JP2005327769A - Calculation method, adjustment method, exposure method, exposure apparatus, image forming state adjustment system, program, and information recording medium - Google Patents

Abstract

An image forming state is adjusted by a projection optical system so that predetermined imaging performance such as line width is optimized.
A specification representing a relationship between a plurality of adjustment amounts used in an adjustment device under a target exposure condition and a predetermined imaging performance of the projection optical system based on the target exposure condition and the wavefront aberration of the projection optical system. A partial differential coefficient (Zernike sensitivity) obtained by partially differentiating the function by the coefficient of each term of the Zernike polynomial is calculated (step 296). Next, a target exposure condition based on an imaging performance calculation function indicating a relationship between the plurality of adjustment amounts, a difference with respect to a target value of a current predetermined imaging performance, a calculated Zernike sensitivity, and a wavefront aberration change table The optimum values of the plurality of adjustment amounts below are calculated (step 302). Then, by adjusting the adjustment device based on the calculation result, the image forming state is adjusted by the projection optical system so that the predetermined imaging performance such as the line width is optimal (step 320).
[Selection] Figure 10

Description

  The present invention relates to a calculation method, an adjustment method, an exposure method and an exposure apparatus, an image formation state adjustment system, a program, and an information recording medium, and more particularly, an object of a pattern image projected onto an object by a projection optical system. The calculation method for calculating the optimum value of the adjustment amount used in the adjustment device for adjusting the formation state above, the adjustment method for adjusting the image formation state using the calculation method, and the formation state of the projected image of the pattern An exposure method and an exposure apparatus using a projection optical system provided with an adjusting apparatus for adjusting, an image forming state adjusting system for optimizing an image forming state of a pattern by the projection optical system used in the exposure apparatus, and a control system for the exposure apparatus The present invention relates to a program for causing a computer to optimize the imaging state of a pattern, and an information recording medium on which the program is recorded.

  Conventionally, when a semiconductor element or a liquid crystal display element or the like is manufactured by a photolithography process, a pattern of a photomask or a reticle (hereinafter, collectively referred to as “reticle”) is formed on the surface of a photoresist or the like via a projection optical system. A projection exposure apparatus that transfers onto a substrate such as a wafer or glass plate coated with a photosensitive agent, such as a step-and-repeat type reduction projection exposure apparatus (so-called stepper), or a step-and-scan type scanning projection exposure. An apparatus (so-called scanning stepper) or the like is used.

  By the way, when manufacturing semiconductor devices, etc., it is necessary to form different circuit patterns by stacking them on the substrate, so that they are already formed on the reticle on which the circuit pattern is formed and each shot region on the substrate. It is important to accurately overlay the formed pattern. In order to perform such superposition accurately, the imaging performance of the projection optical system is adjusted to a desired state (for example, to correct a magnification error of a transfer image of a reticle pattern with respect to a shot area (pattern) on a substrate). It is indispensable to be done. Even when the first layer reticle pattern is transferred to each shot area on the substrate, the imaging performance of the projection optical system is used to accurately transfer the second and subsequent reticle patterns to each shot area. It is desirable to adjust.

  In order to adjust the imaging performance (a kind of optical characteristics) of this projection optical system, it is necessary to accurately measure (or detect) the imaging performance, and conventionally, measurement in which a predetermined measurement pattern is formed. Image formation performance, specifically Seidel based on measurement results obtained by measuring a transfer image obtained by developing a substrate on which a projection image of a measurement pattern is transferred and developed, for example, a resist image. A printing method for calculating the five aberrations (distortion, distortion, astigmatism, curvature of field, coma), and a measurement pattern formed by a projection optical system that illuminates a measurement reticle with illumination light The aerial image measurement method of measuring the aerial image (projected image) and calculating the five aberrations based on the measurement result has been mainly used.

  Recently, however, circuit patterns are becoming increasingly finer as semiconductor devices are highly integrated, and it is not sufficient to correct Seidel's five aberrations (lower order aberrations). Therefore, it has been required to adjust the overall imaging performance of the projection optical system including this aberration.

  For the adjustment of the pattern imaging performance or imaging state of the projection optical system, for example, an imaging performance adjustment mechanism for adjusting the position and inclination of an optical element such as a lens element constituting the projection optical system is used. However, the imaging performance depends on exposure conditions such as illumination conditions (such as illumination σ) and N. A. (Numerical aperture), and changes depending on the pattern used. Therefore, the adjustment position or the like of each optical element by the optimum imaging performance adjustment mechanism under a certain exposure condition is not always the optimum adjustment position or the like under other exposure conditions.

  Under such a background, arbitrary exposure conditions, for example, N.I. A. Recently, an invention related to an image formation state adjustment system for quickly calculating an adjustment position of each optical element by an image formation performance adjustment mechanism that draws out an optimum image formation performance for a combination of illumination σ and a target pattern has recently been developed. (See Patent Document 1 below). In the invention described in Patent Document 1, the root mean square optimization method (linearly combined matrix) representing the relationship between the adjustment amount (adjustment position and the like of each optical element) of the adjustment device and the imaging performance is used. By applying an optimization method such as the method of least squares, the adjustment position of each optical element is calculated.

  However, in some imaging performance, the relationship between the adjustment amount (adjustment position of each optical element, etc.) of the adjusting device and the imaging performance cannot be expressed by a linear function. For example, it is known that the line width of the pattern image to be exposed is generally not in a linear relationship with the adjustment amount of the adjustment device (see, for example, Patent Document 2). For this reason, in the image forming state adjustment system disclosed in the above-mentioned Patent Document 1, for the purpose of adjusting the imaging performance which is not linearly related to the adjustment amount of the adjustment device, as represented by the above line width. In addition, it is difficult to calculate the optimum adjustment amount of the adjustment device. Naturally, the image forming state adjustment system disclosed in the above-mentioned Patent Document 1 does not have a linear relationship with the adjustment amount of the adjustment device such as the line width based on the adjustment amount of the adjustment device under an arbitrary exposure condition. The imaging performance could not be calculated.

International Publication No. 03/065428 Pamphlet International Publication No. 03/075328 Pamphlet

  The present invention has been made under the above circumstances. From the first viewpoint, the present invention is used in an adjustment device that adjusts the formation state of an image of a pattern projected onto an object by the projection optical system on the object. A calculation method for calculating an optimum value of an adjustment amount to be generated, and an imaging performance calculation approximation function in which a nonlinear function representing a relationship between a plurality of adjustment amounts and a predetermined imaging performance of the projection optical system is linearly approximated is created A calculation method including: an approximate function creating step; and a calculation step of calculating optimum values of the plurality of adjustment amounts based on the imaging performance calculation approximate function.

  According to this, through the step of creating an imaging performance calculation approximation function that linearly approximates a nonlinear function representing the relationship between a plurality of adjustment amounts and the predetermined imaging performance of the projection optical system, the created imaging performance A method of calculating an optimum value of the adjustment amount based on a calculation approximation function by an appropriate optimization calculation method is employed. Therefore, it is possible to easily calculate the optimum value of the adjustment amount (optimum adjustment amount) that can be used to adjust the imaging performance that is not linearly related to the adjustment amount of the adjustment device such as the line width of the pattern image described above. Is possible.

  In this case, a first sub-step of creating a new imaging performance calculation near-order function that linearly approximates the nonlinear function corresponding to the calculated optimum values of the latest plurality of adjustment amounts, and the new imaging The method may further include a processing step of performing a series of processing with the second sub-step of calculating the optimum values of the plurality of adjustment amounts based on a performance calculation approximate function at least once. In this case, in the processing step, the series of processes may be performed only once, or the series of processes may be repeated a plurality of times to derive an optimum solution of the adjustment amount. . Particularly in the latter case, the optimum solution of the adjustment amount is asymptotically derived by repeating the process.

  According to a second aspect of the present invention, there is provided an adjustment method for adjusting a formation state of an image of a pattern projected on an object by a projection optical system on the object using an adjustment device. An adjustment method comprising: calculating an optimum value of a plurality of adjustment amounts using a calculation method; and adjusting the adjustment device based on the calculated optimum values of the plurality of adjustment amounts.

  According to this, by the calculation method of the present invention, a plurality of adjustment amounts of the adjustment device that can be used to adjust the imaging performance that is not linearly related to the adjustment amount of the adjustment device such as the line width of the pattern image described above. The optimum value is easily calculated, and the adjustment device is adjusted based on the calculated optimum values of the plurality of adjustment amounts. As a result, the image formation state can be adjusted so that the imaging performance of the projection optical system, such as the line width of the pattern image projected onto the object by the projection optical system, is in an optimal state. .

  According to a third aspect of the present invention, there is provided a step of adjusting a formation state of the image of the pattern on the object by the adjustment method of the invention; and after the adjustment of the formation state of the image is performed, Transferring a pattern onto the object using the projection optical system.

  According to this, the adjustment method according to the present invention can be adjusted so that the imaging performance of the projection optical system such as the line width of the image of the pattern projected onto the object by the projection optical system is in an optimal state (image forming state). After the adjustment is performed, the pattern is transferred onto the object using the adjusted projection optical system. As a result, a pattern image (transfer image) can be accurately formed on the object.

  According to a fourth aspect of the present invention, there is provided an exposure method for transferring a predetermined pattern onto an object using a projection optical system provided with an adjusting device for adjusting a formation state of a projected image of the pattern. Represents a relationship between a plurality of adjustment amounts used in the adjustment device under the target exposure condition and a predetermined imaging performance of the projection optical system based on the target exposure condition and information on the wavefront of the projection optical system. A Zernike sensitivity calculation step of calculating a Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function by a coefficient of each term of the Zernike polynomial that expands the wavefront; and the plurality of adjustment amounts; A difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance; a Zernike sensitivity of the calculated predetermined imaging performance; The plurality of adjustments under the target exposure condition based on an imaging performance calculation function showing a relationship between a wavefront aberration change table composed of a parameter group indicating a relationship between each of the adjustment amount and a change in the wavefront aberration of the projection optical system An adjustment amount calculating step for calculating an optimum value of the amount; and the projection optical system in a state where the adjustment device is adjusted based on the calculation result of the optimum values of the plurality of adjustment amounts under the target exposure condition. And a transfer step of transferring onto the object using a second exposure method.

  According to this, based on given target exposure conditions and information on the wavefront of the projection optical system, a plurality of adjustment amounts used in the adjustment device under the target exposure conditions and predetermined imaging performance of the projection optical system The partial differential coefficient obtained by partial differentiation of the specific function representing the relationship with the coefficient of each term of the Zernike polynomial that expands the wavefront, that is, the Zernike sensitivity of a predetermined imaging performance is calculated (Zernike sensitivity calculating step). Here, the Zernike sensitivity can be calculated regardless of whether the specific function is a linear function or a nonlinear function.

  Next, the plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, the calculated Zernike sensitivity, and the wavefront aberration change Under a target exposure condition based on an imaging performance calculation function showing a relationship between a table (table data including a parameter group indicating a relationship between each of the plurality of adjustment amounts and a change in wavefront aberration of the projection optical system) An optimum value of a plurality of adjustment amounts is calculated (adjustment amount calculation step). Here, when the specific function is a linear function, the imaging performance calculation function is substantially the same function (including a function obtained by adding a fixed offset value (including zero)), and When the specific function is a nonlinear function, the imaging performance calculation function is a linear approximation function of the nonlinear function.

  In any case, the pattern is transferred onto the object using the projection optical system in a state where the adjustment device is adjusted based on the calculation results of the optimum values of the plurality of adjustment amounts (transfer process). As a result, in the state in which the image formation state is adjusted by the projection optical system so that the predetermined imaging performance such as the line width of the image of the pattern is in an optimal state, the pattern is formed using the projection optical system. Transcribed above. Therefore, a pattern image (transfer image) can be accurately formed on the object.

  In this case, when the specific function is a nonlinear function, the imaging performance calculation function is a linear approximation function of the nonlinear function, so the adjustment device is adjusted according to the calculation result of the optimum value of the plurality of adjustment amounts. However, the predetermined imaging performance may be insufficient.

  Therefore, prior to the transfer step, an evaluation step for evaluating the optimization result based on the calculation result of the optimum value of the plurality of adjustment amounts and the imaging performance calculation function; and as a result of the evaluation, further optimization Is necessary based on the calculation result of the optimum value of the plurality of adjustment amounts and the information on the new wavefront calculated based on the wavefront aberration change table and the target exposure condition. A Zernike sensitivity recalculation step for newly calculating the Zernike sensitivity of the predetermined imaging performance in the system; the plurality of adjustment amounts; the predetermined imaging performance of the projection optical system under a predetermined exposure condition; and the imaging The target exposure condition based on an imaging performance calculation function indicating a relationship between a difference from a predetermined target value of performance, a Zernike sensitivity of the newly calculated predetermined imaging performance, and the wavefront aberration change table Before And adjustment amount recalculation process for newly calculating an optimum value of a plurality of adjustment amounts; can be further comprise. In such a case, the pattern is transferred onto the object using the projection optical system in a state where the adjustment device is adjusted based on the optimum values of the plurality of newly calculated adjustment amounts.

  In this case, a series of processes of the evaluation process, the Zernike sensitivity recalculation process, and the adjustment amount recalculation process can be repeated a plurality of times. In such a case, the optimum solution of the adjustment amount is asymptotically derived by repeating the plurality of times.

  According to a fifth aspect of the present invention, there is provided an imaging performance calculation method for calculating a predetermined imaging performance of a projection optical system that forms a projected image of a pattern on an object, wherein the exposure condition is at least one reference. Based on information on a plurality of adjustment amounts used in an adjustment device that adjusts the formation state of the projection image below and information on the wavefront of the projection optical system, the plurality of adjustment amounts under the arbitrary exposure conditions The Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating the specific function representing the relationship with the predetermined imaging performance of the projection optical system by the coefficient of each term of the Zernike polynomial that expands the wavefront. Calculating the Zernike sensitivity to be calculated; and based on the wavefront aberration of the projection optical system and the Zernike sensitivity of the predetermined imaging performance, the location of the projection optical system under the arbitrary exposure conditions And imaging performance calculating step of calculating the imaging performance of; a imaging performance calculation method comprising.

  According to this, based on the information on the plurality of adjustment amounts used in the adjustment device for adjusting the formation state of the projected image under the exposure condition serving as at least one reference and the information on the wavefront of the projection optical system, any arbitrary The Zernike sensitivity of predetermined imaging performance under the exposure conditions is calculated (Zernike sensitivity calculating step). Then, based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance, the predetermined imaging performance of the projection optical system under the arbitrary exposure conditions is calculated (imaging performance) Calculation step). Therefore, for example, it is possible for anyone to easily evaluate whether or not the predetermined imaging performance of the projection optical system should be satisfied based on the calculation result of the imaging performance.

  According to a sixth aspect of the present invention, there is provided an exposure method for transferring a pattern onto an object via a projection optical system, wherein a plurality of setting information in the transfer is obtained using the imaging performance calculation method of the present invention. The third exposure method includes a step of calculating the imaging performance of the projection optical system under a plurality of exposure conditions having different setting values with respect to the setting information to be noticed.

  According to this, it becomes possible to easily determine the exposure condition in which the setting value relating to the setting information to be focused on, that is, the best exposure condition, is optimal based on the imaging performance calculated for each exposure condition.

  From a seventh aspect, the present invention is an exposure apparatus that illuminates a mask with an energy beam and transfers a pattern formed on the mask onto an object via a projection optical system, An adjustment device that adjusts the formation state on the object; and a plurality of adjustment amounts of the adjustment device and the projection under a target exposure condition based on a given target exposure condition and information on a wavefront of the projection optical system Calculates the Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating the specific function representing the relationship with the predetermined imaging performance of the optical system by the coefficient of each term of the Zernike polynomial that expands the wavefront. A first calculation device that performs the plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the first calculation. Equipment FIG. 5 shows a relationship between the Zernike sensitivity of the predetermined imaging performance calculated by the calculation and a wavefront aberration change table including a parameter group indicating a relationship between each of the plurality of adjustment amounts and a change in the wavefront aberration of the projection optical system. A second calculation device that calculates an optimum value of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function; and a calculation result of the optimum values of the plurality of adjustment amounts in transferring the pattern And a processing device for adjusting the adjustment device based on the first exposure apparatus.

  According to this, the Zernike sensitivity of the predetermined imaging performance under the target exposure condition is calculated by the first calculation device based on the given target exposure condition and information on the wavefront of the projection optical system. Here, the Zernike sensitivity of the predetermined imaging performance can be calculated regardless of whether the specific function is a linear function or a nonlinear function.

  In addition, the second calculating device may calculate the plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the calculated Zernike. Based on the imaging performance calculation function indicating the relationship between the sensitivity and the wavefront aberration change table, optimum values of a plurality of adjustment amounts under the target exposure conditions are calculated. Then, when the pattern is transferred by the processing device, the adjustment device so that a predetermined imaging performance such as the line width of the image of the pattern is in an optimum state based on the calculation result of the optimum value of the plurality of adjustment amounts. Is adjusted.

  Therefore, in the state after this adjustment, the pattern is transferred onto the object using the projection optical system, so that an image of the pattern (transfer image) is formed on the object with high accuracy.

  According to an eighth aspect of the present invention, there is provided an exposure apparatus that illuminates a mask with an energy beam and transfers a pattern formed on the mask onto an object via a projection optical system. An adjustment device that adjusts the formation state of the projection optical system; arbitrary exposure based on information on a plurality of adjustment amounts used in the adjustment device and information on the wavefront of the projection optical system under at least one reference exposure condition The specific function representing the relationship between the plurality of adjustment amounts and the predetermined imaging performance of the projection optical system under the condition is a partial differential coefficient obtained by partial differential with the coefficient of each term of the Zernike polynomial that expands the wavefront. A first calculation device for calculating Zernike sensitivity of the predetermined imaging performance; a wavefront aberration of the projection optical system and the Zernike of the predetermined imaging performance calculated by the first calculation device; A second exposure apparatus comprising a; based on the degree, the arbitrary second calculation device for calculating a predetermined imaging performance of the projection optical system in the exposure conditions.

  According to this, for example, based on the calculation result of the imaging performance, anyone can easily evaluate whether or not the predetermined imaging performance of the projection optical system should be satisfied.

  According to a ninth aspect of the present invention, there is provided a method for optimizing a formation state of the projection image on an object used in an exposure apparatus that forms a projection image of a predetermined pattern on the object using a projection optical system. An image formation state adjustment system, comprising: an adjustment device that adjusts a formation state of the projection image on an object; and a computer connected to the exposure apparatus via a communication path, the computer being provided Specific function representing a relationship between a plurality of adjustment amounts of the adjusting device and a predetermined imaging performance of the projection optical system under the target exposure condition based on the target exposure condition and information on the wavefront of the projection optical system A first function for calculating Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partial differentiation with respect to a coefficient of each term of the Zernike polynomial that expands the wavefront; and the plurality of adjustment amounts; A difference between the predetermined imaging performance of the projection optical system under exposure conditions and a predetermined target value of the imaging performance, a Zernike sensitivity of the calculated predetermined imaging performance, and the plurality of adjustment amounts. Optimum of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship between a wavefront aberration change table including a parameter group indicating a relationship between each and a change in wavefront aberration of the projection optical system And a second function for calculating a value; and a first image forming state adjusting system.

  According to this, the computer calculates the Zernike sensitivity of the predetermined imaging performance under the target exposure condition based on the given target exposure condition and information on the wavefront of the projection optical system, and a plurality of An adjustment amount, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, a calculated Zernike sensitivity of the predetermined imaging performance, and a wavefront Based on the imaging performance calculation function indicating the relationship with the aberration change table, the optimum values of the plurality of adjustment amounts under the target exposure condition are calculated. Then, the adjustment device is adjusted based on the calculation results of the optimum values of a plurality of adjustment amounts (image formation by a projection optical system in which a predetermined imaging performance such as the line width of the pattern image is optimal) When the state is adjusted), the pattern is transferred onto the object using the projection optical system, and a pattern image (transfer image) is accurately formed on the object using the projection optical system. Will be.

  According to a tenth aspect of the present invention, there is provided a method for optimizing the formation state of the projection image on an object used in an exposure apparatus that forms a projection image of a predetermined pattern on the object using a projection optical system. An image forming state adjusting system, comprising: an adjusting device that adjusts a forming state of the projected image on an object; and the exposure device that is connected to the exposure device via a communication path and that is at least one reference exposure condition. A relationship between the plurality of adjustment amounts and a predetermined imaging performance of the projection optical system under an arbitrary exposure condition based on information on a plurality of adjustment amounts used in the adjustment apparatus and information on the wavefront of the projection optical system Calculating the Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function representing the Zernike polynomial by a coefficient of each term of the Zernike polynomial that expands the wavefront, and the projection optics A computer that calculates the predetermined imaging performance of the projection optical system under the arbitrary exposure conditions based on the wavefront aberration of the projection and the calculated Zernike sensitivity of the predetermined imaging performance. An image forming state adjusting system.

  According to this, on the basis of information on a plurality of adjustment amounts used in the adjustment apparatus and information on the wavefront of the projection optical system under the exposure condition serving as at least one reference, a predetermined predetermined condition under the exposure condition can be obtained. The Zernike sensitivity of the imaging performance is calculated, and based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance, the predetermined result of the projection optical system under the arbitrary exposure condition is calculated. Image performance is calculated. Therefore, for example, by displaying the calculation result of the imaging performance on the screen, anyone can easily evaluate whether or not the predetermined imaging performance of the projection optical system should be satisfied. .

  In this case, the computer calculates the predetermined imaging performance for a plurality of exposure conditions having different setting values with respect to setting information of interest among a plurality of setting information related to a projection condition of a pattern to be projected by the projection optical system. , And the exposure condition that optimizes the setting value related to the focused setting information can be determined based on the imaging performance calculated for each exposure condition.

  According to an eleventh aspect of the present invention, there is provided an adjustment device that forms a projection image of a predetermined pattern on an object using a projection optical system and adjusts the formation state of the projection image on the object. A program for causing a computer constituting a part of a control system of an exposure apparatus to execute predetermined processing, based on given target exposure conditions and information on the wavefront of the projection optical system, under target exposure conditions Partial differentiation obtained by partially differentiating a specific function representing a relationship between a plurality of adjustment amounts used in the adjustment device and a predetermined imaging performance of the projection optical system by a coefficient of each term of a Zernike polynomial in which the wavefront is expanded Calculating a Zernike sensitivity of the predetermined imaging performance that is a coefficient; the plurality of adjustment amounts; the predetermined imaging performance of the projection optical system under a predetermined exposure condition; and the imaging performance A wavefront comprising a parameter group indicating a relationship between a difference from a predetermined target value, a calculated Zernike sensitivity of the predetermined imaging performance, each of the plurality of adjustment amounts, and a change in wavefront aberration of the projection optical system And a procedure for calculating an optimum value of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship with an aberration change table.

  When information about the target exposure condition and the wavefront of the projection optical system is input to the computer in which this program is installed, in response to this, the computer performs a predetermined process under the target exposure condition based on the input information. The Zernike sensitivity of the imaging performance is calculated, and a plurality of adjustment amounts and a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance are calculated. An optimum value of the plurality of adjustment amounts under the target exposure condition is calculated based on an imaging performance calculation function indicating a relationship between the Zernike sensitivity of the predetermined imaging performance and a wavefront aberration change table. Therefore, by adjusting the adjustment device based on this adjustment amount, the image formation with a nonlinear relationship with the predetermined imaging performance of the projection optical system under any target exposure condition (the adjustment amount such as the line width of the pattern image) (Including performance) can be quickly optimized.

  From a twelfth aspect, the present invention includes an adjustment device that forms a projection image of a predetermined pattern on an object using a projection optical system and adjusts the formation state of the projection image on the object. A program for causing a computer constituting a part of a control system of an exposure apparatus to execute a predetermined process, information on a plurality of adjustment amounts used in the adjustment apparatus and the projection under at least one reference exposure condition Based on information on the wavefront of the optical system, a specific function representing the relationship between the plurality of adjustment amounts and the predetermined imaging performance of the projection optical system under an arbitrary exposure condition is expressed by a Zernike polynomial that expands the wavefront. A procedure for calculating the Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partial differentiation with the coefficient of each term; and the predetermined wavefront aberration calculated for the projection optical system A second program for executing the computer; based on the Zernike sensitivity of image performance, procedures and for calculating the predetermined imaging performance of the projection optical system in the arbitrary exposure conditions.

  When information on a plurality of adjustment amounts and information on the wavefront of the projection optical system are input to a computer in which this program is installed, at least one reference exposure condition, in response, the computer The Zernike sensitivity of a predetermined imaging performance under an arbitrary exposure condition is calculated on the basis of the information of the above, and the arbitrary value is calculated based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance. The predetermined imaging performance of the projection optical system under the exposure conditions is calculated. Therefore, for example, by displaying the calculation result of the imaging performance on the screen, anyone can easily evaluate whether or not the predetermined imaging performance of the projection optical system should be satisfied. . In the second program, the best exposure condition can be easily determined by inputting various exposure conditions as the target exposure condition and outputting the calculation result of the imaging performance.

  The first and second programs of the present invention can be targeted for sale in a state of being recorded on an information recording medium. Therefore, from the thirteenth viewpoint, the present invention can be said to be an information recording medium that can be read by a computer on which either the first or second program of the present invention is recorded.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS.

  FIG. 1 shows an overall configuration of an image forming state adjustment system 10 according to an embodiment of the present invention. The image formation state adjustment system 10 shown in FIG. 1 is an in-house LAN system built in a semiconductor factory of a device manufacturer (hereinafter referred to as “maker A” as appropriate), who is a user of a device manufacturing apparatus such as an exposure apparatus. is there. The image forming state adjustment system 10 includes a first communication server 920 and a lithography system 912 installed in a clean room, and a local area network (LAN) as a communication path to the first communication server 920 constituting the lithography system 912. And a second communication server 930 as a computer connected via 926.

The lithography system 912 includes a first communication server 920, a first exposure apparatus 922 ₁ , a second exposure apparatus 922 ₂ , and a third exposure apparatus 922 ₃ (hereinafter referred to as “exposure” as appropriate). Device 922 ").

FIG. 2 shows a schematic configuration of the first exposure apparatus (hereinafter, also referred to as “exposure apparatus” as appropriate) 922 ₁ . The exposure apparatus 922 ₁ is a step-and-scan reduction projection exposure apparatus (so-called scanner) using a pulse laser light source as an exposure light source (hereinafter referred to as “light source”).

The exposure apparatus 922 ₁ is a reticle stage as a mask stage for holding an illumination system including a light source 16 and an illumination optical system 12 and a reticle R as a mask illuminated by exposure illumination light EL as an energy beam from the illumination system. RST, projection optical system PL that projects exposure illumination light EL emitted from reticle R onto wafer W (image plane) as an object, and Z tilt stage 58 as an object stage that holds wafer W are mounted. Wafer stage WST and control system thereof are provided.

As the light source 16, a pulsed ultraviolet light source that outputs pulsed light in the vacuum ultraviolet region, such as an ArF excimer laser (output wavelength 193 nm) or an F ₂ laser (output wavelength 157 nm), is used here. The light source 16 may be a light source that outputs pulsed light in the far ultraviolet region or ultraviolet region, such as a KrF excimer laser (output wavelength 248 nm).

  The light source 16 is actually a clean room in which a chamber 11 in which an exposure apparatus main body including the constituent elements of the illumination optical system 12 and the reticle stage RST, the projection optical system PL, the wafer stage WST, and the like is housed is installed. It is installed in another low clean room, and is connected to the chamber 11 via a light transmission optical system (not shown) including at least a part of an optical axis adjusting optical system called a beam matching unit. In this light source 16, based on the control information TS from the main controller 50, an internal controller turns on / off the output of the laser beam LB, energy per pulse of the laser beam LB, oscillation frequency (repetition frequency), The center wavelength, the spectrum half width (wavelength width), and the like are controlled.

  The illumination optical system 12 includes a beam shaping / illuminance uniformizing optical system 20 including a cylinder lens, a beam expander (all not shown), an optical integrator (homogenizer) 22, and the like, an illumination system aperture stop plate 24, a first relay lens. 28A, a second relay lens 28B, a fixed reticle blind 30A, a movable reticle blind 30B, an optical path bending mirror M, a condenser lens 32, and the like. As the optical integrator, a fly-eye lens, a rod integrator (an internal reflection type integrator), a diffractive optical element, or the like can be used. In the present embodiment, since a fly-eye lens is used as the optical integrator 22, it is also referred to as a fly-eye lens 22 below.

  The beam shaping / illuminance uniformity optical system 20 is connected to a light transmission optical system (not shown) through a light transmission window 17 provided in the chamber 11. The beam shaping / illuminance equalizing optical system 20 shapes the cross-sectional shape of the laser beam LB that is pulsed by the light source 16 and incident through the light transmission window 17 using, for example, a cylinder lens or a beam expander. The fly-eye lens 22 located on the exit end side in the beam shaping / illumination uniformity optical system 20 is irradiated with a laser beam whose cross-sectional shape is shaped in order to illuminate the reticle R with a uniform illumination distribution. A surface light source (secondary light source) composed of a large number of point light sources (light source images) is formed on the exit-side focal plane arranged so as to substantially coincide with the pupil plane of the illumination optical system 12. Hereinafter, the laser beam emitted from the secondary light source is referred to as “illumination light EL”.

  An illumination system aperture stop plate 24 made of a disk-like member is disposed in the vicinity of the exit-side focal plane of the fly-eye lens 22. The illumination system aperture stop plate 24 is provided with an aperture stop (small aperture) made up of, for example, a normal circular aperture, and an aperture stop (small size) for reducing the σ value that is a coherence factor made up of a small circular aperture at substantially equal angular intervals. σ stop), an annular aperture stop for annular illumination (annular stop), and a modified aperture stop (two types of which are shown in FIG. Only the aperture stop is shown). The illumination system aperture stop plate 24 is rotated by a drive device 40 such as a motor controlled by the main control device 50, whereby any aperture stop is selectively placed on the optical path of the illumination light EL. The light source surface shape in Koehler illumination, which will be described later, is limited to an annular zone, a small circle, a large circle, or the fourth.

  In place of or in combination with the aperture stop plate 24, for example, a plurality of diffractive optical elements that are exchanged and disposed in the illumination optical system that distributes illumination light to different regions on the pupil plane of the illumination optical system, A plurality of prisms (conical prisms, polyhedral prisms, etc.) having at least one movable along the optical axis IX of the illumination optical system, that is, a variable interval in the optical axis direction of the illumination optical system, and at least one of the zoom optical system; An optical unit including the optical unit 22 is disposed between the light source 16 and the optical integrator 22. When the optical integrator 22 is a fly-eye lens, the intensity distribution of illumination light on the incident surface, and the optical integrator 22 is an internal reflection type integrator. In some cases, illumination optics can be changed by changing the incident angle range of the illumination light to the incident surface. Light amount distribution of the illumination light on the pupil plane of the (size and shape of the secondary light source), i.e. it is desirable to suppress the loss of light due to a change of the illumination condition of the reticle R. In the present embodiment, a plurality of light source images (virtual images) formed by the internal reflection type integrator are also called secondary light sources.

  A relay optical system including the first relay lens 28A and the second relay lens 28B is disposed on the optical path of the illumination light EL emitted from the illumination system aperture stop plate 24 with the fixed reticle blind 30A and the movable reticle blind 30B interposed therebetween. Yes. The fixed reticle blind 30A is arranged slightly defocused from the conjugate plane with respect to the pattern surface of the reticle R, and a rectangular opening that defines a rectangular illumination area IAR on the reticle R is formed. Further, a movable reticle blind 30B having an opening whose position and width are variable in the direction corresponding to the scanning direction (the Y-axis direction which is the left-right direction in the drawing in FIG. 2) is disposed in the vicinity of the fixed reticle blind 30A. By further limiting the illumination area via the movable reticle blind 30B at the start and end of exposure, exposure of unnecessary portions is prevented. Further, the movable reticle blind 30B has a variable opening width in a direction corresponding to a non-scanning direction (X-axis direction which is a direction perpendicular to the paper surface in FIG. 2) orthogonal to the scanning direction, and should be transferred onto the wafer W. The width of the illumination area in the non-scanning direction can be adjusted according to the pattern of the reticle R.

  On the optical path of the illumination light EL behind the second relay lens 28B constituting the relay optical system, a bending mirror M that reflects the illumination light EL that has passed through the second relay lens 28B toward the reticle R is disposed. A condenser lens 32 is disposed on the optical path of the illumination light EL behind the mirror M.

  In the above configuration, the entrance surface of the fly-eye lens 22, the placement surface of the movable reticle blind 30B, and the pattern surface of the reticle R are optically conjugate with each other and formed on the exit-side focal plane of the fly-eye lens 22. The light source plane (pupil plane of the illumination optical system) and the Fourier transform plane (exit pupil plane) of the projection optical system PL are optically conjugate with each other to form a Kohler illumination system.

  The operation of the illumination system configured in this way will be briefly described. The laser beam LB pulsed from the light source 16 is incident on the beam shaping / illuminance equalizing optical system 20 and its cross-sectional shape is shaped. Thereafter, the light enters the fly-eye lens 22. Thereby, the secondary light source described above is formed on the exit-side focal plane of the fly-eye lens 22.

  The illumination light EL emitted from the secondary light source passes through one of the aperture stops on the illumination system aperture stop plate 24, then reaches the fixed reticle blind 30A through the first relay lens 28A, and the fixed reticle blind. After passing through the aperture 30A and the movable reticle blind 30B and the second relay lens 28B, the optical path is bent vertically downward by the mirror M, then passes through the condenser lens 32, and on the reticle R held on the reticle stage RST. Illuminate the rectangular illumination area IAR with a uniform illuminance distribution.

  A reticle R is loaded on the reticle stage RST, and is held by suction via an electrostatic chuck (or vacuum chuck) (not shown). Reticle stage RST can be finely driven in an XY plane perpendicular to an optical axis IX of an illumination system (corresponding to optical axis AX of projection optical system PL described later) by a reticle stage driving unit (not shown) including, for example, a linear motor. (Including rotation around the Z axis) and can be driven at a scanning speed designated in a predetermined scanning direction (here, the Y axis direction).

  The position of the reticle stage RST in the XY plane is set to, for example, 0.5 to 1 nm by a reticle laser interferometer (hereinafter referred to as “reticle interferometer”) 54R through a reflective surface provided or formed on the reticle stage RST. It is always detected with a resolution of the order. Position information of reticle stage RST from reticle interferometer 54R is supplied to main controller 50 installed outside main body chamber 11. Main controller 50 drives and controls reticle stage RST via a reticle stage drive unit (not shown) based on position information of reticle stage RST.

  As the projection optical system PL, for example, a double telecentric reduction system is used. The projection magnification of the projection optical system PL is, for example, 1/4, 1/5, or 1/6. Therefore, as described above, when the illumination area IAR on the reticle R is illuminated by the illumination light EL, a reduced image of the circuit pattern or the like of the reticle R in the illumination area IAR is projected via the projection optical system PL. It is formed in the irradiation area (exposure area) IA of the illumination light EL on the wafer W conjugate with the illumination area IAR.

As the projection optical system PL, as shown in FIG. 2, a refraction system including only a plurality of, for example, about 10 to 20 refractive optical elements (lens elements) 13 is used. Of a plurality of lens elements 13 that constitute the projection optical system PL, a plurality of the object plane side (reticle R side) (here, five in order to simplify the description) lens elements 13 _1, Reference numerals 13 ₂ , 13 ₃ , 13 ₄ , and 13 ₅ are movable lenses that can be driven from the outside by the imaging performance correction controller 48. The lens elements 13 _{1 to} 13 ₅ are held by the lens barrel via respective double structure lens holders (not shown). These lens elements 13 _{1 to} 13 ₅ are respectively held by the inner lens holder, and these inner lens holders are supported by the driving element (not shown) such as a piezo element with respect to the outer lens holder at three points in the gravitational direction. Yes. By independently adjusting the voltages applied to these drive elements, shift driving each of the lens elements _{131-134 5} in the Z axis direction is the optical axis direction of the projection optical system PL, and the inclination with respect to the XY plane It can be driven (tilted) in a direction (that is, a rotation direction (θx) around the X axis and a rotation direction (θy) around the Y axis).

The other lens elements 13 are held by the lens barrel via a normal lens holder. Not only the lens elements 13 _{1 to} 13 _5, but also aberrations that correct aberrations of the lens disposed in the vicinity of the pupil plane of the projection optical system PL or near the image plane, or the projection optical system PL, in particular, non-rotationally symmetric components. A correction plate (optical plate) or the like may be driven. Furthermore, the degrees of freedom (movable directions) of these drivable optical elements are not limited to three, but may be one, two, or four or more.

  Further, a pupil aperture stop 15 capable of continuously changing the numerical aperture (NA) within a predetermined range is provided in the vicinity of the pupil plane of the projection optical system PL. As this pupil aperture stop 15, for example, a so-called iris stop is used. The pupil aperture stop 15 is controlled by the main controller 50.

  Wafer stage WST is disposed below projection optical system PL, and is freely driven in an XY two-dimensional plane by wafer stage drive unit 56 including a linear motor and the like. On the Z tilt stage 58 mounted on the wafer stage WST, the wafer W is held by electrostatic chucking (or vacuum chucking) or the like via a wafer holder (not shown). Wafer stage WST is not only moved in the scanning direction (Y-axis direction), but also in a scanning direction so that a plurality of shot areas on wafer W can be moved relative to exposure area IA to perform scanning exposure. It is also configured to be movable in a non-scanning direction (X-axis direction) orthogonal to each other, whereby an operation for scanning (scanning) exposing each shot area on the wafer W and starting acceleration for the exposure of the next shot A step-and-scan operation that repeats the operation of moving (stepping) to a position is possible.

  The Z tilt stage 58 is positioned on the wafer stage WST in the XY direction, and is moved in the Z axis direction by an unillustrated drive system and tilted with respect to the XY plane (that is, the rotational direction (θx) around the X axis) and Y It is configured to be drivable (tiltable) in the rotation direction (θy) around the axis. Thereby, the surface position (Z-axis direction position and inclination with respect to the XY plane) of the wafer W held on the Z tilt stage 58 is set to a desired state.

  Further, a movable mirror 52W is fixed on the Z tilt stage 58, and a wafer laser interferometer (hereinafter abbreviated as “wafer interferometer”) 54W arranged outside is used to detect the X tilt direction of the Z tilt stage 58 in the Y direction. Positions in the axial direction and the θz direction (rotation direction around the Z axis) are measured, and position information measured by the wafer interferometer 54W is supplied to the main controller 50. Main controller 50 determines the wafer stage via wafer stage drive unit 56 (including all of the drive system of wafer stage WST and the drive system of Z tilt stage 58) based on the measurement value of wafer interferometer 54W. WST (and Z tilt stage 58) is controlled. Instead of providing the movable mirror 52W, for example, the end surface (side surface) of the Z tilt stage 58 may be mirror-finished to form a reflecting surface.

  On the Z tilt stage 58, a reference mark plate FM on which a reference mark such as a reference mark for so-called baseline measurement of an alignment system ALG to be described later is formed has a surface substantially the same height as the surface of the wafer W. It is fixed to become.

  A wavefront aberration measuring instrument 80, which is a detachable portable wavefront measuring device, is attached to the side surface of the Z tilt stage 58 on the + X side (the right side in the drawing in FIG. 2).

  As shown in FIG. 3, the wavefront aberration measuring instrument 80 includes a casing 82 having an L-shaped YZ cross section and a space formed therein, and an objective disposed in the casing 82 in a predetermined positional relationship. A light receiving optical system 84 including a lens 84a, a relay lens 84b, a bending mirror 84c, a collimator lens 84d, and a microlens array 84e, and a light receiving portion 86 disposed at the + Y side end inside the housing 82 are provided. .

  A circular opening in a plan view (viewed from above) is provided at the uppermost portion (+ Z direction end portion) of the housing 82 so that light from above the housing 82 enters the internal space of the housing 82. 82a is formed. A cover glass 88 is provided so as to cover the opening 82 a from the inside of the housing 82. On the upper surface of the cover glass 88, a light shielding film having a circular opening in the center is formed by vapor deposition of a metal such as chromium, and the light shielding film is unnecessary from the surroundings when measuring the wavefront aberration of the projection optical system PL. Light is blocked from entering the light receiving optical system 84.

  The light receiving unit 86 is composed of a light receiving element such as a two-dimensional CCD and an electric circuit such as a charge transfer control circuit. The light receiving element has a sufficient area to receive all of the light beams incident on the objective lens 84a and emitted from the microlens array 84e. Note that the measurement data obtained by the light receiving unit 86 is output to the main controller 50 via a signal line (not shown) or by wireless transmission.

  By using the wavefront aberration measuring instrument 80 described above, the wavefront aberration of the projection optical system PL is measured on-body (that is, in a state where the projection optical system PL is incorporated in the exposure apparatus), as will be described later. be able to.

Returning to FIG. 2, the exposure apparatus 922 ₁ of this embodiment has a light source that is controlled to be turned on and off by the main controller 50, and has a large number of pinholes or slits toward the image plane of the projection optical system PL. An irradiation system 60a that irradiates an image forming light beam for forming the image of the image from an oblique direction with respect to the optical axis AX, and a light receiving system 60b that receives a reflected light beam on the surface of the wafer W of the image forming light beam. An incident-type multipoint focal position detection system (hereinafter simply referred to as “focus detection system”) is provided. As the focus detection system (60a, 60b), for example, one having the same configuration as that disclosed in Japanese Patent Laid-Open No. 6-283403 (corresponding US Pat. No. 5,448,332) is used.

  In main controller 50, during scanning exposure or the like, wafer W is placed on wafer W so that the defocus is zero (or within the depth of focus) based on a defocus signal (defocus signal) from light receiving system 60b, for example, an S curve signal. By controlling the Z position and the inclination with respect to the XY plane via the wafer stage driving unit 56, autofocus (automatic focusing) and autoleveling are executed. In addition, the main controller 50 measures and aligns the Z position of the wavefront aberration measuring instrument 80 using the focus detection system (60a, 60b) when measuring the wavefront aberration described later. At this time, the inclination measurement of the wavefront aberration measuring instrument 80 may be performed as necessary.

Further, the exposure apparatus 922 ₁ is an off-axis method used for position measurement of the alignment mark on the wafer W held on the wafer stage WST and the reference mark formed on the reference mark plate FM. The alignment system ALG is provided. As this alignment system ALG, for example, the target mark is irradiated with a broadband detection light beam that does not sensitize the resist on the wafer, and the target mark image formed on the light receiving surface by the reflected light from the target mark and an index (not shown) An image processing type FIA (Field Image Alignment) type sensor that captures the image of the image using an image sensor (CCD or the like) and outputs the imaged signals is used.

Further, in exposure apparatus 922 ₁ of the present embodiment, although not shown, above the reticle R, and the reference mark on the reference mark plate and the corresponding reticle marks on the reticle R through the projection optical system PL A pair of reticle alignment detection systems comprising a TTR (Through The Reticle) alignment system using light of an exposure wavelength for simultaneously observing the light is provided. As these reticle alignment detection systems, for example, those having the same configuration as that disclosed in Japanese Patent Laid-Open No. 7-176468 (corresponding US Pat. No. 5,646,413) are used.

  The control system is mainly configured by the main controller 50 in FIG. The main controller 50 includes a so-called workstation (or microcomputer) including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. In addition to performing the above control operation, the entire apparatus is controlled in an integrated manner. Main controller 50 controls, for example, step-to-shot stepping of wafer stage WST, exposure timing, and the like so that the exposure operation is performed accurately.

  The main controller 50 includes, for example, a storage device 42 composed of a hard disk, an input device 45 including a pointing device such as a keyboard and a mouse, a display device 44 such as a CRT display (or liquid crystal display), and a CD. A drive device 46 of an information recording medium such as (compact disc), DVD (digital versatile disc), MO (magneto-optical disc) or FD (flexible disc) is connected externally. Further, the main controller 50 is connected to the LAN 918 described above.

In the storage device 42, before the projection optical system PL is incorporated into the exposure apparatus main body at the manufacturing stage of the exposure apparatus, for example, the wavefront aberration (hereinafter referred to as "single unit") of the projection optical system PL measured by a wavefront aberration measuring instrument is used. Measurement data of “wavefront aberration” is stored. Further, in this storage device 42, the projection image formed on the wafer W by the projection optical system PL, for example, is optimally formed under a plurality of reference exposure conditions as will be described later (for example, the aberration is zero or an allowable value). The position of the lens element (movable lens) 13 _{1 to} 13 _{5 in} the three-degree-of-freedom direction, the Z position and inclination of the wafer W (Z tilt stage 58), and the wavelength λ of the illumination light are set so that In the adjusted state, wavefront aberration data (or wavefront aberration correction amount (difference between wavefront aberration and the above-mentioned single wavefront aberration) data) measured by the wavefront aberration measuring instrument 80, and information on the adjustment amount at that time, That is, the position information of each of the movable lenses 13 _{1 to} 13 _{5 in the} direction of 3 degrees of freedom, the position information of the wafer W in the direction of 3 degrees of freedom, and the information on the wavelength of the illumination light are stored. Here, since each of the above-described exposure conditions serving as the reference is managed by ID as identification information, hereinafter, each reference exposure condition is referred to as a reference ID. That is, the storage device stores adjustment amount information and wavefront aberration (or wavefront aberration correction amount) data for a plurality of reference IDs.

  The positional deviation amount measured by using the wavefront aberration measuring instrument 80 as described later on an information recording medium (in the following description, a CD-ROM for convenience) set in the drive device 46 is used for each term of the Zernike polynomial. Stores a conversion program for conversion into coefficients.

The second and third exposure apparatuses 922 ₂ and 922 ₃ are configured in the same manner as the first exposure apparatus 922 ₁ described above.

Next, a description will be given first to third measuring methods of the wavefront aberration in the exposure apparatus 922 _{1 to 922 3} to be performed, such as during maintenance. In the following description, for simplification of description, it is assumed that the aberration of the light receiving optical system 84 in the wavefront aberration measuring instrument 80 is negligibly small.

  It is assumed that the conversion program in the CD-ROM set in the drive device 46 is installed in the storage device 42.

  During normal exposure, the wavefront aberration measuring instrument 80 is removed from the Z tilt stage 58. Therefore, when measuring the wavefront, first, an operator or a service engineer (hereinafter referred to as “operator etc.” as appropriate) Z tilt stage 58. An operation of attaching the wavefront aberration measuring instrument 80 to the side surface of the lens is performed. At the time of mounting, a bolt or a magnet or the like is provided on a predetermined reference surface (here, the + X side surface) so that the wavefront aberration measuring instrument 80 is within the moving stroke of the wafer stage WST (Z tilt stage 58) during wavefront measurement. Fixed through.

  After completion of the above attachment, in response to an input of a measurement start command by an operator or the like, main controller 50 passes wafer stage drive unit 56 so that wavefront aberration measuring instrument 80 is positioned below alignment system ALG. To move wafer stage WST. In main controller 50, alignment system ALG detects an alignment mark (not shown) provided in wavefront aberration measuring instrument 80, and the position is determined based on the detection result and the measured value of wafer interferometer 54W at that time. The position coordinates of the alignment mark are calculated, and the exact position of the wavefront aberration measuring instrument 80 is obtained. Then, after measuring the position of the wavefront aberration measuring instrument 80, the main controller 50 measures the wavefront aberration as follows.

  First, main controller 50 loads a measurement reticle (not shown) on which a pinhole pattern is formed by a reticle loader (not shown) (hereinafter referred to as “pinhole reticle”) onto reticle stage RST. This pinhole reticle is a reticle in which pinholes (pinholes that generate a spherical wave as an almost ideal point light source) are formed at a plurality of points in the same area as the illumination area IAR of the pattern surface. For example, when the pinhole reticle is set so that the center coincides with the optical axis AX of the projection optical system PL, the plurality of pinholes are arranged in the illumination area IAR, and the projection image thereof is the projection optical system PL. It is formed at a plurality of points (first to nth measurement points described later) at which wavefront aberration should be measured within the field of view.

  The pinhole reticle used here is provided with a diffusion surface on the upper surface, for example, so that light from the pinhole pattern is distributed over almost the entire pupil plane of the projection optical system PL. It is assumed that wavefront aberration is measured over the entire pupil surface. In this embodiment, since the aperture stop 15 is provided in the vicinity of the pupil plane of the projection optical system PL, the wavefront aberration is measured at the pupil plane substantially defined by the aperture stop 15.

  After loading the pinhole reticle, main controller 50 uses the above-described reticle alignment detection system to detect the reticle alignment mark formed on the pinhole reticle, and based on the detection result, the pinhole reticle is Align to position. Thereby, the center of the pinhole reticle and the optical axis of the projection optical system PL substantially coincide.

  Thereafter, the main controller 50 gives the control information TS to the light source 16 to emit the laser beam LB. Thereby, the illumination light EL from the illumination optical system 12 is irradiated to the pinhole reticle. Then, light emitted from a plurality of pinholes of the pinhole reticle is condensed on the image plane via the projection optical system PL, and an image of the pinhole is formed on the image plane.

  Next, the main controller 50 sets the opening 82a of the wavefront aberration measuring instrument 80 at an image formation point where an image of any pinhole on the pinhole reticle (hereinafter referred to as a pinhole of interest) is formed. Wafer stage WST is moved via wafer stage drive unit 56 while monitoring the measurement value of wafer interferometer 54W so that the centers substantially coincide. At this time, in the main controller 50, based on the detection result of the focus detection system (60a, 60b), the upper surface of the cover glass 88 of the wavefront aberration measuring instrument 80 should be aligned with the image plane on which the pinhole image is formed. The Z tilt stage 58 is slightly driven in the Z-axis direction via the wafer stage drive unit 56. At this time, the tilt angle of the Z tilt stage 58 is also adjusted as necessary. As a result, the image of the pinhole of interest enters the light receiving optical system 84 through the central opening of the cover glass 88 and is received by the light receiving element constituting the light receiving unit 86.

  More specifically, a spherical wave is generated from a focused pinhole on the pinhole reticle, and this spherical wave forms an objective lens constituting the projection optical system PL and the light receiving optical system 84 of the wavefront aberration measuring instrument 80. 84a, relay lens 84b, mirror 84c, and collimator lens 84d are converted into parallel light fluxes to irradiate the microlens array 84e. Thereby, the pupil plane of the projection optical system PL is relayed to the microlens array 84e and divided. Then, each light (divided light) is condensed on the light receiving surface of the light receiving element by each lens element of the microlens array 84e, and a pinhole image is formed on the light receiving surface.

  At this time, if the projection optical system PL is an ideal optical system without wavefront aberration, the wavefront on the pupil plane of the projection optical system PL becomes an ideal wavefront (here, a plane), and as a result, a microlens array. The parallel light flux incident on 84e becomes a plane wave, and its wavefront should be an ideal wavefront. In this case, as shown in FIG. 4A, a spot image (hereinafter also referred to as “spot”) is formed at a position on the optical axis of each lens element constituting the microlens array 84e.

  However, since there is usually wavefront aberration in the projection optical system PL, the wavefront of the parallel light beam incident on the microlens array 84e deviates from the ideal wavefront, and the deviation, that is, the inclination of the wavefront with respect to the ideal wavefront, As shown in FIG. 4B, the imaging position of each spot is shifted from the position on the optical axis of each lens element of the microlens array 84e. In this case, the position shift from the reference point of each spot (the position on the optical axis of each lens element) corresponds to the inclination of the wavefront.

Then, the light (spot image light flux) incident on each light condensing point on the light receiving element constituting the light receiving unit 86 is photoelectrically converted by the light receiving element, and the photoelectric conversion signal is transmitted to the main controller 50 via the electric circuit. Sent. The main controller 50 calculates the imaging position of each spot based on the photoelectric conversion signal, and further calculates the positional deviation (Δξ, Δη) using the calculation result and the position data of a known reference point. And stored in the RAM. At this time, the measurement values (X _i , Y _i ) at that time of the wafer interferometer 54W are supplied to the main controller 50.

  As described above, when the measurement of the positional deviation of the spot image by the wavefront aberration measuring device 80 at the focusing point of one focused pinhole image is completed, the main controller 50 forms the next pinhole image. Wafer stage WST is moved so that the substantially center of opening 82a of wavefront aberration measuring instrument 80 coincides with the point. When this movement is completed, the main controller 50 emits the laser beam LB from the light source 16 in the same manner as described above, and the main controller 50 similarly calculates the imaging position of each spot. Thereafter, the same measurement is sequentially performed at other imaging points of the pinhole image.

In this way, at the stage where necessary measurement is completed, the RAM of the main controller 50 stores the above-described positional deviation data (Δξ, Δη) at the image formation point of each pinhole image and the coordinates of each image formation point. Data (measured values (X _i , Y _i ) of wafer interferometer 54W when measurement is performed at the image formation point of each pinhole image) is stored. In addition, the illumination light EL may be irradiated to all the pinholes simultaneously at the time of the measurement. However, using the movable reticle blind 30B, only the focused pinhole on the reticle, or at least a partial region including the focused pinhole. For example, the position and size of the illumination area on the reticle may be changed for each pinhole so that only the illumination light EL is illuminated.

Next, the main controller 50 loads the conversion program into the main memory, and the positional deviation data (Δξ, Δη) at the image point of each pinhole image stored in the RAM and the coordinates of each image point. Based on the data, according to the principle described below, corresponding to the pinhole image formation point, that is, from the first measurement point (evaluation point) to the nth measurement point (evaluation point) in the field of the projection optical system PL. Corresponding wavefronts (wavefront aberrations), here, coefficients of each term (Zernike term) of the fringe Zernike polynomial (hereinafter, abbreviated as “Zernike polynomial” as appropriate) of the formula (3) described later, for example, the first term The coefficient Z ₁ to the coefficient Z ₃₇ of the 37th term are calculated according to the conversion program.

  In the present embodiment, the wavefront of the projection optical system PL is obtained by calculation according to the conversion program based on the above-described positional deviations (Δξ, Δη). That is, the positional deviation (Δξ, Δη) is a value that directly reflects the inclination of the wavefront with respect to the ideal wavefront, and conversely, the wavefront can be restored based on the positional deviation (Δξ, Δη). As is clear from the physical relationship between the positional deviations (Δξ, Δη) and the wavefront, the wavefront calculation principle in this embodiment is the well-known Shack-Hartmann wavefront calculation principle.

  Next, a method for calculating the wavefront based on the above positional deviation will be briefly described.

  As described above, the positional deviation (Δξ, Δη) corresponds to the inclination of the wavefront, and by integrating this, the shape of the wavefront (strictly, the deviation from the reference plane (ideal wavefront)) is obtained. When the wavefront (deviation of the wavefront from the reference plane) is W (x, y) and the proportionality coefficient is k, the following relational expressions (1) and (2) are established.

スポット位置のみでしか与えられていない波面の傾きをそのまま積分するのは容易ではないため、面形状を級数に展開して、これにフィットするものとする。この場合、級数は直交系を選ぶものとする。ツェルニケ多項式は軸対称な面の展開に適した級数で、円周方向は三角級数に展開する。すなわち、波面Ｗを極座標系（ρ，θ）で表すと、次式（３）のように展開できる。

Since it is not easy to integrate the slope of the wavefront given only by the spot position as it is, the surface shape is developed into a series and fitted to this. In this case, an orthogonal system is selected as the series. The Zernike polynomial is a series suitable for expansion of an axisymmetric surface, and the circumferential direction is expanded to a triangular series. That is, when the wavefront W is expressed in the polar coordinate system (ρ, θ), it can be developed as the following equation (3).

直交系であるから各項の係数Ｚ_iを独立に決定することができる。ｉを適当な値で切ることはある種のフィルタリングを行うことに対応する。なお、一例として第１項〜第３７項までのｆ_i（ｆ_i（ρ，θ）：ρを独立変数とする動径多項式）を係数Ｚ_iとともに例示すると、次の表１のようになる。但し、表１中の第３７項は、実際のツェルニケ多項式では、第４９項に相当するが、本明細書では、ｉ＝３７の項（第３７項）として取り扱うものとする。すなわち、本発明において、ツェルニケ多項式の項の数は、特に限定されるものではない。

Since it is an orthogonal system, the coefficient Z _i of each term can be determined independently. Cutting i by an appropriate value corresponds to performing some kind of filtering. As an example, f _i (f _i (ρ, θ): radial polynomial with ρ as an independent variable) from the first term to the 37th term is illustrated together with the coefficient Z _i as shown in Table 1 below. . However, the 37th term in Table 1 corresponds to the 49th term in the actual Zernike polynomial, but is treated as a term of i = 37 (the 37th term) in this specification. That is, in the present invention, the number of terms of the Zernike polynomial is not particularly limited.

実際には、その微分が上記の位置ずれとして検出されるので、フィッティングは微分係数について行う必要がある。極座標系（ｘ＝ρｃｏｓθ，ｙ＝ρｓｉｎθ）では、次式（４）、（５）のように表される。

Actually, since the differentiation is detected as the above-described positional deviation, the fitting needs to be performed on the differential coefficient. In the polar coordinate system (x = ρcos θ, y = ρsin θ), the following expressions (4) and (5) are used.

ツェルニケ多項式の微分形は直交系ではないので、フィッティングは最小自乗法で行う必要がある。１つのスポット像の結像点の情報（ずれ量）はＸ方向とＹ方向につき与えられるので、ピンホールの数をｎ（ｎは、投影光学系ＰＬの視野内の計測点（評価点）の数に対応しており、本実施形態では、説明の簡略化のためにｎは例えば３３とする）とすると、上記式（１）〜（５）で与えられる観測方程式の数は２ｎ（＝６６）となる。

Since the differential form of the Zernike polynomial is not an orthogonal system, the fitting must be performed by the method of least squares. Since the information (deviation amount) of the image point of one spot image is given for the X direction and the Y direction, the number of pinholes is n (n is the number of measurement points (evaluation points) in the field of the projection optical system PL). In this embodiment, assuming that n is 33 for the sake of simplification of description, the number of observation equations given by the above formulas (1) to (5) is 2n (= 66). )

  Each term in the Zernike polynomial corresponds to an optical aberration. Moreover, the low-order terms (terms with a small i) substantially correspond to Seidel aberration. By using the Zernike polynomial, the wavefront aberration of the projection optical system PL can be obtained.

The calculation procedure of the conversion program is determined according to the principle as described above, and the wavefront corresponding to the first measurement point to the nth measurement point in the field of the projection optical system PL is calculated by the calculation process according to the conversion program. information (wavefront aberration), where the coefficients of the terms of the Zernike polynomial, for example, the first term of the coefficient Z ₁ ~ paragraph 37 of coefficient Z ₃₇ is obtained.

Returning to FIG. 1, target information to be achieved by the _first to third exposure apparatuses 922 _{1 to} 922 ₃ , for example, resolution (resolution), practical minimum line width (device) Rule), the wavelength of illumination light EL (center wavelength and wavelength width, etc.), information on the pattern to be transferred, and other information related to the projection optical system that determines the performance of other exposure apparatuses 922 _{1 to} 922 ₃ , which is the target value The information to get is stored. Further, in the hard disk or the like provided in the first communication server 920, target information in an exposure apparatus scheduled to be introduced in the future, for example, information on a pattern planned to be used is stored as target information.

  On the other hand, an optimization program that optimizes the formation state of a pattern projection image on an object under an arbitrary target exposure condition is installed in a storage device such as a hard disk included in the second communication server 930. In addition, a first database and a second database attached to the optimization program are stored. That is, the optimization program, the first database, and the second database are recorded on an information recording medium such as a CD-ROM, and the information recording medium is a CD-ROM drive provided in the second communication server 930 or the like. The optimization program is installed in a storage device such as a hard disk, and the first database and the second database are copied from the drive device.

The first database is a database of wavefront aberration change tables for each type of projection optical system (projection lens) provided in an exposure apparatus such as the exposure apparatuses 922 _{1 to} 922 ₃ . Here, the wavefront aberration change table is simulated using a model substantially equivalent to the projection optical system PL, and the formation state of the pattern projection image on the object obtained as a result of the simulation is optimized. Change of the unit adjustment amount of the adjustment parameter that can be used to convert the image, and imaging performance corresponding to each of a plurality of measurement points in the field of the projection optical system PL, specifically, wavefront data, for example, the first of the Zernike polynomial It is a change table which consists of the data group which arranged the data which show the relationship with the variation | change_quantity of the coefficient of a term-the 37th term according to the predetermined rule.

In the present embodiment, the adjustment parameters include the driving amounts z ₁ , θx ₁ , θy ₁ of the movable lenses 13 ₁ , 13 ₂ , 13 ₃ , 13 ₄ , 13 _{5 in} the respective degrees of freedom directions (driveable directions). , Z ₂ , θx ₂ , θy ₂ , z ₃ , θx ₃ , θy ₃ , z ₄ , θx ₄ , θy ₄ , z ₅ , θx ₅ , θy ₅ and the wafer W surface (Z tilt stage 58) A total of 19 parameters are used, such as the drive amount Wz, Wθx, Wθy in the direction of the angle and the wavelength shift amount Δλ of the illumination light EL.

Here, a procedure for creating a database of the wavefront aberration change table will be briefly described. The simulation computer a particular optical software is installed, first, the exposure apparatus 922 ₁ of the optical conditions (e.g., the design value of the projection optical system PL (including numerical aperture N.A. and the lens data), coherence factor σ values (Illumination σ) or the numerical aperture NA of the illumination optical system, and the wavelength (exposure wavelength) λ of the illumination light EL) are input. Next, data of an arbitrary first measurement point in the visual field of the projection optical system PL is input to the simulation computer.

Next, unit amount data for each of the degrees of freedom (movable direction) of the movable lenses 13 _{1 to} 13 ₅ , each of the degrees of freedom of the surface of the wafer W, and the shift amount of the wavelength of the illumination light is input. For example, if you enter a command that the movable lens 13 ₁ is driven by a unit amount with respect to the + direction of the Z-direction shift, the simulation computer, the first wave front of the first measurement point determined in advance within the field of projection optical system PL Data on the amount of change from the ideal wavefront, for example, the amount of change in the coefficient of each term (for example, the first to 37th terms) of the Zernike polynomial is calculated, and the data on the amount of change is displayed on the display screen of the simulation computer. At the same time, the amount of change is stored in the memory as a parameter PARA1P1.

Then, if you enter a command that the movable lens 13 ₁ is driven by a unit amount with respect to the + direction of the Y-direction tilt (X-axis of rotation [theta] x), the simulation computer, the second wavefront data for the first measurement point, For example, the change amount of the coefficient of each term of the Zernike polynomial is calculated, the change amount data is displayed on the display screen, and the change amount is stored in the memory as the parameter PARA2P1.

Then, if you enter a command that the movable lens 13 ₁ is driven by a unit amount with respect to the + direction of the X-direction tilt (Y-axis of rotation [theta] y), the simulation computer, third wavefront data for the first measurement point, For example, the change amount of the coefficient of each term of the Zernike polynomial is calculated, and the change amount data is displayed on the screen of the display, and the change amount is stored in the memory as the parameter PARA3P1.

Thereafter, in the same procedure as above, the input of each measurement point to the second measurement point through n th measurement point is performed, Z-direction shift of the movable lens 13 _1, Y-direction tilt command input X-direction tilt respectively Each time the simulation is performed, the simulation computer calculates the first wavefront, second wavefront, and third wavefront data at each measurement point, for example, the amount of change in the coefficient of each term in the Zernike polynomial, and the amount of change data is calculated. In addition to being displayed on the display screen, parameters PARA1P2, PARA2P2, PARA3P2,..., PARA1Pn, PARA2Pn, PARA3Pn are stored in the memory.

For the other movable lenses 13 ₂ , 13 ₃ , 13 ₄ , and 13 ₅ , the input of each measurement point and the command input for driving in the + direction by the unit amount with respect to each direction of freedom are performed in the same procedure as described above. In response to this, each of the first to n-th measurement points when the movable lenses 13 ₂ , 13 ₃ , 13 ₄ , and 13 ₅ are driven by a unit amount in the directions of degrees of freedom by the simulation computer. , For example, the amount of change in the coefficient of each term of the Zernike polynomial is calculated, parameters (PARA4P1, PARA5P1, PARA6P1,..., PARA15P1), parameters (PARA4P2, PARA5P2, PARA6P2,..., PARA15P2),. , Parameters (PARA4Pn, PARA5Pn, PARA6Pn, ..., PARA15Pn) Stored in memory.

  Also for wafer W, in the same procedure as described above, input of each measurement point and command input for driving in the + direction by a unit amount for each direction of freedom are performed. Wavefront data for each of the first to nth measurement points when the wafer W is driven by a unit amount in each direction of freedom of Z, θx, θy by a computer, for example, the amount of change in the coefficient of each term of the Zernike polynomial Are calculated and parameters (PARA16P1, PARA17P1, PARA18P1), parameters (PARA16P2, PARA17P2, PARA18P2),..., Parameters (PARA16Pn, PARA17Pn, PARA18Pn) are stored in the memory.

  Further, with respect to wavelength shift, in the same procedure as described above, input of each measurement point and command input for shifting the wavelength in the + direction by the unit amount are performed, and in response to this, the wavelength is shifted by the simulation computer. Wavefront data for each of the first to n-th measurement points when the value is shifted by a unit amount in the + direction, for example, the amount of change in the coefficient of each term of the Zernike polynomial is calculated, and PARA19P1, PARA19P2,. Stored in memory.

  Here, each of the parameters PARAiPj (i = 1 to 19, j = 1 to n) is a 37 × 1 column matrix (vertical vector). That is, when n = 33, the adjustment parameter PARA1 is expressed by the following equation (6). Note that the parameters PARAiPj are all column matrices, but in the following equation (6) and the following equations, an expression form as if it is a row matrix is adopted for convenience.

また、調整パラメータＰＡＲＡ２について、次式（７）のようになる。

Further, the adjustment parameter PARA2 is expressed by the following equation (7).

同様に、他の調整パラメータＰＡＲＡ３〜ＰＡＲＡ１９についても、次式（８）のようになる。

Similarly, the other adjustment parameters PARA3 to PARA19 are expressed by the following equation (8).

そして、このようにしてメモリ内に記憶されたツェルニケ多項式の各項の係数の変化量から成る列マトリクス（縦ベクトル）ＰＡＲＡ１Ｐ１〜ＰＡＲＡ１９Ｐｎは、調整パラメータ及び計測点について並べ替えが行われる。その結果、列マトリクス（縦ベクトル）ＰＡＲＡ１Ｐ１〜ＰＡＲＡ１９Ｐｎを要素とする次式（９）のマトリクス（行列）Ｏで示される波面収差変化表が作成される。なお、式（９）では、ｍ＝１９である。

The column matrices (vertical vectors) PARA1P1 to PARA19Pn that are composed of the change amounts of the coefficients of the terms of the Zernike polynomial thus stored in the memory are rearranged with respect to the adjustment parameters and the measurement points. As a result, a wavefront aberration change table represented by a matrix (matrix) O of the following equation (9) having column matrices (vertical vectors) PARA1P1 to PARA19Pn as elements is created. In Equation (9), m = 19.

  A database composed of the wavefront aberration change table for each type of projection optical system created in this manner is stored as a first database in a hard disk or the like included in the second communication server 930. In this embodiment, one wavefront aberration change table is created for the same type (same design data) of projection optical system. However, regardless of the type of projection optical system, each projection optical system (that is, in units of exposure apparatuses) is used. ) A wavefront aberration change table may be created.

Next, the second database will be described. In this second database, the following expression (10) expressing each imaging performance (imaging evaluation index) at each measurement point, which is used when optimizing the formation state of a projected image of a pattern to be described later on the wafer. ), A specific function (specific expression) having a coefficient (Zernike coefficient) C _{i, n} of each term of the Zernike polynomial in which the wavefront (wavefront aberration) at each measurement point (measurement point number n) is expanded as an independent variable In addition to the non-linear coefficient and the linear coefficient, data such as an allowable value of imaging performance is stored.

The above formula (10) is an estimation formula for imaging performance (imaging evaluation index) consisting only of nonlinear terms for each Zernike coefficient, similar to the estimation formula for the line width disclosed in the above-mentioned pamphlet of WO 03/075328. This is a formula representing a nonlinear function obtained by adding a linear term to (calculation formula). To calculate this formula (10), A, B, C, D, T _i ^α , T _{i, j} ^β , T _{i are used.} A total of 855 coefficients ^γ , T _i ^δ , S _i (here, i = 1 to 37), a coefficient of each term of the Zernike polynomial that develops the focus Z and the wavefront (wavefront aberration) of the projection optical system ( Zernike coefficient) Ci _{, n} (C1 _{, n to} C37 _{, n} ) is required. The Zernike coefficient C _{i, n} refers to the above-described coefficient Z _i at the n-th measurement point. The Zernike coefficient C _{i, n} is measured as described above, or can be calculated based on the single wavefront aberration and the wavefront aberration correction amount. As will be described later, the focus Z is set as an allowable value of DOF (depth of focus) by the operator as necessary. Therefore, for each of the reference IDs (exposure IDs), A, B, C, D, T _i ^α , T _{i, j} ^β , T _i ^γ , T _i ^δ , S _i (here, i = 1 to 37). A total of 855 coefficients are obtained in advance by simulation using simulation software such as an imaging simulator and stored as a part of the second database in a hard disk or the like included in the second communication server 930.

  In the above equation (10), A, B, C, and D are constants determined by exposure conditions and are not dependent on aberrations. Here, the exposure conditions are optical conditions (exposure wavelength, numerical aperture NA of the projection optical system (maximum NA, NA set at the time of exposure, etc.)) and illumination conditions (illumination NA). (Numerical aperture NA of illumination optical system) or illumination σ (coherence factor), aperture shape of illumination system aperture stop plate 24 (light quantity distribution of illumination light on pupil plane of illumination optical system, ie secondary light source) )))) And evaluation items (mask type, line width, evaluation amount, pattern information, etc.).

T _i ^α is the nonlinear coefficient of the focus shift α, T _{i, j} ^β is the nonlinear coefficient of the line width offset β, T _i ^γ is the nonlinear coefficient of the third-order asymmetry γ, and T _i ^δ is the second-order symmetry δ. It is a nonlinear coefficient. S _i is each term of the Zernike polynomial (for example, each of the first to 37th terms) of each imaging performance (for example, various aberrations (or index values thereof) or (imaging evaluation index)) of the projection optical system. Is the Zernike sensitivity, which is a value when 1λ is given. This Zernike sensitivity indicates the sensitivity of each imaging performance to each Zernike term. In the following description, Zernike sensitivity is also called Zernike Sensitivity or ZS.

In the present embodiment, as the imaging performance for which Zernike sensitivity is calculated, the following 12 types of linear aberrations that are linear imaging performance with respect to each Zernike coefficient, that is, distortion Dis in the X-axis direction and Y-axis direction are displayed. _x , Dis _y , line width abnormal values CM _V , CM _H , CM _R , CM _L which are index values of four types of coma aberration, CF _V , CF _H , CF _R , CF _L which are four types of field curvatures Thirteen types of imaging performance, including SA _V and SA _H which are two types of spherical aberration, and a line width CD which is nonlinear imaging performance for each Zernike coefficient are included. Here, the line width as the non-linear imaging performance for each Zernike coefficient includes the line width of the image of the line pattern formed on the image plane by the projection optical system PL, the line pattern extending in the vertical direction, and the horizontal Although there are line width differences with line patterns extending in the direction, line width differences between isolated lines and dense lines, etc., the line width CD of the image of the line pattern will be described below as a representative example. .

Next, using the aforementioned optimization program for a method of optimizing the formation conditions on the wafer of the projected image of the reticle pattern in such first to third exposure apparatus 922 _{1 to 922 3,} the second communication server The processing algorithm of the processor included in 930 will be described with reference to the flowchart of FIG. 5 (and FIGS. 6 to 10 and FIGS. 16 to 22).

  The flowchart shown in FIG. 5 starts when, for example, an exposure apparatus (unit) to be optimized is specified by an e-mail or the like from the operator of the exposure apparatus in the clean room via the first communication server 920. Is sent, and the operator on the second communication server 930 side inputs an instruction to start processing to the second communication server 930.

  First, in step 102, a target machine designation screen is displayed on the display.

In the next step 104, the system waits for the designation of the number machine, and when the number machine designated by the operator in the previous e-mail, for example, the exposure device 922 ₁ is designated via a pointing device such as a mouse, Proceed to 106 to store the designated number. The memory of this machine is, for example, the device No. It is done by memorizing.

  In the next step 108, a mode selection screen is displayed on the display. In this embodiment, since any one of mode 1 to mode 3 can be selected, for example, selection buttons for mode 1, mode 2, and mode 3 are displayed on the mode selection screen.

In the next step 110, it waits for a mode to be selected. When the operator selects a mode with the mouse or the like, the process proceeds to step 112 to determine whether or not the selected mode is mode 1. If mode 1 is selected, the process proceeds to a subroutine for performing mode 1 processing in step 118 (hereinafter also referred to as “mode 1 processing routine”). Here, mode 1 is a mode in which optimization is performed based on an existing ID. The mode 1 is the adjusted state under exposure condition as a certain reference (reference ID), while using the exposure apparatus 922 _1, for example, lighting conditions and the numerical aperture of the projection optical system (N.A.) such as This is mainly selected when changing.

In the processing routine of this mode 1 (hereinafter also referred to as “first mode”), first, in step 202 of FIG. 6, the exposure condition to be optimized (hereinafter also referred to as “optimized exposure condition” as appropriate). Get information about. Specifically, the first communication server 920 (or target Unit via the first communication server 920 (exposure apparatus 922 ₁₎ of the main control unit 50), the current projection of the target Unit (exposure apparatus 922 ₁₎ N. of the optical system. A. Inquires and acquires setting information such as illumination conditions (illumination NA or illumination σ, aperture stop type, etc.) and target pattern type.

In the next step 204, for the first communication server 920 (or the main controller 50 of the target number machine (exposure apparatus 922 ₁ ) via the first communication server 920), the reference ID closest to the optimized exposure condition described above. (Hereinafter simply abbreviated as “reference ID” where appropriate) and the projection optical system N.D. A. And setting information such as illumination conditions (for example, illumination NA or illumination σ, type of aperture stop).

In the next step 206, from the first communication server 920 (or from the main controller 50 of the target machine (exposure device 922 ₁ ) via the first communication server), the necessary information on the single wavefront aberration and the reference ID, specifically, Acquires the value of the adjustment amount (adjustment parameter) in the reference ID, the wavefront aberration correction amount for the single wavefront aberration in the reference ID, and the like.

  Normally, the single wavefront aberration of the projection optical system PL and the wavefront aberration of the projection optical system PL after being incorporated in the exposure apparatus (hereinafter referred to as wavefront aberration in the on body) do not coincide with each other for some reason. For the sake of simplification of explanation, it is assumed that this correction is made for each reference ID (reference exposure condition) at the time of starting up the exposure apparatus or by adjustment in the manufacturing stage.

In the next step 208, from the first communication server 920 (or the main controller 50 of the target machine (exposure apparatus 922 ₁ ) via the first communication server 920), the model name, exposure wavelength, and maximum N. of the projection optical system. A. Get device information.

In the next step 210, based on the single wavefront aberration acquired in step 206 and the wavefront aberration correction amount in the reference ID, for each measurement point (measurement point numbers are n = 1, 2,... 33), Information on the wavefront aberration, for example, the coefficient C _{i, n} (i = 1 to 37) of each term of the Zernike polynomial is calculated and stored in the memory. As a result, the wavefront aberration data Wa indicated by the matrix of 37 rows and 33 columns of the following equation (11) is stored in the memory.

  Next, in step 220 of FIG. 7, a screen for specifying an allowable value (target value) relating to the imaging performance (the above-mentioned 12 types of linear aberration and nonlinear imaging performance (line width)) is displayed on the display. At this time, regarding the line width performance optimization, the designated area of the depth of focus DOF and the allowable value of the line width variation is displayed. Based on the depth of focus DOF, the focus Z in the above equation (10) is determined.

  In step 222, it is determined whether or not an allowable value has been input. If this determination is negative, the process proceeds to step 226 and whether or not a certain time has elapsed since the input screen for the allowable value was displayed. If this determination is negative, the routine returns to step 222. On the other hand, if an allowable value is specified by the operator via the keyboard or the like in step 222, the allowable value related to the specified imaging performance is stored in a memory such as a RAM and then the process proceeds to step 226. To do. That is, such a loop of step 222 → 226 or a loop of step 222 → 224 → 226 is repeated, and it waits for a predetermined time until an allowable value is designated.

  Here, the tolerance values for the 12 types of linear aberrations and the tolerance values for the line width variation are not necessarily used for the optimization calculation itself (in this embodiment, calculation of the adjustment amount of the adjustment parameter using the merit function Φ as described later). It is not necessary, but it is necessary when evaluating the calculation results. In particular, the line width is basically more important for evaluation than the absolute value. On the other hand, the allowable value of the depth of focus DOF is the reference for the focus Z described above, and is essential when optimizing nonlinear imaging performance such as line width.

  Then, when a certain time has elapsed, the process proceeds to step 228, and a default setting value of an allowable value related to the imaging performance that has not been specified is read from the second database. As a result, the allowable value related to the designated imaging performance and the allowable value of the remaining aberration read from the second database are stored in the memory. Here, when the allowable value of the depth of focus DOF is not specified, it is a case where optimization of the line width is not required. Therefore, the default setting value of the allowable value of the depth of focus DOF is set to zero. When the set value is read from the second database, the focus Z is set to zero.

  In the next step 230, after the constraint condition designation screen is displayed on the display, it is determined whether or not the constraint condition is input in step 232, and if this determination is negative, the process proceeds to step 236. Then, it is determined whether or not a certain period of time has elapsed since the above constraint condition designation screen was displayed. If this determination is denied, the process returns to step 232. On the other hand, if a constraint condition is designated by the operator via the keyboard or the like in step 232, the process proceeds to step 234, and after the constraint condition of the designated adjustment parameter is stored in a memory such as a RAM, Control goes to step 236. That is, such a loop of step 232 → 236 or a loop of step 232 → 234 → 236 is repeated to wait for a predetermined time until the constraint condition is designated.

Here, the constraint conditions are the above-described allowable movable ranges of the movable lenses 13 _{1 to} 13 _{5 in} the respective degrees of freedom, the allowable movable ranges of the Z tilt stage 58 in the three degrees of freedom, the allowable range of wavelength shift, and the like. This means an allowable variable range of each adjustment amount (adjustment parameter).

  Then, when a certain period of time has passed, the process proceeds to step 238, and according to the default setting, as a restriction condition for the adjustment parameter that has not been specified, a movable range (driveable range) calculated based on the current value of each adjustment parameter Range) is calculated and stored in a memory such as a RAM. As a result, the restriction conditions for the designated adjustment parameter and the calculated restriction conditions for the remaining adjustment parameters are stored in the memory.

  Next, in step 240 of FIG. 8, an imaging performance weight designation screen is displayed on the display. Here, in the case of the present embodiment, designation of weights for imaging performance is performed by 33 evaluation points (measurements) in the field of view of the projection optical system (usually, a rectangular region corresponding to the illumination region described above). Since it is necessary to specify the above-mentioned 13 types of imaging performance with respect to (point), it is necessary to specify 33 × 13 = 429 weights. For this reason, on the weight designation screen, first, a weight designation screen for 13 types of imaging performance is displayed so that weights can be designated in two stages, and then weights at each evaluation point in the field of view are designated. The screen is displayed.

  In step 242, it is determined whether any imaging performance weight is designated. If the weight is designated by the operator via the keyboard or the like, the process proceeds to step 244 to store the designated imaging performance weight in a memory such as a RAM and then proceeds to step 248. In this step 248, it is determined whether or not a fixed time has elapsed since the start of the display of the above-described weight designation screen. If this determination is negative, the process returns to step 242.

  On the other hand, if the determination in step 242 is negative, the process proceeds to step 248.

  In the present embodiment, by repeating the loop of step 242 → 248 or the loop of step 242 → 244 → 248, the display of the imaging performance weight designation screen is started when the imaging performance weight is designated. Wait for a certain time from. When at least one imaging performance weight is designated, the designated imaging performance weight is stored. Then, after a certain period of time elapses in this way, the process proceeds to step 253, where the weight of each imaging performance not designated is set to 1 according to the default setting, and then the process proceeds to step 254.

  As a result, the designated imaging performance weight and the remaining imaging performance weight (= 1) are stored in the memory.

  In the next step 254, a screen for designating the weight at the evaluation point (measurement point) in the field of view is displayed on the display. In step 256, it is determined whether or not the weight at the evaluation point is specified. In this case, the process proceeds to step 260, and it is determined whether or not a certain time has elapsed since the start of the display of the screen for designating the weight at the evaluation point (measurement point). If the determination is negative, the process returns to step 256.

  On the other hand, in step 256, when a weight for one of the evaluation points (usually, an evaluation point for which improvement is particularly desired is selected) is specified by the operator via a keyboard or the like, the process proceeds to step 258, where After setting the weight at the evaluation point and storing it in a memory such as a RAM, the routine proceeds to step 260.

  That is, by repeating the loop of step 256 → 260 or the loop of step 256 → 258 → 260, it waits for a certain period of time from the start of display of the weight designation screen at the above-mentioned evaluation point until the weight of the evaluation point is designated. .

  Then, when the predetermined time has elapsed, the process proceeds to step 262, and the weights at all evaluation points not designated are set to 1 according to the default setting, and then the process proceeds to step 264 in FIG.

  As a result, the designated value of the weight at the designated evaluation point and the weight (= 1) at the remaining evaluation points are stored in the memory.

  In step 264 of FIG. 9, a screen for designating target values (targets) of the above-described 13 types of imaging performance at each evaluation point in the field of view is displayed on the display. Here, in the case of this embodiment, the imaging performance target needs to be specified for the 13 types of imaging performance described above for 33 evaluation points (measurement points) in the field of view of the projection optical system. Therefore, it is necessary to specify 33 × 13 = 429 targets. Hereinafter, the line width target is also referred to as “line width target CDt”.

  In the next step 266, waiting for a target to be designated for a predetermined time (that is, determining whether or not the target has been designated), and if no target has been designated (if the judgment is negative), The process proceeds to step 272, where it is determined whether or not a predetermined time has elapsed since the display of the target designation screen was started. If this determination is negative, the process returns to step 266.

  On the other hand, when any one of the imaging performance targets at any of the evaluation points is specified by the operator via the keyboard or the like in step 266, the determination in step 266 is affirmed, and the process proceeds to step 268. After the designated target is set and stored in a memory such as a RAM, the process proceeds to step 272.

  That is, in the present embodiment, the loop of step 266 → 272 or the loop of step 266 → 268 → 272 is repeated to wait for a predetermined time from the start of display of the target designation screen described above. When one or more imaging performance targets at one or more evaluation points are designated, the designated imaging performance targets at the designated evaluation points are stored. Then, after a certain period of time elapses in this way, the process proceeds to step 274, and after setting all of the imaging performance targets at the evaluation points not designated to 0 according to the default settings, the process proceeds to step 284. To do. Note that the line width target CDt being zero means that the line width cannot be zero, and therefore optimization is not performed for the line width.

As a result, in the memory, the target of the specified imaging performance at the specified evaluation point and the remaining target (= 0) of the imaging performance are, for example, 33 rows 13 as shown in the following equation (12). It is stored in the form of a column of the matrix f _t.

  In the present embodiment, the imaging performance at the evaluation point where the target is not specified is not considered in the optimization calculation. Therefore, it is necessary to evaluate the imaging performance again after obtaining the solution.

  In the next step 284, the screen for designating the optimized field range is displayed on the display, and then the loop from step 286 to step 290 is repeated, and the field range is displayed for a predetermined time from the start of the screen for designating the optimized field range. Wait for it to be specified. Here, in the scanning exposure apparatus such as the scanning stepper as in the present embodiment, the optimization field range can be specified. The imaging performance or the transfer of the pattern on the object in the entire field of view of the projection optical system. Depending on the size of the reticle or its pattern area (that is, the whole or a part of the pattern area used for exposure of the wafer) to be used even if it is a so-called stepper, the state is not necessarily optimized. This is because it is not always necessary to optimize the imaging performance or the pattern transfer state on the wafer in the entire field of view of the optical system.

  If the optimization field range is designated within a predetermined time, the process proceeds to step 288, the designated range is stored in a memory such as a RAM, and then the process proceeds to step 292 in FIG. On the other hand, if the optimization field range is not specified, the process proceeds to step 292 without performing anything.

  In step 292, the count value m of the counter that defines the number of iterations of the linear approximation calculation (optimization calculation) is initialized to 1 (m ← 1).

In the next step 294, 13 types of imaging performance at the present time, that is, before optimization, are calculated for each measurement point based on the above-described equation (10), and stored in a temporary storage area in the memory. In the calculation in step 294, the wavefront aberration data Wa for each measurement point calculated in step 210 described above, and the nonlinear coefficient and ZS in the reference ID in the second database are used. Regarding the 12 types of linear aberration, since all of the nonlinear coefficients A, B, C, D, T _i ^α , T _{i, j} ^β , T _i ^γ and T _i ^δ are zero, the equation (10) The calculation is substantially the same as the calculation of the following equation (10) ′.

  As a result of the processing of step 294, data of the imaging performance f indicated by a matrix of 13 rows and 33 columns of the following equation (13) is stored in the temporary storage area in the memory.

  In the next step 296, the following a. ~ C. According to the above procedure, a Zernike Sensitivity file (ZS file) and an imaging performance change table are created for each measurement point.

a. First, Zernike Sensitivity corresponding to the above-described optimized exposure conditions is calculated for each measurement point (n = 1 to 33) based on the following equation (14). In the present embodiment, linear aberrations (distortion Dis _x , Dis _{y in} the X-axis direction and Y-axis direction) for the 12 types of Zernike terms, line width abnormal values CM _V , CM _H , which are index values of the four types of coma aberration, CM _R , CM _L , four types of curvature of field CF _V , CF _H , CF _R , CF _L , two types of spherical aberration SA _V , SA _H ), and at least one type of non-linearity for each Zernike coefficient ZS is calculated for each of the 13 types of imaging performance with a good imaging performance, here, the line width CD.

ここで、Ｓⁿ _p,iは、ｎ番目の計測点におけるｐ番目（ｐ＝１〜１３）の結像性能のZernike Sensitivityを指す。ここで、ｐ＝１はDis_x、ｐ＝２はDis_y、ｐ＝３はＣＭ_V、ｐ＝４はＣＭ_H、ｐ＝５はＣＭ_R、ｐ＝６はＣＭ_L、ｐ＝７はＣＦ_V、ｐ＝８はＣＦ_H、ｐ＝９はＣＦ_R、ｐ＝１０はＣＦ_L、ｐ＝１１はＳＡ_V、ｐ＝１２はＳＡ_H、ｐ＝１３はＣＤ、にそれぞれ対応する。また、ＥＶⁿ _p（ｐ＝１〜１２）は、上式（１０）’に基準ＩＤにおける１２種類の線形収差それぞれのＺＳを代入した各線形収差を表す関数（各ツェルニケ係数に対する線形関数）に相当する。これらの線形収差の場合、ＺＳが波面収差（各ツェルニケ係数）の影響を受けないので、ここでの関数は、カウント値ｍの変化にかかわらず同じ関数のままである。一方、ＥＶⁿ ₁₃は、前述の式（１０）において、第２データベース内の基準ＩＤにおける合計８５５個の係数を代入したｎ番目の計測点についての線幅を表す関数（各ツェルニケ係数に対する非線形関数）に相当する。線幅は、そのＺＳが波面収差の影響を受けて変化するので、後述するようにカウント値ｍの増加に応じてステップ３０２でその都度算出される複数の調整量の最適値と波面収差変化表とから算出される各ツェルニケ係数の大きさに従って、ＺＳが変化することになる。すなわち、このステップ２９６では、カウント値ｍがインクリメントされる度に、複数の調整量の最適値に応じて線幅のＺＳが新たに算出される。このとき、図１４に示されるように、算出された最新の複数の調整量の最適値（例えばΔＰ₁）に対応する、前記非線形関数を線形近似する新たな結像性能計算近次関数（図１４中のＢ’１参照）を作成することになる。

Here, S ⁿ _{p, i} indicates the Zernike Sensitivity of the p-th (p = 1 to 13) imaging performance at the n-th measurement point. Here, p = 1 is Dis _x , p = 2 is Dis _y , p = 3 is CM _V , p = 4 is CM _H , p = 5 is CM _R , p = 6 is CM _L , and p = 7 is CF _V , p = 8 corresponds to CF _H , p = 9 corresponds to CF _R , p = 10 corresponds to CF _L , p = 11 corresponds to SA _V , p = 12 corresponds to SA _H , and p = 13 corresponds to CD. EV ⁿ _p (p = 1 to 12) is a function (linear function for each Zernike coefficient) representing each linear aberration obtained by substituting ZS of each of the 12 types of linear aberrations in the reference ID into the above equation (10) ′. Equivalent to. In the case of these linear aberrations, ZS is not affected by wavefront aberration (each Zernike coefficient), so the function here remains the same regardless of the change in the count value m. On the other hand, EV ⁿ ₁₃ is a function (a non-linear function for each Zernike coefficient) representing the line width at the nth measurement point in which a total of 855 coefficients in the reference ID in the second database are substituted in the above-described equation (10). ). Since the ZS changes under the influence of wavefront aberration, the line width changes, and as will be described later, the optimum value of the plurality of adjustment amounts and the wavefront aberration change table calculated each time in step 302 in accordance with the increase in the count value m. ZS changes according to the magnitude of each Zernike coefficient calculated from the above. That is, in this step 296, every time the count value m is incremented, the line width ZS is newly calculated according to the optimum values of the plurality of adjustment amounts. At this time, as shown in FIG. 14, a new imaging performance calculation near-order function (FIG. 14) that linearly approximates the nonlinear function corresponding to the calculated optimum values (for example, ΔP ₁ ) of the latest plurality of adjustment amounts. 14) (see B′1 in FIG. 14).

b. Next, using each ZS calculated above as an element, a ZS file for each measurement point represented by a matrix of 13 rows and 37 columns of the following equation (15) is created.

In the above equation (15), S ⁿ _{p, q} (p = 1 to 13, q = 1 to 37) indicates each element of the ZS file for the nth measurement point. Specifically, S ⁿ _{1, q} is the change in Dis _x per 1λ of the q-th term of the Zernike polynomial that develops the wavefront aberration (wavefront) at the n-th measurement point, and S ⁿ _{2, q} is the q-th term. Change of Dis _y per 1λ, S ⁿ _{3, q} is change of CM _V per 1λ of q-th term, S ⁿ _{4, q} is change of CM _H per 1λ of q-th term, S ⁿ _{5, q} is Change in CM _R per 1λ of q-th term, S ⁿ _{6, q} is change in CM _L per 1λ in q-th term, S ⁿ _{7, q} is change in CF _V per 1λ in q-th term, S ⁿ _{8, q} is the change in CF _H per 1λ of the q term, S ⁿ _{9, q} is the change in CF _R per 1λ of the q term, and S ⁿ _{10, q} is the change in CF _L per 1λ of the q term. Change, S ⁿ _{11, q} is the change in SA _V per 1λ of the q term, S ⁿ _{12, q} is the change in SA _H per 1λ of the q term, S ⁿ _{13, q} is per 1λ of the q term The change in CD (linear approximation) is shown.

Here _{, the reason why} only the change S ⁿ _{13, q} of the CD is (linear approximate value) is that the remaining aberration is a linear aberration, and thus the change is not an approximate value. That is, when calculating the ZS of linear aberration for each of the 12 types of Zernike coefficients described above, all of A, B, C, D, T _i ^α , T _{i, j} ^β , T _i ^γ and T _i ^δ Since it is zero, the ZS of the 12 types of linear aberrations calculated by the above equation (15) matches the ZS of each linear aberration in the reference ID. Moreover, since these ZS are not influenced by the aberration, they have the same value at all measurement points.

c. The ZS file for the n-th measurement point created above and the wavefront aberration change table for the corresponding measurement point (a matrix of 37 rows and 19 columns corresponding to the n-th row of the matrix of the above equation (9)). Using this, an imaging performance change table for each measurement point is created. This can be expressed by the following equation (16).

Imaging Performance Change Table = Wavefront Aberration Change Table / ZS File (16)
Since the calculation of the equation (16) is a multiplication of the ZS file (matrix with 13 rows and 37 columns) and the wavefront aberration change table (matrix with 37 rows and 19 columns), imaging at the first measurement point obtained is obtained. The performance change table B1 is, for example, a matrix of 13 rows and 19 columns represented by the following equation (17).

  The imaging performance change table is calculated for every 33 measurement points. As a result, 33 imaging performance change tables B1 to B33 each having a matrix of 13 rows and 19 columns are obtained.

In the next step 298, the imaging performance f and its target _ft are lined up (one-dimensional). Here, a row of A, these f is a matrix of 13 rows 33 columns, the f _t, which means that the format conversion in a matrix of 429 rows and 1 column. The f and f _t after the alignment are as shown in the following equations (18) and (19), respectively.

  In the next step 300, the imaging performance change table for each of the 33 measurement points created in step 296 is two-dimensionalized. Here, the two-dimensionalization means that 33 types of imaging performance change tables, each of which is a matrix of 13 rows and 19 columns, are converted into a column for each adjustment parameter and converted into a format of 429 rows and 19 columns. . The imaging performance change table after the two-dimensionalization is, for example, B shown in the following equation (20).

  After the two-dimensionalization of the imaging performance change table as described above, the process proceeds to step 302, and the optimum value of the adjustment parameter change amount (adjustment amount) is calculated without considering the above-described constraint conditions. To do.

  Hereinafter, the processing in step 302 will be described in detail.

  The arbitrary imaging performance at the nth measurement point can be expressed by the above-described equation (10). For example, the line width CD for the nth measurement point can be expressed by the following equation (21).

上式（２１）に、既知の非線形係数、及びＺＳ、並びにツェルニケ係数Ｃ_i,nを代入することで、基準線幅計算値を求めることができる。

By substituting a known nonlinear coefficient, ZS, and Zernike coefficient C _{i, n} into the above equation (21), the calculated reference line width can be obtained.

By the way, since it is difficult to apply the root mean square optimization method to a function represented by a non-linear expression, Equation (21) is expressed as Zernike coefficient C _i of wavefront aberration using the above-mentioned reference line width calculation value as an offset. _{, n} is transformed into a linear approximation formula, the following formula (22) is obtained.

ここで、線幅線形近似計算値をｃｄ_nと表記している。

Here, the line width linear approximation calculation value is expressed as cd _n .

ΔC _{i, n} can be expressed by the following equation (23) using each element of the wavefront aberration change table for the n-th measurement point and the adjustment amount dx _k of each adjustment parameter.

上式（２２）、（２３）より、線幅線形近似計算値ｃｄ_nは、次式（２４）のように表せる。

From the above equations (22) and (23), the line width linear approximation calculation value cd _n can be expressed as the following equation (24).

ここで、２次元化後の結像性能変化表Ｂ中のｎ番目の計測点における線幅変化に対応する要素ｈⁿ _p,k（ｐ＝１３）は、次式（２５）のように定義できる。

Here, the element h ⁿ _{p, k} (p = 13) corresponding to the line width change at the nth measurement point in the imaging performance change table B after the two-dimensionalization is defined as the following equation (25). it can.

上式（２４）、（２５）より、ｎ番目の計測点における線幅線形近似計算値ｃｄ_nは、次式（２６）のように表せる。

From the above equations (24) and (25), the line width linear approximate calculation value cd _n at the _nth measurement point can be expressed as the following equation (26).

ｎ（＝３３）点の計測点における線幅線形近似計算値ｃｄ₁〜ｃｄ₃₃は、次式（２７）のように表せる。

n (= 33) linewidth linear approximation Calculated cd ₁ at the measurement point of the point ～Cd ₃₃ can be expressed as the following equation (27).

上式（２７）と同様の関係式で、他の結像性能、ここでは前述の１２種類の線形収差も表すことができる。そこで、上式（２７）を他の結像性能をも含むように拡張するものとして、１３種類の結像性能の線形近似計算値をｅｖ、基準結像性能計算値をＥＶとすると、これらと２次元化後の結像性能変化表Ｂ、及び１９種類の調整パラメータの調整量（ｄｘとする）との間には、次式（２８）の関係が成立する。

Other imaging performance, here, the above-mentioned 12 types of linear aberrations can also be expressed by the same relational expression as the above expression (27). Therefore, assuming that the above equation (27) is extended to include other imaging performances, ev is a linear approximation calculation value of 13 types of imaging performance, and EV is a reference imaging performance calculation value. The relationship of the following equation (28) is established between the imaging performance change table B after two-dimensionalization and the adjustment amounts (dx) of 19 types of adjustment parameters.

ev = EV + B · dx (28)
In the above equation (28), ev is a column matrix (vertical vector) of 429 rows and 1 column consisting of 13 types of linear approximation calculation values of imaging performance for n (= 33) points. EV is a column matrix (vertical vector) of 429 rows and 1 column composed of reference imaging performance calculation values of 13 types of imaging performance for n (= 33) points. Dx is a matrix of 19 rows and 1 column represented by the following equation (29) having the adjustment amount dx _k of each adjustment parameter as an element.

ここで、基準結像性能計算値ＥＶをステップ２９４で算出された結像性能とした場合に、上式（２８）で表される結像性能の線形近似計算値ｅｖと結像性能のターゲットとの差が最小（例えば零）となる、ｄｘの各要素を求めることが、ここでの最適化に他ならない。そこで、上式（２８）のｅｖを前述の一列化後の結像性能のターゲットｆ_tと置き換え、ＥＶを一列化後の結像性能ｆと置き換えるとともに式の変形を行うと、次式（３０）のような関係が成立する。

Here, when the reference imaging performance calculation value EV is the imaging performance calculated in step 294, the linear approximation calculation value ev of the imaging performance expressed by the above equation (28), the imaging performance target, Finding each element of dx that minimizes the difference between the two is an optimization here. Therefore, replacing the ev of the equation (28) and the target f _t of the imaging performance after a row of the foregoing, when the deformation of the formula is replaced with the imaging performance f after a row of the EV, the following equation (30 ) Is established.

(F _t −f) = B · dx (30)
In the above equation (30), ( _ft− f) is a matrix of 429 rows and 1 column represented by the following equation (31).

上式（３０）を最小自乗法で解くと、次式のようになる。

When the above equation (30) is solved by the least square method, the following equation is obtained.

dx = (B ^T · B) ⁻¹ · B ^T · ( _ft −f) (32)
Here, B ^T is a transposed matrix of the aforementioned imaging performance change table B, and (B ^T · B) ⁻¹ is an inverse matrix of (B ^T · B).

  However, when there is no designation of weight (all weights = 1), it is rare and normally there is designation of a weight. Therefore, the merit function Φ which is a weighting function represented by the following equation (33) is minimized. It will be solved by the square method.

ここで、ｆ_tiは、ｆ_tの要素であり、ｆ_iはｆの要素である。上式を変形すると、次のようになる。

Here, f _ti is an element of f _t , and f _i is an element of f. The above equation is transformed as follows.

従って、ｗ_i ^1/2・ｆ_iを新たな結像性能ｆ_i’とし、ｗ_i ^1/2・ｆ_tiを新たなターゲートｆ_ti’とすると、メリット関数Φは、次のようになる。

Therefore, if w _i ^1/2 · f _i is a new imaging performance f _i ′ and w _i ^1/2 · f _ti is a new targe f _ti ′, the merit function Φ is as follows.

従って、上記式（３５）を最小自乗法で解いても良い。但し、この場合、結像性能変化表として、次式で示される結像性能変化表を用いる必要がある。

Therefore, the above equation (35) may be solved by the method of least squares. However, in this case, it is necessary to use an imaging performance change table represented by the following equation as the imaging performance change table.

このようにして、ステップ３０２では、制約条件を考慮することなく、最小自乗法により、ｄｘの１９個の要素、すなわち前述の１９個の調整パラメータの調整量の最適値を求める。

Thus, in step 302, the optimum value of the adjustment amount of 19 elements of dx, that is, the above-described 19 adjustment parameters is obtained by the least square method without considering the constraint condition.

In the next step 304, as in step 294 described above, 13 types of imaging performance at each element of the matrix f, that is, all evaluation points, are calculated and stored in the temporary storage area in the memory. In the calculation of step 304, each measurement calculated based on the optimum value of the adjustment amount of the latest 19 adjustment parameters and the wavefront aberration change table obtained in either step 302 or step 310 described later. Information on wavefront aberration for the point, for example, the coefficient C _{i, n} (i = 1 to 37, n = 1 to 33) of each term of the Zernike polynomial and the ZS related to each imaging performance created in the previous step 296 are used. It is done.

  In the next step 306, it is determined whether or not the 13 types of imaging performance at all of the calculated evaluation points are within the range of the individual allowable values set previously. At this time, regarding the line width, it is determined whether or not the calculation result of the line width is within an allowable value of the line width variation. If the determination in step 306 is negative, the process proceeds to step 312 to determine whether the count value m of the counter is equal to or greater than a predetermined value M. If this determination is negative, the process proceeds to step 314, the count value m is incremented by 1, and the process returns to step 296.

In step 296, a ZS file and an imaging performance change table are created for each measurement point according to the above-described procedure, and the processing in step 298 and thereafter is repeated thereafter. In this step 296, when the count value m is 2 or more, when calculating Zernike Sensitivity, the optimum value of the adjustment amount and wavefront aberration of the latest 19 adjustment parameters obtained in the above step 302 (or step 310 described later) are calculated. Information on wavefront aberration for each measurement point calculated based on the change table, for example, coefficients C _{i, n} (i = 1 to 37, n = 1 to 33) of each term of the Zernike polynomial are used.

  In this manner, the loop process of step 296 → 298 → 300 → 302 → 304 → 306 → 312 → 314 is repeatedly executed until the determination in either step 306 or step 312 is affirmed. Every time the processing of this loop is repeated, in step 302, the optimum value of the adjustment amount of 19 adjustment parameters for simultaneously optimizing the imaging performance to be optimized among the 13 types of imaging performance is obtained. In particular, in the case of non-linear imaging performance with respect to each Zernike coefficient, here, the target CDt of the line width is not zero, the optimum value of the adjustment amount of the 19 adjustment parameters calculated in step 302 is a true optimum solution. Asymptotically. On the other hand, when the line width target CDt is zero and only the linear imaging performance is targeted for optimization with respect to each Zernike coefficient, the weight, imaging performance target, and other setting values are not changed. The calculation result in step 302 does not change.

Here, the principle of the above-described method for asymptotically obtaining the optimum solution will be described. Here, a case where one lens element is driven using the first lens element driving mechanism and the second lens element driving mechanism to optimize the line width at three measurement points in the field of view of the projection optical system. An example will be described with reference to FIGS. The first lens element drive mechanism, and the second lens element driving mechanism refers to adjusting mechanism for adjusting the line width of the projected image of the pattern by the projection optical system, for example, any of the movable lens _{131-134 5} above The one-degree-of-freedom direction driving mechanism and the second lens element driving mechanism can be considered to correspond to another degree-of-freedom-direction driving mechanism of the movable lens.

In FIG. 11, the driving amount ΔP ₁ of the first lens element driving mechanism is taken as a horizontal axis, and is nonlinear with respect to the driving amount ΔP ₁ at any one measurement point (evaluation point) in the field of view of the projection optical system. A nonlinear function A1 representing the amount of change in line width, which is a kind of imaging performance, that is, ΔCD = f ₁ (ΔP ₁ ) is indicated by a solid line, and approximated by a tangent at a point of ΔP ₁ = 0 of the nonlinear function A1. The linear approximation function A′1 is indicated by a broken line. The linear approximation function A′1 indicated by the broken line is expressed by the following equation (37).

ここで、ΔＣＤ^linは線形近似関数Ａ’１で計算される近似線幅変化量を、Ｆ₁は第１レンズエレメント駆動機構の駆動量と線幅変化量との関係を表す線形近似関数Ａ’１を、ｆ₁は第１レンズエレメント駆動機構の駆動量と線幅変化量との関係を示す非線形関数Ａ１を、（∂ｆ₁（ΔＰ₁）／∂ΔＰ₁）_@ΔP1=0はΔＰ₁＝０での非線形関数ｆ₁の偏微分係数（微分係数）を、それぞれ表わす。

Here, ΔCD ^lin is an approximate line width change amount calculated by the linear approximation function A′1, and F ₁ is a linear approximation function A ′ representing the relationship between the drive amount of the first lens element drive mechanism and the line width change amount. 1, f ₁ is a non-linear function A1 indicating the relationship between the driving amount of the first lens element driving mechanism and the line width change amount, and (∂f ₁ (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} is ΔP ₁ The partial differential coefficients (differential coefficients) of the nonlinear function f ₁ at = 0 are represented respectively.

Similarly to the above, the linear approximation function of the driving amount of the second lens element driving mechanism (denoted by ΔP ₂ ) and the line width change amount is expressed by the following equation.

ここで、Ｆ₂は第２レンズエレメント駆動機構の駆動量ΔＰ₂と線幅変化量との関係を示す線形近似関数を、ｆ₂は第２レンズエレメント駆動機構の駆動量と線幅変化量との関係を示す非線形関数を、（∂ｆ₂（ΔＰ₂）／∂ΔＰ₂）_@ΔP2=0はΔＰ₂＝０での非線形関数ｆ₂の偏微分係数（微分係数）を、それぞれ表わす。線幅の変化が式（３７）と式（３８）との線形和で表されるとすると、次式（３９）が成立する。

Here, F ₂ is a linear approximation function indicating the relationship between the driving amount [Delta] P ₂ and line width variation amount of the second lens element drive mechanism, f ₂ is a drive amount and the change in line width of the second lens element driving mechanism (∂f ₂ (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} represents a partial differential coefficient (differential coefficient) of the nonlinear function f _{2 when} ΔP ₂ = 0. If the change in line width is expressed by the linear sum of Expression (37) and Expression (38), the following Expression (39) is established.

これを、マトリクス表示すれば、次式（４０）のようになる。

If this is displayed in matrix, the following equation (40) is obtained.

一方、イニシャルの線幅性能は、実際に露光を行いウエハ上に形成されたパターンの転写像（例えばレジスト像）などの線幅を計測することで求めることができる。このイニシャルの線幅性能をＣＤⁱⁿⁱとすると、第１レンズエレメント駆動機構と第２レンズエレメント駆動機構とをともに駆動したときの線幅の線形近似計算値ＣＤ^linが、次式（４１）によって予測できる。

On the other hand, the initial line width performance can be obtained by actually measuring the line width of a transfer image (for example, a resist image) of a pattern formed on the wafer after exposure. When the line width performance of this initial is CD ⁱⁿⁱ , the linear approximate calculation value CD ^lin of the line width when both the first lens element driving mechanism and the second lens element driving mechanism are driven is predicted by the following equation (41). it can.

  Here, when optimizing the line widths at three measurement points (first, second, and third measurement points) in the field of view of the projection optical system, the above equation (41) is expressed by the following equation (41) 42).

Here, CD ₁ ^lin , CD ₂ ^lin , and CD ₃ ^lin are line widths at the first, second, and third measurement points when the first lens element driving mechanism and the second lens element driving mechanism are driven together. The linear approximation calculation values of are respectively shown. CD ₁ ⁱⁿⁱ , CD ₂ ⁱⁿⁱ , and CD ₃ ⁱⁿⁱ indicate initial line widths at the first, second, and third measurement points, respectively. ΔCD ₁ ^lin , ΔCD ₂ ^lin , and ΔCD ₃ ^lin are line width changes at the first, second, and third measurement points when the first lens element driving mechanism and the second lens element driving mechanism are driven together. The linear approximation calculation value of quantity is shown, respectively. f _1,1 , f _2,1 , and f _3,1 are nonlinear functions indicating the line width changes at the first, second, and third measurement points, respectively, when the first lens element driving mechanism is driven. Show. Further, (∂f _1,1 (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} , (∂f _2,1 (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} , (∂f _3,1 (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} indicates a partial differential coefficient (differential coefficient) of each of the nonlinear functions f _1,1 , f _2,1 , f _3,1 at ΔP ₁ = 0. F _1,2 , f _2,2 and f _3,2 are nonlinear functions indicating the line width change amounts at the first, second and third measurement points when the second lens element driving mechanism is driven. , Respectively. Also, (∂f _1,2 (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} , (∂f _2,2 (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} , (∂f _3,2 (ΔP ₂ / ∂ΔP ₂ ) _{@ ΔP2 = 0} indicates the partial differential coefficient (differential coefficient) of each of the nonlinear functions f _1,2 , f _2,2 and f _3,2 at ΔP ₂ = 0.

In the above equation (42), the adjustment amount of the adjustment parameter of the adjustment device (the drive amount of the lens element driving mechanism) and the imaging performance of the projection optical system are similar to the above-described equation (28) or equation (30). They are connected by a linear matrix. Therefore, using the least square method (square mean optimization method), the adjustment values ΔP ₁ and ΔP ₂ of the adjustment parameters for optimizing the imaging performance are set to optimum values (referred to as ΔP ₁ ¹ and ΔP ₂ ¹ ). Can be requested.

  However, the result of optimization using the above equation (42) is only a linear approximation function, and the calculated line width is not exactly accurate. Therefore, the line width when the first lens element driving mechanism and the second lens element driving mechanism are driven by the optimum driving amount (optimal driving amount) calculated by the linear approximation optimization calculation is calculated using a non-linear expression. To do.

FIG. 12 schematically shows a linear approximation optimization calculation result and a post-optimization line width change calculation result using a nonlinear equation. In FIG. 12, the nonlinear function A1 and the linear approximation function A′1 are the same as those in FIG. Now, the above linear approximation optimization calculation results, the optimal value [Delta] P ₁ ¹ driving amount of the first lens element driving mechanism is obtained as the value as shown in FIG. In this case, the linear approximation optimization calculation, the variation of the line width when the first lens element driving mechanism driven by the optimum value [Delta] P ₁ ¹ of the drive amount calculated in linear approximation optimization calculation point Q in FIG. 12 It is calculated as the line width variation amount [Delta] CD _Q. That is, ΔP ₁ ¹ is substituted into the equation (37), and can be expressed as the following equation (43).

ここで、ΔＣＤ^lin_1は線形近似最適化計算による線幅変化量を示す。同様に第２レンズエレメント駆動機構を線形近似最適化計算で算出した駆動量の最適値ΔＰ₂ ¹だけ駆動したときの線幅変化量ΔＣＤ^lin_1は、次式（４４）で表される。

Here, ΔCD ^{lin — 1} indicates the amount of change in line width by linear approximation optimization calculation. Similarly the line width variation amount [Delta] CD ^LIN_1 when the second lens element driving mechanism driven by the optimum value [Delta] P ₂ ¹ drive amount calculated in linear approximation optimization calculated is expressed by the following equation (44).

しかし、例えば、実際の第１レンズエレメント駆動機構を線形近似最適化計算で算出した駆動量の最適値だけ駆動した時の線幅変化量は、図１２の非線形関数Ａ１上の点Ｒにおける線幅変化量ΔＣＤ_Rになっているはずである。すなわち、次式（４５）が成立する。

However, for example, the line width change amount when the actual first lens element driving mechanism is driven by the optimum value of the driving amount calculated by the linear approximation optimization calculation is the line width at the point R on the nonlinear function A1 in FIG. it should have become variation [Delta] CD _R. That is, the following equation (45) is established.

ΔCD ^nonlin_1 = f ₁ (ΔP ₁ ¹ ) (45)
Here, [Delta] CD ^Nonlin_1 the line width variation amount calculated by non-linear function A1 when driving the first lens element driving mechanism by the optimum value [Delta] P ₁ ¹ of the drive amount calculated in linear approximation optimization calculation, i.e. 12 in ΔCD _R of Similarly the line width variation amount when the second lens element driving mechanism driven by the optimum value [Delta] P ₂ ¹ drive amount calculated in linear approximation optimization calculated is given by the following equation (46).

ΔCD ^nonlin_1 = f ₂ (ΔP ₂ ¹ ) (46)
Here, the amount of change in the line width when the first lens element driving mechanism and the second lens element driving mechanism are driven is the same as when the first lens element driving mechanism and the second lens element driving mechanism are individually driven. If it is expressed by the sum of the line width changes, the following equation (47) is established.

ここで、ＣＤ₁ ^nonlin_1、ＣＤ₂ ^nonlin_1、ＣＤ₃ ^nonlin_1は、第１レンズエレメント駆動機構と第２レンズエレメント駆動機構を、線形近似最適化計算で算出した駆動量の最適値だけそれぞれ駆動したときの第１、第２、第３計測点での線幅の非線形計算値をそれぞれ示す。また、ΔＣＤ₁ ^nonlin_1、ΔＣＤ₂ ^nonlin_1、ΔＣＤ₃ ^nonlin_1は、第１レンズエレメント駆動機構と第２レンズエレメント駆動機構を線形近似最適化計算で算出した駆動量の最適値だけそれぞれ駆動したときの第１、第２、第３計測点での線幅変化量の非線形計算値を、それぞれ示す。

Here, CD ₁ ^nonlin_1 , CD ₂ ^nonlin_1 , and CD ₃ ^nonlin_1 are obtained when the first lens element driving mechanism and the second lens element driving mechanism are respectively driven by the optimum values of the driving amounts calculated by the linear approximation optimization calculation. The nonlinear calculated values of the line widths at the first, second, and third measurement points are respectively shown. ΔCD ₁ ^nonlin_1 , ΔCD ₂ ^nonlin_1 , and ΔCD ₃ ^nonlin_1 are the first ^values when the first lens element driving mechanism and the second lens element driving mechanism are respectively driven by the optimum values of the driving amounts calculated by the linear approximation optimization calculation. The non-linear calculation values of the line width change amounts at the second and third measurement points are respectively shown.

^Lines when CD ₁ ^nonlin_1 , CD ₂ ^nonlin_1 and CD ₃ ^nonlin_1 drive the first lens element driving mechanism and the second lens element driving mechanism by the optimum driving amount calculated by the linear approximation optimization calculation, respectively. This is a calculated value of the width (optimization calculation result).

However, since the optimization calculation result given by the above equation (47) is an optimization calculation result using a linear approximation function to the last, the line width performance is improved as compared with before optimization, but the real optimization Line width performance may not be achieved. Therefore, it is considered that the linear approximation optimization calculation is executed once again with the state of Expression (47) as a reference. First, the nonlinear function A1 representing the relationship between the driving amount of the first lens element driving mechanism and the change in line width is determined as the optimum driving amount of the first lens element driving mechanism at the time of the first linear approximation optimization calculation described above. Replace the value ΔP ₁ ¹ with the reference. That is, the nonlinear function A1 in FIG. 12 is translated by -ΔP ₁ ^{1 in} the horizontal axis direction and by -ΔCD _{R in the} vertical axis direction (the point R (ΔP ₁ ¹ , ΔCD _R ) on the nonlinear function A1 is the origin (0 , 0).

  In FIG. 13, the non-linear functions A1 and B1 before and after the parallel movement are shown by a solid line and a dotted line, respectively. In FIG. 13, a point R ′ (0, 0) on the nonlinear function B1 after translation corresponds to a point R on the nonlinear function A1 before translation. Here, the nonlinear function after translation, that is, the line width change amount calculating nonlinear function B1 after the first line-type approximate optimization is expressed by the following equation (48).

ΔCD ² = f ₁ ² (ΔP ₁ ) = f ₁ (ΔP ₁ + ΔP ₁ ¹ ) −f ₁ (ΔP ₁ ¹ ) (48)
Here, ΔCD ² is the amount of change in line width due to the driving of the first lens element driving mechanism during the second line type approximate optimization from the first line type approximate optimization line width, and f ₁ ² is the second line. A nonlinear function B1 indicating the relationship between the driving amount of the first lens element driving mechanism and the line width change amount at the time of shape approximation optimization, and ΔP ₁ is the horizontal axis of FIG. 13, that is, the first line shape after the first line shape approximation optimization. The driving amounts of the first lens element driving mechanism at the second optimization from the driving position of the one lens element driving mechanism are respectively shown.

Similarly, with respect to the second lens element driving mechanism, the line width change amount ΔCD ² due to the driving of the lens element driving mechanism at the time of the second line type approximate optimization from the first line type approximate optimization line width is expressed by the following equation: (49).
ΔCD ² = f ₂ ² (ΔP ₂ ) = f ₂ (ΔP ₂ + ΔP ₂ ¹ ) −f ₂ (ΔP ₂ ¹ ) (49)
Here, f ₂ ² is a nonlinear function indicating the relationship between the driving amount of the second lens element driving mechanism and the line width change amount at the time of the second line type approximate optimization, and ΔP ₂ is the value after the first line type approximate optimization. A driving amount of the second lens element driving mechanism at the time of second line type approximate optimization from the driving position of the second lens element driving mechanism is represented.

  Since the optimization by the least square method is difficult if the nonlinear function remains as it is, consider transforming the equations (48) and (49) into linear approximation functions.

In FIG. 14, the nonlinear function B1 representing the relationship between the driving amount of the first lens element driving mechanism and the change amount of the line width in the second line type approximate optimization calculation is indicated by a dotted line, and ΔP of the nonlinear function B1 A linear approximation function B′1 approximated by a tangent at a point where ₁ = 0 is indicated by a broken line. The approximate function B′1 indicated by the broken line is expressed by the following equation (50).

ここで、ΔＣＤ^lin_2は第２回線形近似関数Ｂ’１で計算される近似線幅変化量を、Ｆ₁ ²は第２回線形近似最適化時の第１レンズエレメント駆動機構の駆動量と線幅変化量との関係を示す線形近似関数Ｂ’１を、（∂ｆ₁ ²（ΔＰ₁）／∂ΔＰ₁）_@ΔP1=0はΔＰ₁＝０での非線形関数ｆ² ₁の偏微分係数（微分係数）を、それぞれ示す。

^Here, ΔCD lin_2 is an approximate line width change amount calculated by the second line type approximation function B'1, F ₁ ² is a driving amount of the first lens element driving mechanism during the second line-shaped approximate optimization lines The linear approximation function B′1 indicating the relationship with the amount of change in width is expressed as follows: (∂f ₁ ² (ΔP ₁ ) / ＰΔP ₁ ) _{@ ΔP1 = 0} is the partial differential coefficient of the nonlinear function f ² _{1 when} ΔP ₁ = 0 (Differential coefficients) are shown respectively.

  Similarly, a linear approximation function indicating the relationship between the driving amount of the second lens element driving mechanism and the line width change amount at the time of the second line type approximate optimization calculation is expressed by the following equation (51).

ここで、ΔＣＤ^lin_2は第２回線形近似関数で計算される線幅変化量を、Ｆ₂ ²は第２回線形近似最適化時の第２レンズエレメント駆動機構の駆動量と線幅変化量との関係を示す線形近似関数を、（∂ｆ₂ ²（ΔＰ₂）／∂ΔＰ₂）_@ΔP2=0はΔＰ₂＝０での非線形関数ｆ₂ ²の偏微分係数（微分係数）を、それぞれ示す。線幅の変化が式（５０）と式（５１）の線形和で表されるとすると、次式（５２）が成立する。

^Here, ΔCD lin_2 the line width variation amount calculated by the second line type approximation function, F ₂ ² is a driving amount and the change in line width of the second lens element driving mechanism during the second line type approximation optimization (∂f ₂ ² (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} is the partial differential coefficient (derivative coefficient) of the nonlinear function f ₂ ^{2 when} ΔP ₂ = 0, Show. If the change in line width is expressed by the linear sum of Expression (50) and Expression (51), the following Expression (52) is established.

上式（５２）をマトリクス表示すれば、次式（５３）のようになる。

If the above equation (52) is displayed in matrix, the following equation (53) is obtained.

  Here, as in the case of the first line-type approximate optimization calculation described above, considering the line width change at the first to third measurement points, the above equation (53) is expanded as the following equation (54): it can.

Here, ΔCD ₁ ^lin_2 , ΔCD ₂ ^lin_2 , and ΔCD ₃ ^lin_2 are the first and second ^values when the first lens element driving mechanism and the second lens element driving mechanism at the time of the second line type approximate optimization calculation are driven. The linear approximate calculation value of the line width change amount at the third measurement point is shown respectively. F _1,1 ² , f _2,1 ² , and f _3,1 ² are the first, second, and third _values when the first lens element driving mechanism is driven in the second line type approximate optimization calculation. Each nonlinear function indicating the amount of change in line width at each measurement point is shown. Also, (∂f _1,1 ² (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} , (∂f _2,1 ² (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} , (∂f _3,1 ² (ΔP ₁ ) / ∂ΔP ₁ ) _{@ ΔP1 = 0} is the partial differential coefficient (differential coefficient) of each of the nonlinear functions f _1,1 ² , f _2,1 ² , f _3,1 ² at ΔP ₁ = 0. Are shown respectively. F _1,2 ² , f _2,2 ² , and f _3,2 ² are the first, second, and third _values when the second lens element driving mechanism is driven in the second line type approximate optimization calculation. Each nonlinear function indicating the amount of change in line width at each measurement point is shown. Further, (∂f _1,2 ² (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} , (∂f _2,2 ² (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} , (∂f _3,2 ² (ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP2 = 0} is the partial differential coefficient (differential coefficient) of each of the nonlinear functions f _1,2 ² , f _2,2 ² , f _3,2 ² at ΔP ₂ = 0. Are shown respectively.

  On the other hand, the line width performance after the first line type approximate optimization calculation is expressed by the above-described equation (47). In order to predict the line width when the first lens element driving mechanism and the second lens element driving mechanism are driven simultaneously in the second line type approximate optimization calculation by combining the expressions (47) and (54). The following formula (55) is obtained.

ここで、ＣＤ₁ ^lin_2は、ＣＤ₂ ^lin_2、ＣＤ₃ ^lin_2は、第２回線形近似最適化計算時の第１レンズエレメント駆動機構と第２レンズエレメント駆動機構とを駆動したときの第１、第２、第３計測点での線幅の線形近似計算値を、それぞれ示す。

Here, CD ₁ ^lin_2 is CD ₂ ^lin_2 , and CD ₃ ^lin_2 is the first and second lens element driving mechanisms when the first lens element driving mechanism and the second lens element driving mechanism are driven in the second line type approximate optimization calculation. 2 shows linear approximation calculation values of the line width at the third measurement point.

  In the above equation (55), the adjustment amount of the adjusting device (the driving amount of the lens element driving mechanism) and the line width performance of the projection optical system are combined with a linear matrix in the same manner as the above equation (28) or equation (30). ing. Therefore, as described above, optimizing the driving amount and line width performance of the lens element driving mechanism can be realized by using the mean square optimization method (least square method).

  However, the result of optimization using Expression (55) is obtained only by approximation calculation using a linear approximation function, and the line width calculation value is not strictly accurate. Therefore, the line width when the first lens element driving mechanism and the second lens element driving mechanism are driven by the optimum value of the driving amount calculated by the second line type approximate optimization calculation is calculated using a non-linear expression.

FIG. 14 schematically shows the result of the second line type approximate optimization calculation and the post-optimization line width change calculation using a nonlinear expression. Now, the second line type approximation optimization calculation results, the optimum value [Delta] P ₁ ² driving amount of the first lens element driving mechanism is obtained as the value as shown in FIG. 14. At this time, in the second line type approximation optimization calculation, the change in line width when the first lens element driving mechanism driven by the optimum value [Delta] P ₁ ² driving amount calculated by the second line type optimization calculation 14 It is calculated as the line width change amount ΔCD _S of the point S on the linear approximation function B′1. That is, ΔP ₁ ² is substituted into the equation (50), and can be expressed as the following equation (56).

ここで、ΔＣＤ^lin_2は第２回線形近似最適化計算による線幅変化量を表す。同様に、第２レンズエレメント駆動機構を第２回目線形近似最適化計算で算出した駆動量の最適値ΔＰ₂ ²だけ駆動した時の線幅変化量は、次式（５７）で表される。

Here, ΔCD ^{lin —} 2 represents the line width change amount by the second line type approximate optimization calculation. Similarly, the line width variation amount when the second lens element driving mechanism second round linear approximation optimization calculation only optimum value [Delta] P ₂ ² drive amount of which is calculated to drive is represented by the following formula (57).

ここで、ΔＰ₂ ²は第２回線形近似最適化計算で算出した、第２レンズエレメント駆動機構の駆動量の最適値を示す。視野内の第１、第２、第３計測点での最適化線幅は、式（５５）にΔＰ₁ ²、ΔＰ₂ ²を代入して、次式（５８）で表される。

Here, ΔP ₂ ² indicates the optimum value of the driving amount of the second lens element driving mechanism calculated by the second line type approximate optimization calculation. The optimized line widths at the first, second, and third measurement points in the field of view are expressed by the following equation (58) by substituting ΔP ₁ ² and ΔP ₂ ² into equation (55).

Here, CD ₁ ^lin_2 , CD ₂ ^lin_2 , and CD ₃ ^lin_2 are the second line type approximate optimization calculation for the first lens element driving mechanism and the second lens element driving mechanism at the time of the second line type approximate optimization calculation, respectively. The linear approximate calculation values of the line widths at the first, second, and third measurement points when the calculated drive amount is the optimum value are shown. ΔCD ₁ ^lin_2 , ΔCD ₂ ^lin_2 , and ΔCD ₃ ^lin_2 are calculated by the second line type approximate optimization calculation for the first lens element driving mechanism and the second lens element driving mechanism at the time of the second line type approximate optimization calculation, respectively. The linear approximation calculation values of the line width change amounts at the first, second, and third measurement points when the optimum driving amount is driven are shown.

However, for example, the line width variation amount [Delta] CD ^Nonlin_2 when driven actual first lens element driving mechanism by the optimum value [Delta] P ₁ ² of the calculated driving amount in the second line type approximation optimization calculation, the non-linear function of FIG. 14 It should be the line width change amount ΔCD _T at the point T on B1. That is, the following equation (59) should be satisfied.
ΔCD ^nonlin_2 = f ₁ ² (ΔP ₁ ² ) (59)
Here, [Delta] CD ^Nonlin_2 the line width variation amount calculated by the nonlinear function B1 when driven by the optimum value [Delta] P ₁ ² for driving amount calculated for the first lens element driving mechanism in the second line type approximation optimization calculation, namely ΔCD _T is represented. Similarly the line width variation amount when the second lens element driving mechanism is driven by the optimum value [Delta] P ₂ ² drive amount of which is calculated in the second line type approximation optimization calculated is given by the following equation (60).
ΔCD ^nonlin_2 = f ₂ ² (ΔP ₂ ² ) (60)

  Here, the amount of change in line width when the first lens element driving mechanism and the second lens element driving mechanism are driven simultaneously is the same as when the first lens element driving mechanism and the second lens element driving mechanism are individually driven. Is expressed by the sum of the line width change amounts, the following equation (61) is established for the first, second, and third measurement points.

Here, CD ₁ ^nonlin_2 , CD ₂ ^nonlin_2 , and CD ₃ ^nonlin_2 are the second line type approximate optimization calculation for the first lens element drive mechanism and the second lens element drive mechanism at the time of the second line type approximate optimization calculation, respectively. The non-linear calculated values of the line widths at the first, second, and third measurement points when driven by the optimum value of the calculated drive amount are respectively shown. ΔCD ₁ ^nonlin_2 , ΔCD ₂ ^nonlin_2 , and ΔCD ₃ ^nonlin_2 are calculated by the second line type approximate optimization calculation for the first lens element driving mechanism and the second lens element driving mechanism at the time of the second line type approximate optimization calculation, respectively. The non-linear calculated values of the line width change amounts at the first, second, and third measurement points when the drive amount is the optimum value are shown. When the above CD ₁ ^nonlin_2 , CD ₂ ^nonlin_2 , and CD ₃ ^nonlin_2 drive the first lens element drive mechanism and the second lens element drive mechanism by the optimum drive amount calculated by the second line-type approximate optimization calculation The line width calculation result (optimization calculation result).

By the way, as apparent from comparing δ ₁ in FIG. 12 and δ _{2 in} FIG. 14, the line width change amount calculated by the optimum value of the driving amount calculated by the linear approximation optimization calculation and the nonlinear function The difference δ between the optimum value of the driving amount calculated by the linear approximation optimization calculation and the line width change amount calculated by the linear approximation function is the second line type approximation compared to the case of the first line type approximation optimization calculation. The optimization calculation is clearly smaller (δ ₁ > δ ₂ ). Furthermore, it is clear that the difference δ is further reduced by performing the third line type optimization calculation based on the second line type approximate optimization calculation result. In this way, the line width performance gradually converges to an optimal solution by sequentially repeating the linear approximation optimization calculation.

  By the way, in the description using FIGS. 11 to 14 described above, for the sake of convenience, the linear approximate line width change amount when the first lens element driving mechanism and the second lens element driving mechanism are driven together is the first lens. The element driving mechanism and the second lens element driving mechanism are expressed by the linear sum of the linear approximation functions of the nonlinear functions of the respective line width changes when the element driving mechanism and the second lens element driving mechanism are individually moved. That is, the imaging performance calculation approximation function is a linear approximation change amount of the predetermined imaging performance expressed as a linear sum of linear approximation functions of nonlinear functions representing the relationship between the respective adjustment amounts and the predetermined imaging performance. (Refer to the above-mentioned formulas (42) and (55)). However, strictly speaking, the equations (42) and (55) are not correct.

  That is, if a linear approximation function using a partial differentiation of a nonlinear function such as the following equation (62) is used instead of the equation (42) at the time of the first line approximation optimization described above, it is optimal with sufficient accuracy. Calculation can be performed.

Here, f ₁ , f ₂ , and f ₃ are the first, second, and third measurements when both the first lens element driving mechanism and the second lens element driving mechanism are driven at the time of the first line type approximate optimization. The non-linear functions of the line width change amount at points are respectively shown. Also, (∂f ₁ (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₂ (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} , (∂ f ₃ (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} is a partial differential coefficient related to ΔP _{1 when} ΔP ₁ = ΔP ₂ = 0 of each of the nonlinear functions f ₁ , f ₂ , and f _3. , Respectively. Further, (∂f ₁ (ΔP _1, ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₂ (ΔP _1, ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP1 = ΔP2 = 0} , (∂ _{f 3 (ΔP 1, ΔP 2} ) / ∂ΔP 2) @ ΔP1 = ΔP2 = 0 , the partial differential coefficients for [Delta] P ₂ of a non-linear function f _1, f _2, f ₃ each ΔP ₁ = ΔP ₂ = 0 , Respectively.

  Similarly, the following equation (63) may be used instead of the equation (55) at the time of the second line type approximate optimization.

Here, f ₁ ² , f ₂ ² , and f ₃ ² are the first, second, and second values when both the first lens element driving mechanism and the second lens element driving mechanism at the time of the second line type approximate optimization are driven. The nonlinear functions of the line width change amount at the third measurement point are respectively shown. Further, (∂f ₁ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₂ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₃ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₁ ) _{@ ΔP1 = ΔP2 = 0} means that ΔP ₁ = ΔP ₂ = 0 of each of the nonlinear functions f ₁ ² , f ₂ ² , and f ₃ ² _The partial differential coefficients for ₁ are shown respectively. Also, (∂f ₁ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₂ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP1 = ΔP2 = 0} , (∂f ₃ ² (ΔP _1, ΔP ₂ ) / ∂ΔP ₂ ) _{@ ΔP1 = ΔP2 = 0} indicates that ΔP ₁ = ΔP ₂ = 0 of each of the nonlinear functions f ₁ ² , f ₂ ² , and f ₃ ² _The partial differential coefficients for ₂ are shown respectively.

  The above calculation is generally performed even when there are more measurement points in the field of view (field) of the projection optical system and more lens element driving mechanisms (adjustment parameters of the adjustment device). This can be done by expanding the matrix.

Assuming that the above description is compared with the above equation (62) and the above equation (27), the equation (27) is obtained by converting the equation (62) into the field of view (field) of the projection optical system. This is nothing but an expanded formula with n (= 33) points and 19 adjustment amounts dx _{1 to} dx ₁₉ . Further, as described above, Expression (28) is obtained by extending Expression (27) to include other imaging performance. Therefore, by repeating the processing of the above-described loop of FIG. 10 (loop of steps 296 → 298 → 300 → 302 → 304 → 306 → 312 → 314), the optimum solution of the adjustment amount is asymptotically explained as described above. It can be seen that

  Returning to the flowchart of FIG. 10, if the determination in step 312 is affirmative, the optimization is not possible by repeating the linear approximation calculation a predetermined number of times (M times). To display the result on the display. In this case, an OK button and an NG button are displayed together with an optimization failure display.

  On the other hand, if the determination in step 306 is affirmed, the process proceeds to step 308, and the optimum value of the adjustment amount of the 19 adjustment parameters calculated in step 302 (or step 310) is set to the previously set constraint condition. Determine if there is a violation. Note that the constraint conditions and the determination method to be determined here are the same as those disclosed in the pamphlet of International Publication No. 03/065428, and thus detailed description thereof is omitted.

  If this determination is affirmed, the process proceeds to step 310, and the setting of the constraint conditions is sequentially performed in the same manner as disclosed in the above-mentioned WO 03/065428. After performing optimization again and obtaining the adjustment amount, the process returns to step 304.

  On the other hand, if the determination in step 308 is negative, that is, if there is no constraint condition violation or if the constraint condition violation is resolved, the process proceeds to step 316 and the result is displayed on the display. In this case, the adjustment amount of 19 adjustment parameters (in this case, the amount of change from the position in the reference ID), the value of each adjustment parameter after adjustment, and the imaging performance after optimization (13 types of imaging performance) A value, a wavefront aberration correction amount (same value as the wavefront aberration correction amount in the reference ID), an OK button, and an NG button are displayed.

  Then, looking at the display screen of the result, when the operator points the NG button with a mouse or the like, the process returns to the above-described step 240. Here, the NG button is selected, for example, when the target or weight is set again and the optimization is performed again, and the set weight and the target allowable value are obtained. There is a case where the operator wants to further improve the imaging performance at a certain evaluation point, or to reset the weight and optimize again.

On the other hand, when the operator looks at the result display screen and points the OK button with the mouse or the like, the process proceeds to step 320, and the main control of the first communication server 920 and the exposure apparatus 922 ₁ based on the calculated adjustment amount. Each adjustment unit (at least one of the Z position and inclination of the movable lenses 13 _{1 to} 13 ₅ and the wafer W and the wavelength shift amount of the illumination light) is controlled via the apparatus 50.

In this case, Z, θx (rotation around the X axis), and θy (rotation around the Y axis) are displacements in three degrees of freedom as adjustment amounts of the lens element (movable lens) 13 _i (i = 1 to 5). When the amounts are calculated, these adjustment amounts are calculated by geometrical calculation of the movable lens 13 _i (i = 1 to 5) in the same manner as disclosed in the pamphlet of International Publication No. 03/065428. It converts into the drive amount of each drive shaft. That is, in the second communication server 930, for example, a command value indicating that the movable lenses 13 _{1 to} 13 ₅ should be driven in the directions of degrees of freedom is given to the imaging performance correction controller 48 based on the conversion result. Thereby, the imaging performance correction controller 48 controls the applied voltage to each drive element that drives the movable lenses 13 _{1 to} 13 ₅ in the respective degrees of freedom.

  In the present embodiment, the aforementioned adjustment parameters include the driving amounts Wz, Wθx, Wθy of the wafer W, and the wavelength shift amount Δλ of the illumination light EL, and the adjustment amounts corresponding to these four adjustment parameters are also first described. It has been calculated. The adjustment amounts of these four adjustment parameters are stored in the memory in association with the above-described optimized exposure conditions (including illumination conditions), and from the memory when the pattern is transferred to the wafer under the exposure conditions. It is read and used. That is, the adjustment amounts of the three adjustment parameters relating to the wafer are used in the focus leveling control of the wafer using the focus detection system described above, and the adjustment amount of the adjustment parameter relating to the wavelength of the illumination light is the center wavelength of the illumination light in the light source 16 It will be used for setting. The adjustment amount or drive amount of the movable lens described above is also stored in the memory in association with the optimized exposure conditions described above, and is read from the memory when the pattern is transferred to the wafer under the exposure conditions. The movable lens may be driven.

The control of each adjustment portion of the exposure apparatus 922 ₁ is optimized, formation state on the wafer W of the projected image of the reticle pattern at the time of exposure is to be optimized.

  Thereafter, the processing routine of the first mode (mode 1) is terminated, and the process returns to step 122 of the main routine of FIG.

On the other hand, if the operator selects mode 2 with the mouse or the like in step 110, the determination in step 114 is affirmed and a subroutine for performing mode 2 processing in step 116 (hereinafter referred to as “mode 2 processing routine”). (Also called). Here, the mode 2 is a mode in which optimization is performed based on actually measured data of wavefront information (for example, the coefficient of each term of the Zernike polynomial described above) under an arbitrary exposure condition (arbitrary ID). This mode 2 is mainly selected when a new ID is newly added. According to an optimized result by the mode 1 and as described above in a state where each of the control sections of the above is adjusted, while using the exposure apparatus 922 _1, for example, a service engineer or the like, such as during maintenance, the wavefront aberration of the projection optical system When measurement is performed, the processing of mode 2 described below is performed based on the actual measurement data of the wavefront aberration, and as a result, errors such as calculation adjustment amounts in mode 1 can be corrected. .

  When this mode 2 is selected, the premise is that the wavefront aberration of the projection optical system PL is measured with the current ID (optimization target ID) of the target machine. Therefore, here, it is assumed that information indicating that the wavefront aberration has been measured is sent together with the designation of the exposure apparatus (unit) to be optimized and the optimization instruction by the above-described e-mail or the like.

In the processing routine of mode 2 (hereinafter also referred to as “second mode”), first, in step 402 of FIG. 15, information on the exposure condition to be optimized is acquired. Specifically, the first communication server 920 (or target Unit via the first communication server 920 (exposure apparatus 922 ₁₎ of the main control unit 50), the current projection of the target Unit (exposure apparatus 922 ₁₎ N. of the optical system. A. Inquires and acquires setting information such as illumination conditions (illumination NA or illumination σ, aperture stop type, etc.) and target pattern type.

In the next step 406, new wavefront aberration measurement data (first measurement point to first measurement data) from the first communication server 920 (or the main controller 50 of the target machine (exposure device 922 ₁ ) via the first communication server 920). The terms of the Zernike polynomial (for example, the first to 37th terms) in which the wavefront corresponding to the n measurement points is expanded, and necessary information related thereto, specifically, the adjustment amount at the time of measuring the wavefront aberration ( The value of the adjustment parameter) is acquired by communication. The value of this adjustment amount, that is, the position information in the three-degree-of-freedom direction of the movable lenses 13 _{1 to} 13 ₅ , etc., usually coincides with the current value, that is, the value under the exposure condition to be optimized.

  Hereinafter, in this step 406, it is assumed that the wavefront aberration measurement data Wa ′ represented by the following equation (64) is acquired.

上式（６４）において、Ｃ_i,n’は、ｎ番目の計測点における波面を展開したツェルニケ多項式の第ｉ項（ｉ＝１〜３７）の係数を示す。

In the above equation (64), C _{i, n} ′ indicates the coefficient of the i-th term (i = 1 to 37) of the Zernike polynomial that expands the wavefront at the n-th measurement point.

  In the next step 408, as in the above-described step 208, the model name of the target machine, the exposure wavelength, and the maximum N.D. A. Get device information.

  Next, in steps 420 to 438 in FIG. 16, processing (including determination) similar to that in steps 220 to 238 described above is performed. Thereby, the allowable value of the imaging performance and the restriction condition of the adjustment amount are set.

  Next, in steps 440 to 462 in FIG. 17, the same processing (including determination) as in steps 240 to 262 described above is performed. As a result, 13 types of imaging performance weights at 33 evaluation points (measurement points) in the field of view of the projection optical system are set in the same manner as described above.

  Next, in steps 464 to 490 in FIG. 18, processing (including determination) similar to that in steps 264 to 290 described above is performed. As a result, when 13 kinds of target values (targets) of the imaging performance at 33 evaluation points in the field of view of the projection optical system and the optimization field range are designated, the settings (to the memory) are set. Is stored).

  Next, in step 492 of FIG. 19, the count value m of the counter that defines the number of iterations of the linear approximation calculation (optimization calculation) is initialized to 1 (m ← 1).

In the next step 494, as in step 294 described above, 13 types of imaging performance at the present time, that is, before optimization, are calculated for each measurement point based on the above-described equation (10). Store in the storage area. In the calculation in step 494, the wavefront aberration data (measured data) Wa ′ for each measurement point acquired in step 406 described above, and the nonlinear coefficient and ZS in the reference ID in the second database are used. That is, the second mode is different from the first mode (mode 1) in that actually measured data is used for calculating the imaging performance. In calculating the imaging performance, C _{i, n} ′ _, which is an element of Wa ′, is used instead of C _{i, n} in the equation (10).

Also in the case of the second mode, for the 12 types of linear aberration, all of the nonlinear coefficients A, B, C, D, T _i ^α , T _{i, j} ^β , T _i ^γ , and T _i ^δ are zero. The calculation of the above equation (10) is substantially the same as the calculation of the following equation (10) ″.

In the next step 496, a Zernike Sensitivity file (ZS file) and an imaging performance change table are created for each measurement point in the same procedure as in step 296 described above. At this time (when the count value m = 1), in this step 496, calculation of Zernike Sensitivity is performed by replacing C _{i, n} with C _{i, n} '.

In the next step 498, similarly to the above-described step 298, the imaging performance f and its target _ft are lined up (one-dimensionalized).

  Next, in step 500, the imaging performance change table for each of the 33 measurement points created in step 496 is two-dimensionalized in the same manner as in step 300 described above. Similarly, the change amount (adjustment amount) of the adjustment parameter is calculated without considering the constraint condition.

  In the next step 504, 13 kinds of imaging performances are calculated for each element of the matrix f, that is, for all evaluation points, in the same manner as in step 304 described above.

  In the next step 506, in the same manner as in the above-described step 306, it is determined whether or not the 13 types of imaging performances at all the calculated evaluation points are within the respective allowable values set previously. If NO is determined, the process proceeds to step 512 to determine whether or not the count value m of the counter is equal to or greater than a predetermined value M. If this determination is negative, the process proceeds to step 514 to increment the count value m by 1, and then returns to step 296.

In step 296, a ZS file and an imaging performance change table are created for each measurement point according to the above-described procedure, and the processing in step 298 and thereafter is repeated thereafter. In this step 496, when the count value m is 2 or more, when calculating Zernike Sensitivity, the optimum value and wavefront aberration of the latest 19 adjustment parameters obtained in step 502 (or step 310 described later) are calculated. Information on wavefront aberration for each measurement point calculated based on the change table, for example, coefficients C _{i, n} (i = 1 to 37, n = 1 to 33) of each term of the Zernike polynomial are used.

  In this way, until the determination in either step 506 or step 512 is affirmed, the loop process of steps 496 → 498 → 500 → 502 → 504 → 506 → 512 → 514 is repeatedly executed. Each time this loop processing is repeated, every time this loop processing is repeated, in step 502, 19 adjustment parameters for simultaneously optimizing the imaging performance to be optimized among the 13 types of imaging performance are set. The optimum value of the adjustment amount is obtained. In particular, when the nonlinear imaging performance with respect to each Zernike coefficient, in this case, the line width target CDt is not zero, the adjustment amount of the 19 adjustment parameters calculated in step 502 is calculated. The optimal value asymptotically approaches the true optimal solution. On the other hand, when the line width target CDt is zero and only the linear imaging performance is targeted for optimization with respect to each Zernike coefficient, the weight, imaging performance target, and other setting values are not changed. The calculation result in step 502 does not change.

  On the other hand, if the determination in step 512 is affirmed, it is impossible to optimize by repeating the linear approximation calculation a predetermined number of times (M times). Show on the display. In this case, an OK button and an NG button are displayed together with an optimization failure display.

  On the other hand, if the determination in step 506 is affirmed, the process proceeds to step 508, where it is determined whether or not the adjustment amounts of the 19 adjustment parameters calculated in step 502 violate the previously set constraint conditions. Judgment is made in the same manner as described above. If this determination is affirmed, the process proceeds to step 510, the constraint conditions are taken into consideration, the constraint conditions are sequentially set and optimized again, the adjustment amount is obtained, and then the process returns to step 504.

  On the other hand, when the determination in step 508 is negative, that is, when there is no constraint condition violation or when the constraint condition violation is resolved, the process proceeds to step 516 and the result is displayed on the display. In this case, the adjustment amount of 19 adjustment parameters (in this case, the amount of change from the initial value), the value of each adjustment parameter after adjustment, the value of imaging performance after optimization (13 types of imaging performance), And a wavefront aberration correction amount, and an OK button and an NG button are displayed.

  Then, looking at the display screen of the result, when the operator points the NG button with a mouse or the like, the process returns to step 440 described above.

On the other hand, when the operator looks at the result display screen and points the OK button with the mouse or the like, the process proceeds to step 520 and the main control of the first communication server 920 and the exposure apparatus 922 ₁ based on the calculated adjustment amount. Each adjustment unit (at least one of the Z position and inclination of the movable lenses 13 _{1 to} 13 ₅ and the wafer W and the wavelength shift amount of the illumination light) is controlled through the apparatus 50 in the same manner as described above. As a result, the exposure apparatus 922 ₁ is optimized, and the formation state of the projected image of the reticle pattern on the wafer W at the time of exposure is optimized.

  Thereafter, the processing routine of the second mode (mode 2) is terminated, and the process returns to step 122 of the main routine of FIG.

  Furthermore, if the operator selects mode 3 with the mouse or the like in step 110, the determination in step 114 is denied, and a subroutine for performing mode 3 processing in step 120 (hereinafter referred to as “mode 3 processing routine”). To call). Here, mode 3 refers to imaging performance under an arbitrary exposure condition (arbitrary ID) in a state where the wavefront aberration in a reference state is known and the value of the adjustment parameter at that time is fixed. In this case, the above-described 13 types of imaging performance) are obtained. This mode 3 is suitable not only for device manufacturers but also for improving imaging performance and bringing it closer to a desired target, for example, when adjusting the optical characteristics of the projection optical system in the manufacturing stage at an exposure apparatus manufacturer. Can be used.

In the processing routine of mode 3 (hereinafter also referred to as “third mode”), first, in step 602 of FIG. 20, the target machine (exposure device 922 ₁₎ via the first communication server 920 (or the first communication server 920). ), The value of the adjustment amount (adjustment parameter) in the current state, the single wavefront aberration, and the wavefront aberration correction amount for the single wavefront aberration are acquired. This acquired information becomes information in the reference state of this mode 3.

In the next step 604, the model name, exposure wavelength, and maximum N. of the projection optical system from the first communication server 920 (or the main control device 50 of the target machine (exposure device 922 ₁ ) via the first communication server 920). A. Get device information.

  In the next step 606, after the target pattern information input screen is displayed on the display, the process proceeds to step 608 to wait for the target pattern information to be input.

  Then, information on the target pattern (type of blank pattern or remaining pattern, type of dense pattern or isolated pattern, pitch, line width, isolated line in case of dense lines (line and space, etc.) via the keyboard or the like by the operator Line width in case of contact, length in width in case of contact hole, width, distance between hole patterns (pitch, etc.), phase shift pattern (including halftone type) or phase shift reticle and its type (for example, spatial frequency) If a modulation type, halftone type, etc.) are input, the process proceeds to step 610 and the input pattern information is stored in a memory such as a RAM.

  In the next step 612, after the illumination condition input screen is displayed, the process proceeds to step 614 to wait for the input of the illumination condition information. Then, information on illumination conditions, for example, illumination N.D. A. Alternatively, when information such as illumination σ, annular ratio, aperture shape of illumination system aperture stop (secondary light source shape) is input, the input illumination condition is stored in a memory such as a RAM in step 615.

  In the next step 616, after the NA input screen of the projection optical system is displayed on the display, the process proceeds to the next step 617 and the N.A. A. Wait for input. When the operator inputs N.A. via a keyboard or the like, the process proceeds to step 618 (FIG. 21), and the input N.A. is stored in a memory such as a RAM.

  In the next step 619, a designated screen for imaging performance (hereinafter referred to as “evaluation imaging performance” as appropriate) is displayed on the display, and then the process proceeds to step 620. It is determined whether or not the imaging performance is designated. Here, the designation completion button is displayed together with the imaging performance designation screen to be evaluated.

  When one of the 13 types of imaging performance described above is specified as the imaging performance of the evaluation target by the operator via a keyboard or the like, the specified imaging performance of the evaluation target is stored in a memory such as a RAM. After that, the routine proceeds to step 624, where it is determined whether designation completion is instructed. If this determination is denied, the process returns to step 620. On the other hand, if the determination in step 620 is negative, the process proceeds to step 624.

  In other words, in this embodiment, the loop of step 620 → 622 → 624 or the loop of step 620 → 624 is repeated to wait for the completion of the designation of the imaging performance to be evaluated. When the operator points to the designation completion button via the mouse or the like, the process proceeds to step 626. At this time, a plurality of imaging performances (evaluation items) for evaluation may be designated.

  In step 626, a ZS file corresponding to the evaluation condition is created. Here, the evaluation condition is an evaluation under the conditions to be evaluated, that is, under the exposure conditions (hereinafter referred to as “target exposure conditions” as appropriate) determined by the information input in steps 610, 615, and 618, respectively. This means a condition for evaluating the imaging performance of the item (here, the imaging performance of the evaluation target specified in step 620 and stored in the memory in step 622).

  The creation of the ZS file in step 626 is performed in the same manner as the creation of the ZS file in step 296 described above.

  In the next step 634, the imaging performance of the evaluation item (here, the imaging performance of the evaluation target specified in step 620 and stored in the memory in step 622) under the target exposure condition is calculated as follows. .

  That is, by substituting the wavefront aberration data obtained from the information obtained in step 602 and the ZS file data created in step 626 into the aforementioned equation (10), each evaluation point in the field of view is obtained. The imaging performance at is calculated.

  In the next step 636, the calculated imaging performance information is displayed on the display. At this time, an OK button and a redo button are displayed together with information on the imaging performance on the display.

  By displaying the imaging performance described above, the operator can recognize the imaging performance that is an evaluation item under the target exposure condition specified by the operator.

  For example, when the imaging performance under the target exposure condition should be sufficiently satisfied, the operator who views the display points the OK button using a mouse or the like. As a result, the processing in the third mode ends, and the process returns to step 122 of the main routine of FIG.

  On the other hand, if the image formation performance under the target exposure condition is not sufficiently satisfied by looking at the display content, the operator can set the redo button to a mouse or the like to know the image formation performance under another target exposure condition. Use to point. As a result, the process returns to step 606, the pattern information input screen is displayed again, and the processing (including judgment) after step 608 is repeated.

  Here, in the third mode, the operator can easily determine the best exposure condition by repeatedly pressing the redo button and calculating and displaying the imaging performance by setting various exposure conditions as the target exposure conditions. That is, for example, while the designation information other than the pattern information input in step 608 is fixed, the pattern information is gradually changed and the redo button is repeatedly pressed to create the above ZS file and the imaging performance (evaluation target). By repeatedly calculating the (imaging performance) and sequentially checking the display of the calculation results in step 636, by finding pattern information that minimizes (or optimizes) the imaging performance (imaging performance to be evaluated) An optimum pattern can be determined as the best exposure condition.

  Similarly, with the remaining designation information fixed, while gradually changing only certain specific conditions, repeatedly press the Redo button to create the ZS file and calculate the imaging performance (imaging performance to be evaluated). Are repeatedly performed, and the display of the calculation result in step 636 is sequentially confirmed to find the specific condition that optimizes the imaging performance, thereby determining the optimal specific condition as the best exposure condition.

  Returning to the description of FIG. 5, in step 122, a screen for selecting whether to end or continue is displayed on the display. When continue is selected, the process returns to step 102. On the other hand, when the end is selected, a series of processing of this routine is ended.

  In the first mode processing, the wavefront aberration correction amount in the reference ID may be unknown, and in this case, the wavefront aberration correction amount can be estimated from this imaging performance. This will be described below.

Here, the correction amount of the wavefront aberration is estimated on the assumption that the deviation between the single wavefront aberration and the on-body wavefront aberration corresponds to the adjustment amount deviation Δx ′ of the adjustment parameters of the movable lenses 13 _{1 to} 13 ₅ described above.

When the single wavefront aberration and the on-body wavefront aberration are the same, the adjustment amount is Δx, the adjustment amount is Δx ′, the ZS file is ZS, and the theoretical imaging performance with reference ID (on-body wavefront) Theoretical imaging performance when there is no aberration deviation) is K ₀ , the actual imaging performance with the reference ID (same adjustment parameter value) is K ₁ , the wavefront aberration change table is H, and the imaging performance change table is When H ′, the single wavefront aberration is Wp, and the wavefront aberration correction amount is ΔWp, the following two formulas (65) and (66) hold.

K ₀ = ZS · (Wp + H · Δx) (65)
K ₁ = ZS · (Wp + H · (Δx + Δx ′)) (66)
Than this,
K ₁ −K ₀ = ZS · H · Δx ′ = H ′ · Δx ′ (67)
From this, when the above equation (67) is solved by the least square method,
The correction amount Δx ′ of the adjustment amount can be expressed as the following equation (68).

Δx ′ = (H ′ ^T · H ′) ⁻¹ · H ′ ^T · (K ₁ −K ₀ ) (68)
Further, the wavefront aberration correction amount ΔWp can be expressed by the following equation (69).

ΔWp = H · Δx ′ (69)
Each reference ID has this wavefront aberration correction amount ΔWp.

  Further, the actual on body wavefront aberration is expressed by the following equation (70).

  Actual on-body wavefront aberration = Wp + H · Δx + ΔWp (70)

By the way, in the exposure apparatuses 922 _{1 to} 922 _{3 of} this embodiment, when manufacturing a semiconductor device, a reticle R for device manufacture is loaded on the reticle stage RST, and then reticle alignment, so-called baseline measurement, and EGA (enhanced) are performed.・ Preparation work such as wafer alignment such as global alignment is performed.

  The preparation work such as reticle alignment and baseline measurement described above is disclosed in detail in, for example, Japanese Patent Laid-Open No. 7-176468 (corresponding US Pat. No. 5,646,413) and the like. Subsequent EGA is disclosed in detail in JP-A-61-44429 (corresponding US Pat. No. 4,780,617) and the like.

  Thereafter, step-and-scan exposure is performed based on the wafer alignment result. The operation during exposure does not differ from that of a normal scanning stepper (scanner), and a detailed description thereof will be omitted.

As is apparent from the above description, in this embodiment, the movable lenses 13 _{1 to} 13 ₅ , the positions of the Z tilt stage 58 in the Z, θx, and θy directions (or their variations), and the illumination light from the light source 16 The amount of wavelength shift is the adjustment amount. The movable lenses 13 _{1 to} 13 ₅ , the Z tilt stage 58 and the light source 16, the driving element and imaging performance correction controller 48 for driving the movable lens, the wafer stage driving unit 56 for driving the Z tilt stage 58, and the connection The image performance correction controller 48, the wafer stage drive unit 56, and the main controller 50 that controls the light source 16 constitute an adjustment device. However, the configuration of the adjustment device is not limited to this, and for example, only the movable lenses 13 _{1 to} 13 ₅ may be included as the adjustment unit. This is because even in such a case, the imaging performance (various aberrations) of the projection optical system can be adjusted.

  The second communication server 930 includes a first calculation device, a second calculation device, a processing device, an evaluation device, a Zernike sensitivity recalculation device, an adjustment amount recalculation device, and a determination device.

  Further, in the description so far, the measurement of the wavefront aberration performed when the projection optical system PL is adjusted is based on the aerial image formed through the pinhole and the projection optical system PL using the wavefront aberration measuring instrument 80. However, the present invention is not limited to this. For example, a measurement mask having a special structure disclosed in US Pat. No. 5,978,085 is used, and each of a plurality of measurement patterns on the mask is used. Bake on the object through the pinhole and projection optical system provided individually one after another, and print the reference pattern on the mask onto the object through the projection optical system without going through the condenser lens and pinhole, The registration image of each of the plurality of measurement patterns obtained as a result of each printing is measured with respect to the registration image of the reference pattern, and a predetermined calculation is performed. Aberration may be calculated a.

  Further, the wavefront aberration may be measured using a PDI (Point Deflection Interferometer) disclosed in, for example, Japanese Patent Application Laid-Open No. 2000-97617. Further, for example, the phase recovery method disclosed in Japanese Patent Laid-Open No. 10-284368, US Pat. No. 4,309,602 and the like, and the halftone phase shift disclosed in, for example, Japanese Patent Laid-Open No. 2000-146757, etc. A technique using a mask can also be used. Further, for example, JP-A-10-170399, Jena Review 1991/1, pp8-12 "Wavefront analysis of photolithographic lenses" Wolfgang Freitaget al., Applied Optics Vol. 31, No.13, May 1, 1992, pp2284-2290 As disclosed in “Aberration analysis in aerial images formed by lithographic lenses”, Wolfgang Freitag et al., And Japanese Patent Application Laid-Open No. 2002-22609, the light beam passing through a part of the pupil of the projection optical system is reflected. The technique used can also be used.

  As described above, according to the image forming state adjustment system 10 according to the present embodiment, when the first mode or the second mode described above is selected, the second communication server 930 gives the target exposure conditions given, Based on the information about the wavefront of the projection optical system, the Zernike sensitivity (ZS) of the predetermined imaging performance under the target exposure condition is calculated (see step 296 in FIG. 10 and step 496 in FIG. 19)). A plurality of adjustment amounts (for example, all (or part of 19 adjustment amounts) of the adjustment device) and a predetermined imaging performance of the projection optical system under a predetermined exposure condition (the above-described 12 types of linear aberrations) And the imaging performance selected from the line width) and a predetermined target value of the imaging performance, the calculated Zernike sensitivity of the predetermined imaging performance, and the wavefront aberration change table. Show Optimum values of the plurality of adjustment amount in said target exposure conditions based on the image performance calculation functions (see the above equations (30)) is calculated.

  Further, the second communication server 930 adjusts the adjustment device described above via the first communication server 920 based on the adjustment amount calculated in the second mode. Therefore, according to the image formation state adjustment system 10 of the present embodiment, it is possible to quickly optimize the formation state of the projection image on the wafer W by the projection optical system PL of the reticle pattern under an arbitrary target exposure condition. It has become.

  Then, as described above, the adjustment device is adjusted (a state in which the image forming state is adjusted by the projection optical system PL so that predetermined imaging performance such as the line width of the pattern image is optimal) The pattern is transferred onto the wafer using a projection optical system. Therefore, a pattern image (transfer image) is accurately formed on the wafer using the projection optical system PL.

  Here, in the second mode, the adjustment amount is calculated on the basis of the actually measured value of the wavefront aberration, so that it is possible to calculate the optimum value of the adjustment amount with the same or higher accuracy than in the first mode. Become.

  In addition, according to the image forming state adjustment system 10 of the present embodiment, the second communication server 930 is an adjustment device under the target exposure condition based on the target exposure condition given and information on the wavefront of the projection optical system. A specific function representing a relationship between a plurality of adjustment amounts used and a predetermined imaging performance of the projection optical system is partially differentiated by a coefficient of each term of the Zernike polynomial that expands the wavefront, that is, a predetermined result. The Zernike sensitivity of the image performance is calculated (see step 296 etc.). Here, the Zernike sensitivity can be calculated regardless of whether the specific function is a linear function or a nonlinear function.

  Next, the plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, the calculated Zernike sensitivity, and the wavefront aberration change Based on the imaging performance calculation function indicating the relationship with the table, optimum values of a plurality of adjustment amounts under the target exposure conditions are calculated (see step 302 and the like). Here, when the specific function is a linear function, the imaging performance calculation function is substantially the same function (including a function obtained by adding a fixed offset value (including zero)), and When the specific function is a nonlinear function, the imaging performance calculation function is a linear approximation function of the nonlinear function.

  Further, according to the present embodiment, as shown in FIG. 11, an imaging performance calculation approximate function A obtained by linearly approximating a nonlinear function A1 representing the relationship between a plurality of adjustment amounts and the predetermined imaging performance of the projection optical system PL. Through the process of creating '1 (see step 296 in FIG. 10 (or step 496 in FIG. 19), etc.), the optimum value of the adjustment amount is calculated based on the created imaging performance calculation approximation function, for example, the least square method. (See step 302 in FIG. 10 (or step 502 in FIG. 19) and the like).

  Therefore, the adjustment amount of the adjustment amount that can be used for adjustment of imaging performance that is not linearly related to the adjustment amount of the adjustment device, such as the line width of the image of the pattern described above (in other words, non-linear with respect to each Zernike coefficient). It is possible to easily calculate the optimum value (optimum adjustment amount).

  Further, the optimization result is evaluated based on the calculation result of the optimum values of the plurality of adjustment amounts and the imaging performance calculation function (see step 306 in FIG. 10). As a result of this evaluation, when further optimization is required, the loop processing of steps 296 to 314 in FIG. 10 is repeated each time the count value m is incremented. Then, for each iteration, a new imaging performance that linearly approximates the nonlinear function corresponding to the optimum values of the latest plurality of adjustment amounts calculated in step 302 (or step 310) in advance in step 296. A calculated near-order function is created, and optimum values of the plurality of adjustment amounts are calculated in step 302 based on the new imaging performance calculation near-order function. That is, at each iteration, in step 296, based on the information on the new wavefront calculated based on the calculation result of the optimum value of the plurality of adjustment amounts and the wavefront aberration change table, and the target exposure condition, The Zernike sensitivity of the predetermined imaging performance under the exposure condition is newly calculated. In step 302, the plurality of adjustment amounts, the predetermined imaging performance of the projection optical system under the predetermined exposure condition, and the imaging The target exposure condition based on an imaging performance calculation function indicating a relationship between a difference from a predetermined target value of performance, a Zernike sensitivity of the newly calculated predetermined imaging performance, and the wavefront aberration change table The optimum values of the plurality of adjustment amounts below are newly calculated.

  In addition, by setting the predetermined number of times M in step 312 to 2 times, the processing of the loop can be performed only once, or by setting the predetermined number of times M to 3 times or more, As a result of the evaluation, as long as further optimization is required, a series of processes including the above steps 306, 296, and 302 can be repeated a plurality of times. In such a case, the optimum solution of the adjustment amount is asymptotically derived by repeating the plurality of times.

  In any case, the pattern of the reticle R is transferred onto the wafer using the projection optical system PL in a state where the above-described adjustment device is adjusted based on the calculation results of the optimum values of the plurality of adjustment amounts. In this case, the pattern is formed on the wafer using the projection optical system in a state in which the image formation state is adjusted by the projection optical system so that the predetermined imaging performance such as the line width of the pattern image is optimal. Transcribed above. Therefore, a pattern image (transfer image) can be formed on the wafer with high accuracy.

  In addition, according to the image forming state adjustment system 10 according to the present embodiment, when the above-described third mode is selected, the second communication server 930 performs the above-described operation under at least one reference exposure condition (reference ID). The Zernike sensitivity of predetermined imaging performance under an arbitrary exposure condition is calculated based on information on a plurality of adjustment amounts used in the adjustment apparatus and information on the wavefront of the projection optical system (see step 626 in FIG. 21). ), The predetermined imaging performance of the projection optical system under the arbitrary exposure conditions is calculated based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance (FIG. 21). Step 634). Then, the calculation result is displayed on the screen (see step 636 in FIG. 21). Accordingly, by looking at the display on the screen, anyone can easily evaluate whether or not the predetermined imaging performance of the projection optical system should be satisfied.

  Further, according to the image formation state adjustment system 10 according to the present embodiment, the wavefront of the projection optical system PL is self-measured by the wavefront aberration measuring instrument 80 provided in the exposure apparatus 922. The first communication server 920 transmits the measurement result of the wavefront of the projection optical system PL measured by the wavefront aberration measuring instrument 80 to the second communication server 930 via the communication path. The second communication server 930 controls the adjustment device described above using the wavefront measurement result. Therefore, the imaging performance of the projection optical system PL is accurately adjusted using information on the wavefront on the pupil plane of the projection optical system, that is, comprehensive information passing through the pupil plane. As a result, adjustment is made so that the image formation state of the pattern by the projection optical system is optimized. In this case, the second communication server 930 can be disposed at a position away from the exposure apparatus 922 and the first communication server 920 connected thereto, and in such a case, the image of the projection optical system PL is remotely controlled. It is possible to adjust the performance, and consequently the image formation state of the pattern by the projection optical system PL with high accuracy.

  Further, when an in-house LAN system as shown in FIG. 1 is built in an exposure apparatus manufacturer, for example, on the clean room side of the research and development department, for example, a place where the exposure apparatus is assembled and adjusted (hereinafter referred to as “site”). The first communication server 920 is installed, and the second communication server 930 is installed in a laboratory away from the site. Then, the technician on the site side measures the wavefront aberration described above and the exposure condition information (including pattern information) of the exposure apparatus at the experimental stage via the first communication server 920 in the second communication on the laboratory side. Send to server 930. Then, a laboratory engineer uses the second communication server 930 in which a software program designed by himself / herself is installed in advance, and based on the sent information, the imaging performance of the projection optical system PL of the exposure apparatus 922 Is automatically corrected from a remote location and the measurement results of the wavefront aberration of the projection optical system after the adjustment of the imaging performance is received, so that the effect of the adjustment of the imaging performance can be confirmed. It can also be used for the development stage.

  Note that the processing algorithm of the second communication server described in the above embodiment is merely an example, and the image forming state adjustment system of the present invention is not limited to this.

  For example, the above-mentioned weight (imaging performance weight, weight of each evaluation point in the field of view), target (target value of imaging performance at each evaluation point in the field of view), optimization field range The designation or the like may not necessarily be possible. This is because these can be dealt with by specifying in advance by default settings as described above. For the same reason, it is not always necessary to specify an allowable value or a constraint condition.

  On the other hand, other functions not described above may be added. For example, even if the line width performance (line width variation) is good only on a specific focus surface, it is not preferable that the line width performance deteriorates on other focus surfaces within the depth of focus. Therefore, in order to simultaneously optimize the line width performance on a plurality of focus surfaces within the depth of focus, the Z position of the plurality of focus surfaces within the depth of focus is substituted for Z in Equation (10), and a line for each focus surface is obtained. A processing algorithm that performs width calculation and optimizes all the results simultaneously may be employed, particularly in the first and second modes. In the first and second modes, the weight is reset when the operator sees the result of the optimization calculation displayed on the screen and determines that it is necessary. A processing algorithm that resets weights based on a predetermined number of times may be employed.

  In the above embodiment, the imaging performance calculation near-order function used for obtaining the optimum value of the adjustment amount of the adjusting device is the plural (19) adjustment amounts and the predetermined imaging performance described above, specifically, The nonlinear function representing the relationship with the line width is assumed to be a function including a linear approximation change amount of a predetermined imaging performance expressed as a linear sum of linear approximation functions obtained by partial differentiation with respect to each of the plurality of adjustment amounts. (See equation (27) above). However, if the required accuracy is not so severe, or if the imaging performance of the projection optical system is accurately adjusted at the manufacturing stage, the above-mentioned imaging performance calculation approximate function is The linear approximation change amount of the predetermined imaging performance expressed as a linear sum of the linear approximation functions of the nonlinear functions representing the relationship between the respective adjustment amounts and the predetermined imaging performance, such as the equation (42). It is also possible to use a function including

  Further, in the above embodiment, the wavefront aberration calculated in the reference ID is used in the mode 1, the wavefront aberration actually measured in the mode 2 is used, and the wavefront aberration data similar to that in the mode 1 is obtained in the mode 3. For example, the wavefront aberration actually measured in the case of mode 3 may be used. That is, based on the actually measured wavefront aberration, the above-mentioned 13 types of imaging performance under various exposure conditions may be obtained by calculation, and if the above-mentioned best exposure conditions are determined based on the calculation results, Based on the actual measurement data, it is possible to determine the best exposure condition more accurately.

  Further, in the case of mode 1 and mode 3, instead of using the calculated wavefront aberration in the reference ID, the actually measured wavefront aberration may be used. In short, wavefront aberration data may be used for the above-described optimization calculation.

  In the above embodiment, the second communication server can set three modes from mode 1 to mode 3, but only mode 1, only mode 2, only mode 1 and mode 2, only mode 1 Only mode 3 and mode 2 and mode 3 may be settable.

  In the description so far, from the viewpoint of avoiding more complicated explanation than necessary, it is caused by fluctuations in the atmospheric pressure of the environment where the exposure apparatus is installed and the amount of energy of illumination light irradiated on the projection optical system. The point that the imaging performance of the projection optical system changes, that is, the so-called atmospheric pressure fluctuation and the so-called irradiation fluctuation of the imaging performance is not particularly mentioned. Also good. These basic data can be obtained by experiments or high-precision optical simulation.

  On the other hand, in the above-described embodiment, when creating a database such as a wavefront aberration change table for the reference ID, the atmospheric pressure, the irradiation amount, etc. are assumed to serve as reference values, and these are taken into account by the above simulation. Create a database such as a wavefront aberration change table. For example, when the above-described mode 1 is selected, the second communication server 930 assumes that the calculated wavefront aberration in the reference ID is used, that is, when the image forming state is optimized, Measurement data of a sensor that measures the atmospheric pressure in the chamber 11 (or in the clean room) of the exposure apparatus 922 that is an adjustment amount calculation target, and irradiation in log data collected by the main controller 50 of the exposure apparatus 922 History data is taken in via the first communication server 920. Next, the second communication server 930 calculates the reference atmospheric pressure and the amount of variation from the irradiation amount based on these data, and the imaging performance of the projection optical system based on the calculation result. Atmospheric pressure fluctuation and irradiation fluctuation are calculated. Then, the second communication server 930 may perform the optimization process using the calculated wavefront aberration in the reference ID of mode 1 described above in consideration of the calculation result.

  In the case of mode 2 as well as mode 3, similarly, the atmospheric pressure fluctuation or irradiation fluctuation of the imaging performance of the projection optical system described above may be taken into consideration. This also applies to the modified examples described later.

  The above-described various changes in the processing algorithm of the second communication server can be easily realized by changing the software.

  The system configuration described in the above embodiment is merely an example, and the image forming state adjustment system according to the present invention is not limited to this. For example, a system configuration having a communication path including a public line as a part thereof may be adopted.

  Moreover, although the said embodiment demonstrated the case where the above-mentioned optimization program was stored in the 2nd communication server 930, it is not restricted to this, The optimization program is in the CD-ROM drive with which the 1st communication server 920 is provided. And a CD-ROM in which a database attached thereto is loaded, and an optimization program and a database attached thereto are installed and copied from a CD-ROM drive into a storage device such as a hard disk provided in the first communication server 920. You can leave it. In this way, the first communication server 920 can perform the aforementioned optimization processing and the like only by receiving information from the exposure apparatus 922.

  Alternatively, a CD-ROM storing an optimization program and a database attached thereto is loaded into the drive device 46 provided in the exposure apparatus 922, and the optimization program and the database attached thereto are stored from the CD-ROM drive into a storage device such as a hard disk. It may be installed and copied in 42. In this way, it is possible to perform the above-described optimization processing and the like with the exposure apparatus 922 alone. Instead of inputting pattern information by an operator, pattern information is obtained from a host computer of a device manufacturing factory of manufacturer A, or a barcode or a two-dimensional code attached to a reticle on which a pattern to be transferred to a wafer is formed. The exposure apparatus may read pattern information to obtain pattern information, and automatic adjustment of the projection optical system PL by the exposure apparatus may be possible without intervention of an operator or service engineer. In this case, the main controller 50 constitutes a first calculation device, a second calculation device, a processing device, an evaluation device, a Zernike sensitivity recalculation device, an adjustment amount recalculation device, and a determination device.

  That is, the main controller 50 executes the above-described mode 1 process (including determination), and the adjustment information of the adjustment device and the information on the wavefront of the projection optical system under the reference exposure condition (reference ID). The optimal adjustment amount of the adjustment device under the target exposure condition is calculated based on the above, and the adjustment device is controlled based on the calculated adjustment amount. As a result, the formation state of the pattern projection image on the wafer under an arbitrary target exposure condition is optimized almost automatically.

  Further, main controller 50 executes the process of mode 2 described above, and under the target exposure condition based on the measurement data of the adjustment information of the adjustment device and the wavefront information of the projection optical system under the predetermined target exposure condition. An optimum adjustment amount of the adjustment device is calculated, and the adjustment device is controlled based on the calculated adjustment amount. In this case, the formation state of the pattern projection image on the wafer under an arbitrary target exposure condition is optimized almost automatically. In this case, the adjustment device is controlled based on a more accurate adjustment amount than in the first mode.

  In the above embodiment, a wavefront aberration measuring instrument having an overall shape that can be exchanged with the wafer holder may be used as the wavefront aberration measuring instrument. In such a case, this wavefront aberration measuring instrument uses a transfer system (such as a wafer loader) that loads a wafer or wafer holder onto wafer stage WST (Z tilt stage 58) and unloads it from wafer stage WST (Z tilt stage 58). Can be automatically conveyed. Note that the wavefront aberration measuring instrument carried into the wafer stage may not include all of the wavefront aberration measuring instrument 80 described above, for example, and only a part of the wavefront aberration measuring instrument 80 is provided outside the wafer stage. May be. Furthermore, in the above embodiment, the wavefront aberration measuring instrument 80 is detachable from the wafer stage, but may be permanently installed. At this time, only a part of the wavefront aberration measuring instrument 80 may be placed on the wafer stage, and the rest may be placed outside the wafer stage. Furthermore, in the above embodiment, the aberration of the light receiving optical system of the wavefront aberration measuring instrument 80 is ignored, but the wavefront aberration of the projection optical system may be determined in consideration of the wavefront aberration. Further, when the measurement reticle disclosed in, for example, the aforementioned US Pat. No. 5,978,085 is used for measuring the wavefront aberration, the latent image of the measurement pattern transferred and formed on the resist layer on the wafer is used. The positional deviation of the reference pattern with respect to the latent image may be detected by, for example, an alignment system ALG provided in the exposure apparatus. When detecting a latent image of a measurement pattern, a photoresist may be used as a photosensitive layer on an object such as a wafer, or a magneto-optical material may be used. In addition, the exposure device and coater / developer are connected in-line, and the resist image obtained by developing the wafer or other object to which the above-mentioned measurement pattern is transferred, and the etching image obtained by etching are exposed. You may detect with the alignment system ALG of an apparatus. By such various ideas, it is possible to automatically perform the above-described automatic adjustment of the imaging performance of the projection optical system PL by the image forming state adjustment system 10 without involving an operator or a service engineer. It is. Similarly, by storing the optimization program in the first communication server, the above-described automatic adjustment of the imaging performance of the projection optical system PL can be performed by the first communication server without intervention of an operator or service engineer. Can do. Similarly, by installing an optimization program in the storage device 42 of the exposure apparatus 922, the above-described automatic adjustment of the imaging performance of the projection optical system PL can be performed by the exposure apparatus alone without intervention of an operator or service engineer. It is also possible to do this.

  In addition, the first communication server 920 and the second communication server 930 may be connected by a wireless line.

  In the above embodiment, 13 types of imaging performance are optimized, but the type (number) of imaging performance is not limited to this, and the type of exposure condition to be optimized is changed. By doing so, more or less imaging performance may be optimized. For example, as nonlinear imaging performance for each Zernike coefficient, instead of or in addition to the line width CD of the image of the line pattern described in the above embodiment, the line width difference between vertical and horizontal lines, isolated lines and dense lines The line width difference may be taken as an evaluation object or an optimization object.

  In the above embodiment, 12 types of aberrations that are linear imaging performance with respect to each Zernike coefficient and line widths that are non-linear imaging performance with respect to each Zernike coefficient are calculated using the same optimization calculation method. The case of processing has been described. For example, the calculation method for optimizing linear aberration disclosed in International Publication No. 03/065428 is simpler than the method described in this embodiment, and the time required for the calculation is as follows. Also very short. Therefore, if the mode can be set according to the type of imaging performance to be optimized and only linear optimization is performed, the optimization calculation disclosed in the above-mentioned WO 03/065428 is performed. In other cases, the optimization calculation described above may be executed.

In the above embodiment, all the coefficients of the first to nth terms of the Zernike polynomial are used. However, the coefficients may not be used in at least one of the first to nth terms. For example, the corresponding imaging performance may be adjusted as usual without using the coefficients of the second to fourth terms. In this case, when the coefficients of the second to fourth terms are not used, the corresponding imaging performance is adjusted by adjusting the position of at least one of the movable lenses 13 _{1 to} 13 ₅ in the three-degree-of-freedom direction. However, it may be performed by adjusting the Z position and tilt of the wafer W (Z tilt stage 58).

  Further, in the above embodiment, after linear approximation calculation (ZS calculation), optimization is performed by the least square method (Least Square Method) or the attenuated least square method (Damped Least Square Method). For example, (1) Gradient methods such as Steepest Decent Method and Conjugate Gradient Method, (2) Flecible Method, (3) Variable by Variable Method, (4) Orthonomalization Method, (5) Adaptive Method, (6 ) Quadratic differentiation, (7) global optimization by simulated annealing, (8) global optimization by biological evolution, and (9) genetic algorithm (see US2001 / 0053962A).

  In the above embodiment, a case where a LAN, or a LAN and a public line, and other signal lines are used as a communication path has been described. However, the present invention is not limited to this, and the signal line and the communication path may be wired or wireless.

  In the above embodiment, as illumination condition information, a σ value (coherence factor) is used for normal illumination, and an annular ratio is used for annular illumination, but in addition to or in addition to the annular ratio in annular illumination, Instead, an inner diameter or an outer diameter may be used, and in modified illumination such as quadrupole illumination (also called SHRINC or multipolar illumination), the light amount distribution of illumination light on the pupil plane of the illumination optical system is a part thereof, that is, Since the amount of light is increased in a plurality of partial areas whose light intensity centroids are set at positions where the distance from the optical axis of the illumination optical system is substantially equal, position information of the plurality of partial areas (light intensity centroids) on the pupil plane of the illumination optical system (For example, coordinate values in a coordinate system with the optical axis as the origin on the pupil plane of the illumination optical system, etc.), the distance between a plurality of partial regions (light intensity centroids) and the optical axis of the illumination optical system, and the size of the partial region ( equivalent to σ value) Also good.

  Further, in the above embodiment, the imaging performance is adjusted by moving the optical element of the projection optical system PL, but the imaging performance adjustment mechanism is not limited to the driving mechanism of the optical element, and the driving mechanism In addition to or instead of this, for example, the pressure of the gas between the optical elements of the projection optical system PL is changed, the reticle R is moved or tilted in the optical axis direction of the projection optical system, or between the reticle and the wafer. For example, a mechanism for changing the optical thickness of the plane parallel plate disposed on the plate may be used. However, in this case, the number of degrees of freedom in the above embodiment can be changed.

In the above embodiment, a case has been described in which a plurality of exposure apparatuses 922 are provided and the second communication server 930 is commonly connected to the plurality of exposure apparatuses 922 _{1 to} 922 ₃ via a communication path. However, the present invention is not limited to this, and a single exposure apparatus may of course be used.

  In the above embodiment, the case where a scanning stepper is used as the exposure apparatus has been described. However, the present invention is not limited to this, and the present invention may be applied to a stepper that performs exposure while the mask and the wafer are stationary.

  Further, in the above embodiment, the plurality of exposure apparatuses have the same configuration, but exposure apparatuses having different wavelengths of the illumination light EL may be mixed, or exposure apparatuses having different configurations, for example, a static exposure method An exposure apparatus (such as a stepper) and a scanning exposure type exposure apparatus (such as a scanner) may be mixed. A part of the plurality of exposure apparatuses may be an exposure apparatus that uses a charged particle beam such as an electron beam or an ion beam. Further, for example, an immersion type exposure apparatus disclosed in International Publication WO99 / 49504 or the like in which a liquid is filled between the projection optical system PL and the wafer may be used.

  The use of the exposure apparatus in this case is not limited to the exposure apparatus for semiconductor manufacturing, but for example, an exposure apparatus for liquid crystal that transfers a liquid crystal display element pattern to a square glass plate, a plasma display, an organic EL, or the like The present invention can be widely applied to an exposure apparatus for manufacturing a display device, an image sensor (CCD, etc.), a thin film magnetic head, a micromachine, a DNA chip, and the like. Further, in order to manufacture reticles or masks used in not only microdevices such as semiconductor elements but also light exposure apparatuses, EUV exposure apparatuses, X-ray exposure apparatuses, electron beam exposure apparatuses, etc., glass substrates or silicon wafers, etc. The present invention can also be applied to an exposure apparatus that transfers a circuit pattern.

The light source of the exposure apparatus of the above embodiment is not limited to an ultraviolet pulse light source such as an F ₂ laser, ArF excimer laser, or KrF excimer laser, but a continuous light source such as g-line (wavelength 436 nm), i-line (wavelength 365 nm), etc. It is also possible to use an ultra-high pressure mercury lamp that emits a bright line. Further, X-rays, particularly EUV light, etc. may be used as the illumination light EL.

In addition, a single wavelength laser beam oscillated from a DFB semiconductor laser or fiber laser is amplified by a fiber amplifier doped with, for example, erbium (or both erbium and ytterbium), and a nonlinear optical crystal is obtained. It is also possible to use harmonics that have been converted into ultraviolet light. Further, the magnification of the projection optical system may be not only a reduction system but also an equal magnification or an enlargement system. The projection optical system is not limited to a refraction system, and may be a catadioptric system (catadioptric system) having a reflection optical element and a refraction optical element or a reflection system using only a reflection optical element. When a catadioptric system or a reflective system is used as the projection optical system PL, the imaging performance of the projection optical system is improved by changing the position of the reflective optical element (such as a concave mirror or a reflective mirror) as the movable optical element described above. adjust. Further, when Ar ₂ laser light, EUV light or the like is used as the illumination light EL, the projection optical system PL may be an all reflection system composed of only a reflective optical element. However, when using Ar ₂ laser light or EUV light, the reticle R is also of a reflective type.

  For semiconductor devices, the step of designing the function and performance of the device, the step of manufacturing a reticle based on this design step, the step of manufacturing a wafer from a silicon material, and the pattern of the reticle on the wafer by the exposure apparatus of the above-described embodiment And a device assembly step (including a dicing process, a bonding process, and a packaging process), an inspection step, and the like. According to this device manufacturing method, since exposure is performed in the lithography process using the exposure apparatus of the above-described embodiment, the imaging performance is adjusted according to the target pattern, or the result is based on the measurement result of the wavefront aberration. Since the pattern of the reticle R is transferred onto the wafer W via the projection optical system PL whose image performance is adjusted with high accuracy, it becomes possible to transfer the fine pattern onto the wafer W with good overlay accuracy. Therefore, the yield of the device as the final product is improved, and the productivity can be improved.

  As described above, the calculation method of the present invention is suitable for calculating the adjustment amount used in the adjustment device that adjusts the formation state of the pattern image projected onto the object by the projection optical system. The adjustment method of the present invention is suitable for adjusting the formation state of the pattern image on the object. The exposure method and exposure apparatus of the present invention are suitable for transferring a pattern onto an object with high accuracy. The image formation state adjustment system of the present invention is suitable for quickly optimizing the formation state of a pattern projection image on an object. The program and the information recording medium of the present invention are suitable for causing a computer constituting a part of a control system of an exposure apparatus to execute processing for optimizing the formation state of a pattern projection image on an object. Yes.

It is a figure which shows the structure of the image formation state adjustment system which concerns on one Embodiment of this invention. It is a figure which shows schematically the structure of the 1st exposure apparatus 922 ₁ of FIG. It is sectional drawing which shows an example of a wavefront aberration measuring device. 4A shows a light beam emitted from the microlens array when there is no aberration in the optical system, and FIG. 4B shows a light beam emitted from the microlens array when there is aberration in the optical system. FIG. It is a flowchart which shows the process algorithm performed by CPU in a 2nd communication server. It is a flowchart (the 1) which shows the process in step 118 of FIG. It is a flowchart (the 2) which shows the process in step 118 of FIG. 6 is a flowchart (No. 3) showing a process in step 118 of FIG. 6 is a flowchart (No. 4) showing a process in step 118 of FIG. 6 is a flowchart (No. 5) showing a process in step 118 of FIG. FIG. 5 is a diagram (part 1) for explaining the principle of a method for asymptotically obtaining an optimal solution for an adjustment amount; FIG. 6 is a diagram (part 2) for explaining the principle of a method for asymptotically obtaining an optimal solution for an adjustment amount; FIG. 10 is a diagram (No. 3) for explaining the principle of a method for asymptotically obtaining an optimal solution for an adjustment amount; FIG. 14 is a diagram (No. 4) for explaining the principle of a technique for asymptotically obtaining an optimal solution for an adjustment amount; It is a flowchart (the 1) which shows the process in step 116 of FIG. It is a flowchart (the 2) which shows the process in step 116 of FIG. It is a flowchart (the 3) which shows the process in step 116 of FIG. 6 is a flowchart (No. 4) showing a process in step 116 of FIG. It is a flowchart (the 5) which shows the process in step 116 of FIG. It is a flowchart (the 1) which shows the process in step 120 of FIG. It is a flowchart (the 2) which shows the process in step 120 of FIG.

Explanation of symbols

10 ... imaging condition adjustment system, _{131-134 5} ... (part of the adjustment device) movable lens, 16 ... (part of the adjustment device) light source, (part of the adjusting device) 48 ... imaging performance correction controller, 50... Main control device (part of adjustment device) 56... Wafer stage drive unit (part of adjustment device) 58... Z tilt stage (part of adjustment device) 922 ₁ , 922 ₂ , 922 ₃ . Device, 930 ... second communication server (computer, first calculation device, second calculation device, processing device, evaluation device, Zernike sensitivity recalculation device, adjustment amount recalculation device, determination device), EL ... illumination light (energy beam) ), R ... reticle (mask), PL ... projection optical system, W ... wafer (object).

Claims (31)

A calculation method for calculating an optimum value of an adjustment amount used in an adjustment device for adjusting a formation state of an image of a pattern projected on an object by a projection optical system on the object,
An approximation function creating step for creating an imaging performance calculation approximation function that linearly approximates a nonlinear function representing a relationship between a plurality of adjustment amounts and the predetermined imaging performance of the projection optical system;
A calculation step of calculating an optimum value of the plurality of adjustment amounts based on the imaging performance calculation approximation function.   A first sub-step of creating a new imaging performance calculation proximity function that linearly approximates the nonlinear function corresponding to the calculated optimum values of the plurality of latest adjustment amounts; and the new imaging performance calculation proximity The calculation method according to claim 1, further comprising a processing step of performing a series of processing with the second sub-step of calculating the optimum values of the plurality of adjustment amounts based on a function at least once.   The calculation method according to claim 2, wherein in the processing step, the series of processing is repeated a plurality of times to derive an optimal solution of the adjustment amount.   The imaging performance calculation approximation function is a linear approximation change amount of the predetermined imaging performance expressed as a linear sum of a linear approximation function of a nonlinear function representing a relationship between each adjustment amount and the predetermined imaging performance. The calculation method according to claim 1, wherein the calculation method is a function including.   The imaging performance calculation proximity function is expressed as a linear sum of linear approximation functions obtained by partially differentiating a nonlinear function representing the relationship between the plurality of adjustment amounts and the predetermined imaging performance with each of the plurality of adjustment amounts. The calculation method according to claim 1, wherein the calculation method is a function including a linear approximate change amount of the predetermined imaging performance. An adjustment method for adjusting a formation state of an image of a pattern projected on an object by a projection optical system on the object using an adjustment device,
Calculating an optimum value of a plurality of adjustment amounts using the calculation method according to claim 1;
Adjusting the adjusting device based on the calculated optimum values of the plurality of adjustment amounts. Adjusting the formation state of the image of the pattern on the object by the adjustment method according to claim 6;
And a step of transferring the pattern onto the object using the projection optical system after adjusting the image formation state. An exposure method for transferring a predetermined pattern onto an object using a projection optical system provided with an adjusting device for adjusting a formation state of a projected image of a pattern,
Based on given target exposure conditions and information on the wavefront of the projection optical system, a relationship between a plurality of adjustment amounts used in the adjustment device under the target exposure conditions and predetermined imaging performance of the projection optical system A Zernike sensitivity calculating step of calculating Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function representing the Zernike polynomial by a coefficient of each term of the Zernike polynomial that expands the wavefront;
The plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the calculated Zernike of the predetermined imaging performance The target exposure condition based on an imaging performance calculation function indicating a relationship between sensitivity and a wavefront aberration change table including a parameter group indicating a relationship between each of the plurality of adjustment amounts and a change in wavefront aberration of the projection optical system An adjustment amount calculation step of calculating an optimum value of the plurality of adjustment amounts below;
A transfer step of transferring the pattern onto the object using the projection optical system in a state where the adjustment device is adjusted based on the calculation result of the optimum values of the plurality of adjustment amounts under the target exposure condition; An exposure method comprising: An evaluation step of evaluating an optimization result based on a calculation result of an optimum value of the plurality of adjustment amounts and the imaging performance calculation function prior to the transfer step;
As a result of the evaluation, when further optimization is required, information on the new wavefront calculated based on the calculation result of the optimum value of the plurality of adjustment amounts and the wavefront aberration change table and the target exposure condition A Zernike sensitivity recalculation step for newly calculating a Zernike sensitivity of the predetermined imaging performance under the target exposure condition;
The plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the newly calculated predetermined imaging An adjustment amount recalculation step for newly calculating optimum values of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship between Zernike sensitivity of performance and the wavefront aberration change table; The exposure method according to claim 8, further comprising:   The exposure method according to claim 8, wherein a series of processes of the evaluation step, the Zernike sensitivity recalculation step, and the adjustment amount recalculation step are repeated a plurality of times.   The exposure method according to claim 8, wherein the predetermined exposure condition is an exposure condition serving as at least one reference.   12. The exposure method according to claim 11, wherein the information about the wavefront of the projection optical system is information about the wavefront of the projection optical system after adjustment under the reference exposure conditions.   The information on the wavefront aberration of the projection optical system is calculated based on information on the single wavefront aberration of the projection optical system and the imaging performance of the projection optical system under the reference exposure conditions. The exposure method according to claim 11.   The exposure method according to claim 8, wherein the predetermined exposure condition is the target exposure condition.   15. The exposure method according to claim 14, wherein the information on the wavefront of the projection optical system is actually measured data of wavefront aberration under the target exposure condition. An imaging performance calculation method for calculating a predetermined imaging performance of a projection optical system that forms a projected image of a pattern on an object,
Based on information on a plurality of adjustment amounts used in the adjustment device that adjusts the formation state of the projection image under exposure conditions serving as at least one reference, and information on the wavefront of the projection optical system, The predetermined function is a partial differential coefficient obtained by partially differentiating a specific function representing a relationship between the plurality of adjustment amounts and a predetermined imaging performance of the projection optical system with a coefficient of each term of a Zernike polynomial in which the wavefront is expanded. A Zernike sensitivity calculating step of calculating a Zernike sensitivity of the imaging performance of;
An imaging performance calculation step of calculating the predetermined imaging performance of the projection optical system under the arbitrary exposure conditions based on the wavefront aberration of the projection optical system and the Zernike sensitivity of the predetermined imaging performance; Imaging performance calculation method including An exposure method for transferring a pattern onto an object via a projection optical system,
The imaging performance calculation method according to claim 16 is used to calculate the imaging performance of the projection optical system respectively under a plurality of exposure conditions having different setting values with respect to setting information of interest among a plurality of setting information in the transfer. An exposure method including steps. An exposure apparatus that illuminates a mask with an energy beam and transfers a pattern formed on the mask onto an object via a projection optical system,
An adjusting device for adjusting a formation state of the projected image of the pattern on the object;
Based on given target exposure conditions and information on the wavefront of the projection optical system, a relationship between a plurality of adjustment amounts used in the adjustment device under the target exposure conditions and predetermined imaging performance of the projection optical system A first calculation device that calculates Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function that represents a specific function by a coefficient of each term of a Zernike polynomial that expands the wavefront;
The plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the Zernike sensitivity calculated by the first calculation device Based on an imaging performance calculation function indicating a relationship between each of the plurality of adjustment amounts and a wavefront aberration change table including a parameter group indicating a relationship between a change in wavefront aberration of the projection optical system. A second calculation device for calculating an optimum value of the plurality of adjustment amounts in;
An exposure apparatus comprising: a processing device that adjusts the adjustment device based on a calculation result of the optimum values of the plurality of adjustment amounts when transferring the pattern. Prior to the adjustment by the processing device, the optimization result is evaluated based on the calculation result of the optimum value of the plurality of adjustment amounts and the imaging performance calculation function, and it is determined whether further optimization is necessary. An evaluation device to perform;
When the evaluation device determines that further optimization is necessary, it calculates new wavefront information based on the calculation results of the optimum values of the plurality of adjustment amounts and the wavefront aberration change table, and the new A Zernike sensitivity recalculation device that newly calculates a Zernike sensitivity of the predetermined imaging performance under the target exposure condition on the basis of information relating to a correct wavefront and the target exposure condition;
The plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the newly calculated predetermined imaging An adjustment amount recalculation device that newly calculates an optimum value of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship between Zernike sensitivity of performance and the wavefront aberration change table; The exposure apparatus according to claim 18, further comprising: An exposure apparatus that illuminates a mask with an energy beam and transfers a pattern formed on the mask onto an object via a projection optical system,
An adjusting device for adjusting the formation state of the projected image on the object;
Based on information on a plurality of adjustment amounts used in the adjustment device and information on the wavefront of the projection optical system under at least one reference exposure condition, the plurality of adjustment amounts under the arbitrary exposure conditions The Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating the specific function representing the relationship with the predetermined imaging performance of the projection optical system by the coefficient of each term of the Zernike polynomial that expands the wavefront. A first calculating device for calculating;
A second calculation device for calculating the predetermined imaging performance of the projection optical system under the arbitrary exposure conditions based on the wavefront aberration of the projection optical system and the Zernike sensitivity calculated by the first calculation device; An exposure apparatus.   Using the first and second calculation devices, the projection is performed under a plurality of exposure conditions having different setting values with respect to setting information to be noticed among a plurality of setting information related to the projection conditions of the pattern to be projected by the projection optical system. A determination device that calculates the predetermined imaging performance of the optical system, and determines an exposure condition in which a setting value related to the focused setting information is optimal based on the imaging performance calculated for each exposure condition; The exposure apparatus according to claim 20. An image formation state adjustment system for optimizing the formation state of the projection image on an object used in an exposure apparatus that forms a projection image of a predetermined pattern on the object using a projection optical system,
An adjusting device for adjusting the formation state of the projected image on the object;
A computer connected to the exposure apparatus via a communication path;
The computer
Based on given target exposure conditions and information on the wavefront of the projection optical system, a relationship between a plurality of adjustment amounts used in the adjustment device under the target exposure conditions and predetermined imaging performance of the projection optical system A first function for calculating a Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function representing the Zernike polynomial by a coefficient of each term of the Zernike polynomial that expands the wavefront;
The plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the calculated Zernike of the predetermined imaging performance The target exposure condition based on an imaging performance calculation function indicating a relationship between sensitivity and a wavefront aberration change table including a parameter group indicating a relationship between each of the plurality of adjustment amounts and a change in wavefront aberration of the projection optical system A second function of calculating an optimum value of the plurality of adjustment amounts below; and an image forming state adjustment system characterized by comprising: The computer
A third evaluation for evaluating the optimization result based on the calculation result of the optimum values of the plurality of adjustment amounts and the imaging performance calculation function, and determining whether further optimization is necessary based on the evaluation result; Function and;
When it is determined that further optimization is necessary, information on a new wavefront is calculated based on the calculation results of the optimum values of the plurality of adjustment amounts and the wavefront aberration change table, and information on the new wavefront A fourth function for newly calculating the Zernike sensitivity of the predetermined imaging performance under the target exposure condition based on the target exposure condition;
The plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the newly calculated predetermined imaging A fifth function for newly calculating optimum values of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship between Zernike sensitivity of performance and the wavefront aberration change table; The image forming state adjustment system according to claim 22, further comprising: An image formation state adjustment system for optimizing the formation state of the projection image on an object used in an exposure apparatus that forms a projection image of a predetermined pattern on the object using a projection optical system,
An adjusting device for adjusting the formation state of the projected image on the object;
Based on information on a plurality of adjustment amounts used in the adjustment device and information on the wavefront of the projection optical system under an exposure condition that is connected to the exposure device via a communication path and serves as at least one reference. A partial differential coefficient obtained by partially differentiating a specific function representing the relationship between the plurality of adjustment amounts and the predetermined imaging performance of the projection optical system under the exposure condition by a coefficient of each term of the Zernike polynomial that expands the wavefront Zernike sensitivity is calculated, and based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance, the predetermined result of the projection optical system under the arbitrary exposure conditions is calculated. An image forming state adjustment system comprising: a computer that calculates image performance.   The computer executes the calculation of the predetermined imaging performance for a plurality of exposure conditions having different setting values with respect to setting information to be noted among a plurality of setting information related to the projection conditions of a pattern to be projected by the projection optical system. 25. The image forming state adjustment system according to claim 24, wherein an exposure condition in which a setting value related to the focused setting information is optimal is determined based on the imaging performance calculated for each exposure condition.   The image forming state adjustment system according to any one of claims 22 to 25, wherein the computer is a control computer that controls each component of the exposure apparatus. A projection image of a predetermined pattern is formed on an object using a projection optical system, and a part of a control system of an exposure apparatus including an adjustment device that adjusts a formation state of the projection image on the object is configured. A program for causing a computer to execute predetermined processing,
Based on given target exposure conditions and information on the wavefront of the projection optical system, a relationship between a plurality of adjustment amounts used in the adjustment device under the target exposure conditions and predetermined imaging performance of the projection optical system A procedure for calculating Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating a specific function that represents a specific function by a coefficient of each term of a Zernike polynomial that expands the wavefront;
The plurality of adjustment amounts, the difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the calculated Zernike of the predetermined imaging performance The target exposure condition based on an imaging performance calculation function indicating a relationship between sensitivity and a wavefront aberration change table including a parameter group indicating a relationship between each of the plurality of adjustment amounts and a change in wavefront aberration of the projection optical system A program for causing the computer to execute a procedure for calculating optimal values of the plurality of adjustment amounts below. A procedure for evaluating an optimization result based on a calculation result of an optimum value of the plurality of adjustment amounts and the imaging performance calculation function, and determining whether further optimization is necessary based on the evaluation result;
When it is determined that further optimization is necessary, information on a new wavefront is calculated based on the calculation results of the optimum values of the plurality of adjustment amounts and the wavefront aberration change table, and information on the new wavefront A procedure for newly calculating the Zernike sensitivity of the predetermined imaging performance under the target exposure condition based on the target exposure condition;
The plurality of adjustment amounts, a difference between the predetermined imaging performance of the projection optical system under a predetermined exposure condition and a predetermined target value of the imaging performance, and the newly calculated predetermined imaging performance A step of newly calculating optimum values of the plurality of adjustment amounts under the target exposure condition based on an imaging performance calculation function indicating a relationship between the Zernike sensitivity of the lens and the wavefront aberration change table; The program according to claim 27 to be executed. A projection image of a predetermined pattern is formed on an object using a projection optical system, and a part of a control system of an exposure apparatus including an adjustment device that adjusts a formation state of the projection image on the object is configured. A program for causing a computer to execute predetermined processing,
Based on information on a plurality of adjustment amounts used in the adjustment device and information on the wavefront of the projection optical system under at least one reference exposure condition, the plurality of adjustment amounts under the arbitrary exposure conditions The Zernike sensitivity of the predetermined imaging performance, which is a partial differential coefficient obtained by partially differentiating the specific function representing the relationship with the predetermined imaging performance of the projection optical system by the coefficient of each term of the Zernike polynomial that expands the wavefront. A procedure for calculating;
Calculating the predetermined imaging performance of the projection optical system under the arbitrary exposure conditions based on the wavefront aberration of the projection optical system and the calculated Zernike sensitivity of the predetermined imaging performance; A program to be executed by the computer. The computer executes the calculation of the predetermined imaging performance for a plurality of exposure conditions having different setting values with respect to setting information of interest among a plurality of setting information related to the projection conditions of the pattern to be projected by the projection optical system. As well as
30. The method according to claim 29, further causing the computer to execute a procedure for determining an exposure condition at which a setting value relating to the setting information of interest is optimal based on the imaging performance calculated for each of the exposure conditions. The listed program. A computer-readable information recording medium on which the program according to any one of claims 27 to 30 is recorded.

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