JP2014075444A - Method and program of determining lighting conditions, exposure method and manufacturing method for device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To determine an effective light source quickly without causing indefiniteness or instability of calculation results.SOLUTION: An effective light source for confining an evaluation value, indicating the difference between the distribution of a function obtained by multiplying the convolution integral of an effective light source, i.e., the light intensity distribution to be formed on the pupil surface of an illumination optical system, and the pupil function of a projection optical system by a complex conjugate of the diffraction light distribution of the pattern of a mask, and an ideal diffraction light distribution defined as a function determined by performing Fourier transformation of a target pattern on the image surface of the projection optical system, within an allowable range is determined as the lighting conditions used in an exposure device.

Description

  The present invention relates to a method and program for determining illumination conditions, an exposure method, and a device manufacturing method.

  2. Description of the Related Art An exposure apparatus has been conventionally used when manufacturing a fine semiconductor device such as a semiconductor memory or a logic circuit by using a photolithography technique. The exposure apparatus projects a pattern (circuit pattern) drawn on an original mask (reticle) onto a substrate such as a wafer by a projection optical system, and transfers the pattern onto the substrate. In recent years, miniaturization of semiconductor devices has progressed, and in an exposure apparatus, it is necessary to form a pattern having a dimension smaller than the wavelength of exposure light. In the formation of such a fine pattern, since the quality of the pattern transferred to the substrate differs depending on the illumination condition (effective light source) for illuminating the mask, it is important to set an optimal effective light source.

  For this reason, a method of calculating an exact optical image (aerial image) and selecting an effective light source is generally performed by assuming a plurality of illumination conditions by trial and error. However, it takes time and effort. Therefore, a method for efficiently determining an effective light source is needed. In general, calculation of an optical image is required to determine an effective light source. For example, the light source is two-dimensionally divided into a plurality of elements, and the plurality of elements are regarded as point light sources. Optimizes the effective light source by calculating the optical image when the light from one point light source passes through the mask and projection optical system and reaches the image plane, and selects the light that contributes to the pattern image formation. (See Patent Documents 1 to 3). However, since this method has to calculate an optical image (aerial image), it takes a long time to determine an effective light source.

  In order to solve this problem, Patent Document 4 proposes a method of determining an effective light source by an operation based on an analytical expression without repeating aerial image calculation. However, in the method described in Patent Document 4, the calculation for determining the effective light source may include division by 0 and a minute number, resulting in indefiniteness and instability of the calculation result.

JP-A-6-120119 JP 2002-334836 A JP 2004-128108 A JP 2011-129985 A

  Therefore, an object of the present invention is to determine an effective light source quickly and without causing indefiniteness or instability of a calculation result.

  The present invention relates to illumination conditions used in an exposure apparatus that illuminates a mask with light emitted from an illumination optical system, and projects the pattern of the illuminated mask onto a substrate via a projection optical system to expose the substrate. A complex conjugate of the diffracted light distribution of the mask pattern to the convolution integral of the effective light source that is the light intensity distribution to be formed on the pupil plane of the illumination optical system and the pupil function of the projection optical system. An effective light source that makes an evaluation value indicating a difference between the distribution represented by the function multiplied by the ideal diffracted light distribution defined as a function obtained by Fourier transforming the target pattern on the image plane of the projection optical system within an allowable range The illumination condition is determined.

  According to the present invention, an effective light source can be determined quickly and without causing indefiniteness or instability of a calculation result.

Flowchart diagram of a method for determining an effective light source Diagram showing the formula used to determine the effective light source and its definition The figure which shows the target pattern in Example 1, the initial effective light source, the determined effective light source, the pattern of the mask containing an auxiliary pattern, and a two-dimensional image The figure which shows the comparison of the effective light source determined in Example 2, the pattern of the mask containing an auxiliary pattern, a two-dimensional image, and a defocus characteristic Diagram showing exposure equipment Conceptual diagram of initial effective light source and trial effective light source The figure which shows the effective light source determined in Example 3, the pattern of the mask containing an auxiliary pattern, and a two-dimensional image

  The present invention relates to original data (mask pattern) used in the manufacture of various devices such as semiconductor chips such as IC and LSI, display elements such as liquid crystal panels, detection elements such as magnetic heads, imaging elements such as CCDs, and micromechanics. Can be applied when generating Here, the micromechanics refers to a technique for creating a micron-unit mechanical system having advanced functions by applying a semiconductor integrated circuit manufacturing technique to the manufacture of a fine structure, and the mechanical system itself. The present invention provides, for example, data on an original (mask pattern) used in an exposure apparatus having a projection optical system having a large numerical aperture (NA) or an immersion exposure apparatus that fills a space between the final surface of the projection optical system and a wafer with a liquid. ) Can be used as a method of determining an effective light source for illuminating.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In addition, in each figure, the same reference number is attached | subjected about the same member and the overlapping description is abbreviate | omitted. The relationship between the mask pattern and the wafer pattern in the exposure apparatus is a partial coherent imaging relationship. In partial coherent imaging, information on the effective light source is required to know the coherence on the mask surface. Here, coherency is the degree of interference according to the distance on the mask surface, and means so-called spatial coherence. The effective light source is a light intensity distribution formed on the pupil of the projection optical system when there is no mask. That is, determining the effective light source is calculating the light intensity distribution to be formed on the pupil plane of the illumination optical system.

The imaging performance of the partially coherent imaging system is expressed using TCC (Transmission Cross Coefficient). TCC is defined by the pupil plane of the projection optical system, and is an overlapping portion of the effective light source, the pupil function of the projection optical system, and the complex conjugate of the pupil function of the projection optical system. If the coordinates on the pupil plane of the projection optical system are (f, g), the function expressing the effective light source is S (f, g), and the pupil function is P (f, g), TCC is Can be expressed as: However, in Formula 1, * represents a complex conjugate and the integration range is from −∞ to ∞.

The pupil function is a function representing the pupil plane of the projection optical system, and has information such as the shape, size, and aberration of the pupil. Since aberrations of the projection optical system, polarization of illumination light, resist information, and the like can be incorporated into the pupil function P (f, g), in this specification, the polarization, aberration, and resist information are simply described as the pupil function. May contain. As shown in Equation 1, TCC is originally a four-dimensional function, but may be simply abbreviated as TCC in the text. In order to obtain the function I (x, y) that expresses the aerial image using TCC, a function that expresses the spectral distribution (diffracted light distribution) of the mask pattern on the pupil plane of the projection optical system is represented by And quadruple integration may be performed as shown in Equation 2. A function a (f, g) representing the diffracted light distribution of the mask pattern is a function F (m (x, y)) obtained by Fourier transform of the function m (x, y) representing the mask pattern. However, in Formula 2, * represents a complex conjugate and the integration range is from −∞ to ∞. M.M. Born, E.M. Wolf, “Principles of Optics”, Cambridge University Press, 1999, 7th (extended) edition, p. 554-632 has a detailed description of Equation 2.

Equation 2, that is, a function I (x, y) representing an aerial image is represented by a discretized variable, and transformed into Equation 3 and Equation 4. In Formula 4, F ⁻¹ represents an inverse Fourier transform.

W _{f ′, g ′} (f ″, g ″) in Expression 4 is defined by Expression 5 for a certain fixed coordinate (f ′, g ′).

Now, W _{f ′, g ′} (f ″, g ″) is referred to as a two-dimensional mutual transmission coefficient. When (f ′, g ′) = (0, 0), the pupil function of the projection optical system and the effective light source overlap. Therefore, it is clear that W _0,0 (f ″, g ″) has the largest influence among all the two-dimensional mutual transmission coefficients. Hereinafter, a case where the aberration of the pupil function is extremely small will be considered. At this time, the pupil function whose center is fixed at the origin in Equation 1 takes almost the value 1 within the radius of the pupil, so S (f, g) P (f, g) = S (f, g) Can be approximated. Therefore, W _0,0 (f ″, g ″) is expressed by Equation 6. S * P represents the convolution integral of S and P.

Under the approximation that the aberration of the pupil function is extremely small, W _0,0 (f ″, g ″) is expressed by a convolution of the effective light source S and the pupil function P. In Patent Document 4, W _0,0 (f ″, g ″) is used in place of W _{f ′, g ′} (f ″, g ″) in Equation 4, and Y _f thus obtained is used. I (x, y) that is the result of adding _{', g'} (x, y) as shown in Equation 3 is referred to as approximate aerial image I '(x, y).

The approximate aerial image I ′ (x, y) is calculated as Equation 7 by substituting Equation 6 into Equation 2.
I ′ (x, y) = F ⁻¹ [(S * P) · a ^* ] · m (7)

Equation 7 includes a mask pattern m as a factor. The intensity of the aerial image should originally change continuously from a place where the intensity is high to a place where the intensity of the peripheral portion is low. However, in the approximate aerial image calculated by Equation 7, the image intensity changes discontinuously at the boundary of the light transmittance distribution of the mask pattern. Further, when the effective light source S is obtained from Equation 7, division by the mask pattern m occurs. In particular, if the mask pattern m is a binary mask, an indefinite division by zero occurs. This has caused the instability and indeterminacy of the calculation in the determination of the effective light source S by Expression 7. Therefore, the present invention proposes the form of Equation 8 as a new approximate aerial image I ″.
I ″ (x, y) = (Γ · ASF) * m = F ⁻¹ [(S * P) · a ^* ] (8)

  In the above equation, Γ is the mutual intensity and is in a Fourier transform relationship with the effective light source S. ASF is an amplitude distribution function and is in a Fourier transform relationship with the pupil function P. The new approximate aerial image I ″ has a shape in which the mask pattern m is convolved with the ASF modulated by Γ. This reflects the shape of the mask pattern m. It is guaranteed that Further, as shown in the rightmost side of Equation 8, I ″ can be written in a form in which a factor m is dropped from I ′. For this reason, I ″ has a discontinuous intensity change as seen in I ′. There is nothing.

Next, consider using the concept of the approximate aerial image I ″ to optimize the effective light source S. Instead of optimizing the effective light source S using the exact aerial image I, the approximate aerial image I is considered. ”Is used to optimize the effective light source S. For this purpose, the concept of ideal diffracted light distribution a ₀ is prepared. The ideal diffracted light distribution a ₀ is a light intensity distribution of diffracted light whose inverse Fourier transform is an ideal aerial image (target pattern) T in consideration of the diffraction limit of the pupil.

For example, the target pattern T subjected to Fourier transform and multiplied by a circular function with a radius of 2 centered at the origin can be used as the ideal diffracted light distribution a ₀ . Here, when the wavelength of light emitted from the illumination optical system is λ, the radius of the pupil of the projection optical system is normalized by (NA / λ). The circular function is a function having a value of 1 on the circumference and inside of the circle and a value of 0 on the outside of the circle, and using the variable s indicating the radial radius of the pupil of the projection optical system, circ ( 0.5s). Since the circ function has a value with an argument of 1 or less, it has a value up to a radius s = 2.

The target pattern T may or may not coincide with the mask pattern m actually used for exposure. When the ideal diffracted light distribution a ₀ is expressed by a mathematical expression, the mathematical expression 9 is obtained.
a ₀ = circ (0.5 s) · F [T] (9)

On the other hand, when the diffracted light distribution “a” of the simple mask pattern is expressed by a mathematical expression, the mathematical expression 10 is obtained.
a = F [m] (10)

Since an evaluation function (evaluation value) is necessary for actual optimization, it is considered to define it. Looking at the right side of Equation 8, if the distribution represented by the inverse Fourier transform function (S * P) · a ^* is the ideal diffracted light distribution a ₀ defined above, the obtained approximate aerial image I ″ is It turns out that it becomes an ideal aerial image (target pattern) Based on this consideration, we propose what is expressed by Equation 11 as the evaluation function H.

That is, the shape of the effective light source S is set so that the evaluation value indicating the difference between the distribution represented by the inverse Fourier transform function (S * P) · a ^* and the ideal diffracted light distribution a ₀ is within an allowable range, for example, the minimum. It will change. In Formula 11, the integrand exponent is exemplarily set to 2, but this is not necessarily so, and the integrand shows a difference between the distribution represented by (S * P) · a ^* and the ideal diffracted light distribution. It only needs to be the norm of the evaluation value. Expressions 8 and 11 are important concepts that form the basis of the present invention.

FIG. 2 schematically shows these mathematical formulas and the concept of optimizing the effective light source in the present invention. By optimizing the effective light source S so that the evaluation function H is minimized, the distribution represented by (S * P) · a ^* is brought close to the ideal diffracted light distribution a ₀ , and the approximate aerial image I is thereby obtained. It approaches the target pattern T. In this way, the effective light source S is determined. The target pattern is usually composed of a plurality of figures. At this time, with respect to the intensity of the ideal diffracted light distribution a ₀ , it is possible to consider weighting for each corresponding figure pitch. The diffracted light distribution is a superposition of the frequency components of the pitches of various figures constituting the pattern, and the diffracted light corresponding to the pitches of some figures having a high appearance frequency on the pattern becomes stronger. Accordingly, when it is important to resolve a graphic even though the frequency of appearance of the graphic is low, the intensity of diffracted light corresponding to the pitch of the graphic is increased. In general, the resolution of the minimum pitch is often emphasized, so it is preferable to increase the diffracted light positioned outside the pupil.

It goes without saying that aberrations can be considered in optimizing the effective light source of the present invention. In this case, in the pupil function P (f, g), when aberration is taken into consideration, the aberration function can be expressed as Equation 12 with Φ.
P (f, g) = exp [-2πi / λ · φ (f, g)] (12)
For example, when only defocus is considered as the aberration, the aberration function Φ is expressed by the following Expression 13. Now, it is assumed that the projection optical system considers only defocus aberration and does not consider the resist applied to the substrate (wafer). The defocus amount of the image plane is def (nm). Here, n represents the refractive index of the medium.

In general, when the aberration function Φ is expanded with a Zernike coefficient, the aberration function Φ can also be expressed by the following Expression 14. The coordinates of the pupil are polar coordinates (ρ, θ) (0 ≦ ρ ≦ 1, 0 ≦ θ ≦ 2π).

Here, n and m are integers, n ≧ m ≧ 1, and A _nm is a coefficient. R _n ^m (ρ) cosmθ is an orthogonal function system. If these Formula 13 and Formula 14 are used for the pupil function, the effective light source can be optimized even under the condition where there is aberration.

  As specific optimization methods, various existing methods can be used. Hereinafter, a specific method for calculating the image function will be exemplarily described. FIG. 1 is a schematic block diagram illustrating a method for calculating a light intensity distribution to be formed on the pupil plane of an illumination optical system, that is, determining an effective light source, and causes a computer to execute the program. It is assumed that the effective light source is divided into minute light source elements of arbitrary fineness.

The method for determining the effective light source of FIG. 1 is based on the method of FIG. In S1, the user sets the initial state (initial effective source) S ₀ and the control parameter C of effective light source, the computer stores the information entered. The initial effective light source S ₀ is an effective light source used as a starting point for optimization so that the entire surface inside the pupil or the shape of the solution can be predicted, and the light intensity is within that range. The control parameter C is a non-negative amount used for adjusting a determination criterion for determining whether or not to adopt a certain light source element, as will be described in detail in S5. Of course, it may be zero.

In S2 the computer calculates the ideal diffracted light distribution _{a 0.} As the ideal diffracted light distribution a ₀ , as expressed in Formula 9, a target pattern obtained by performing a Fourier transform and multiplying it by a circular function with a radius of 2 having a center at the origin can be used. In S3 the computer calculates a value called the reference value H _0. The reference value H ₀ is an integral value calculated using the initial effective light source S ₀ as the effective light source S in Equation 11.

Computer in S4, among the initial effective light source S ₀ which is divided into a plurality of light sources element, the light intensity of a single light source element varies tentatively 0 make trial effective light source S '. For schematic explanation, FIG. 6A shows an example of the initial effective light source S ₀ , and FIG. 6B shows an example of the trial effective light source S ′. Next, the trial effective light source S ′ is substituted into Equation 12 to calculate a value called trial value H ′. In S5, the computer compares the value obtained by adding the control parameter C to the trial value H ′ with the reference value H ₀ . If (trial value H ′ + C) falls below the reference value H ₀ in S5, the computer determines in S6 that the trial effective light source S ′ is improved from the initial effective light source S ₀ , and temporarily sets the light intensity to zero. It is determined that the light intensity of the changed light source element is zero. Conversely, if (trial value H ′ + C) exceeds the reference value H ₀ in S5, the computer determines in S7 that the trial effective light source S ′ is lower than the initial effective light source S ₀ , and temporarily sets it to 0. the light intensity of the fluctuating light source element decides to return to the value of the initial effective light source S _0.

A series of operations ranging to S4 to step S7 is repeated until it has tried all the light source elements of the initial effective light source S _0. When the operations of S4 to S7 are completed for all the light source elements, the computer adopts a set of light source elements whose light intensity is not 0 as the optimized effective light source S, and determines the adopted effective light source as the illumination condition. To do. Note that the specific calculation method of the effective light source in S4 to S7 is an example, and other methods may be used.

  Hereinafter, details of optimization using these processes will be described with reference to examples. In the embodiment, the NA of the projection optical system of the exposure apparatus is 1.35, and the wavelength of the exposure light is 193 nm. The length of the mask pattern is represented by the length on the image plane multiplied by the magnification of the projection optical system. All light sources are shown as effective light sources on the pupil, with the pupil radius shown as one. Further, the NA ratio between the projection optical system and the illumination optical system will be all 1 hereinafter. Also, the half pitch HP (nm) of the target pattern is normalized by the exposure light wavelength λ (nm), NA, and expressed as k1 = HP (nm) / (λ (nm) / NA).

[Example 1]
Hereinafter, Example 1 which is a method for determining an effective light source will be described with reference to FIGS. FIG. 3A shows a target pattern to be formed on the substrate. Here, the minimum half pitch HP of the pattern is 50 nm. The target size of each hole is also 50 nm. When the exposure light wavelength λ = 193 nm and NA = 1.35, the process factor k1 of the target pattern is about 0.35. Assuming that the mask is a binary mask, the transmittance of the pattern is 1 and the transmittance around the pattern is 0%. The target pattern consists of holes that are closely packed in the horizontal direction and isolated holes. It is not a simple periodic pattern but includes isolated holes, and it is difficult to balance the size of isolated holes and dense holes. The vertical axis and horizontal axis of FIG. 3A showing the pattern are all shown in length (nm) converted to the length on the image plane. In all the following, the horizontal axis is the X axis and the vertical axis is the Y axis.

It is assumed that the pupil plane is divided into 63 × 63 minute elements. The pupil radius is 1. In general, when the narrowest half-pitch HP appearing in a pattern is expressed as HP = k ₁ λ / NA, it is known that the optimum light source for resolving this pattern has an intensity peak at a position of 1/4 k ₁ from the center. Yes. Therefore, as the initial effective light source, annular illumination having an inner diameter of (1/4 k ₁ −0.2) and an outer diameter of (1/4 k ₁ +0.2) was employed as shown in FIG. The control parameter C = 0 was set for the initial effective light source and optimization was performed. The ideal diffracted light distribution was defined as the product of the target pattern shown in FIG. A specific light source optimization method followed the procedure shown in FIG. FIG. 3C shows an effective light source suitable for resolving the target pattern, which is derived as a result of optimization using Equation 11 as an evaluation function.

  In the method described in Japanese Patent Application Laid-Open No. 2008-040470 for obtaining a mask pattern from a target pattern, an effective light source has been given first. However, if the present invention is used, an effective light source can be directly obtained from the target pattern, and a mask pattern can be obtained from the obtained effective light source by using the method described in JP-A-2008-040470. Therefore, the method of the present invention can be said to be a method for obtaining an effective light source in the method for obtaining a mask pattern from a target pattern. FIG. 3D shows a mask pattern determined by the method described in Japanese Patent Laid-Open No. 2008-040470. The effective light source shown in FIG. 3C was used as the effective light source. The main patterns are all 50 nm and are not biased. When this mask pattern is imaged by the above-described exposure apparatus with illumination light using the effective light source of FIG. 3C as illumination conditions, an image as shown in FIG. 3G is obtained. In Japanese Patent Laid-Open No. 2008-040470, Equation 7 is used to obtain an approximate aerial image, but Equation 8 may be used instead.

  Next, the effect of the present invention is verified by an imaging simulation. When the method described in Japanese Patent Laid-Open No. 2008-040470 is applied to the target pattern shown in FIG. 3A using quadrupole illumination as shown in FIG. 3E, the result shown in FIG. The mask pattern as shown is obtained. When the pattern of this mask is imaged by the above-described exposure apparatus with illumination light using the effective light source of FIG. 3E as illumination conditions, an image as shown in FIG. 3H is obtained. 3 (G) and 3 (H) are contour lines of an intensity distribution in which the intensity value at which the horizontal width of the reference pattern is 50 nm and the intensity value of ± 10% are slice levels. The polarization distribution of the light source was non-polarized light. Comparing FIGS. 3 (G) and (H), all the holes are resolved in both cases, but in FIG. 3 (G), the hole shape is uniform and the image performance is improved. .

[Example 2]
In the second embodiment, the effective light source is determined when defocus aberration is present. The effective light source is determined under the same conditions as in Example 1 except for considering the amount of aberration. The pupil function is expressed by Expression 12, and the aberration function in Expression 13 is expressed by Expression 14. Here, the defocus amount def is def = 25 (nm), and the refractive index n of the medium is a pure water value of 1.44. When defocus aberration is taken into consideration, a light source distribution different from that in the case where aberration is not taken into consideration as shown in FIG. FIG. 4B shows a mask pattern determined to further improve the resolution by the method disclosed in Japanese Patent Application Laid-Open No. 2008-040470 for this light source distribution. A two-dimensional image obtained using the effective light source of FIG. 4A and the mask pattern of FIG. 4B is as shown in FIG.

  Next, the performance is verified by an imaging simulation using these light source distributions and mask patterns. In the imaging simulation, the exposure light wavelength λ = 193 nm and NA = 1.35 is used to form an image of the mask pattern shown in FIG. 3A, and the light source shown in FIG. Compare the imaging performance with the light source of FIG. The imaging simulation was performed by changing the defocus.

  The performance was evaluated by determining the change in the line width (CD) of the two-dimensional image when the defocus was changed. Hereinafter, the x direction and the y direction mean the horizontal direction and the vertical direction in the figure, respectively. First, from the aerial image obtained with the best focus, an intensity value such that the width of the reference pattern in the x direction was 50 nm was obtained as the reference slice level. Next, for each defocus, the aerial image was obtained as a two-dimensional image by using contour lines at the reference slice level, and the line width (CD) of the two-dimensional image was obtained. FIG. 4D is a diagram for explaining FIGS. 4E and 4F. In the figure, a, b, and c indicate the positions of holes serving as evaluation points. FIG. 4E shows the result when the effective light source shown in FIG. 3C and the mask pattern shown in FIG. 3D are used. FIG. 4F shows the result shown in FIG. This is a result when the effective light source and the mask pattern shown in FIG. The symbol x or y in the graph means the CD in the x direction and the CD in the y direction at each evaluation hole position.

  Comparing FIG. 4 (E) and FIG. 4 (F), it can be seen that the graph shown in FIG. 4 (F) has better CD uniformity of each hole. Therefore, it is suggested that the light source distribution in consideration of the aberration mitigates the deterioration of the imaging performance due to the aberration. In the present embodiment, the light source distribution considering the defocus aberration is shown. However, the light source distribution can be calculated using an arbitrary aberration function using Expression 14.

[Example 3]
In the third embodiment, an effective light source accompanied by enhancement of the intensity of the ideal diffracted light distribution is determined. The effective light source is determined under the same conditions as in Example 1 except for considering the enhancement of the intensity of the ideal diffracted light distribution. The ideal diffracted light distribution a ₀ uses the form of Equation 15. That is, in the third embodiment, the ideal diffracted light distribution used in the first and second embodiments is multiplied by a function that increases the intensity toward the outside of the pupil.
a ₀ = circ (0.5 s) · F [T] · (0.1 s) ^0.5 (15)

  When the intensity of the ideal diffracted light distribution is manipulated, a light source distribution as shown in FIG. 7A is obtained. FIG. 7B shows a mask pattern optimized for improving the resolving power by the method described in Japanese Patent Laid-Open No. 2008-040470 with respect to this light source distribution. A two-dimensional image obtained using the effective light source of FIG. 7A and the mask pattern of FIG. 7B is as shown in FIG. The dense holes corresponding to the minimum pitch width are well separated.

  Needless to say, in Examples 1 to 3, the process for optimizing the effective light source had no instability and indefiniteness. The computation time is about 3 minutes on a workstation equipped with a CPU having a clock frequency of 3.2 GHz, and the calculation time can be shortened from half to one-quarter considering the symmetry of the light source.

[Exposure equipment]
With reference to FIG. 6, an exposure apparatus 100 that illuminates an original with light emitted from an illumination optical system, projects a pattern of the illuminated original on a substrate via a projection optical system, and exposes the substrate will be described. . FIG. 6 is a schematic block diagram showing the configuration of the exposure apparatus 100. Here, the exposure apparatus 100 forms an effective light source corresponding to the effective light source data generated by executing the above-described generation program in the illumination optical system 180. The exposure apparatus 100 illuminates the mask 120 created based on the light source data generated by executing the above-described generation program. In this embodiment, the exposure apparatus 100 is a projection exposure apparatus that exposes the pattern of the mask 120 onto the wafer (substrate) 140 by a step-and-scan method. However, the exposure apparatus 100 can also apply a step-and-repeat method and other exposure methods. As illustrated in FIG. 6, the exposure apparatus 100 includes an illumination device 110, a reticle stage (not shown) that supports the mask 120, a projection optical system 130, and a wafer stage (not shown) that supports the wafer 140. . The illumination device 110 illuminates the mask 120 on which a transfer circuit pattern is formed, and includes a light source 160 and an illumination optical system 180. As the light source 160, for example, an excimer laser such as an ArF excimer laser having a wavelength of about 193 nm or a KrF excimer laser having a wavelength of about 248 nm is used. However, the light source 160 is not limited to an excimer laser, and an F2 laser having a wavelength of about 157 nm, a narrow band mercury lamp, or the like may be used.

  The illumination optical system 180 is an optical system that illuminates the mask 120 using light from the light source 160. In the present embodiment, an effective light source corresponding to the effective light source data generated by executing the above-described generation program is formed. Then, the mask 120 is illuminated. The illumination optical system 180 includes a routing optical system 181, an optical system 182 that shapes a beam, a polarization control unit 183, a phase control unit 184, an optical element 185 that stores an emission angle, a relay optical system 186, A light beam generation unit 187. The illumination optical system 180 includes a polarization state adjustment unit 188, a computer generated hologram 189, a relay optical system 190, an aperture 191, a zoom optical system 192, a multi-beam generation unit 193, an aperture stop 194, and an irradiation unit. 195. The drawing optical system 181 guides the light from the light source 160 to the optical system 182 that deflects the light and shapes the beam. The optical system 182 for shaping the beam converts the aspect ratio of the cross-sectional shape of the light from the light source 160 into a desired value (for example, changes the cross-sectional shape from a rectangle to a square), and cross-sections the light from the light source 160. Shape the shape into the desired shape. The optical system 182 for shaping the beam forms a light beam having a size and a divergence angle necessary for illuminating the multi-beam generation unit 187.

  The polarization controller 183 is composed of a linear polarizer or the like, and has a function of removing unnecessary polarization components. By minimizing the polarization component removed (shielded) by the polarization controller 183, the light from the light source 160 can be efficiently converted into desired linearly polarized light. The phase control unit 184 converts the light that has been linearly polarized by the polarization control unit 183 into a circularly polarized light by giving a phase difference of λ / 4. The optical element 185 that stores the emission angle is constituted by, for example, an optical integrator (such as a fly-eye lens or a fiber bundle made up of a plurality of minute lenses), and emits light at a constant divergence angle. The relay optical system 186 focuses the light emitted from the optical element 185 that stores the emission angle on the multi-beam generation unit 187. The exit surface of the optical element 185 that stores the exit angle and the entrance surface of the multi-beam generation unit 187 are in a Fourier transform relationship (relationship between the object plane and the pupil plane or between the pupil plane and the image plane) by the relay optical system 186. ing. The multi-beam generation unit 187 includes an optical integrator (such as a fly-eye lens or a fiber bundle composed of a plurality of microlenses) for uniformly illuminating the polarization state adjustment unit 188 and the computer generated hologram 189. The exit surface of the multi-beam generation unit 187 forms a light source surface composed of a plurality of point light sources. The light emitted from the multibeam generation unit 187 enters the polarization state adjustment unit 188 as circularly polarized light.

  The polarization state adjustment unit 188 gives a phase difference of λ / 4 to the light that has been circularly polarized by the phase control unit 184, and converts it into linearly polarized light having a desired polarization direction. The light emitted from the polarization state adjusting unit 188 enters the computer generated hologram 189 as a diffractive optical element as linearly polarized light. Although the polarization state adjustment unit 188 is arranged on the light source side with respect to the computer generated hologram 189, the front and rear may be interchanged. Further, the polarization state adjusting unit may be configured by SWS (Sub Wavelength Structure) and integrated with the diffractive optical element. That is, one element can be formed to have the functions of the polarization state adjusting unit and the diffractive optical element. When circularly polarized light is incident, the light that has passed through the polarization state adjusting unit 188 is converted into linearly polarized light having a desired polarization direction, is incident on a predetermined portion of the computer generated hologram 189, and has an arbitrary polarization direction. An arbitrary light source distribution is formed.

  The computer generated hologram 189 forms a desired light intensity distribution such as an effective light source having tangential polarization at the position of the aperture 191 via the relay optical system 190. Further, the computer generated hologram 189 can form annular illumination, quadrupole illumination, and the like, and implements a desired light polarization distribution such as tangential polarization and radial polarization in combination with the polarization state adjustment unit 188. be able to. A plurality of computer generated holograms 189 forming these different effective light sources are arranged in a switching unit such as a turret. The polarization state adjustment unit 188 can also be switched. Then, by arranging the computer generated hologram 189 corresponding to the effective light source data generated by the processing device (computer) in the optical path of the illumination optical system 180, various effective light sources can be expressed.

  The aperture 191 has a function of passing only the light intensity distribution formed by the computer generated hologram 189. The computer generated hologram 189 and the aperture 191 are arranged so as to have a Fourier transform plane relationship with each other. The zoom optical system 192 enlarges the light intensity distribution formed by the computer generated hologram 189 at a predetermined magnification and projects it onto the multi-beam generation unit 193. The multibeam generation unit 193 is disposed on the pupil plane of the illumination optical system 180 and forms a light source image (effective light source distribution) corresponding to the light intensity distribution formed at the position of the aperture 191 on the exit surface. In the present embodiment, the multi-beam generation unit 193 is configured by an optical integrator such as a fly-eye lens or a cylindrical lens array. Note that an aperture stop 194 is disposed in the vicinity of the exit surface of the multi-beam generation unit 193. The irradiation unit 195 includes a condenser optical system and the like, and illuminates the mask 120 with an effective light source distribution formed on the exit surface of the multi-beam generation unit 193.

  The mask 120 is created based on mask data generated by the processing apparatus, and has a circuit pattern (main pattern) to be transferred and an auxiliary pattern. The mask 120 is supported and driven by a mask stage (not shown). Diffracted light emitted from the mask 120 is projected onto the wafer 140 via the projection optical system 130. Since the exposure apparatus 100 is a step-and-scan exposure apparatus, the pattern of the mask 120 is transferred to the wafer 140 by scanning the mask 120 and the wafer 140. The projection optical system 130 is an optical system that projects the pattern of the mask 120 onto the wafer 140. The projection optical system 130 can use a refractive system, a catadioptric system, or a reflective system. The wafer 140 is a substrate onto which the pattern of the mask 120 is projected (transferred), and is supported and driven by a wafer stage (not shown). However, a glass plate or other substrate can be used instead of the wafer 140. A photoresist is applied to the wafer 140. In the exposure, the light emitted from the light source 160 illuminates the mask 120 by the illumination optical system 180. The light reflecting the pattern of the mask 120 forms an image on the wafer 140 by the projection optical system 130. At this time, the mask 120 created based on the mask data generated by the processing apparatus is illuminated with an effective light source corresponding to the effective light source data generated by the processing apparatus. Therefore, the exposure apparatus 100 can provide high-quality devices (semiconductor elements, LCD elements, imaging elements (CCDs, etc.), thin film magnetic heads, etc.) with high throughput and economical efficiency by multiple exposure.

[Device manufacturing method]
Next, a method for manufacturing a device (semiconductor device, liquid crystal display device, etc.) according to an embodiment of the present invention will be described. Here, a method for manufacturing a semiconductor device will be described as an example. A semiconductor device is manufactured through a pre-process for producing an integrated circuit on a wafer and a post-process for completing an integrated circuit chip on the wafer produced in the pre-process as a product. The pre-process includes a step of exposing a wafer coated with a photosensitive agent using the above-described exposure apparatus, and a step of developing the wafer. The post-process includes an assembly process (dicing and bonding) and a packaging process (encapsulation). In addition, a liquid crystal display device is manufactured by passing through the process of forming a transparent electrode. The step of forming the transparent electrode includes a step of applying a photosensitive agent to a glass substrate on which a transparent conductive film is deposited, a step of exposing the glass substrate on which the photosensitive agent is applied using the above-described exposure apparatus, and a glass substrate. The process of developing is included. According to the device manufacturing method of the present embodiment, it is possible to manufacture a higher quality device than before.

[Other Embodiments]
The present invention can also be realized by executing the following processing. That is, software (program) that realizes the functions of the above-described embodiments is supplied to a system or apparatus via a network or various storage media, and a computer (or CPU, MPU, or the like) of the system or apparatus reads the program. It is a process to be executed. In this case, the program and the storage medium storing the program constitute the present invention.

  The preferred embodiments of the present invention have been described above, but the present invention is not limited to these embodiments, and various modifications and changes can be made within the scope of the gist.

Claims (9)

A method for determining illumination conditions used in an exposure apparatus that illuminates a mask with light emitted from an illumination optical system, projects a pattern of the illuminated mask onto a substrate via a projection optical system, and exposes the substrate Because
A distribution represented by a function obtained by multiplying a convolution integral of an effective light source that is a light intensity distribution to be formed on the pupil plane of the illumination optical system and a pupil function of the projection optical system by a complex conjugate of the diffracted light distribution of the mask pattern And an effective light source that determines an evaluation value indicating a difference between an ideal diffracted light distribution defined as a function of Fourier transform of a target pattern on the image plane of the projection optical system within an allowable range as the illumination condition. Feature method. The coordinates on the pupil plane of the projection optical system are (f, g), the effective light source is S (f, g), the pupil function is P (f, g), and the diffracted light distribution of the mask pattern is a (f , G), when the ideal diffracted light distribution is expressed as a ₀ (f, g), the convolution integral is expressed as ^*, and the complex conjugate is expressed as ^* , the function that gives the evaluation value is
The method of claim 1, wherein: A first step of setting an initial state of the effective light source including a plurality of light source elements and the ideal diffracted light distribution;
A second step of obtaining the evaluation value as a reference value when the effective light source is in the initial state;
A third step of determining the light intensity of each light source element by comparing the evaluation value in a state where the light intensity of each of the plurality of light source elements is changed from the initial state and the reference value;
The method according to claim 1 or 2, comprising:   When the numerical aperture of the projection optical system is NA and the wavelength of light emitted from the illumination optical system is λ, the ideal diffracted light distribution is a function obtained by Fourier transforming the target pattern, and (NA / λ) 2. A function obtained by multiplying a function in which a value on the circumference and an inside of a circle having a radius of 2 is 1 and a value on the outside of the circle is 0 on the pupil plane normalized by (1). The method according to any one of 1 to 3. The target pattern is composed of a plurality of figures,
When the numerical aperture of the projection optical system is NA and the wavelength of light emitted from the illumination optical system is λ, the ideal diffracted light distribution is a function obtained by Fourier transforming the target pattern, and (NA / λ) For a function obtained by multiplying a function in which the value on the circumference and the inside of the circle having a radius of 2 is 1 and the value outside the circle is 0 on the pupil plane normalized by 4. The method according to claim 1, wherein the function is a function weighted so as to emphasize the intensity of diffracted light corresponding to some of the figures.   When the wavelength of the light emitted from the illumination optical system is λ, the coordinate on the pupil plane is (f, g), and the aberration of the projection optical system is φ (f, g), the pupil function is exp [ The method according to claim 1, wherein the method is represented by −2πi / λ · φ (f, g)].   The program which makes a computer perform the method of any one of Claims 1 thru | or 6. An exposure method for exposing a substrate,
A mask is illuminated using illumination conditions determined using the method according to claim 1, and the illuminated mask pattern is projected onto the substrate via a projection optical system. An exposure method comprising a step of exposing the substrate. A method of manufacturing a device comprising:
Exposing the substrate using the exposure method according to claim 8;
Developing the substrate exposed in the step;
A method comprising the steps of: