CN114488719B - OPC method based on three-dimensional feature reinforcement - Google Patents
OPC method based on three-dimensional feature reinforcement Download PDFInfo
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Abstract
Description
技术领域Technical field
本发明属于光学临近校正技术领域,更具体地,涉及一种基于三维特征强化的OPC方法。The invention belongs to the technical field of optical proximity correction, and more specifically, relates to an OPC method based on three-dimensional feature enhancement.
背景技术Background technique
光刻是半导体集成电路、MEMS、微纳光学等众多领域中的一个重要工艺,是对半导体晶圆表面的掩蔽物(如二氧化硅)进行刻蚀或沉积等,以便进行杂质的定域扩散的一种加工技术。其昂贵的设备制造和维护成本约占集成电路总生产成本的一半。其中掩膜制造消耗成本巨大,为降低成本,无掩膜光刻技术如电子束光刻、离子束光刻以及扫描激光光刻逐渐兴起。Photolithography is an important process in many fields such as semiconductor integrated circuits, MEMS, micro-nano optics, etc. It is the etching or deposition of masks (such as silicon dioxide) on the surface of semiconductor wafers to facilitate localized diffusion of impurities. a processing technology. Its expensive equipment manufacturing and maintenance costs account for about half of the total integrated circuit production costs. Among them, mask manufacturing costs are huge. In order to reduce costs, maskless lithography technologies such as electron beam lithography, ion beam lithography and scanning laser lithography are gradually emerging.
扫描激光光刻系统主要包含:激光光源、聚焦调制系统、步进系统、扫描系统和涂有光刻胶的硅晶圆。其中,激光束被聚焦到目标尺寸的光斑大小,并且在光刻胶表面扫描的同时调制光束功率(灰度光刻胶曝光深度随着曝光能量非线性增加,常用s形曲线近似),然后在扫描方向上以设定的步长进行扫描,扫描一个周期结束后在步进方向上步进一次继续进行反向扫描。The scanning laser lithography system mainly includes: laser light source, focus modulation system, stepping system, scanning system and silicon wafer coated with photoresist. Among them, the laser beam is focused to the spot size of the target size, and the beam power is modulated while scanning the photoresist surface (the exposure depth of the grayscale photoresist increases nonlinearly with the exposure energy, commonly used as an s-shaped curve approximation), and then in Scan with the set step size in the scanning direction. After scanning for one period, step once in the step direction to continue scanning in the reverse direction.
在扫描光刻成像的过程中,由于来自其他扫描区域能量的叠加因此需要对成像进行优化。另外随着关键尺寸(Critical dimension,简称CD)的持续减小,扫描激光光刻的特征尺寸受到了制约。在扫描激光光刻系统中,每个位置的曝光剂量都可以被精确地控制,因此可以通过对曝光剂量的分布进行模拟和计算对叠加的能量进行规划和补偿,使得成像分辨率增强得以实现。In the process of scanning lithography imaging, the imaging needs to be optimized due to the superposition of energy from other scanning areas. In addition, as the critical dimension (CD) continues to decrease, the feature size of scanning laser lithography is restricted. In a scanning laser lithography system, the exposure dose at each position can be precisely controlled, so the superimposed energy can be planned and compensated by simulating and calculating the exposure dose distribution, so that imaging resolution enhancement can be achieved.
扫描激光光刻的光学临近校正技术(Optical proximity correction,OPC)通常利用光刻机和光刻胶参数搭建非线性数值模型,使用非线性规划方法或基于梯度的优化算法寻找最优曝光剂量分布,从而最小化期望图案和曝光图案之间的差异(主要包含图案误差(PE)和边缘放置误差(EPE)),实现输出图案的优化。在3D厚膜光刻中,对于高度的优化有重要意义,3D结构不只包含水平面上的尺寸精度,还包含高度上的尺寸精度。高度上的变化更加容易受到衍射极限的影响导致边缘不清晰,过度边缘圆角尺寸大,最终影响产品质量,因此3D结构的高度参数往往在结构发挥作用中起着关键作用。Optical proximity correction (OPC) technology for scanning laser lithography usually uses photolithography machine and photoresist parameters to build a nonlinear numerical model, and uses nonlinear programming methods or gradient-based optimization algorithms to find the optimal exposure dose distribution. Thereby minimizing the difference between the desired pattern and the exposed pattern (mainly including pattern error (PE) and edge placement error (EPE)), the output pattern is optimized. In 3D thick film lithography, optimization of height is of great significance. 3D structures not only include dimensional accuracy on the horizontal plane, but also include dimensional accuracy on the height. Changes in height are more susceptible to the influence of the diffraction limit, resulting in unclear edges and excessive edge fillet sizes, which ultimately affect product quality. Therefore, the height parameters of 3D structures often play a key role in the function of the structure.
现有的基于矢量矩阵的3D光刻优化方法虽然减小了整体的计算代价,但是仍存在如下缺陷:(1)优化对象是针对全曝光区域的整体性优化,对于图案边缘的优化一并处理,没有着重优化图案边缘(即光刻时目标图案和刻蚀掉的部分的交界处),无法进一步提高优化速度和精度。(2)缺少对3D光刻z轴(即高度方向)的局域优化,结构高度特征优化不充分。Although the existing vector matrix-based 3D lithography optimization method reduces the overall calculation cost, it still has the following defects: (1) The optimization object is the overall optimization of the entire exposure area, and the optimization of the pattern edges is also processed. , without focusing on optimizing the pattern edge (that is, the interface between the target pattern and the etched part during photolithography), it is impossible to further improve the optimization speed and accuracy. (2) There is a lack of local optimization of the z-axis (i.e., height direction) of 3D lithography, and the structural height characteristics are not fully optimized.
发明内容Contents of the invention
本发明通过提供一种基于三维特征强化的OPC方法,解决现有技术中高度特征优化缺失,优化速度和精度有待提高的问题。By providing an OPC method based on three-dimensional feature enhancement, the present invention solves the problems in the prior art that the high-level feature optimization is lacking and the optimization speed and accuracy need to be improved.
本发明提供一种基于三维特征强化的OPC方法,主要包括以下步骤:The present invention provides an OPC method based on three-dimensional feature enhancement, which mainly includes the following steps:
步骤S1、根据光刻胶曝光数据和光刻胶的化学反应函数得到优化的光刻胶函数模型;根据光刻机参数,将目标图案转化为目标像素化图案;Step S1: Obtain an optimized photoresist function model based on the photoresist exposure data and the chemical reaction function of the photoresist; convert the target pattern into a target pixelated pattern according to the photolithography machine parameters;
步骤S2、采用Sobel算子对所述目标像素化图案在两个不同的梯度阈值下进行边缘提取,得到对应的边缘特征矩阵,将边缘特征矩阵的数值作为目标图案矩阵的数值;Step S2: Use the Sobel operator to perform edge extraction on the target pixelated pattern under two different gradient thresholds to obtain the corresponding edge feature matrix, and use the value of the edge feature matrix as the value of the target pattern matrix;
步骤S3、根据光刻机参数和优化的光刻胶函数模型,得到初始的成像图案矩阵;Step S3: Obtain the initial imaging pattern matrix according to the photolithography machine parameters and the optimized photoresist function model;
步骤S4、构建第一代价函数和约束条件,根据所述约束条件对曝光剂量分布和成像图案矩阵的数值进行更新;Step S4: Construct the first cost function and constraint conditions, and update the values of the exposure dose distribution and imaging pattern matrix according to the constraint conditions;
步骤S5、根据更新判断条件对梯度阈值进行自动更新;Step S5: Automatically update the gradient threshold according to the update judgment conditions;
步骤S6、判断是否满足循环结束条件;若不满足,则返回至步骤S2;若满足,则结束循环。Step S6: Determine whether the loop end condition is satisfied; if not, return to step S2; if satisfied, end the loop.
优选的,所述步骤S1包括以下子步骤:Preferably, step S1 includes the following sub-steps:
步骤S11、根据实际测量得到的光刻胶曝光数据,结合光刻胶的化学反应函数建立第二代价函数;Step S11: Establish a second cost function based on the actual measured photoresist exposure data and the chemical reaction function of the photoresist;
所述第二代价函数表示为:The second cost function is expressed as:
其中,H表示第二代价函数,PR表示实际测量得到的光刻胶曝光数据,Sig(·)表示光刻胶的化学反应函数;Among them, H represents the second cost function, PR represents the actual measured photoresist exposure data, and Sig(·) represents the chemical reaction function of the photoresist;
步骤S12、根据所述第二代价函数,使用最优化算法对光刻胶参数进行优化,直至所述第二代价函数最小,获得最优的光刻胶参数,所述光刻胶参数包括刻蚀速度和刻蚀阈值;Step S12: According to the second cost function, use an optimization algorithm to optimize the photoresist parameters until the second cost function is minimum and obtain optimal photoresist parameters. The photoresist parameters include etching Speed and etch threshold;
步骤S13、基于最优的刻蚀速度和最优的刻蚀阈值得到优化的光刻胶函数模型;Step S13: Obtain an optimized photoresist function model based on the optimal etching speed and the optimal etching threshold;
所述优化的光刻胶函数模型表示为:The optimized photoresist function model is expressed as:
其中,a表示最优的刻蚀速度,tr表示最优的刻蚀阈值;Among them, a represents the optimal etching speed, t r represents the optimal etching threshold;
步骤S14、输入光刻机参数,将目标图案转化为目标像素化图案。Step S14: Input photolithography machine parameters to convert the target pattern into a target pixelated pattern.
优选的,在采用Sobel算子进行边缘提取之前,还包括:对所述目标像素化图案进行高斯平滑处理。Preferably, before using the Sobel operator for edge extraction, the method further includes: performing Gaussian smoothing on the target pixelated pattern.
优选的,高斯平滑卷积核如下:Preferably, the Gaussian smooth convolution kernel is as follows:
通过使用所述高斯平滑卷积核与目标像素化图案做卷积运算,实现对目标像素化图案进行高斯平滑处理。By using the Gaussian smoothing convolution kernel and the target pixelated pattern to perform a convolution operation, Gaussian smoothing processing is performed on the target pixelated pattern.
优选的,所述步骤S2包括以下子步骤:Preferably, the step S2 includes the following sub-steps:
步骤S21、采用Sobel算子与所述目标像素化图案做卷积运算,得到图案梯度变化图;Sobel算子卷积核如下:Step S21: Use the Sobel operator to perform a convolution operation with the target pixelated pattern to obtain a pattern gradient change map; the Sobel operator convolution kernel is as follows:
x方向:x direction:
y方向:y direction:
G=|Gx|+|Gy|G=|Gx|+|Gy|
其中,Gx表示目标像素化图案和x方向的Sobel算子卷积核卷积后得到的每个像素在x轴方向上的梯度大小,Gy表示目标像素化图案和y方向的Sobel算子卷积核卷积后得到的每个像素在y轴方向上的梯度大小;G表示每个像素的高度梯度大小,G的值为每个像素在x、y轴方向上梯度值的绝对值之和;Among them, Gx represents the gradient size of each pixel in the x-axis direction obtained by convolving the target pixelated pattern with the Sobel operator convolution kernel in the x direction, and Gy represents the convolution of the target pixelated pattern with the Sobel operator in the y direction. The gradient size of each pixel in the y-axis direction obtained after kernel convolution; G represents the height gradient size of each pixel, and the value of G is the sum of the absolute values of the gradient values of each pixel in the x- and y-axis directions;
步骤S22、基于所述图案梯度变化图,根据设定的两个梯度阈值β1、β2,分别提取大于梯度阈值的两个梯度分布矩阵作为边缘特征矩阵Sz1、Sz2;Step S22: Based on the pattern gradient change map, according to the two set gradient thresholds β 1 and β 2 , extract two gradient distribution matrices greater than the gradient threshold as edge feature matrices S z1 and S z2 respectively;
针对每一个梯度阈值,若Sij≥β,则SZij=Sij,否则,SZij=0;For each gradient threshold, if S ij ≥ β, then S Zij =S ij , otherwise, S Zij =0;
其中,Sij表示图案梯度变化图中第i行第j列像素点的坐标值,Szij表示边缘特征矩阵中第i行第j列像素点的坐标值;Among them, S ij represents the coordinate value of the pixel point in the i-th row and j-th column in the pattern gradient change map, and S zij represents the coordinate value of the pixel point in the i-th row and jth column in the edge feature matrix;
将边缘特征矩阵的数值作为目标图案矩阵Z(x,y)的数值。The value of the edge feature matrix is used as the value of the target pattern matrix Z(x, y).
优选的,所述步骤S3包括以下子步骤:Preferably, step S3 includes the following sub-steps:
步骤S31、根据所述光刻机参数,对所述目标图案进行像素化处理,得到曝光剂量分布矩阵:Step S31: Perform pixelation processing on the target pattern according to the lithography machine parameters to obtain an exposure dose distribution matrix:
其中,E(x,y)表示曝光剂量分布矩阵,曝光剂量分布矩阵的初始值来自于目标图案矩阵Z(x,y)对应像素点位置的数值,(x,y)表示一个曝光点的位置坐标,单个曝光点的位置坐标等于对应像素点的位置坐标,θ表示无约束优化变量;Among them, E(x, y) represents the exposure dose distribution matrix. The initial value of the exposure dose distribution matrix comes from the value of the corresponding pixel position of the target pattern matrix Z(x, y). (x, y) represents the position of an exposure point. Coordinates, the position coordinate of a single exposure point is equal to the position coordinate of the corresponding pixel point, θ represents the unconstrained optimization variable;
步骤S32、获得高斯光束矩阵:Step S32: Obtain the Gaussian beam matrix:
其中,B(x,y)表示高斯光束矩阵,P表示整体曝光功率,ω0为焦平面处激光光斑的半径;Among them, B(x, y) represents the Gaussian beam matrix, P represents the overall exposure power, and ω 0 is the radius of the laser spot at the focal plane;
步骤S33、根据所述曝光剂量分布矩阵及所述高斯光束矩阵得到曝光能量分布矩阵:Step S33: Obtain the exposure energy distribution matrix according to the exposure dose distribution matrix and the Gaussian beam matrix:
其中,D(x,y)表示曝光能量分布矩阵,表示卷积符号;Among them, D(x, y) represents the exposure energy distribution matrix, Represents the convolution symbol;
步骤S34、根据所述曝光能量分布矩阵和所述优化的光刻胶函数模型,得到所述初始的成像图案矩阵:Step S34: Obtain the initial imaging pattern matrix according to the exposure energy distribution matrix and the optimized photoresist function model:
其中,表示初始的成像图案矩阵。in, Represents the initial imaging pattern matrix.
优选的,所述步骤S4中,结合最优化算法,构建第一代价函数和约束条件,对曝光剂量分布矩阵和成像图案矩阵进行迭代优化:Preferably, in step S4, the first cost function and constraints are constructed in combination with an optimization algorithm, and the exposure dose distribution matrix and imaging pattern matrix are iteratively optimized:
其中,FZ表示经光刻胶成像之后的图案误差,FE表示系统总的输出剂量,F表示第一代价函数,Z(x,y)表示目标图案矩阵,表示成像图案矩阵,E(x,y)表示曝光剂量分布矩阵;Among them, F Z represents the pattern error after photoresist imaging, F E represents the total output dose of the system, F represents the first cost function, Z (x, y) represents the target pattern matrix, represents the imaging pattern matrix, and E(x, y) represents the exposure dose distribution matrix;
对曝光剂量分布矩阵进行迭代优化:Iteratively optimize the exposure dose distribution matrix:
其中,s表示最优化算法中更新的步长。Among them, s represents the updated step size in the optimization algorithm.
优选的,步骤S5中,所述更新判断条件包括第一条件和第二条件;所述第一条件为F2-F1>0,所述第二条件为F2-F1≤0;F1表示在梯度阈值β1下用边缘特征矩阵构建的第一代价函数,F2表示在梯度阈值β2下用边缘特征矩阵构建的第一代价函数;Preferably, in step S5, the update judgment condition includes a first condition and a second condition; the first condition is F 2 -F 1 >0, and the second condition is F 2 -F 1 ≤0; F 1 represents the first cost function constructed with the edge feature matrix under the gradient threshold β 1 , and F 2 represents the first cost function constructed with the edge feature matrix under the gradient threshold β 2 ;
若满足所述第一条件,则对梯度阈值按下述原则进行自动更新:If the first condition is met, the gradient threshold is automatically updated according to the following principles:
β2=β1,β1=β1-α(F2-F1)β 2 =β 1 , β 1 =β 1 -α(F 2 -F 1 )
若满足所述第二条件,则对梯度阈值按下述原则进行自动更新:If the second condition is met, the gradient threshold is automatically updated according to the following principles:
β1=β2,β2=β2+α(F2-F1)β 1 =β 2 , β 2 =β 2 +α(F 2 -F 1 )
其中,α表示设定步长。Among them, α represents the set step size.
优选的,步骤S6中,若结束循环,取β1和β2中较小的数值作为最优梯度阈值,取所述最优梯度阈值对应的边缘特征矩阵作为最优边缘特征矩阵,将所述最优边缘特征矩阵对应的曝光剂量分布矩阵和曝光能量分布矩阵作为全局最优分布。Preferably, in step S6, if the loop ends, the smaller value of β 1 and β 2 is taken as the optimal gradient threshold, the edge feature matrix corresponding to the optimal gradient threshold is taken as the optimal edge feature matrix, and the The exposure dose distribution matrix and exposure energy distribution matrix corresponding to the optimal edge feature matrix are regarded as the global optimal distribution.
优选的,步骤S6中,所述循环结束条件为达到优化次数或所述第一代价函数的数值小于优化阈值。Preferably, in step S6, the loop end condition is that the number of optimization times is reached or the value of the first cost function is less than the optimization threshold.
本发明中提供的一个或多个技术方案,至少具有如下技术效果或优点:One or more technical solutions provided in the present invention have at least the following technical effects or advantages:
在本发明中,根据光刻胶曝光数据和光刻胶的化学反应函数得到优化的光刻胶函数模型;根据光刻机参数,将目标图案转化为目标像素化图案;采用Sobel算子对目标像素化图案在两个不同的梯度阈值下进行边缘提取,得到对应的边缘特征矩阵,将边缘特征矩阵的数值作为目标图案矩阵的数值;根据光刻机参数和优化的光刻胶函数模型,得到初始的成像图案矩阵;构建第一代价函数和约束条件,根据约束条件对曝光剂量分布和成像图案矩阵的数值进行更新;根据更新判断条件对梯度阈值进行自动更新;更新后判断是否满足循环结束条件;若不满足,则返回至边缘提取的步骤;若满足,则结束循环。传统的曝光剂量分布求解是针对整个图案进行求解,即优化对象是针对全曝光区域的整体性优化,导致单次计算量大、优化速度慢。本发明对特征的边缘进行求解,采用Sobel算子提取边缘矩阵,进行针对性地优化,能够提升优化效果和速度。本发明基于Sobel算子边缘提取的高度优化方法对曝光剂量分布进行三维结构优化,解决了现有适量矩阵优化方法中高度优化缺失的问题。本发明在两个不同的梯度阈值下进行边缘提取,根据更新判断条件对梯度阈值进行自动更新,进而得到最优梯度阈值,即本发明提出了一种自动寻找最优阈值方法,解决了灰度梯度阈值人为无法设置最优值的问题。In the present invention, an optimized photoresist function model is obtained based on the photoresist exposure data and the chemical reaction function of the photoresist; the target pattern is converted into a target pixelated pattern according to the photolithography machine parameters; the Sobel operator is used to calculate the target The edges of the pixelated pattern are extracted under two different gradient thresholds to obtain the corresponding edge feature matrix. The value of the edge feature matrix is used as the value of the target pattern matrix. According to the photolithography machine parameters and the optimized photoresist function model, we obtain Initial imaging pattern matrix; construct the first cost function and constraint conditions, update the exposure dose distribution and imaging pattern matrix values according to the constraint conditions; automatically update the gradient threshold according to the update judgment conditions; determine whether the loop end condition is met after the update ; If not satisfied, return to the edge extraction step; if satisfied, end the loop. The traditional exposure dose distribution solution is based on the entire pattern, that is, the optimization object is the overall optimization of the entire exposure area, resulting in a large amount of single calculation and slow optimization speed. The present invention solves the edges of features, uses the Sobel operator to extract the edge matrix, and performs targeted optimization, which can improve the optimization effect and speed. The present invention performs three-dimensional structural optimization of exposure dose distribution based on a highly optimized method of Sobel operator edge extraction, and solves the problem of missing height optimization in existing appropriate matrix optimization methods. The present invention performs edge extraction under two different gradient thresholds, automatically updates the gradient threshold according to the update judgment conditions, and then obtains the optimal gradient threshold. That is, the present invention proposes an automatic search for the optimal threshold method, which solves the problem of grayscale The gradient threshold is artificially unable to set the optimal value.
附图说明Description of the drawings
图1为本发明实施例提供的一种基于三维特征强化的OPC方法的流程图。Figure 1 is a flow chart of an OPC method based on three-dimensional feature enhancement provided by an embodiment of the present invention.
具体实施方式Detailed ways
为了更好的理解上述技术方案,下面将结合说明书附图以及具体的实施方式对上述技术方案进行详细的说明。In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation modes.
本实施例提供了一种基于三维特征强化的OPC方法,参见图1,包括以下步骤:This embodiment provides an OPC method based on three-dimensional feature enhancement, see Figure 1, which includes the following steps:
步骤S1、根据光刻胶曝光数据和光刻胶的化学反应函数得到优化的光刻胶函数模型;根据光刻机参数,将目标图案转化为目标像素化图案。Step S1: Obtain an optimized photoresist function model based on the photoresist exposure data and the chemical reaction function of the photoresist; convert the target pattern into a target pixelated pattern according to the photolithography machine parameters.
其中,所述步骤S1包括以下子步骤:Among them, the step S1 includes the following sub-steps:
步骤S11、根据实际测量得到的光刻胶曝光数据,结合光刻胶的化学反应函数建立第二代价函数;Step S11: Establish a second cost function based on the actual measured photoresist exposure data and the chemical reaction function of the photoresist;
所述第二代价函数表示为:The second cost function is expressed as:
其中,H表示第二代价函数,PR表示实际测量得到的光刻胶曝光数据,包括曝光能量和留膜率;Sig(·)表示光刻胶的化学反应函数。Among them, H represents the second cost function, PR represents the actual measured photoresist exposure data, including exposure energy and film retention rate; Sig(·) represents the chemical reaction function of the photoresist.
步骤S12、根据所述第二代价函数,使用最优化算法对光刻胶参数进行优化,直至所述第二代价函数最小,获得最优的光刻胶参数,所述光刻胶参数包括刻蚀速度和刻蚀阈值。Step S12: According to the second cost function, use an optimization algorithm to optimize the photoresist parameters until the second cost function is minimum and obtain optimal photoresist parameters. The photoresist parameters include etching Speed and etch threshold.
步骤S13、基于最优的刻蚀速度和最优的刻蚀阈值得到优化的光刻胶函数模型;Step S13: Obtain an optimized photoresist function model based on the optimal etching speed and the optimal etching threshold;
所述优化的光刻胶函数模型表示为:The optimized photoresist function model is expressed as:
其中,a表示最优的刻蚀速度,tr表示最优的刻蚀阈值。Among them, a represents the optimal etching speed, and tr represents the optimal etching threshold.
步骤S14、输入光刻机参数,将目标图案转化为目标像素化图案。Step S14: Input photolithography machine parameters to convert the target pattern into a target pixelated pattern.
其中,光刻机参数包括分辨率、扫描速度、步进速度、光源尺寸等。Among them, the lithography machine parameters include resolution, scanning speed, stepping speed, light source size, etc.
步骤S2、采用Sobel算子对所述目标像素化图案在两个不同的梯度阈值下进行边缘提取,得到对应的边缘特征矩阵,将边缘特征矩阵的数值作为目标图案矩阵的数值。Step S2: Use the Sobel operator to perform edge extraction on the target pixelated pattern under two different gradient thresholds to obtain the corresponding edge feature matrix, and use the value of the edge feature matrix as the value of the target pattern matrix.
其中,所述步骤S2包括以下子步骤:Among them, the step S2 includes the following sub-steps:
步骤S21、采用Sobel算子与所述目标像素化图案做卷积运算,得到图案梯度变化图;Sobel算子卷积核如下:Step S21: Use the Sobel operator to perform a convolution operation with the target pixelated pattern to obtain a pattern gradient change map; the Sobel operator convolution kernel is as follows:
x方向:x direction:
y方向:y direction:
G=|Gx|+|Gy|G=|Gx|+|Gy|
其中,Gx表示目标像素化图案和x方向的Sobel算子卷积核卷积后得到的每个像素在x轴方向上的梯度大小,Gy表示目标像素化图案和y方向的Sobel算子卷积核卷积后得到的每个像素在y轴方向上的梯度大小;G表示每个像素的高度梯度大小,G的值为每个像素在x、y轴方向上梯度值的绝对值之和。Among them, Gx represents the gradient size of each pixel in the x-axis direction obtained by convolving the target pixelated pattern with the Sobel operator convolution kernel in the x direction, and Gy represents the convolution of the target pixelated pattern with the Sobel operator in the y direction. The gradient size of each pixel in the y-axis direction obtained after kernel convolution; G represents the height gradient size of each pixel, and the value of G is the sum of the absolute values of the gradient values of each pixel in the x- and y-axis directions.
步骤S22、基于所述图案梯度变化图,根据设定的两个梯度阈值β1、β2,分别提取大于梯度阈值的两个梯度分布矩阵作为边缘特征矩阵Sz1、Sz2;Step S22: Based on the pattern gradient change map, according to the two set gradient thresholds β 1 and β 2 , extract two gradient distribution matrices greater than the gradient threshold as edge feature matrices S z1 and S z2 respectively;
针对每一个梯度阈值,若Sij≥β,则SZij=Sij,否则,SZij=0;For each gradient threshold, if S ij ≥ β, then S Zij =S ij , otherwise, S Zij =0;
其中,Sij表示图案梯度变化图中第i行第j列像素点的坐标值,Szij表示边缘特征矩阵中第i行第j列像素点的坐标值;Among them, S ij represents the coordinate value of the pixel point in the i-th row and j-th column in the pattern gradient change map, and S zij represents the coordinate value of the pixel point in the i-th row and jth column in the edge feature matrix;
将边缘特征矩阵的数值作为目标图案矩阵Z(x,y)的数值。The value of the edge feature matrix is used as the value of the target pattern matrix Z(x, y).
步骤S3、根据光刻机参数和优化的光刻胶函数模型,得到初始的成像图案矩阵。Step S3: Obtain an initial imaging pattern matrix based on the photolithography machine parameters and the optimized photoresist function model.
其中,所述步骤S3包括以下子步骤:Among them, the step S3 includes the following sub-steps:
步骤S31、根据所述光刻机参数,对所述目标图案进行像素化处理,得到曝光剂量分布矩阵:Step S31: Perform pixelation processing on the target pattern according to the lithography machine parameters to obtain an exposure dose distribution matrix:
其中,E(x,y)表示曝光剂量分布矩阵,曝光剂量分布矩阵的初始值来自于目标图案矩阵Z(x,y)对应像素点位置的数值,(x,y)表示一个曝光点的位置坐标,单个曝光点的位置坐标等于对应像素点的位置坐标,θ表示无约束优化变量。Among them, E(x, y) represents the exposure dose distribution matrix. The initial value of the exposure dose distribution matrix comes from the value of the corresponding pixel position of the target pattern matrix Z(x, y). (x, y) represents the position of an exposure point. Coordinates, the position coordinates of a single exposure point are equal to the position coordinates of the corresponding pixel point, and θ represents the unconstrained optimization variable.
步骤S32、获得高斯光束矩阵:Step S32: Obtain the Gaussian beam matrix:
其中,B(x,y)表示高斯光束矩阵,P表示整体曝光功率,ω0为焦平面处激光光斑的半径;高斯光束矩阵的数学形式跟光刻机参数相关,因为光刻机的参数固定,因此接下来的步骤中高斯光束矩阵的数值也固定。Among them, B (x, y) represents the Gaussian beam matrix, P represents the overall exposure power, and ω 0 is the radius of the laser spot at the focal plane; the mathematical form of the Gaussian beam matrix is related to the parameters of the lithography machine, because the parameters of the lithography machine are fixed. , so the value of the Gaussian beam matrix is also fixed in the next steps.
步骤S33、根据所述曝光剂量分布矩阵及所述高斯光束矩阵得到曝光能量分布矩阵:Step S33: Obtain the exposure energy distribution matrix according to the exposure dose distribution matrix and the Gaussian beam matrix:
其中,D(x,y)表示曝光能量分布矩阵,表示卷积符号;Among them, D(x, y) represents the exposure energy distribution matrix, Represents the convolution symbol;
步骤S34、根据所述曝光能量分布矩阵和所述优化的光刻胶函数模型,得到所述初始的成像图案矩阵:Step S34: Obtain the initial imaging pattern matrix according to the exposure energy distribution matrix and the optimized photoresist function model:
其中,表示初始的成像图案矩阵。in, Represents the initial imaging pattern matrix.
步骤S4、构建第一代价函数和约束条件,根据所述约束条件对曝光剂量分布和成像图案矩阵的数值进行更新。Step S4: Construct a first cost function and constraint conditions, and update the exposure dose distribution and imaging pattern matrix values according to the constraint conditions.
具体的,结合最优化算法,构建第一代价函数和约束条件,对曝光剂量分布矩阵和成像图案矩阵进行迭代优化:Specifically, combined with the optimization algorithm, the first cost function and constraints are constructed, and the exposure dose distribution matrix and imaging pattern matrix are iteratively optimized:
其中,FZ表示经光刻胶成像之后的图案误差,FE表示系统总的输出剂量,F表示第一代价函数,Z(x,y)表示目标图案矩阵,表示成像图案矩阵,E(x,y)表示曝光剂量分布矩阵。Among them, F Z represents the pattern error after photoresist imaging, F E represents the total output dose of the system, F represents the first cost function, Z (x, y) represents the target pattern matrix, represents the imaging pattern matrix, and E(x, y) represents the exposure dose distribution matrix.
对曝光剂量分布矩阵进行迭代优化:Iteratively optimize the exposure dose distribution matrix:
其中,s表示最优化算法中更新的步长。Among them, s represents the updated step size in the optimization algorithm.
步骤S5、根据更新判断条件对梯度阈值进行自动更新。Step S5: Automatically update the gradient threshold according to the update judgment condition.
其中,所述更新判断条件包括第一条件和第二条件;所述第一条件为F2-F1>0,所述第二条件为F2-F1≤0;F1表示在梯度阈值β1下用边缘特征矩阵构建的第一代价函数,F2表示在梯度阈值β2下用边缘特征矩阵构建的第一代价函数。Wherein, the update judgment condition includes a first condition and a second condition; the first condition is F 2 -F 1 > 0, and the second condition is F 2 -F 1 ≤ 0; F 1 represents the gradient threshold The first cost function constructed with the edge feature matrix under β 1 , F 2 represents the first cost function constructed with the edge feature matrix under the gradient threshold β 2 .
若满足所述第一条件,则对梯度阈值按下述原则进行自动更新:If the first condition is met, the gradient threshold is automatically updated according to the following principles:
β2=β1,β1=β1-α(F2-F1)β 2 =β 1 , β 1 =β 1 -α(F 2 -F 1 )
若满足所述第二条件,则对梯度阈值按下述原则进行自动更新:If the second condition is met, the gradient threshold is automatically updated according to the following principles:
β1=β2,β2=β2+α(F2-F1)β 1 =β 2 , β 2 =β 2 +α(F 2 -F 1 )
其中,α表示设定步长。Among them, α represents the set step size.
步骤S6、判断是否满足循环结束条件;若不满足,则返回至步骤S2;若满足,则结束循环。Step S6: Determine whether the loop end condition is satisfied; if not, return to step S2; if satisfied, end the loop.
其中,若结束循环,取β1和β2中较小的数值作为最优梯度阈值,取所述最优梯度阈值对应的边缘特征矩阵作为最优边缘特征矩阵,将所述最优边缘特征矩阵对应的曝光剂量分布矩阵和曝光能量分布矩阵作为全局最优分布。Among them, if the loop is ended, the smaller value of β 1 and β 2 is taken as the optimal gradient threshold, the edge feature matrix corresponding to the optimal gradient threshold is taken as the optimal edge feature matrix, and the optimal edge feature matrix is The corresponding exposure dose distribution matrix and exposure energy distribution matrix are used as the global optimal distribution.
所述循环结束条件为达到优化次数或所述第一代价函数的数值小于优化阈值。The loop end condition is that the number of optimization times is reached or the value of the first cost function is less than the optimization threshold.
此外,优选的方案中,在采用Sobel算子进行边缘提取之前,还包括:对所述目标像素化图案进行高斯平滑处理。In addition, in a preferred solution, before using the Sobel operator for edge extraction, the method further includes: performing Gaussian smoothing on the target pixelated pattern.
具体的,高斯平滑卷积核如下:Specifically, the Gaussian smooth convolution kernel is as follows:
通过使用所述高斯平滑卷积核与目标像素化图案做卷积运算,实现对目标像素化图案进行高斯平滑处理。By using the Gaussian smoothing convolution kernel and the target pixelated pattern to perform a convolution operation, Gaussian smoothing processing is performed on the target pixelated pattern.
本发明采用Sobel算子对灰度图进行处理,提取到图像边缘以后,通过对图像边缘进行反向光刻计算,求得图像边缘的曝光剂量分布,因为求解的计算复杂度随像素点的个数的增加而迅速增加,在此过程中,本发明提供的方法减少了需要求解的像素点个数,从而减少了计算复杂度。此外,梯度阈值的大小影响着代价函数函数的大小,并且不同的图案合适的梯度阈值也不一定相同,合适的梯度阈值并不能事先确定,面对人为设定阈值无从下手的困难,本发明采用了自动寻优的算法,在给定两个不同的初始梯度阈值的情况下,通过优化步骤能够自动调整梯度阈值到最优值,进一步减少了求解时的困难。因此,本发明提供的技术方案具有快速、高效、操作简单的优点,能够大大提升反向光刻的速度。The present invention uses the Sobel operator to process the grayscale image. After extracting the image edge, the exposure dose distribution of the image edge is obtained by performing reverse photolithography calculation on the image edge, because the computational complexity of the solution varies with the individual pixels. The number increases rapidly. In this process, the method provided by the present invention reduces the number of pixel points that need to be solved, thereby reducing the computational complexity. In addition, the size of the gradient threshold affects the size of the cost function, and the appropriate gradient thresholds for different patterns are not necessarily the same. The appropriate gradient threshold cannot be determined in advance. Faced with the difficulty of artificially setting the threshold, the present invention adopts It adopts an automatic optimization algorithm. When two different initial gradient thresholds are given, the gradient threshold can be automatically adjusted to the optimal value through the optimization step, further reducing the difficulty in solving the problem. Therefore, the technical solution provided by the present invention has the advantages of speed, efficiency, and simple operation, and can greatly increase the speed of reverse lithography.
本发明实施例提供的一种基于三维特征强化的OPC方法至少包括如下技术效果:An OPC method based on three-dimensional feature enhancement provided by the embodiment of the present invention at least includes the following technical effects:
本发明通过局域优化解决了现有优化方法对整体优化导致单次计算量大的问题;提供针对三维高度特征的局域优化方法对曝光剂量分布进行优化,解决了现有适量矩阵优化方法中高度优化缺失的问题,同时能够自动寻找最优阈值,解决了灰度梯度阈值人为无法设置最优值的问题。The present invention solves the problem of large single calculation amount caused by existing optimization methods for overall optimization through local optimization; provides a local optimization method for three-dimensional height characteristics to optimize exposure dose distribution, and solves the problem of existing appropriate matrix optimization methods. It highly optimizes the missing problem and can automatically find the optimal threshold, solving the problem that the gray gradient threshold cannot be manually set to the optimal value.
最后所应说明的是,以上具体实施方式仅用以说明本发明的技术方案而非限制,尽管参照实例对本发明进行了详细说明,本领域的普通技术人员应当理解,可以对本发明的技术方案进行修改或者等同替换,而不脱离本发明技术方案的精神和范围,其均应涵盖在本发明的权利要求范围当中。Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to examples, those of ordinary skill in the art will understand that the technical solutions of the present invention can be carried out. Modifications or equivalent substitutions without departing from the spirit and scope of the technical solution of the present invention shall be included in the scope of the claims of the present invention.
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