Photoetching imaging fidelity enhancement method and system based on information theory

Abstract

The invention discloses a photoetching imaging fidelity enhancement method and system based on an information theory, and constructs a photoetching informatics model and system by analyzing graphic characteristics of a mask and a wafer image in photoetching and counting pixel density. By applying the model and the system, the optimal probability distribution of the mask can be given, and the theoretical limit of the imaging precision of the photoetching algorithm can be calculated. Meanwhile, the invention provides an improved method of a computational lithography technology based on the model and the system, the update iteration of the mask is guided according to the optimal probability distribution of the mask, and the algorithm is beneficial to improving the convergence precision of a computational lithography algorithm. According to the method, the fidelity of photoetching imaging can be enhanced, the convergence precision of a calculation photoetching algorithm is improved, and a theoretical basis is provided for optimization of a calculation photoetching technology under an advanced node.

Description

Technical Field

[0001] The present invention relates to the technical field of computational lithography, and particularly to a method and system for enhancing lithography imaging fidelity based on information theory. Background Art

[0002] Lithography technology is one of the core processes in integrated circuit manufacturing. In this technology, a short-wavelength light source is first used to irradiate a mask on which the circuit layout to be printed is engraved. After the light passes through the mask, it is collected by a projection objective and projected onto a silicon wafer coated with photoresist on the surface. Then, through processes such as exposure, development, and etching, the circuit layout is replicated on the silicon wafer.

[0003] The imaging accuracy of a lithography system is affected by optical effects such as light diffraction and interference, as well as lithography processes. Therefore, the integrated circuit manufacturing industry widely uses computational lithography technology to compensate for the lithography process, so as to minimize the distortion and distortion of the circuit layout projected onto the silicon wafer and improve lithography resolution and imaging fidelity. Computational lithography technology is an advanced technology that comprehensively applies mathematical methods, physical models, and numerical simulations to optimize and improve the lithography imaging process.

[0004] In recent years, in order to explore the informatics essence of computational lithography technology and the theoretical limit of imaging accuracy that computational lithography algorithms can achieve, researchers have constructed a computational lithography model based on information theory, given the theoretical limit of imaging accuracy of some computational lithography technologies under this model framework, and improved the convergence accuracy of existing computational lithography algorithms. However, the current computational lithography model based on information theory has theoretical defects. When analyzing the mask pixel distribution pattern, it relies on the idealized assumption of using uniform pattern density to simplify the mathematical derivation. Specifically, the uniform pattern density assumption states that for a mask (or wafer image) region containing a fixed number of pixels, the distribution pattern of these pixels is random and equally probable. In fact, this assumption is not consistent with the actual situation. The mask (or wafer image) always contains geometric features similar to the target circuit layout, pixels always tend to aggregate, and isolated pixels are uncommon. Therefore, the occurrence probability of some pixel distribution patterns is extremely low, which does not conform to the uniform pattern density assumption. Therefore, the theoretical limit of imaging accuracy of computational lithography algorithms obtained under the uniform pattern density assumption is not accurate, and there is room for further optimization of the developed computational lithography technology. To address this problem and also to provide a more complete theoretical basis for the research and development of computational lithography technology at advanced nodes, it is necessary to establish a lithography informatics model and system based on pixel density statistics. And apply this model and system to give an accurate theoretical limit of imaging accuracy of computational lithography algorithms and a technical solution to further improve the imaging fidelity of computational lithography algorithms. Summary of the Invention

[0005] In view of this, the present invention provides a method and system for enhancing the fidelity of lithographic imaging based on information theory, which can solve the problems that the existing computational lithography model based on information theory has theoretical defects and the calculation of the theoretical limit result of imaging accuracy is inaccurate.

[0006] To achieve the above object, the method for enhancing the fidelity of lithographic imaging based on information theory provided by the present invention includes the following technical steps:

[0007] S1: For a given binary mask M, rasterize it and perform a point spread operation on each pixel point to obtain a vector composed of pixels covered by the point spread function on the mask M Subsequently, use a typical lithographic imaging model to simulate the mask M to obtain the wafer image Z, and also perform a point spread operation on each pixel point on the wafer image Z to obtain a vector composed of pixels covered by the point spread function on the wafer image Z

[0008] S2: For the pixels covered by the point spread function on the mask M and the wafer image Z, take the degree of pixel aggregation as the pixel density PD; count the vector corresponding to each pixel point on the mask M the number N of elements with pixel value 1 in x and the pixel density PD x , count the vector corresponding to the corresponding pixel point on the wafer image Z the number N of elements with pixel value 1 in y and the pixel density PD y .

[0009] S3: Collect the statistical results of all pixel points, the probability of the event {N x =m, PD x =a} is p ma , the probability of the event {N y =n, PD y =b} is q nb ; construct a vector representing the probability distribution of the mask M according to the probability p ma construct a vector representing the probability distribution of the wafer image Z according to the probability q At the same time, the vector nb and the vector satisfy where T is the probability transition matrix between the vector and the vector . and the vector .

[0010] S4: Construct the first cost function

[0011] S5: Use the steepest descent method to solve the optimization problem Obtain the optimal mask probability distribution Further obtain the imaging accuracy limit of the computational lithography algorithm.

[0012] S6: Based on the optimal mask probability distribution Design a mask optimization algorithm for enhancing imaging fidelity. During the mask optimization process, construct a second cost function to control the insertion of sub-resolution assist features.

[0013] S7: According to the optimal mask probability distribution and the mask M, solve the optimization problem using the steepest descent method to obtain the optimized actual wafer image Z and the optimized mask M * which is obtained by adding sub-resolution assist features to M.

[0014] 2. A method for enhancing lithography imaging fidelity based on information theory according to claim 1, wherein the specific method for determining the pixel density PD is as follows:

[0015] S201: For the coverage area C determined by the point spread function p , there are a total of K pixels; randomly generate S n regions containing n one-valued pixels in C p , where n < K, and among them, the distribution of all one-valued pixels in each C p region is random and unique.

[0016] S202: For all one-valued pixels in each C p , use the k-means clustering algorithm to determine their cluster centers, k = 1, calculate the Euclidean distance d from all one-valued pixels to the cluster center, then the average distance from each one-valued pixel to the cluster center is Arrange all the d n obtained from the S p regions of C aver in ascending order to obtain the sequence D:

[0017]

[0018] S203: Divide the sequence D into E + 1 intervals, corresponding to pixel density PD = 0 to PD = E from left to right; the division rule is: from left to right, the number of elements in each interval increases geometrically with a ratio of 2 times, that is, the interval with PD = 0 contains S n / 2 E elements, the interval with PD = 1 contains S n / 2 E-1 elements, and so on, the interval with PD = E contains S n / 2 elements; record the first element in each interval and the last element of sequence D, a total of E + 2 elements, to form a new sequence D':

[0019] D' = {d a ′ ver1 , d a ′ ver2 ,..., d a ′ ver(E+2)}

[0020] S204: Use sequence D' to calculate the PD of any given C that contains n one-valued pixels. The calculation method is to, according to the second step, calculate the d of the given C p region, and based on sequence D', construct a mapping G p : aver n

[0021] PD = G n (d aver ) = g - 1, d a ′ verg ≤ d aver < d a ′ ver(g+1) .

[0022] 3. The method for enhancing lithography imaging fidelity based on information theory according to claim 1, wherein the method for obtaining the probability transition matrix T between vector and vector is as follows:

[0023] S301: The probability distribution vectors of the mask and the wafer image are respectively represented as vector vector

[0024] The probability transition matrix T is a square matrix with (K + 1)×(E + 1) rows and (K + 1)×(E + 1) columns.

[0025] S302: Given the lithography system parameters and process parameters, select several groups of training masks M # = {M 1 , M 2 , M 3 ,...} and their wafer images Z # = {Z 1 , Z 2 , Z 3 ,...}; Through steps S1 and S2, count the number N # of one-valued pixels and the pixel density PD of the region C p covered by the point spread function corresponding to each pixel of all masks M x to obtain the event {Nx = m, PD x The occurrence frequency of the event {N # , event {N y = n, PD y = b} is v. Similarly, for the wafer image group Z

[0026] S303: Based on more than a set number of training samples, it is considered that under the condition that the event {N x = m, PD x = a} occurs, the occurrence probability of the event {N y = n, PD y = b} is v / u; this probability is used as the value in the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T. By traversing all N x , N y , PD x , PD y the entire probability transition matrix T is obtained.

[0027] Furthermore, the first cost function includes a main function and three penalty functions, which are respectively used to evaluate the mutual information, mathematical specification, imaging fidelity, and manufacturability corresponding to the optimized mask probability distribution ; among them, the mutual information is the mutual information between the mask layout and the wafer image, representing the information transmission efficiency in the lithography system; the mathematical specification means that the optimized mask probability distribution should satisfy that the sum of elements is 1; the imaging fidelity represents that the wafer image probability distribution corresponding to the optimized mask probability distribution is closest to the probability distribution of the target circuit layout The manufacturability represents that the pixel density corresponding to the optimized mask probability distribution is the densest and there are no isolated pixel points.

[0028] Furthermore, the mutual information is the mutual information between the mask layout and the wafer image. Specifically, the calculation method of the mutual information between the mask layout and the wafer image is as follows:

[0029] S401: Calculate the information entropy of the vector where P

[0030]

[0031] {·} represents probability, r and represents the number of combinations of taking n elements from K elements.

[0032] S402: Calculate the known vector with respect to the vector conditional entropy

[0033]

[0034] S403: Calculate the mutual information

[0035]

[0036] wherein, T nbma represents the element at the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T, and T nbuv represents the element at the [(E + 1)n + b + 1]-th row and [(E + 1)u + v + 1]-th column of the probability transition matrix T, and p uv represents the vector the [(E + 1)u + v + 1]-th element in

[0037] Furthermore, the second cost function is used to control the insertion of sub-resolution assist features. This cost function includes a main function and three penalty functions, which are respectively used to evaluate the imaging fidelity, quantization error, complexity, and the rationality of the mask probability distribution corresponding to the optimized mask; wherein, the imaging fidelity represents the case where the wafer image Z of the mask is closest to the target circuit layout ; the complexity and quantization error respectively represent the wavelet penalty term and the quadratic penalty term, and the rationality of the mask probability distribution represents the case where the optimized mask probability distribution is closest to the optimal mask probability distribution .

[0038] Another embodiment of the present invention further provides a lithographic imaging fidelity enhancement system based on information theory, including a point spread module, a pixel statistics module, a probability distribution vector construction module, a first cost function construction module, a mask optimization module, a second cost function construction module, and a wafer image optimization module.

[0039] The point spread module is configured to rasterize a given binary mask M and perform a point spread operation on each pixel point to obtain a vector composed of pixels covered by the point spread function on the mask M Subsequently, use a typical lithographic imaging model to simulate the mask M to obtain the wafer image Z, and also perform a point spread operation on each pixel point on the wafer image Z to obtain a vector composed of pixels covered by the point spread function on the wafer image Z

[0040] A pixel statistics module is used to calculate the pixel density PD of the pixels on the mask M and the wafer image Z covered by the point spread function, based on the degree of pixel aggregation; and to count the vector corresponding to each pixel point on the mask M the number N of elements with pixel value 1 in the vector x and the pixel density PD x ; and to count the number N of elements with pixel value 1 in the vector y corresponding to the corresponding pixel point on the wafer image Z y and the pixel density PD y .

[0041] A probability distribution vector construction module is used to collect the statistical results of all pixel points. The probability of the event {N x =m, PD x =a} is p ma , and the probability of the event {N y =n, PD y =b} is q nb ; to construct a vector representing the probability distribution of the mask M according to the probability p ma ; to construct a vector representing the probability distribution of the wafer image Z according to the probability q ; meanwhile, the vector nb and the vector satisfy where T is the probability transition matrix between the vector and the vector . and the vector .

[0042] A first cost function construction module is used to construct a first cost function

[0043] A mask optimization module is used to solve the optimization problem using the steepest descent method to obtain the optimal mask probability distribution and further obtain the imaging accuracy limit of the computational lithography algorithm

[0044] A second cost function construction module designs a mask optimization algorithm for enhancing imaging fidelity based on the optimal mask probability distribution , and constructs a second cost function during the mask optimization process to control the insertion of sub-resolution assist features

[0045] A wafer image optimization module, according to the optimal mask probability distribution and the mask M, solves the optimization problem using the steepest descent method to obtain the optimized actual wafer image Z, and the optimized mask M * is obtained by adding sub-resolution assist features to M

[0046] Further, in the pixel statistics module, the specific method for determining the pixel density PD is as follows:

[0047] S201: For the coverage area C determined by the point spread function p , there are a total of K pixels; randomly generate S n regions of C that contain n one-valued pixels, where n < K. Among them, the distribution of all one-valued pixels in each C p region is random and unique. p

[0048] S202: Use the k-means clustering algorithm to determine the cluster center for all one-valued pixels in each C p . Let k = 1, and calculate the Euclidean distance d from all one-valued pixels to the cluster center. Then, the average distance from each one-valued pixel to the cluster center is Arrange all the d n values obtained from the S p regions of C in ascending order to obtain the sequence D: aver

[0049]

[0050] S203: Divide the sequence D into E + 1 intervals, corresponding to pixel density PD = 0 to PD = E from left to right; the division rule is: from left to right, the number of elements in each interval increases geometrically with a ratio of 2, that is, the interval with PD = 0 contains S n / 2 E elements, the interval with PD = 1 contains S n / 2 E-1 elements, and so on. The interval with PD = E contains S n / 2 elements; record the first element in each interval and the last element of the sequence D, a total of E + 2 elements, to form a new sequence D':

[0051] D' = {d' aver1 , d' aver2 ,..., d' aver(E+2)}

[0052] S204: Use the sequence D' to calculate the PD of any given C p that contains n one-valued pixels. The calculation method is as follows: According to the second step, calculate the d p of the given C aver region, and construct a mapping G n based on the sequence D':

[0053] PD = G n (d aver ) = g - 1, d' averg ≤ d aver < d'​​aver(g+1) .

[0054] Furthermore, in the probability distribution vector construction module, the method for obtaining the probability transition matrix T between vector and vector is as follows:

[0055] S301: The probability distribution vectors of the mask and the wafer image are respectively represented as vector vector

[0056] The probability transition matrix T is a square matrix with (K + 1)×(E + 1) rows and (K + 1)×(E + 1) columns.

[0057] S302: Given the lithography system parameters and process parameters, select several groups of training masks M # ={M 1 , M 2 , M 3 ,...} and their wafer images Z # ={Z 1 , Z 2 , Z 3 ,...}; Through steps S1 and S2, count the number of 1-valued pixels N # and the pixel density PD of the coverage area C p corresponding to each pixel of all masks M x to obtain the occurrence frequency v of the event {N x = m, PD x = a}, and similarly, for the wafer image group Z # , obtain the occurrence frequency u of the event {N y = n, PD y = b}.

[0058] S303: Based on more than a set number of training samples, assume that under the condition that the event {N x = m, PD x = a} occurs, the occurrence probability of the event {N y = n, PD y = b} is v / u; Take this probability as the value of the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T, and traverse all N x , N y , PD x , PD y to obtain the entire probability transition matrix T.

[0059] Furthermore, the first cost function includes a main function and three penalty functions, which are respectively used to evaluate the optimized mask probability distribution The corresponding mutual information, mathematical specification, imaging fidelity, and manufacturability; among them, the mutual information is the mutual information between the mask layout and the wafer imaging, representing the information transmission efficiency in the lithography system; the mathematical specification represents the optimized mask probability distribution should satisfy that the sum of elements is 1; the imaging fidelity represents the optimized mask probability distribution corresponding wafer image probability distribution the probability distribution closest to the target circuit layout the manufacturability represents the optimized mask probability distribution the corresponding pixel density is the densest and there are no isolated pixels

[0060] The mutual information is the mutual information between the mask layout and the wafer imaging. Specifically, the mutual information between the mask layout and the wafer imaging The calculation method is as follows:

[0061] S401: Calculate the information entropy of the vector where \(P\)

[0062]

[0063] where \(\{·\}\) represents probability, r and \(\binom{K}{n}\) represents the combination number of taking \(n\) elements from \(K\) elements

[0064] S402: Calculate the conditional entropy of the known vector with respect to the vector

[0065]

[0066] S403: Calculate the mutual information

[0067]

[0068] where \(T\) nbma represents the element in the \([(E + 1)n + b + 1]\)-th row and \([(E + 1)m + a + 1]\)-th column of the probability transition matrix \(T\), and \(T\) nbuv represents the element in the \([(E + 1)n + b + 1]\)-th row and \([(E + 1)u + v + 1]\)-th column of the probability transition matrix \(T\), and \(p\) uv represents the \([(E + 1)u + v + 1]\)-th element in the vector

[0069] The second cost function ​​​For controlling the insertion of sub-resolution assist features, the cost function includes a main function and three penalty functions, which are used to evaluate the imaging fidelity, quantization error, complexity, and rationality of the mask probability distribution corresponding to the optimized mask respectively; among them, the imaging fidelity represents the case where the wafer image Z of the mask is closest to the target circuit layout ; the complexity and quantization error represent the wavelet penalty term and the quadratic penalty term respectively, and the rationality of the mask probability distribution represents the case where the optimized mask probability distribution is closest to the optimal mask probability distribution .

[0070] Beneficial effects:

[0071] 1. The present invention proposes a method and system for enhancing lithographic imaging fidelity based on information theory. First, aiming at the theoretical defects of the existing computational lithography model based on information theory, a solution method for pixel density analysis is proposed. Subsequently, a computational lithography informatics model is constructed based on pixel density information, and the optimal probability distribution of the mask under the given lithography system and process parameters is solved by a gradient-based numerical algorithm. Finally, the theoretical limit of the imaging accuracy of computational lithography technology is calculated according to the optimal probability distribution, providing a more complete theoretical basis for the further development of current computational lithography technology. That is, the present invention studies the information transmission mechanism and law of the lithography process through mathematical methods, and the constructed lithography informatics model can obtain the theoretical limit of accurate computational lithography imaging accuracy and improve the convergence accuracy of computational lithography algorithms.

[0072] 2. The present invention proposes a lithography informatics model and system applying pixel density statistics and a mask optimization method for enhancing the imaging fidelity of a lithography system. For any mask, under the given lithography system and process parameters, the optimal probability distribution of the mask is solved through the lithography informatics model and system based on pixel density statistics, and combined with the general method of mask optimization, the optimal probability distribution is used to further enhance the lithography imaging fidelity. This method is used to solve the problems in computational lithography technology at advanced nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flowchart of the method and system for enhancing lithographic imaging fidelity based on information theory provided by the present invention;

[0074] Figure 2 is a schematic diagram of the channel model of the lithography system provided by the present invention;

[0075] Figure 3 is a schematic diagram of the principle of calculating pixel density provided by the present invention;

[0076] Figure 4 is a schematic diagram of some training masks and their wafer images of the probability transition matrix provided by the present invention;

[0077] Figure 5 Test mask, optimized mask and schematic diagram of their wafer images of the method and system for enhancing lithographic imaging fidelity based on information theory provided by the present invention;

[0078] Figure 6 Schematic diagram of the convergence curve of the optimal mutual information calculated by using the method and system for enhancing lithographic imaging fidelity based on information theory provided by the present invention for a specific mask;

[0079] Figure 7 Schematic diagram of the optimal probability distribution of the mask calculated by using the method and system for enhancing lithographic imaging fidelity based on information theory provided by the present invention for a specific mask. Detailed implementation manners

[0080] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.

[0081] Example 1:

[0082] Please refer to the attached Figure 1 , the attached Figure 1 shows the flowchart of the method and system for enhancing lithographic imaging fidelity based on information theory, which specifically includes the following steps:

[0083] S1: For a given binary mask M, rasterize it and perform a point spread operation on each pixel. Among them, the point spread operation is: taking the current pixel as the center and with a radius of R, construct a point spread function, and the circular area covered by the point spread function is denoted as C p . The vector composed of the pixels on the mask M covered by C p is denoted as x i = 0 or 1, where K is the total number of pixels on the mask M covered by C p , and x i is the mask pixel value. The pixel value of 0 represents an opaque pixel, and the pixel value of 1 represents a transparent pixel. Subsequently, use a typical lithographic imaging model to simulate the mask M to obtain the wafer image Z, and perform a point spread operation on each pixel of the wafer image Z as well. Denote the K pixels with the same pixel positions as those in the vector as y i = 0 or 1, where y i is the wafer image pixel value. The pixel value of 0 represents a non-imaging pixel, and the pixel value of 1 represents an imaging pixel.

[0084] It should be noted that as shown in the attached Figure 2As shown, the mask M calculates the wafer image Z through a lithographic aerial image model and a photoresist threshold model, where the lithographic aerial image model is the Abbe imaging model. In some embodiments, other lithographic aerial image models can also be used for substitution, such as the Hopkins imaging model. The specific form of the Abbe model is:

[0085]

[0086] where I represents the lithographic aerial image; r represents the spatial coordinates; m represents the point light source; Γ m represents the intensity of the point light source; h m represents the point spread function of the lithographic system; represents the convolution operation.

[0087] The photoresist threshold model can be expressed as a sigmoid function for taking its derivative in a numerical optimization algorithm. The specific form is:

[0088] Z = sig{I, t r} = 1 / {1 + exp[-a r (I - t r )]} (2)

[0089] where t r represents the photoresist threshold, and a r represents the steepness factor of the sigmoid function.

[0090] In addition, it should be supplemented that the initial mask M is a binary image, the lithographic aerial image I itself is a grayscale image, and the wafer image Z obtained through the photoresist threshold model calculation is a binary image. Therefore, all statistical and informatics processing in the present invention is only applicable to binary images.

[0091] S2: For the region C p covered by the point spread function corresponding to each pixel point on the mask M and the wafer image Z, there are several pixels with pixel values of 0 or 1 distributed inside. Define the aggregation degree of these pixels as the pixel density PD. According to the calculation method of PD, the smaller PD is, the denser the pixels are, and the larger PD is, the sparser the pixels are. PD is a discrete variable, which can only take integer values, with the minimum value of 0 and the maximum value of E. The value of E is determined according to the actual application scenario and the calculation efficiency requirements. Statistically count the number of elements with pixel value of 1 and the pixel density in the vector corresponding to each pixel point on the mask M, denoted as N x and PD x , and statistically count the number of elements with pixel value of 1 and the pixel density in the vector corresponding to the corresponding pixel point on the wafer image Z, denoted as N y and PD y .

[0092] In step S2, the specific method for determining the pixel density PD is as follows:

[0093] S201: Assume that for the coverage area C determined by the point spread function p , there are a total of K pixels. Randomly generate S n (S n should be as large as possible) regions of C that contain n (n < K) 1-valued pixels, where the distribution of all 1-valued pixels within each C p region is random and unique. p

[0094] S202: As shown in Figure 3 (a), for all 1-valued pixels within each C p , use the k-means clustering algorithm (k = 1) to determine their cluster centers, and calculate the Euclidean distance d from all 1-valued pixels to the cluster centers. Therefore, the average distance from each 1-valued pixel to the cluster center is Arrange all the d n obtained from the S p regions of C in ascending order to obtain the sequence D: aver

[0095]

[0096] S203: As shown in Figure 3 (b), divide the sequence D into E + 1 intervals, corresponding to pixel density PD = 0 to PD = E from left to right. The division rule is: from left to right, the number of elements in each interval increases geometrically with a ratio of 2, that is, the interval with PD = 0 contains S n / 2 E elements, the interval with PD = 1 contains S n / 2 E-1 elements, and so on. The interval with PD = E contains S n / 2 elements. Record the first element in each interval and the last element of the sequence D, a total of E + 2 elements, to form a new sequence D′:

[0097] D′ = {d′ aver1 , d′ aver2 ,..., d′ aver(E+2)} (4)

[0098] S204: The PD of any given C that contains n 1-valued pixels can be calculated using the sequence D′. The calculation method is to calculate the d p of the given C p region according to step S202, and construct a mapping G aver based on the sequence D′: n : ​​

[0099] PD = G n (d aver ) = g - 1, d′ averg ≤d aver <d′ aver(g+1) (5)

[0100] It should be noted that the calculation of PD is based on the Monte Carlo method. This method is a simplified method for estimating the physical quantity of pixel density by randomly sampling a large number of samples. The reason for using the Monte Carlo method to calculate PD is that: the total number of pixels included in region C p is K. If the number of pixels with value 1 is n, then all pixel distributions total species. Since the value of K is large (a typical value is 317), when the number of pixels with value 1 gradually increases, the value of will become very large, making it very difficult to statistically analyze species of pixel distributions. For example, when n = 10, the value of is 2.4×10^18. Therefore, it is suitable to use the Monte Carlo method to solve. According to step S201, by randomly generating S n (the typical value of S n is 150000) species of pixel distribution methods to replace the statistical analysis of species of pixel distribution methods. The present invention has experimentally verified the accuracy of the Monte Carlo method fitting. As the value of S n gradually increases (the maximum value is 10^8), repeating steps S202 to S204, the experimental results show that the sequence D′ obtained in step S203 becomes stable when S n is above 10^5, that is, the calculation of the pixel density PD for any pixel distribution is not affected by S n .

[0101] S3: Collect the statistical results of all pixel points, and define p ma as the probability of the event {N x = m, PD x = a}, and q nb as the probability of the event {N y = n, PD y = b}. According to the probability p ma a vector representing the probability distribution of the mask M can be constructed According to the probability q nb a vector representing the probability distribution of the wafer image Z can be constructed Meanwhile, the vector and the vector satisfy where T is the vector and the vector The probability transition matrix between them. T is related to the lithography system parameters and process parameters. Among them, the lithography system parameters include the style, wavelength, polarization state, numerical aperture of the lithography system, etc., and the process parameters include the photoresist thickness, anti-reflection layer thickness, baking time and temperature, exposure dose, etc.

[0102] In step S3, the vector and the vector The method for obtaining the probability transition matrix T between them is as follows:

[0103] S301: According to step S3, the probability distribution vectors of the mask and the wafer image can be respectively expressed as the vectors vector Therefore, the probability transition matrix T is a square matrix with the number of rows (K + 1)×(E + 1) and the number of columns (K + 1)×(E + 1).

[0104] S302: As shown in the appendix Figure 4 , given the lithography system parameters and process parameters, select several groups of training masks M # ={M 1 , M 2 , M 3 ,...} and their wafer images Z # ={Z 1 , Z 2 , Z 3 ,...}. By steps S1 and S2, count the number of 1-valued pixels Nx and pixel density PD of the area C # covered by the point spread function corresponding to each pixel of all masks M p , and obtain the occurrence frequency v of the event {N x =m, PD x =a}. Similarly, for the wafer image group Z # , the occurrence frequency u of the event {N y =n, PD y =b} can be obtained.

[0105] S303: Based on a sufficiently large training sample, it can be considered that under the condition that the event {N x =m, PD x =a} occurs, the probability of the event {N y =n, PD y =b} is v / u. Take this probability as the value of the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T, and traverse all N x , N y , PD x , PD y to obtain the entire probability transition matrix T.

[0106] S4: Construct a cost function The cost function includes a main function and three penalty functions, which are used to evaluate the optimized mask probability distribution The corresponding mutual information, mathematical specification, imaging fidelity, and manufacturability. Among them, the mutual information represents the information transmission efficiency in the lithography system; the mathematical specification represents the optimized mask probability distribution should satisfy that the sum of elements is 1; the imaging fidelity represents the optimized mask probability distribution The corresponding wafer image probability distribution should be as close as possible to the probability distribution of the target circuit layout The manufacturability represents the optimized mask probability distribution The corresponding pixel density should be as dense as possible and there should be no isolated pixel points

[0107] In step S4, the mutual information between the mask layout and the wafer imaging is calculated as follows

[0108] S401: Calculate the vector The information entropy of

[0109]

[0110] where P r {·} represents probability, represents the combination number of taking n elements from K elements

[0111] S402: Calculate the conditional entropy of the known vector with respect to the vector when

[0112]

[0113] S403: Calculate the mutual information

[0114]

[0115] where T nbma represents the element in the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T, and T nbuv represents the element in the [(E + 1)n + b + 1]-th row and [(E + 1)u + v + 1]-th column of the probability transition matrix T, and p uv represents the [(E + 1)u + v + 1]-th element in the vector

[0116] In step S4, the cost function ​The calculation method is as follows:

[0117] S405: According to step S4, the cost function has the following specific form:

[0118]

[0119] where Π is a positive integer not greater than CD / c, CD is the critical dimension of the target circuit layout , c represents the side length of each pixel on the mask, and η 1 , η 2 and η 3 are the weight coefficients corresponding to the three penalty functions respectively, represents the two-norm, and max{·,·} represents the maximum operation.

[0120] Among them, the main function represents the mutual information;

[0121] and are the three penalty terms, corresponding to mathematical norms, imaging fidelity, and manufacturability respectively.

[0122] It should be noted that the value range of the independent variable of the cost function is limited to [0,1]. The domain can be relaxed through parameter transformation for iteration. The specific method is: let p ma =(1 + cosΘ ma ) / 2, where Θ ma ∈(-∞, +∞).

[0123] Thus, the cost function is transformed into

[0124] In addition, it should be noted that CD refers to the size of the narrowest part on the target circuit layout , which is a technical term commonly used in this field.

[0125] S5: Use the steepest descent method to solve the optimization problem to obtain the optimal mask probability distribution According to the optimal mask probability distribution the imaging accuracy limit of the computational lithography algorithm can be obtained.

[0126] In step S5, the specific calculation method of the theoretical limit of the imaging accuracy of the computational lithography algorithm is:

[0127] S501: Substitute the optimal mask probability distribution obtained in step S5 into the expression of the mutual information in formula (1), and the optimal mutual information can be calculated

[0128]

[0129] S502: According to the optimal mutual information the optimal macro-pixel side length c can be calculated * , where a macro-pixel is the smallest unit that can transmit 1 bit of information error-free in the lithography system channel, and the optimal macro-pixel side length can be expressed as:

[0130]

[0131] S503: Use PE as an evaluation index to measure the imaging fidelity of the lithography system, and its expression is:

[0132]

[0133] where N represents the total number of pixels on one side of the wafer image, (m, n) represents the pixel coordinates of the wafer image, represents the target circuit layout, and Z represents the actual wafer image. The theoretical limit of the imaging accuracy of the lithography algorithm can be represented by the minimum imaging error PE min PE min The relationship with the macro-pixel side length can be deduced as:

[0134]

[0135] where H t is the total perimeter of all the patterns in the target layout ; A t is the total area of all the patterns in the target layout ; mod{·,·} is the modulo operation. Therefore, according to the optimal macro-pixel side length c*, PE min can be obtained and used as the theoretical limit for calculating the imaging accuracy of the lithography algorithm.

[0136] It should be noted that in the lithography informatics model, the mutual information characterizes the efficiency of the distortion-free transmission of layout information in the channel. Physically, due to the bandwidth limitation of the lithography system, the information on the mask cannot be completely transmitted to the wafer surface. For the vector composed of K pixels on the mask, the average mutual information of each pixel is For the wafer image, each pixel contains log 2 2 = 1 bit of information. Therefore, in order to completely transmit 1 bit of information, at least pixels are required. Assuming that a single pixel is a square with side length c, a macro-pixel is defined as a square area on the imaging surface with side length .

[0137] When using a set of macro - pixels to cover the target circuit layout as much as possible, since the side lengths of the macro - pixels and the single pixels are inconsistent, there may be a deviation between the covered area and the target circuit layout. This deviation exactly reflects the lithographic imaging error caused by information transmission error. Based on this principle, by covering and comparing different macro - pixels with the target circuit layout, formula (25) can be obtained. According to formula (25), when the side length of the macro - pixel is an integer multiple of the side length of the single pixel and satisfies c * ≤CD, the macro - pixel can just coincide with the target circuit layout. Therefore, in order to minimize the imaging error PE, the side length of the macro - pixel should be made equal to an integer multiple of the single pixel as much as possible and satisfy c * ≤CD, that is

[0138] S6: Design a mask optimization algorithm for enhancing imaging fidelity based on the optimal mask probability distribution. During the mask optimization process, use the cost function to control the insertion of sub - resolution assist features. This cost function includes a main function and three penalty functions, which are used to evaluate the imaging fidelity, quantization error, complexity, and rationality of the mask probability distribution corresponding to the optimized mask respectively. Among them, the imaging fidelity means that the wafer image Z of the mask should be as close as possible to the target circuit layout The complexity and quantization error represent the wavelet penalty term and the quadratic penalty term respectively, and the rationality of the mask probability distribution means that the optimized mask probability distribution should be as close as possible to the optimal mask probability distribution

[0139] In step S6, the calculation method of the cost function is as follows:

[0140] S601: According to step S4, the specific form of the cost function is as follows:

[0141]

[0142] where is the main function of the second cost function, μ q R q , μ w R w , are the penalty functions corresponding to the quantization error, complexity, and rationality of the mask probability distribution respectively; μ q μ w μ p represent the weight coefficients of the three penalty functions respectively; R q represents the binary penalty term; R w represents the wavelet penalty term.

[0143] S7: According to the optimal mask probability distribution and the mask M, solve the optimization problem using the steepest descent method to obtain the optimized actual wafer image Z and the optimized mask M * which is obtained by adding sub-resolution assist features to M.

[0144] The implementation examples of the present invention are as follows:

[0145] The target circuit layout of the test mask is as shown in the appendix Figure 5 (a), and the appendix Figure 5 (b) shows the processing of the target layout using a typical computational lithography technology, Inverse Lithography Technology (ILT for short), to obtain the ILT mask of the target layout. The appendix Figure 5 (c) and the appendix Figure 5 (d) respectively show the wafer images of the target circuit layout and the ILT mask, and the imaging errors are PE = 1128 and PE = 56 respectively.

[0146] Perform statistical analysis on the test mask according to steps S1 to S5 to obtain the cost function and minimize the cost function using the steepest descent method to obtain the optimal probability distribution of the test mask The appendix Figure 6 shows the convergence curve of the optimized cost function and the mutual information optimization curve, and the appendix Figure 7 shows the comparison results between the optimal probability distribution of the test mask (appendix Figure 7 (a)) and the initial probability distribution (appendix Figure 7 (b)).

[0147] Through the optimal probability distribution of the test mask, the theoretical limit of the imaging accuracy that the ILT computational lithography technology can achieve for the test mask can be calculated. As shown in Table 1 below, the table also shows the optimal mutual information value corresponding to the theoretical limit of the imaging accuracy.

[0148] Table 1

[0149] Theoretical limit of imaging accuracy Optimal mutual information Test mask 26.18 3.8635

[0150] It can be seen from Table 1 that by using the system in this patent, the imaging accuracy limit of the lithography system that the ILT computational lithography technology can achieve can be calculated, and the mask can be optimized through steps S6 to S7 to improve the convergence accuracy of the existing ILT optimization algorithm, thereby further improving the imaging fidelity of the lithography system.

[0151] Example 2

[0152] An information - theory - based lithography imaging fidelity enhancement system, characterized by comprising a point spread module, a pixel statistics module, a probability distribution vector construction module, a first cost function construction module, a mask optimization module, a second cost function construction module, and a wafer image optimization module.

[0153] The point spread module is used to rasterize a given binary mask M and perform a point spread operation on each pixel point to obtain a vector composed of pixels covered by the point spread function on the mask M. Subsequently, use the typical lithography imaging model to simulate the mask M to obtain the wafer image Z, and also perform a point spread operation on each pixel point on the wafer image Z to obtain a vector composed of pixels covered by the point spread function on the wafer image Z.

[0154] The pixel statistics module is used to take the aggregation degree of pixels covered by the point spread function on the mask M and the wafer image Z as the pixel density PD; count the vector corresponding to each pixel point on the mask M. The number N of elements with pixel value 1 in the vector x and the pixel density PD x , count the vector corresponding to the corresponding pixel point on the wafer image Z. The number N of elements with pixel value 1 in the vector y and the pixel density PD y .

[0155] The probability distribution vector construction module is used to collect the statistical results of all pixel points. The probability of the event {N x =m, PD x =a} is p ma , the probability of the event {N y =n, PD y =b} is q nb ; construct a vector representing the probability distribution of the mask M according to the probability p ma construct a vector representing the probability distribution of the wafer image Z according to the probability q According to the probability q nb construct a vector representing the probability distribution of the wafer image Z At the same time, the vector and the vector satisfy T is the probability transition matrix between the vector and the vector .

[0156] The first cost function construction module is used to construct the first cost function

[0157] The mask optimization module is used to solve the optimization problem using the steepest descent method to obtain the optimal mask probability distribution Further obtain the imaging accuracy limit of the computational lithography algorithm.

[0158] The second cost function construction module, based on the optimal mask probability distribution Design a mask optimization algorithm for enhancing imaging fidelity. During the mask optimization process, construct a second cost function to control the insertion of sub-resolution assist features.

[0159] The wafer image optimization module, according to the optimal mask probability distribution and the mask M, solve the optimization problem using the steepest descent method to obtain the optimized actual wafer image Z and the optimized mask M * which is obtained by adding sub-resolution assist features to M.

[0160] In this embodiment, in the pixel statistics module, the specific method for determining the pixel density PD is as follows:

[0161] S201: For the coverage area C determined by the point spread function p , there are a total of K pixels; randomly generate S n regions containing n one-valued pixels in C p , n < K, where the distribution of all one-valued pixels in each C p region is random and unique.

[0162] S202: For all one-valued pixels in each C p , use the k-means clustering algorithm to determine their cluster centers, k = 1, calculate the Euclidean distance d from all one-valued pixels to the cluster center, then the average distance from each one-valued pixel to the cluster center is Arrange all the d n obtained from the S p regions of C aver in ascending order to obtain the sequence D:

[0163]

[0164] S203: Divide the sequence D into E + 1 intervals, corresponding to pixel density PD = 0 to PD = E from left to right; the division rule is: from left to right, the number of elements in each interval increases geometrically with a ratio of 2, that is, the interval with PD = 0 contains S n / 2 E elements, the interval with PD = 1 contains S n / 2 E-1 elements, and so on, the interval with PD = E contains S n / 2 elements; record the first element in each interval and the last element of the sequence D, a total of E + 2 elements, to form a new sequence D':

[0165] D′ = {d a ′ ver1 , d a ′ ver2 ,..., d a ′ ver(E+2)}

[0166] S204: Calculate the PD of any given C containing n one - valued pixels using the sequence D′. The calculation method is as follows: According to the second step, calculate the d of the given C p region, and construct a mapping G based on the sequence D′ p : aver PD = G n :

[0167] PD = G n (d aver ) = g - 1, d a ′ verg ≤ d aver < d a ′ ver(g+1) .

[0168] In this embodiment, in the probability distribution vector construction module, the method for obtaining the probability transition matrix T between the vector and the vector is as follows:

[0169] S301: The probability distribution vectors of the mask and the wafer image are respectively represented as vectors vector

[0170] The probability transition matrix T is a square matrix with (K + 1)×(E + 1) rows and (K + 1)×(E + 1) columns.

[0171] S302: Given the lithography system parameters and process parameters, select several groups of training masks M different from the initial mask M # = {M 1 , M 2 , M 3 ,...} and their wafer images Z # = {Z 1 , Z 2 , Z 3 ,...}; Through steps S1 and S2, count the number of one - valued pixels N # of each pixel corresponding point spread function coverage region C p for all masks M x and the pixel density PD, and obtain the occurrence frequency v of the event {N x = m, PD x = a}. Similarly, for the wafer image group Z # , the event {N y= n, PD y The occurrence frequency of {N

[0172] S303: Based on more than a set number of training samples, it is considered that for the event {N x = m, PD x = a}, under the condition of its occurrence, the occurrence probability of the event {N y = n, PD y = b} is v / u; this probability is used as the value in the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T. After traversing all N x and N y and PD x and PD y the entire probability transition matrix T is obtained.

[0173] In this embodiment, the first cost function includes one main function and three penalty functions, which are respectively used to evaluate the mutual information, mathematical specification, imaging fidelity, and manufacturability corresponding to the optimized mask probability distribution ; among them, the mutual information is the mutual information between the mask layout and the wafer imaging, representing the information transmission efficiency in the lithography system; the mathematical specification means that the optimized mask probability distribution should satisfy that the sum of elements is 1; the imaging fidelity represents that the wafer image probability distribution corresponding to the optimized mask probability distribution is closest to the probability distribution of the target circuit layout The manufacturability represents that the pixel density corresponding to the optimized mask probability distribution is the densest and there are no isolated pixel points.

[0174] The mutual information is the mutual information between the mask layout and the wafer imaging. Specifically, the calculation method of the mutual information between the mask layout and the wafer imaging is as follows:

[0175] S401: Calculate the information entropy of the vector

[0176]

[0177] where P r {·} represents probability, represents the combination number of taking n elements from K elements.

[0178] S402: Calculate the conditional entropy of the vector with respect to the vector

[0179]

[0180] S403: Calculate the mutual information

[0181]

[0182] where, T nbma represents the element at the [(E + 1)n + b + 1]-th row and [(E + 1)m + a + 1]-th column of the probability transition matrix T, and T nbuv represents the element at the [(E + 1)n + b + 1]-th row and [(E + 1)u + v + 1]-th column of the probability transition matrix T, and p uv represents the ((E + 1)u + v + 1)-th element in the vector.

[0183] The second cost function is used to control the insertion of sub-resolution assist features. This cost function includes a main function and three penalty functions, which are respectively used to evaluate the imaging fidelity, quantization error, complexity, and the rationality of the mask probability distribution corresponding to the optimized mask; where, the imaging fidelity represents the case where the wafer image Z of the mask is closest to the target circuit layout ; the complexity and quantization error respectively represent the wavelet penalty term and the quadratic penalty term, and the rationality of the mask probability distribution represents the case where the optimized mask probability distribution is closest to the optimal mask probability distribution .

[0184] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for enhancing the fidelity of lithography imaging based on information theory, characterized in that: The steps include: S1: For a given binary mask M, rasterize it and perform a point diffusion operation on each pixel to obtain a vector consisting of pixels covered by the point diffusion function on the mask M. Then, the typical photolithography imaging model is used to simulate the mask M to obtain the wafer image Z. The point diffusion operation is also performed on each pixel point on the wafer image Z to obtain the vector composed of pixels covered by the point diffusion function on the wafer image Z. S2: For the pixels covered by the point spread function on the mask M and the wafer image Z, the pixel density PD is taken as the degree of pixel aggregation; the vector corresponding to each pixel point on the mask M is counted The number of elements with pixel value 1 in N x And pixel density PD x , count the vectors corresponding to the corresponding pixel points on the wafer image Z The number of elements with pixel value 1 in N y And pixel density PD y ; S3: Collect the statistical results of all pixels, event {N x =m,PD x =a} has a probability p ma , event {N y =n,PD y =b} has a probability of q nb ; According to the probability p ma Construct a vector representing the probability distribution of mask M According to the probability q nb Construct a vector representing the probability distribution of wafer image Z At the same time, the vector and vector satisfy T is a vector and vector The probability transfer matrix between S4: Construct the first cost function S5: Solving optimization problems using the steepest descent method Get the optimal mask probability distribution Further obtain the imaging accuracy limit of computational lithography algorithms; S6: Based on the optimal mask probability distribution Design a mask optimization algorithm with enhanced imaging fidelity and construct a second cost function during mask optimization To control the insertion of sub-resolution auxiliary graphics; S7: Based on the optimal mask probability distribution And mask M, use the steepest descent method to solve the optimization problem Get the optimized actual wafer image Z and optimized mask M * Obtained by adding sub-resolution auxiliary graphics to M.

2. The method for enhancing the fidelity of lithography imaging based on information theory as claimed in claim 1, characterized in that: The specific method for determining the pixel density PD is: S201: Coverage area C determined by point spread function p , there are K pixels in total; randomly generate S n C contains n 1-valued pixels p Region, n<K, where each C p The distribution of all 1-value pixels in the region is random and unique; S202: For each C p All 1-value pixels in the cluster are clustered using the k-means clustering algorithm to determine their cluster centers, k = 1, and the Euclidean distance d from all 1-value pixels to the cluster center is calculated. The average distance from each 1-value pixel to the cluster center is S n C p All d found in the area aver Arrange in ascending order to get the sequence D: S203: Divide the sequence D into E+1 intervals, corresponding to pixel densities PD=0 to PD=E from left to right; the division rule is: from left to right, the number of elements in each interval increases geometrically, the ratio is 2 times, that is, the interval PD=0 contains S n / 2 E elements, the interval of PD=1 contains S n / 2 E-1 elements, and so on, the interval PD=E contains S n / 2 elements; record the first element in each interval and the last element of sequence D, a total of E+2 elements, to form a new sequence D′: D′={d a ′ ver1 ,d a ′ ver2 ,...,d a ′ ver(E+2) } S204: Use the sequence D′ to calculate any given C containing n 1-valued pixels p The PD is calculated by calculating the given C in the second step. p The area of ​​d aver , construct the mapping G based on the sequence D′ n : PD=G n (d aver )=g-1,d a ′ verg ≤d aver <d a ′ ver(g+1) 。 3. The method for enhancing the fidelity of lithography imaging based on information theory as claimed in claim 1, characterized in that: vector and vector The method for obtaining the probability transfer matrix T between is: S301: The probability distribution vectors of the mask and wafer image are respectively represented as vectors vector The probability transfer matrix T is a square matrix with (K+1)×(E+1) rows and (K+1)×(E+1) columns; S302: Given the lithography system parameters and process parameters, select several sets of training masks M different from the initial mask M # ={M1,M2,M3,...} and its wafer image Z # ={Z1, Z2, Z3, ...}; Statistics M through steps S1 and S2 # Each pixel of all masks corresponds to the point spread function covering area C p The number of 1-valued pixels N x and pixel density PD, we get event {N x =m,PD x =a} has a frequency of occurrence v, and similarly, for the wafer image group Z # , event {N y =n,PD y =b} has an occurrence frequency of u; S303: Based on the training samples exceeding the set number, it is considered that the event {N x =m,PD x = a} occurs, the event {N y =n,PD y = b} is v / u; take this probability as the value of the [(E+1)n+b+1]th row and [(E+1)m+a+1]th column of the probability transfer matrix T, and traverse all N x 、N y , PD x , PD y Then the entire probability transfer matrix T is obtained.

4. The method for enhancing the fidelity of lithography imaging based on information theory as claimed in claim 1, characterized in that: The first cost function Contains a main function and three penalty functions, which are used to evaluate the optimized mask probability distribution. The corresponding mutual information, mathematical specification, imaging fidelity and manufacturability; where the mutual information is the mutual information between the mask layout and the wafer imaging, representing the information transmission efficiency in the lithography system; the mathematical specification represents the optimized mask probability distribution The sum of the elements should be 1; the imaging fidelity represents the optimized mask probability distribution Corresponding wafer image probability distribution Probability distribution of the circuit layout closest to the target Manufacturability represents the optimized mask probability distribution The corresponding pixel density is the densest and there are no isolated pixels.

5. The method for enhancing the fidelity of lithography imaging based on information theory as claimed in claim 4, characterized in that: The mutual information is the mutual information between the mask layout and the wafer imaging. Specifically, the mutual information between the mask layout and the wafer imaging The calculation method is: S401: Calculate vector Information entropy Among them, P r {·} represents probability, It represents the number of combinations of n elements from K elements; S402: Calculate known vectors When about vector The conditional entropy S403: Calculate mutual information Among them, T nbma represents the element in the [(E+1)n+b+1]th row and [(E+1)m+a+1]th column of the probability transfer matrix T, T nbuv represents the element of the [(E+1)n+b+1]th row and [(E+1)u+v+1]th column of the probability transfer matrix T, p uv Representation vector The [(E+1)u+v+1]th element in .

6. The method for enhancing the fidelity of lithography imaging based on information theory as claimed in claim 1, characterized in that: The second cost function Used to control the insertion of sub-resolution auxiliary graphics, the cost function includes a main function and three penalty functions, which are used to evaluate the imaging fidelity, quantization error, complexity and rationality of the mask probability distribution corresponding to the optimized mask; among them, the imaging fidelity represents the wafer image Z of the mask closest to the target circuit layout The complexity and quantization error represent the wavelet penalty term and the quadratic penalty term respectively. The rationality of the mask probability distribution represents that the optimized mask probability distribution is closest to the optimal mask probability distribution. situation.

7. A lithography imaging fidelity enhancement system based on information theory, characterized in that: It includes a point diffusion module, a pixel statistics module, a probability distribution vector construction module, a first cost function construction module, a mask optimization module, a second cost function construction module and a wafer image optimization module; The point diffusion module is used to rasterize a given binary mask M and perform a point diffusion operation on each pixel to obtain a vector consisting of pixels covered by the point diffusion function on the mask M. Then, the typical photolithography imaging model is used to simulate the mask M to obtain the wafer image Z. The point diffusion operation is also performed on each pixel point on the wafer image Z to obtain the vector composed of pixels covered by the point diffusion function on the wafer image Z. The pixel statistics module is used to count the pixels covered by the point spread function on the mask M and the wafer image Z, taking the degree of pixel aggregation as the pixel density PD; and to count the vectors corresponding to each pixel point on the mask M. The number of elements with pixel value 1 in N x And pixel density PD x , count the vectors corresponding to the corresponding pixel points on the wafer image Z The number of elements with pixel value 1 in N y And pixel density PD y ; The probability distribution vector building module is used to collect the statistical results of all pixels, event {N x =m,PD x =a} has a probability p ma , event {N y =n,PD y =b} has a probability of q nb ; According to the probability p ma Construct a vector representing the probability distribution of mask M According to the probability q nb Construct a vector representing the probability distribution of wafer image Z At the same time, the vector and vector satisfy T is a vector and vector The probability transfer matrix between The first cost function building module is used to build a first cost function The mask optimization module is used to solve the optimization problem using the steepest descent method Get the optimal mask probability distribution Further obtain the imaging accuracy limit of computational lithography algorithms; The second cost function construction module is based on the optimal mask probability distribution Design a mask optimization algorithm with enhanced imaging fidelity and construct a second cost function during mask optimization To control the insertion of sub-resolution auxiliary graphics; The wafer image optimization module is based on the optimal mask probability distribution And mask M, use the steepest descent method to solve the optimization problem Get the optimized actual wafer image Z and optimized mask M * Obtained by adding sub-resolution auxiliary graphics to M.

8. The information theory-based lithography imaging fidelity enhancement system according to claim 7, characterized in that: In the pixel statistics module, the specific method for determining the pixel density PD is: S201: Coverage area C determined by point spread function p , there are K pixels in total; randomly generate S n C contains n 1-valued pixels p Region, n<K, where each C p The distribution of all 1-value pixels in the region is random and unique; S202: For each C p All 1-value pixels in the cluster are clustered using the k-means clustering algorithm to determine their cluster centers, k = 1, and the Euclidean distance d from all 1-value pixels to the cluster center is calculated. The average distance from each 1-value pixel to the cluster center is S n C p All d found in the area aver Arrange in ascending order to get the sequence D: S203: Divide the sequence D into E+1 intervals, corresponding to pixel densities PD=0 to PD=E from left to right; the division rule is: from left to right, the number of elements in each interval increases geometrically, the ratio is 2 times, that is, the interval PD=0 contains S n / 2 E elements, the interval of PD=1 contains S n / 2 E-1 elements, and so on, the interval PD=E contains S n / 2 elements; record the first element in each interval and the last element of sequence D, a total of E+2 elements, to form a new sequence D′: D′={d a ′ ver1 ,d a ′ ver2 ,...,d a ′ ver(E+2) } S204: Use the sequence D′ to calculate any given C containing n 1-valued pixels p The PD is calculated by calculating the given C in the second step. p The area of ​​d aver , construct the mapping G based on the sequence D′ n : PD=G n (d aver )=g-1,d a ′ verg ≤d aver <d a ′ ver(g+1) 。 9. The information theory-based lithography imaging fidelity enhancement system according to claim 7, characterized in that: In the probability distribution vector building module, the vector and vector The method for obtaining the probability transfer matrix T between is: S301: The probability distribution vectors of the mask and wafer image are respectively represented as vectors vector The probability transfer matrix T is a square matrix with (K+1)×(E+1) rows and (K+1)×(E+1) columns; S302: Given the lithography system parameters and process parameters, select several sets of training masks M different from the initial mask M # ={M1,M2,M3,...} and its wafer image Z # ={Z1, Z2, Z3, ...}; Statistics M through steps S1 and S2 # Each pixel of all masks corresponds to the point spread function covering area C p The number of 1-valued pixels N x and pixel density PD, we get event {N x =m,PD x =a} has a frequency of occurrence v, and similarly, for the wafer image group Z # , event {N y =n,PD y =b} has an occurrence frequency of u; S303: Based on the training samples exceeding the set number, it is considered that the event {N x =m,PD x = a} occurs, the event {N y =n,PD y = b} is v / u; take this probability as the value of the [(E+1)n+b+1]th row and [(E+1)m+a+1]th column of the probability transfer matrix T, and traverse all N x 、N y , PD x , PD y Then the entire probability transfer matrix T is obtained.

10. The method for enhancing the fidelity of lithography imaging based on information theory according to claim 7, characterized in that: The first cost function Contains a main function and three penalty functions, which are used to evaluate the optimized mask probability distribution. The corresponding mutual information, mathematical specification, imaging fidelity and manufacturability; where the mutual information is the mutual information between the mask layout and the wafer imaging, representing the information transmission efficiency in the lithography system; the mathematical specification represents the optimized mask probability distribution The sum of the elements should be 1; the imaging fidelity represents the optimized mask probability distribution Corresponding wafer image probability distribution Probability distribution of the circuit layout closest to the target Manufacturability represents the optimized mask probability distribution The corresponding pixel density is the densest and there are no isolated pixels; The mutual information is the mutual information between the mask layout and the wafer imaging. Specifically, the mutual information between the mask layout and the wafer imaging The calculation method is: S401: Calculate vector Information entropy Among them, P r {·} represents probability, It represents the number of combinations of n elements from K elements; S402: Calculate known vectors When about vector The conditional entropy S403: Calculate mutual information Among them, T nbma represents the element in the [(E+1)n+b+1]th row and [(E+1)m+a+1]th column of the probability transfer matrix T, T nbuv represents the element of the [(E+1)n+b+1]th row and [(E+1)u+v+1]th column of the probability transfer matrix T, p uv Representation vector The [(E+1)u+v+1]th element in ; The second cost function Used to control the insertion of sub-resolution auxiliary graphics, the cost function includes a main function and three penalty functions, which are used to evaluate the imaging fidelity, quantization error, complexity and rationality of the mask probability distribution corresponding to the optimized mask; among them, the imaging fidelity represents the wafer image Z of the mask closest to the target circuit layout The complexity and quantization error represent the wavelet penalty term and the quadratic penalty term respectively. The rationality of the mask probability distribution represents that the optimized mask probability distribution is closest to the optimal mask probability distribution. situation.

Images