Method, device and equipment for determining dose distribution of electron beam lithography and storage medium

Abstract

The invention provides an electron beam lithography dose distribution determination method and device, equipment and a storage medium, and belongs to the field of computer technology and semiconductor manufacturing. According to the method, the first dose distribution under the low resolution is iteratively updated, and due to the fact that the number of elements included in the first dose distribution is small, the data calculation amount of each updating process is small, and then the calculation time is shortened. After the optimal first dose distribution under the low resolution is obtained, the number of elements contained in the first dose distribution is increased based on the high resolution, and the second dose distribution is obtained, so that the second dose distribution under the high resolution has a good initial value. On the basis, the optimal second dose distribution under the high resolution can be obtained by carrying out iteration updating for a few times, namely, the number of iteration updating times under the high resolution is reduced, and then the calculation time consumption is shortened. Therefore, according to the method, the overall calculation time for determining the dose distribution is shortened, the efficiency is improved, and the calculation cost is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer technology and semiconductor manufacturing, and particularly relates to a method and device for determining an electron beam lithography dose distribution, and a storage medium. BACKGROUND

[0002] With the increasing demand for integrated circuit performance, the feature size of integrated circuits continues to shrink and the number of transistors increases, resulting in smaller and more densely packed patterns on the mask. Therefore, during the manufacture of the mask, the backscattering effect of the electron beam on the photoresist is obvious, causing overexposure in the non-exposed area, which seriously affects the manufacturing accuracy of the mask. The mask refers to one of the key components used to transfer circuit patterns in integrated circuit manufacturing, and the transmittance of the circuit pattern area and the other areas except the circuit pattern area included in the mask is different.

[0003] During the manufacture of the mask, a target mask image is designed and drawn, the target mask image includes a circuit pattern area and other areas except the circuit pattern area, and the wafer with photoresist is exposed to an electron beam based on the target mask image, so that the photoresist in the circuit pattern area of the wafer undergoes a chemical reaction. Then, the wafer is developed, etched, and the like, and finally the mask is obtained. Before the wafer is exposed to the electron beam, the electron beam dose distribution is optimized using an iterative approximation method. By analyzing and deducing various physical effects during the electron beam exposure process, the electron beam dose distribution is iteratively optimized, so that the electron beam dose distribution gradually approaches the optimal electron beam dose distribution. During the optimization of the electron beam dose distribution, the backscattering effect of the electron beam on the photoresist is minimized as much as possible.

[0004] In the above manner, when determining the electron beam dose distribution, multiple iterations of calculation are required, which can result in a long time consumption, and thus the efficiency of determining the electron beam dose distribution is low. SUMMARY

[0005] Embodiments of the present application provide a method, device, and equipment for determining an electron beam lithography dose distribution, and a storage medium, which shortens the overall calculation time for determining the dose distribution, improves the efficiency, and reduces the calculation cost. The technical solutions provided by embodiments of the present application are as follows:

[0006] According to an aspect of an embodiment of the present application, a method for determining an electron beam lithography dose distribution is provided, and the method comprises:

[0007] determining a first predicted imaging image based on a first dose distribution of electron beam lithography, the first predicted imaging image being an image obtained by simulating an electron beam lithography process based on the first dose distribution;

[0008] update the first dose distribution iteratively based on a difference between the first predicted imaging image and a first target imaging image, wherein the first target imaging image has a first resolution, and wherein the first dose distribution is a matrix including a plurality of elements, and each element of the first dose distribution corresponds to a pixel in the first target imaging image;

[0009] increase a number of elements included in the updated first dose distribution based on a second resolution to obtain a second dose distribution, wherein the second resolution is greater than the first resolution;

[0010] determine a second predicted imaging image based on the second dose distribution, wherein the second predicted imaging image is an image obtained by simulating an e-beam lithography process based on the second dose distribution;

[0011] update the second dose distribution iteratively based on a difference between the second predicted imaging image and a second target imaging image, wherein the second target imaging image has the second resolution.

[0012] According to another aspect of the embodiments of the present application, there is provided an apparatus for determining an e-beam lithography dose distribution, the apparatus comprising:

[0013] an image determining module configured to determine a first predicted imaging image based on a first dose distribution of e-beam lithography, wherein the first predicted imaging image is an image obtained by simulating an e-beam lithography process based on the first dose distribution;

[0014] a dose updating module configured to update the first dose distribution iteratively based on a difference between the first predicted imaging image and a first target imaging image, wherein the first target imaging image has a first resolution, and wherein the first dose distribution is a matrix including a plurality of elements, and each element of the first dose distribution corresponds to a pixel in the first target imaging image;

[0015] an element increasing module configured to increase a number of elements included in the updated first dose distribution based on a second resolution to obtain a second dose distribution, wherein the second resolution is greater than the first resolution;

[0016] the image determining module is further configured to determine a second predicted imaging image based on the second dose distribution, wherein the second predicted imaging image is an image obtained by simulating an e-beam lithography process based on the second dose distribution;

[0017] The dose updating module is further configured to iteratively update the second dose distribution based on a difference between the second predicted imaging image and a second target imaging image, to obtain an updated second dose distribution, wherein the second target imaging image has the second resolution.

[0018] In another aspect, a computer device is provided, which includes a processor and a memory, the memory being configured to store a computer program, the computer program being loaded and executed by the processor to implement the method for determining the dose distribution of electron beam lithography in the embodiments of the present application.

[0019] In another aspect, a computer readable storage medium is provided, which stores a computer program, the computer program being loaded and executed by a processor to implement the method for determining the dose distribution of electron beam lithography in the embodiments of the present application.

[0020] In another aspect, a computer program product is provided, which includes a computer program stored in a computer readable storage medium, a processor of a computer device reading the computer program from the computer readable storage medium, and the processor executing the computer program to enable the computer device to perform the method for determining the dose distribution of electron beam lithography according to any of the implementation manners described above.

[0021] The technical solutions provided in the embodiments of the present application have at least the following beneficial effects:

[0022] The method first iteratively updates the first dose distribution at a low resolution. Since the first dose distribution includes a small number of elements, the data calculation amount of each updating process is small, and thus the calculation time is shortened. After obtaining the first dose distribution at the low resolution, the number of elements included in the first dose distribution is increased based on a high resolution to obtain a second dose distribution. In this way, the second dose distribution at the high resolution has a good initial value, and a small number of iterative updates can obtain the second dose distribution at the high resolution, that is, the number of iterative updates at the high resolution is reduced, and thus the calculation time is shortened. Therefore, the method shortens the overall calculation time of determining the dose distribution, improves the efficiency, and reduces the calculation cost. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is a schematic diagram of a scheme implementation environment provided by an embodiment of the present application;

[0024] Figure 2 is a schematic diagram of a scheme implementation environment provided by another embodiment of the present application;

[0025] Figure 3is a flowchart of a method for determining an e-beam lithography dose distribution provided by an embodiment of the present application;

[0026] Figure 4 is a flowchart of a method for determining an e-beam lithography dose distribution provided by another embodiment of the present application;

[0027] Figure 5 is a comparative effect diagram provided by an embodiment of the present application;

[0028] Figure 6 is a flowchart of updating a first dose distribution provided by an embodiment of the present application;

[0029] Figure 7 is a block diagram of a device for determining an e-beam lithography dose distribution provided by an embodiment of the present application;

[0030] Figure 8 is a structural block diagram of a computer device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0032] Reference is made to Figure 1 which shows a schematic diagram of a scheme implementation environment provided by an exemplary embodiment of the present application. The scheme implementation environment can include a computer device 10 and an e-beam lithography device 20.

[0033] The computer device 10 is an electronic device with data calculation, processing and storage functions. The computer device can be a terminal device or a server. The computer device 10 can include but is not limited to electronic devices such as mobile phones, computers, and automated control systems. Exemplarily, the server mentioned above can be a standalone physical server, a server cluster or a distributed system composed of multiple physical servers, a cloud server providing cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms, etc. basic cloud computing services, but is not limited thereto. The computer device 10 is used to determine the dose distribution of e-beam lithography for manufacturing a mask.

[0034] Electron beam lithography equipment 20 is a device that uses an electron beam to expose photoresist to achieve pattern writing. In this application, electron beam lithography equipment 20 is used to manufacture a photomask. Electron beam lithography equipment 20 generates an electron beam based on the dose distribution of electron beam lithography determined by computer device 10, and controls the movement of the electron beam on the substrate surface based on the target imaging image to gradually form the desired target pattern. A photomask refers to a pattern master used in semiconductor manufacturing for selective exposure during the photolithography process. A substrate is a material used to support and carry the target pattern on the photomask. Optionally, the substrate has properties such as high transparency, low coefficient of thermal expansion, and high tensile strength, and may be, but is not limited to, any of the following materials: quartz, glass, and resin, etc. Optionally, the substrate may also include one or more thin films.

[0035] A thin film refers to a functional material covering the surface of a photomask substrate. For example, the substrate surface of a photomask may include one or more of the following thin films: photoresist film, opaque layer, anti-reflective coating, hard mask layer, etc., and may also be thin films with other functions; this application does not limit this. The photoresist layer is a photosensitive material covering the substrate of the photomask, used to form a target pattern on the substrate during the photomask manufacturing process. The opaque layer is used to block some light during the photolithography process for manufacturing integrated circuits, thereby forming a circuit pattern on the substrate used for manufacturing integrated circuits. The opaque layer can be formed on the substrate of the photomask using chromium, other metals, or metal alloys. The anti-reflective coating is used to reduce or eliminate light reflection on the photomask during the photolithography process for manufacturing integrated circuits, thereby improving the contrast and resolution of the circuit pattern on the substrate used for manufacturing integrated circuits. The anti-reflective coating can be formed on the substrate of the photomask using high refractive index materials such as tantalum oxide or silicon nitride. The hard mask layer is used to protect the accuracy of the target pattern on the substrate of the photomask during subsequent etching or processing. Hard mask layers can be generated on the substrate of the mask using etching-resistant materials such as titanium nitride and tantalum oxide.

[0036] For example, such as Figure 1 As shown, the target imaging image 30 is input into the computer device 10, which determines the dose distribution for electron beam lithography based on the target imaging image 30. The electron beam lithography equipment 20 generates an electron beam 21 according to the dose distribution and controls the generated electron beam 21 to move on the substrate 22 used to manufacture the photomask. The photoresist on the substrate 22 exposed by the electron beam 21 undergoes a chemical reaction, changing its solubility. Finally, the substrate 22 is subjected to processes such as development, etching, and metal deposition, and the resulting substrate 22 is the photomask 40.

[0037] The computer device 10 and the electron beam lithography device 20 can communicate with each other via a network. This network can be a wired network or a wireless network.

[0038] Referring to Figure 2 , a schematic diagram of an implementation environment of a method for determining an electron beam lithography dose distribution is shown. The implementation environment can include a computer device 10. The computer device 10 can be a terminal device or a server.

[0039] Exemplarily, as Figure 2 shown, a first target imaging image 31 of a first resolution is input into the computer device 10, and the computer device 10 determines a first dose distribution 32 of electron beam lithography. The computer device 10 simulates an electron beam lithography process based on the first dose distribution 32 to obtain a first predicted imaging image 33, and iteratively updates the first dose distribution 32 based on a difference between the first predicted imaging image 33 and the first target imaging image 31. Based on a second resolution greater than the first resolution, the number of elements contained in the updated first dose distribution 32 is increased to obtain a second dose distribution 34. The computer device 10 simulates an electron beam lithography process based on the second dose distribution 34 to obtain a second predicted imaging image 35, and iteratively updates the second dose distribution 34 based on a difference between the second predicted imaging image 35 and a second target imaging image of the second resolution to obtain an updated second dose distribution 34. An electron beam lithography device 20 is used to perform lithography according to the updated second dose distribution 34 to obtain a mask 40.

[0040] Referring to Figure 3 , a flowchart of a method for determining an electron beam lithography dose distribution is shown. The execution subject of each step of the method can be a computer device, and the method includes at least one of the following steps (310-350).

[0041] Step 310, determining a first predicted imaging image based on a first dose distribution of electron beam lithography, the first predicted imaging image being an image obtained by simulating an electron beam lithography process based on the first dose distribution.

[0042] In the embodiments of the present application, the first dose distribution is a matrix including a plurality of elements, each element in the first dose distribution corresponding to a pixel in the first target imaging image, that is, the plurality of elements contained in the first dose distribution one-to-one correspond to the plurality of pixels in the first target imaging image. The value of each element is the electron beam dose on the corresponding pixel.

[0043] Exemplarily, the matrix includes M*N elements, and the first target imaging image includes M*N pixels, then the element in the i-th row and the j-th column of the matrix corresponds to the pixel in the i-th row and the j-th column of the first target imaging image. M, N, i and j are all positive integers.

[0044] In some embodiments, between performing step 310, a first target imaging image is obtained. Optionally, the first target imaging image is obtained by reducing the resolution of a second target imaging image. The second target imaging image is used to define a target pattern to be formed on a substrate. The resolution of the second target imaging image is a second resolution, and the resolution of the first target imaging image is a first resolution, wherein the second resolution is greater than the first resolution.

[0045] Optionally, the second target imaging image is down-sampled based on the first resolution to obtain the first target imaging image. In this embodiment, by down-sampling the original target imaging image (i.e., the second target imaging image) to obtain a low-resolution target imaging image (i.e., the first target imaging image), it is convenient to quickly convert to the high-resolution target imaging image for iterative calculation of the dose distribution after the iterative calculation of the dose distribution based on the low-resolution target imaging image, without introducing other resolution target imaging images. Moreover, by reducing the resolution of the original target imaging image first, and then performing iterative calculation of the dose distribution based on the low-resolution target imaging image, the amount of data for calculation is reduced, thereby shortening the calculation time. On this basis, iterative calculation of the dose distribution at high resolution can reduce the number of calculations, shorten the calculation time, and improve the calculation efficiency.

[0046] In some embodiments, the second target imaging image is obtained from a target mask file. The target mask file includes the second target imaging image, and the second target imaging image is used to define a target pattern to be formed on a substrate. Optionally, the target mask file also contains information of a mask pattern used in a photolithography or electron beam lithography process, for defining a target pattern etched on a substrate of the mask.

[0047] In some embodiments, the second target imaging image includes a target pattern region and a region other than the target pattern region. The target pattern region refers to a region in the second target imaging image that belongs to the target pattern. It can be understood that the second target imaging image only contains two types of pixels, namely, target pattern and non-target pattern.

[0048] In some embodiments, the second target imaging image is represented by binary data. For example, each numerical value represents a pixel on the target imaging image. For any pixel in the second target imaging image, if its corresponding numerical value is 1, it means that the pixel belongs to the target pattern region, and if its corresponding numerical value is 0, it means that the pixel belongs to the non-target pattern region. Similarly, 0 can also be used to represent the target pattern region, and 1 can be used to represent the non-target pattern region. Optionally, in other embodiments, other numerical values can also be used to represent the target pattern region and the non-target pattern region, which are not limited in the embodiments of the present application.

[0049] In some embodiments, the first dose distribution includes electron beam doses on a plurality of first grids, i.e., the first dose distribution contains a plurality of elements which are electron beam doses on the plurality of first grids. Each first grid corresponds to a pixel in the first target imaging image, i.e., the plurality of first grids one-to-one correspond to the plurality of pixels in the first target imaging image. The electron beam dose on each first grid is also the electron beam dose on the corresponding pixel. The size of each first grid is the size of the corresponding pixel. Further, each first grid is also the grid formed by the area of the corresponding pixel.

[0050] In some embodiments, the first dose distribution for electron beam lithography is initialized before step 310 is performed.

[0051] In some embodiments, the initialized first dose distribution is determined based on the first target imaging image. Wherein, the plurality of first grids which one-to-one correspond to the plurality of pixels in the first target imaging image are first determined based on the first resolution of the first target imaging image, and then the initialized first dose distribution is obtained by assigning an initialized value to each first grid. In the case that a first pixel in at least one pixel contained in the first target imaging image belongs to the target pattern region, the electron beam dose on the first grid corresponding to the first pixel in the initialized first dose distribution is a first value; in the case that the first pixel in at least one pixel contained in the first target imaging image does not belong to the target pattern region, the electron beam dose on the first grid corresponding to the first pixel in the initialized first dose distribution is a second value, and the second value is different from the first value.

[0052] The first pixel is any one of the at least one pixel contained in the first target imaging image. It can be understood that for each pixel contained in the first target imaging image, the electron beam dose on the corresponding first grid in the first dose distribution can be determined in the same way as the first pixel.

[0053] The first dose distribution is a matrix including a plurality of elements. The number of pixels contained in the first target imaging image is the same as the number of elements contained in the first dose distribution. The first value and the second value are preset values, which represent the initial values of the elements corresponding to the target pattern region and the non-target pattern region in the first dose distribution, respectively. Optionally, the first value is 1 and the second value is 0. Optionally, the first value and the second value are set by a relevant technical person according to requirements, and the embodiments of the present application do not limit this.

[0054] In the embodiments of the present application, the process of determining the first predicted imaging image based on the first dose distribution for electron beam lithography includes the following two implementation manners.

[0055] In the first implementation, a first predicted imaging image is obtained based on a first dose distribution using an electron beam lithography physical model. This model is constructed based on a point spread function and the dose distribution, with the point spread function describing the propagation of the electron beam. Further, an energy deposition density distribution is obtained based on the point spread function and the first dose distribution, indicating the energy deposition density of the electron beam at various locations on the photoresist. The first predicted imaging image is then obtained using an activation function based on this energy deposition density distribution.

[0056] The electron beam lithography physical model is a mathematical model used to describe the physical processes of electron beam propagation in the photoresist and substrate during the lithography process. An electron beam refers to a flowing beam composed of high-energy electrons. The physical processes may include at least one of the following: the interaction between the electron beam and the photoresist, electron beam scattering, energy deposition, and development processes, and may also include other physical processes related to electron beam propagation during the lithography process, which are not limited in this application. The interaction between the electron beam and the photoresist refers to the process in which the electron beam, after acceleration and focusing, bombards the photoresist with high energy, causing a chemical change in the exposed photoresist.

[0057] The physical processes associated with the interaction between the electron beam and the photoresist include elastic and inelastic scattering. Elastic scattering of electrons within the photoresist alters the direction of the electron beam propagation without significant energy loss. Inelastic scattering of electrons within the photoresist causes energy transfer between the atoms of the photoresist and excites secondary electrons, which participate in molecular reactions in the photoresist, such as chain breaking or cross-linking.

[0058] The physical processes related to electron beam scattering include forward scattering and backscattering. Forward scattering refers to the elastic scattering of electrons upon entering the photoresist by the atomic nuclei or electrons of the photoresist, causing them to deviate from their original propagation direction, but the electrons still propagate forward. Backscattering refers to the large-angle scattering of electrons after entering the substrate by interacting with the atoms in the substrate, causing some electrons to bounce back into the photoresist for propagation, resulting in a backscattering effect and uneven energy deposition distribution.

[0059] The energy deposition density distribution of the electron beam determines the intensity of the areas where the photoresist undergoes chemical reactions after exposure, affecting the shape and precision of the developed pattern. The development process refers to using a developer to reveal the exposed photoresist. The physical processes associated with development include the diffusion of the developer and the dissolution kinetics of the photoresist. In other words, the electron beam lithography physical model integrates multiple aspects such as the interaction between electrons and matter, electron energy deposition, chemical reactions, and the development process to simulate the process of fabricating a photomask on a substrate using an electron beam. The dose distribution in electron beam lithography refers to the energy distribution of the electron beam deposited on the photoresist on the substrate during the photolithography process of photomask fabrication.

[0060] The first predicted image was obtained by simulating the process of electron beam propagation and energy deposition on the photoresist and substrate using an electron beam lithography physical model and a first dose distribution of electron beam lithography.

[0061] The point spread function describes how the electron beam propagates through the photoresist and its distribution upon reaching the substrate. Because electrons interact with the photoresist or substrate during propagation, resulting in scattering, the effective range of a single electron on the substrate is not a single point, but rather a dispersed region. The point spread function describes the shape and intensity distribution of this dispersed region.

[0062] For example, the following point spread function P can be used:

[0063]

[0064] Where r is the distance between the field point and the source point, measured in nm (nanometers); α and β are the forward scattering coefficient and backscattering coefficient, respectively, measured in nm; η is the ratio of the energy deposition density of the forward scattering portion to the backscattering portion, dimensionless. The point spread function P(r) is used to describe the forward scattering and backscattering physical processes. Optionally, the parameters α, β, and η of the point spread function P(r) can be obtained through experimental calibration or through Monte Carlo simulation of the energy distribution of electrons in the photoresist; this embodiment of the application does not limit this. Optionally, by adjusting the parameters α, β, and η of the point spread function P(r), different point spread phenomena can be fitted and predicted.

[0065] In electron beam lithography, the energy deposition density distribution describes how the electron beam distributes its energy within the photoresist. In electron beam lithography, energy deposition occurs within the photoresist as the electron beam penetrates and interacts with it. The energy deposition density distribution determines the exposure level at different locations within the photoresist, thus affecting the final target pattern formed on the substrate.

[0066] The energy deposition density distribution is obtained by convolving the point spread function and the dose distribution. For example, based on the point spread function P and the dose distribution D, the energy deposition density distribution E can be expressed as:

[0067]

[0068] Wherein, E(r) i ) represents pixel r in the first target imaging image. i Energy deposition density at location, in eV / nm 2 (electron volts per square nanometer); point spread function P(r) i ,r jLet be a vector representation of the point spread function P(r), where r = |r| i -r j |;D(r j ) represents pixel r in the first target imaging image. j Exposure dose at location, in μC / cm 2 (microcoulombs per square centimeter); N is the number of pixels contained in the first target imaging image. Optionally, the value of each element in the energy deposition density distribution ranges from [0,10].

[0069] Activation functions are used to introduce non-linear characteristics, thereby mapping input values ​​from the input to the output. In some embodiments, the activation function is the Sigmoid function. The Sigmoid function maps input values ​​to the range between 0 and 1. Optionally, in other embodiments, the activation function may also be any of the following: ReLU (Rectified Linear Unit), Leaky ReLU, etc., or other activation functions; this application does not limit the specific activation function used.

[0070] For example, the energy deposition density E distribution is transformed using the Sigmoid function to obtain the first predicted imaging image M(x,y):

[0071]

[0072] Where, θ E and E th Using 100 and 0.5 respectively, θ E This refers to the slope parameter, used to control the steepness of M(x,y), E th Used to determine the center position of M(x,y), i.e., when E equals E th When E is greater than E, M(x,y) is 0.5. That is, when E is greater than E... th When M(x,y) takes values ​​in the range (0.5,1), and when E equals E th When M(x,y) takes the value of 0.5, and when E is less than E th When M(x,y) takes values ​​in the range [0,0.5), in this embodiment, the range of M(x,y) and θ... E and E th The values ​​of M(x,y) are only illustrative; in other embodiments, the range of values ​​for M(x,y) and θ are different. E and E th The value can also be set to other values, and this application embodiment does not limit this.

[0073] In the second implementation, a first predicted imaging image is obtained based on a first dose distribution using an image prediction model, which is a neural network model used to predict imaging images based on dose distribution.

[0074] The image prediction model takes a dose distribution as input and outputs an imaging image. The training samples for the image prediction model consist of sample pairs composed of dose distributions and imaging images. The training process of the image prediction model is as follows: Multiple sample pairs are acquired, each pair including the electron beam dose distribution and the corresponding target imaging image. The sample dose distributions from each sample pair are input into the image prediction model, which outputs a predicted imaging image. The gradient of the loss function between the predicted and target imaging images is determined with respect to the model parameters. Based on the mean gradient values ​​of multiple sample pairs, the image prediction model is iteratively trained to obtain the trained image prediction model. The mean gradient value of each sample pair is the mean of the gradient values ​​of at least two sample pairs included in the model.

[0075] In this embodiment of the application, by training a neural network model between dose distribution and imaging image, the corresponding imaging image can be obtained quickly based on the dose distribution, without having to go through multiple calculation steps in the electron lithography physical model to obtain the imaging image, thus shortening the calculation time and improving efficiency.

[0076] Step 320: Based on the difference between the first predicted imaging image and the first target imaging image, iteratively update the first dose distribution to obtain the updated first dose distribution, wherein the resolution of the first target imaging image is the first resolution, and the first dose distribution is a matrix containing multiple elements, each element in the first dose distribution corresponding to a pixel in the first target imaging image.

[0077] In this embodiment of the application, step 320 described above can be found in [reference needed]. Figure 6 The specific implementation examples are not described in detail here.

[0078] Step 330: Based on the second resolution, increase the number of elements contained in the updated first dose distribution to obtain a second dose distribution, where the second resolution is greater than the first resolution.

[0079] In some embodiments, the second resolution is also the resolution of the second target imaging image, which is used to define the target pattern to be formed on the substrate, i.e., the second resolution is the resolution of the final generated mask (imaging image).

[0080] In this embodiment, the second dose distribution is a matrix containing multiple elements. Each element in the second dose distribution corresponds to a pixel in the second target imaging image, meaning that the multiple elements in the second dose distribution correspond one-to-one with the multiple pixels in the second target imaging image. The value of each element is the electron beam dose at the corresponding pixel.

[0081] The resolution of the second target imaging image is the second resolution. Since the second resolution is greater than the first resolution, the number of elements contained in the second dose distribution is greater than the number of elements contained in the first dose distribution.

[0082] In some embodiments, the process of increasing the number of elements contained in the updated first dose distribution based on the second resolution to obtain the second dose distribution includes the following implementation: interpolating the updated first dose distribution based on the second resolution to obtain the second dose distribution.

[0083] The interpolation method can be any of the following: Lagrange interpolation, Newton interpolation, bicubic interpolation, triangular mesh interpolation, spline interpolation, nearest neighbor interpolation, bilinear interpolation, etc. In this embodiment, the second dose distribution is obtained by interpolating the first dose distribution, which not only increases the number of elements contained in the first dose distribution and improves the accuracy of the dose distribution, but also improves efficiency and convenience.

[0084] The second dose distribution includes electron beam doses on multiple second grids; that is, the multiple elements of the second dose distribution are electron beam doses on multiple second grids. Each second grid corresponds to a pixel in the second target imaging image, meaning that the multiple second grids correspond one-to-one with the multiple pixels in the second target imaging image. The electron beam dose on each second grid is also the electron beam dose on the corresponding pixel. The size of each second grid is the size of the corresponding pixel. Further, each second grid is also a grid formed by the region where its corresponding pixel is located.

[0085] In some embodiments, the process of interpolating the updated first dose distribution based on the second resolution to obtain the second dose distribution includes the following steps: determining a plurality of second grids corresponding one-to-one with a plurality of pixels on the second target imaging image based on the second resolution, wherein the size of the second grid is smaller than the size of the first grid and the number of second grids is greater than the number of first grids; obtaining the electron beam dose on the plurality of second grids based on the electron beam dose on the plurality of first grids; and obtaining the second dose distribution based on the electron beam dose on the plurality of second grids.

[0086] The second target image is the same size as the first target image, but has a different resolution, meaning it contains a different number and size of pixels. Multiple first grids form an image of the same size as the first target image, and multiple second grids form an image of the same size as the second target image. Optionally, based on the second resolution, a blank image of the same size as the images containing the multiple first grids is divided into multiple second grids, thus obtaining multiple second grids that correspond one-to-one with the multiple pixels on the second target image.

[0087] In this implementation, based on the second resolution, multiple second grids are determined that correspond one-to-one with multiple pixels in the second target imaging image, and the electron beam doses of the multiple second grids are obtained based on the electron beam doses of the multiple first grids. Thus, the obtained second dose distribution includes the electron beam dose on each pixel in the second target imaging image, which facilitates subsequent iterative calculation of the dose distribution at high resolution.

[0088] In some embodiments, the process of obtaining the electron beam dose on a plurality of second grids based on the electron beam dose on a plurality of first grids includes the following implementation: for each of the plurality of second grids, the electron beam dose on the first grid closest to the second grid is determined as the electron beam dose on the second grid.

[0089] In this embodiment, since the target imaging images corresponding to the multiple first grids and multiple second grids have the same size and correspond one-to-one with pixels, optionally, the positions of pixels in the first target imaging image and the second target imaging image are measured using the same coordinate system. The horizontal and vertical units of this coordinate system can be length units, such as nm. This allows determining the coordinate position of each pixel in the first target imaging image and the coordinate position of each pixel in the second target imaging image. Since multiple pixels in the first target imaging image correspond one-to-one with multiple first grids, the coordinate positions of multiple pixels in the first target imaging image can be determined as the coordinate positions of multiple first grids. Similarly, the coordinate positions of multiple pixels in the second target imaging image can be determined as the coordinate positions of multiple second grids.

[0090] Optionally, for each of the plurality of second grids, based on the coordinate position of the second grid and the positions of the plurality of first grids, the first grid closest to the second grid is determined, and the electron beam dose on the first grid is determined as the electron beam dose on the second grid.

[0091] In this embodiment, for each second grid, the electron beam dose of the nearest first grid is determined as its electron beam dose, reducing calculation steps and improving convenience and efficiency.

[0092] In other embodiments, for each second grid, at least two first grids that are closest to it can be identified, and the mean of the electron beam dose distributions on these at least two first grids can be determined as the electron beam dose distribution on the second grid. Alternatively, the weighted sum of the electron beam dose distributions on these at least two first grids can be determined as the electron beam dose distribution on the second grid. The weight of each first grid is negatively correlated with the distance between the first grid and the second grid; that is, the closer the distance, the greater the weight.

[0093] In some embodiments, the size (side length) of the first grid is an integer multiple of the size of the second grid, that is, the area of ​​the first grid is an exponential multiple of the area of ​​the second grid. The process described above, which interpolates the updated first dose distribution based on the second resolution to obtain the second dose distribution, further includes the following implementation: dividing each first grid into multiple second grids based on the second resolution; determining the electron beam dose on each of the first grids as the electron beam dose on each of the multiple second grids included in the first grid; and obtaining the second dose distribution based on the electron beam doses on the multiple divided second grids.

[0094] Since both the first and second grids are squares, a first grid can only be divided into multiple second grids if the size of the first grid is an integer multiple of the size of the second grid. For example, if the size of the first grid is nδ and the size of the second grid is δ, then one first grid can be divided into n squared second grids. If the size of the first grid is 4nm and the size of the second grid is 1nm, then one first grid can be divided into 16 second grids.

[0095] In this embodiment, the first grid is directly divided into multiple smaller grids, and the electron beam dose on the first grid is directly assigned to the smaller grids it includes, which improves efficiency while ensuring accuracy.

[0096] Step 340: Based on the second dose distribution, determine the second predicted imaging image, which is an image obtained by simulating the electron beam lithography process based on the second dose distribution.

[0097] In this embodiment, the process of determining the second predicted imaging image based on the second dose distribution is the same as the process of determining the first predicted imaging image based on the first dose distribution in step 310, and will not be repeated here.

[0098] Step 350: Based on the difference between the second predicted imaging image and the second target imaging image, the second dose distribution is iteratively updated to obtain the updated second dose distribution, and the resolution of the second target imaging image is the second resolution.

[0099] In this embodiment, the second dose distribution is iteratively updated based on the difference between the second predicted imaging image and the second target imaging image to obtain the updated second dose distribution. The process of iteratively updating the first dose distribution based on the difference between the first predicted imaging image and the first target imaging image in step 320 to obtain the updated first dose distribution is similar and will not be repeated here.

[0100] It should be noted that, since the second dose distribution contains more elements than the first dose distribution, each update process of the second dose distribution involves more data computation and takes longer than each update process of the first dose distribution.

[0101] In some embodiments, the computational complexity of dose optimization can be expressed by the following formula:

[0102]

[0103] in, Let δ represent the computational complexity; N represent the number of grids; δ represent the grid size; and A represent the area of ​​the dose calculation range, i.e., the area of ​​the target pattern region, where AlogA is a constant. The computational complexity is inversely proportional to the square of the grid size; if the grid size doubles, the computation time decreases by a factor of four. Therefore, the dose distribution calculation time is very low under a coarse grid (first grid). Building on this, only a few iterations are needed under a fine grid (second grid), significantly reducing the dose distribution calculation time under the fine grid, ultimately resulting in a significant reduction in overall computation time.

[0104] In some embodiments, the number of iterations for updating the second dose distribution is less than the number of iterations for updating the first dose distribution. Since the first dose distribution contains fewer elements, performing more iterations based on it results in less computation, less time consumption, and a more accurate first dose distribution, which in turn leads to a more accurate second dose distribution. Then, performing fewer iterations on the second dose distribution yields a more accurate second dose distribution, improving efficiency. Furthermore, since the second dose distribution contains more elements, reducing the number of iterations for updating it also reduces computation, saves time, and improves efficiency.

[0105] Optionally, the number of iterations for the second dose distribution is much smaller than the number of iterations for the first dose distribution. For example, the number of iterations for the first dose distribution is a preset multiple of the number of iterations for the second dose distribution, such as 3 times.

[0106] For example, please refer to Figure 4 , Figure 4This is a flowchart of a method for determining the dose distribution in electron beam lithography according to an embodiment of this application. Based on a low-resolution target imaging image, an optimal dose distribution at low resolution is obtained using an inverse electron beam lithography (IEBL) dose distribution optimization algorithm (i.e., steps 310-320). This dose distribution is then interpolated to obtain a high-resolution dose distribution. Finally, the optimal dose distribution at high resolution is obtained using an inverse electron beam lithography dose distribution optimization algorithm (i.e., steps 340-350).

[0107] For example, please refer to Figure 5 , Figure 5 This is a comparative illustration of the effects provided by one embodiment of this application. The first row shows the imaging image (photoresist image) and error diagram obtained through other methods, from left to right: target imaging image, dose distribution, photoresist image, and the difference between the target imaging image and the photoresist image. The second row shows the imaging image and error diagram obtained through the method provided by this embodiment. The comparison shows that the imaging error of the method provided by this embodiment is basically the same as that of other methods. However, the calculation time of the method provided by this embodiment is significantly shortened. Compared with other methods, the calculation time of this method is reduced by about 52%, significantly improving efficiency and reducing computational costs.

[0108] For example, the following imaging error EDE can be used:

[0109]

[0110] Where Length represents the sum of the perimeters of all polygons in the target pattern region of the second target imaging image. The second predicted imaging image M(x,y) represents the imaging image predicted based on the second dose distribution. t (x,y) represents the second target imaging image, and N3 represents the second target imaging image M. t The width of (x,y), i.e., the number of pixels in the horizontal direction, and N4 represents the second target imaging image M. t The height of (x,y) is the number of pixels in the vertical direction.

[0111] In this embodiment, reverse electron beam lithography dose optimization is first performed at a larger grid size to obtain a dose distribution at low resolution. This dose distribution is then interpolated onto a higher resolution grid for fine correction. This process, involving a small number of iterations, yields the optimal dose distribution at high resolution. Because the computational cost of the low-resolution grid is very low and the high-resolution grid requires fewer iterations, the final computation time is significantly reduced.

[0112] The method provided in this application first iteratively updates a first dose distribution at low resolution. Since the first dose distribution includes a small number of elements, the computational load for each update is small, thus shortening the computation time. After obtaining a better first dose distribution at low resolution, the number of elements in the first dose distribution is increased based on high resolution to obtain a second dose distribution. This provides a better initial value for the second dose distribution at high resolution. Based on this, a fewer iterative update is needed to obtain a better second dose distribution at high resolution, thus reducing the number of iterative updates at high resolution and shortening the computation time. Therefore, this method reduces the overall computation time for determining the dose distribution, improves efficiency, and reduces computational costs.

[0113] Please refer to Figure 6 This illustrates a flowchart of updating a first dose distribution according to an embodiment of this application. The execution entity of each step of the method may be a computer device, and the method may include at least one of the following sub-steps (321-325).

[0114] Step 321: Based on the difference between the first predicted imaging image and the first target imaging image, determine the first imaging loss function, which is used to characterize the difference between the first predicted imaging image and the first target imaging image.

[0115] Optionally, the first imaging loss function can be represented by any of the following: mean squared error (MSE), mean absolute error (MAE), cross-entropy loss function, etc. Other loss functions can also be used, but this application embodiment does not limit them.

[0116] In some embodiments, calculating the first imaging loss function means calculating the function value of the first imaging loss function under the first predicted imaging image and the first target imaging image.

[0117] In some embodiments, for a second pixel among at least one pixel in the first predicted imaging image, the difference between the second pixel and the corresponding pixel in the first target imaging image is calculated to obtain the error value of the second pixel; based on the error values ​​of each of the at least one pixel in the first predicted imaging image, the function value of the first imaging loss function is calculated. The second pixel refers to any one of the at least one pixels in the first predicted imaging image. By traversing each pixel in the first predicted imaging image, calculating its error value with the corresponding pixel in the first target imaging image, and then based on the error values ​​of all pixels in the first predicted imaging image, the function value of the first imaging loss function is finally calculated.

[0118] For example, based on the first predicted imaging image M(x,y) and the first target imaging image M t The first imaging loss function L, defined for (x, y), is expressed as follows:

[0119]

[0120] Where N1 represents the first target imaging image M t The width of (x,y), which is the number of pixels in the horizontal direction; N2 represents the first target image M. t The height (x,y) is the number of pixels in the vertical direction. γ is a parameter used to control the nonlinearity of the first imaging loss function L, for example, γ is 2. Optionally, N1 and N2 can be the same or different, and this embodiment does not limit this.

[0121] Step 322: Using automatic differentiation technology, the gradient of the first imaging loss function with respect to the first dose distribution is determined. Automatic differentiation technology is used to decompose the first imaging loss function and then gradually differentiate it to automatically calculate the gradient of the first imaging loss function with respect to the first dose distribution.

[0122] The gradient of the first imaging loss function with respect to the dose distribution indicates the direction in which the value of the first imaging loss function decreases the most. To minimize the value of the first imaging loss function, the dose distribution should be optimized in the direction in which the value of the first imaging loss function decreases the most.

[0123] Automatic differentiation is a method that breaks down the computational process into basic operations (such as addition, multiplication, trigonometric functions, etc.) and uses the chain rule to automatically calculate derivatives. Automatic differentiation includes forward automatic differentiation and backward automatic differentiation. Forward automatic differentiation involves calculating the derivative of each intermediate variable starting from the input variable until the derivative of the final output second imaging loss function is reached. For example, suppose y = f(x1, x2, ..., x...). i ,…,x n ), where x i If it is an input variable, then the forward automatic differentiation starts from x. i Initially, the derivative of each intermediate variable is calculated step by step until the derivative of the final output y is obtained. Backward automatic differentiation is the opposite of forward automatic differentiation; it starts by calculating the derivative of the output y, propagating the gradient according to the chain rule at each step until the derivative of the input is calculated.

[0124] The above method, by employing automatic differentiation technology to calculate the gradient of the first imaging loss function with respect to the first dose distribution, can obtain an accurate gradient of the first imaging loss function with respect to the first dose distribution, avoiding a complex mathematical analytical derivation process and improving the optimization efficiency of the first dose distribution.

[0125] Step 323: In the case of updating the first dose distribution for the kth time, determine the first adjustment amount based on the gradient of the first imaging loss function with respect to the first dose distribution and the first target imaging image. The first adjustment amount is the adjustment amount determined when updating the first dose distribution for the kth time, where k is a positive integer. Based on the first adjustment amount, update the first dose distribution to obtain the updated first dose distribution.

[0126] The first adjustment is used to indicate the optimization direction during the k-th update of the first dose distribution. The optimization direction refers to the direction in which the first dose distribution is updated in each update process. The optimization direction, to a certain extent, determines the speed of gradient convergence of the first imaging loss function with respect to the first dose distribution and the final optimization effect of the first dose distribution.

[0127] In some embodiments, a first adjustment amount is determined based on the gradient of a first imaging loss function with respect to a first dose distribution and a first target imaging image. Exemplarily, this adjustment is based on the gradient g of the first imaging loss function with respect to the first dose distribution. k and the first target imaging image M t The first adjustment amount V is determined by the following formula. k :

[0128]

[0129] In some embodiments, there are two cases for determining the adjustment amount of the first dose distribution for the kth update.

[0130] Case 1: When k equals 1, the first adjustment amount is determined based on the gradient of the first imaging loss function with respect to the first dose distribution and the first target imaging image. During the first update of the first dose distribution, the first adjustment amount is directly calculated based on the gradient of the first imaging loss function with respect to the first dose distribution and the first target imaging image. For example, when k = 1, the first adjustment amount V... k Calculated using the following formula:

[0131]

[0132] in, M is the gradient of the first imaging loss function with respect to the first dose distribution when the first dose distribution is updated for the first time. t This is the image of the first target.

[0133] Case 2: When k is greater than 1, the first adjustment amount is determined based on the gradient of the first imaging loss function with respect to the first dose distribution, the first target image, and the second adjustment amount. The second adjustment amount is the adjustment amount determined during the (k-1)th update of the first dose distribution. After the first update of the first dose distribution, the first adjustment amount retains the previous adjustment amount. By combining the previous adjustment amount to determine the first adjustment amount, the optimization direction indicated by the first adjustment amount is conjugate to the optimization direction indicated by the previous adjustment amount, thereby avoiding repeated optimization in the same direction and improving the convergence speed of the gradient of the first imaging loss function with respect to the first dose distribution.

[0134] For the conjugate gradient method, the initial optimization direction of the first imaging loss function is determined based on the gradient of the first imaging loss function with respect to the first dose distribution, and the optimization direction of the previous step is retained in subsequent optimization directions.

[0135] In some embodiments, a gradient factor is determined based on the gradient of the first imaging loss function with respect to the first dose distribution and a first gradient, the gradient factor being used to maintain the update of the first dose distribution, and the first gradient being the gradient determined during the (k-1)th update of the first dose distribution; a first adjustment amount is determined based on the gradient of the first imaging loss function with respect to the first dose distribution, a second adjustment amount, and the gradient factor.

[0136] The gradient factor, also known as the conjugate gradient factor, ensures that the new first adjustment is in the conjugate direction of the first dose distribution, thus enabling the conjugate gradient method to operate effectively and avoiding optimization stagnation. The gradient factor is automatically adjusted each time the first dose distribution is updated to prevent optimization stagnation.

[0137] For example, when k > 1, the first adjustment amount V k Calculated using the following formula:

[0138] V k =g k -η k V k-1 k>1

[0139]

[0140]

[0141] Among them, g k It is the gradient of the first imaging loss function with respect to the first dose distribution, calculated during the k-th update of the first dose distribution, g. k-1 It is the gradient of the first imaging loss function with respect to the first dose distribution, calculated during the (k-1)th update of the first dose distribution, V. k-1 η is the gradient determined during the (k-1)th update of the first dose distribution. kThe gradient factor determined during the k-th update of the first dose distribution, ‖*‖ 2 This refers to finding the square of the Euclidean norm of matrix *, ∑g k g k-1 This refers to finding g. k and g k-1 The sum of the products of corresponding elements, M t This is the image of the first target.

[0142] In some embodiments, an update step size is determined based on a first adjustment amount, the update step size indicating the adjustment magnitude of the first dose distribution; the first dose distribution is updated according to the first adjustment amount and the update step size to obtain the updated first dose distribution. The update step size, also known as the learning rate, is used to control the magnitude of each adjustment to the first dose distribution. In this application, the update step size is automatically updated each time the first dose distribution is updated. Exemplarily, the update step size ω is updated using the following formula. k :

[0143]

[0144] Where ε is the step size factor, used to control the size of the update step, such as ε being 0.1, max(*) means taking the maximum value in the expression *, |V k | refers to V k Find the absolute value of each element contained in it.

[0145] Based on the above example, based on the first adjustment amount V k and update step size ω k The first dose distribution D is calculated using the following formula. k The update is performed to obtain the updated first dose distribution D. k+1 :

[0146] D k+1 =D k +ω k V k

[0147] The above method, by retaining the adjustment amount from the previous step when determining the adjustment amount for each update of the first dose distribution, can effectively improve the convergence efficiency of the gradient of the first imaging loss function with respect to the first dose distribution.

[0148] In this embodiment, step 323 above achieves the process of iteratively updating the first dose distribution based on the gradient of the first imaging loss function with respect to the first dose distribution, and obtaining the updated first dose distribution. This process can also be achieved in other ways, which will not be elaborated here.

[0149] In some embodiments, step 323 is followed by step 324.

[0150] Step 324: Based on the target imaging image, the minimum threshold value, and the maximum threshold value, correct the updated first dose distribution to obtain the corrected first dose distribution; wherein, the minimum threshold value is the preset minimum value of the first dose distribution, and the maximum threshold value is the preset maximum value of the first dose distribution.

[0151] To constrain the first dose distribution to a preset range, the updated first dose distribution needs to be corrected. Optionally, the preset range is determined by a minimum threshold and a maximum threshold, and is preset by relevant technical personnel based on experiments or requirements; this embodiment does not limit this.

[0152] For example, the preset value range is [D Min D Max The updated first dose distribution D is calculated using the following formula. k+1 Make corrections:

[0153] D k+1 =(D k+1 ×(D Max -D Min )+D Min )×M t

[0154] Where D is on the left side of the equation above. k+1 For the corrected first dose distribution, D on the right side of the equation k+1 For the updated first dose distribution, D Min D is the minimum threshold value for the first dose distribution. Max M is the maximum threshold value of the first dose distribution. t This is the image of the first target. For example, the preset value range is [0,10], D Min D is 0 Max It is 10.

[0155] The above method, by correcting the updated first dose distribution, ensures that the optimized first dose distribution is achievable in the actual physical system.

[0156] In some embodiments, the method further includes step 325.

[0157] Step 325: Determine whether the first dose distribution meets the update stop condition; if the first dose distribution does not meet the update stop condition, based on the updated first dose distribution, start again from the step of calculating the first predicted imaging image based on the first dose distribution of electron beam lithography (i.e., step 310 above); if the first dose distribution meets the update stop condition, stop the update process of the first dose distribution.

[0158] In some embodiments, the update stopping condition includes at least one of the following: the number of iterations reaches a first threshold, or the gradient of the first imaging loss function with respect to the first dose distribution is less than or equal to a second threshold.

[0159] The update stopping condition refers to the criteria for determining when to terminate the update process of the first dose distribution. The first threshold refers to the maximum number of iterations. Optionally, the first threshold for the number of iterations is preset by those skilled in the art. The second threshold represents the minimum acceptable error of the first imaging loss function; this embodiment does not limit this. Optionally, the second threshold for the gradient of the first imaging loss function with respect to the first dose distribution is preset by those skilled in the art; this embodiment does not limit this.

[0160] In other words, if the first dose distribution does not meet the update stop condition, steps 310 to 320 are repeated until the first dose distribution meets the update stop condition, and the first dose distribution obtained from the last update is determined as the optimal dose distribution under low resolution.

[0161] In this embodiment of the application, the first dose distribution corresponding to the first target imaging image is iteratively optimized by an electron beam dose optimization algorithm to obtain an optimized first dose distribution, which makes the optimized first dose distribution highly accurate.

[0162] In some embodiments, a first dose distribution optimized for electron beam lithography is predicted based on a first target imaging image using a deep vision algorithm. A deep vision algorithm refers to an algorithm that utilizes deep learning technology to process and understand visual data (such as images and videos). The deep vision algorithm is used to directly predict the dose distribution of electron beam lithography based on the target imaging image, without simulating the electron beam lithography process using a physical model or calculating the gradient of the imaging loss function with respect to the dose distribution. Optionally, the deep vision algorithm may include any of the following: Convolutional Neural Network (CNN), Generative Adversarial Network (GAN), reinforcement learning in deep learning, etc., or other deep vision algorithms; this application embodiment does not limit this. The above method, by directly predicting the dose distribution of electron beam lithography using a deep vision algorithm, greatly reduces the computational time and cost of proximity effect correction.

[0163] The following are embodiments of the apparatus described in this application, which can be used to execute the embodiments of the method described in this application. For details not disclosed in the apparatus embodiments of this application, please refer to the embodiments of the method described in this application.

[0164] Please refer to Figure 7This diagram illustrates a block diagram of an apparatus for determining the dose distribution in electron beam lithography according to an embodiment of this application. The apparatus has the function of implementing the aforementioned method for determining the dose distribution in electron beam lithography; this function can be implemented in hardware or by hardware executing corresponding software. The apparatus can be the computer device described above, or it can be installed within a computer device. Figure 7 As shown, the device may include: an image determination module 710, a dose update module 720, and an element addition module 730.

[0165] The image determination module 710 is used to determine a first predicted imaging image based on a first dose distribution of electron beam lithography. The first predicted imaging image is an image obtained by simulating the electron beam lithography process based on the first dose distribution.

[0166] The dose update module 720 is used to iteratively update the first dose distribution based on the difference between the first predicted imaging image and the first target imaging image to obtain the updated first dose distribution, wherein the resolution of the first target imaging image is a first resolution, and the first dose distribution is a matrix containing multiple elements, each element in the first dose distribution corresponding to a pixel in the first target imaging image.

[0167] The element addition module 730 is used to increase the number of elements contained in the updated first dose distribution based on the second resolution to obtain a second dose distribution, wherein the second resolution is greater than the first resolution;

[0168] The image determination module 710 is also used to determine a second predicted imaging image based on a second dose distribution, wherein the second predicted imaging image is an image obtained by simulating an electron beam lithography process based on the second dose distribution.

[0169] The dose update module 720 is also used to iteratively update the second dose distribution based on the difference between the second predicted imaging image and the second target imaging image to obtain the updated second dose distribution, wherein the resolution of the second target imaging image is the second resolution.

[0170] In some embodiments, the element-adding module 730 is used for:

[0171] Based on the second resolution, the updated first dose distribution is interpolated to obtain the second dose distribution.

[0172] In some embodiments, the first dose distribution includes electron beam doses on a plurality of first grids;

[0173] Module 730, which adds elements, is used for:

[0174] Based on the second resolution, multiple second grids are determined that correspond one-to-one with multiple pixels on the second target imaging image. The size of the second grid is smaller than the size of the first grid, and the number of second grids is greater than the number of first grids.

[0175] Based on the electron beam doses on multiple first grids, the electron beam doses on multiple second grids are obtained;

[0176] A second dose distribution is obtained based on the electron beam dose on multiple second grids.

[0177] In some embodiments, the element-adding module 730 is used for:

[0178] For each of the multiple second grids, the electron beam dose on the first grid closest to the second grid is determined as the electron beam dose on the second grid.

[0179] In some embodiments, the first dose distribution includes electron beam doses on a plurality of first grids;

[0180] Module 730, which adds elements, is used for:

[0181] Based on the second resolution, each first grid is divided into multiple second grids;

[0182] The electron beam dose on the first grid is determined as the electron beam dose on the multiple second grids included in the first grid;

[0183] The second dose distribution is obtained based on the electron beam dose on the multiple second grids that have been divided.

[0184] In some embodiments, the first target imaging image includes a target pattern region and other regions besides the target pattern region; the apparatus further includes a dose determination module for:

[0185] Based on the first target imaging image, determine the initial first dose distribution;

[0186] Wherein, if the first pixel in at least one pixel in the first target imaging image belongs to the target pattern region, the electron beam dose on the first grid corresponding to the first pixel in the initialized first dose distribution is a first value; if the first pixel in at least one pixel in the first target imaging image does not belong to the target pattern region, the electron beam dose on the first grid corresponding to the first pixel in the initialized first dose distribution is a second value, and the second value is different from the first value.

[0187] In some embodiments, the number of iterations for the second dose distribution is less than the number of iterations for the first dose distribution.

[0188] In some embodiments, the apparatus further includes a downsampling module for:

[0189] Based on the first resolution, the imaging image of the second target is downsampled to obtain the imaging image of the first target.

[0190] In some embodiments, the image determination module 710 is configured to:

[0191] Using an electron beam lithography physical model, a first predicted imaging image is obtained based on a first dose distribution. The electron beam lithography physical model is a physical model constructed based on a point spread function and a dose distribution; the point spread function describes the propagation of the electron beam. Alternatively,

[0192] The first predicted imaging image is obtained by using an image prediction model based on a first dose distribution. The image prediction model is a neural network model used to predict imaging images based on dose distribution.

[0193] In some embodiments, the image determination module 710 is configured to:

[0194] Based on the point spread function and the first dose distribution, the energy deposition density distribution is obtained, which is used to indicate the energy deposition density of the electron beam at various locations on the photoresist.

[0195] The first predicted imaging image is obtained by using an activation function based on the energy deposition density distribution.

[0196] In some embodiments, the dose update module 720 is configured to:

[0197] Based on the difference between the first predicted imaging image and the first target imaging image, a first imaging loss function is determined. The first imaging loss function is used to characterize the difference between the first predicted imaging image and the first target imaging image.

[0198] Automatic differentiation technique is used to determine the gradient of the first imaging loss function with respect to the first dose distribution. The automatic differentiation technique is used to decompose the first imaging loss function and then take derivatives step by step to automatically calculate the gradient of the first imaging loss function with respect to the first dose distribution.

[0199] Based on the gradient of the first imaging loss function with respect to the first dose distribution, the first dose distribution is iteratively updated to obtain the updated first dose distribution.

[0200] In some embodiments, the dose update module 720 is configured to:

[0201] In the case of updating the first dose distribution for the kth time, a first adjustment amount is determined based on the gradient of the first imaging loss function with respect to the first dose distribution and the first target imaging image. The first adjustment amount is the adjustment amount determined when updating the first dose distribution for the kth time, where k is a positive integer.

[0202] Based on the first adjustment amount, the first dose distribution is updated to obtain the updated first dose distribution.

[0203] The device first iteratively updates the first dose distribution at low resolution. Since the first dose distribution includes fewer elements, the computational load for each update is reduced, thus shortening the computation time. After obtaining a better first dose distribution at low resolution, the number of elements in the first dose distribution is increased based on high resolution to obtain a second dose distribution. This provides a better initial value for the second dose distribution at high resolution. Based on this, fewer iterative updates are needed to obtain a better second dose distribution at high resolution, thus reducing the number of iterations and further shortening the computation time. Therefore, this device reduces the overall computation time for determining the dose distribution, improves efficiency, and lowers computational costs.

[0204] It should be noted that the apparatus provided in the above embodiments is only illustrated by the division of the above functional modules when implementing its functions. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0205] Please refer to Figure 8 This diagram illustrates a structural block diagram of a computer device 800 provided in one embodiment of this application. The computer device 800 may be a computer device 10 in an implementation environment, which is used to implement the method for determining the electron beam lithography dose distribution provided in the above embodiments. Specifically:

[0206] Typically, computer device 800 includes a processor 810 and a memory 820.

[0207] Processor 810 may include one or more processing cores, such as a quad-core processor or an octa-core processor. Processor 810 may be implemented using at least one hardware form selected from Digital Signal Processing (DSP), Field Programmable Gate Array (FPGA), and Programmable Logic Array (PLA). Processor 810 may also include a main processor and a coprocessor. The main processor, also known as the central processing unit, is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state. In some embodiments, processor 810 may include a GPU, which is responsible for executing the method steps provided in this application. In some embodiments, processor 810 may also include an AI processor, which is used to handle computational operations related to machine learning.

[0208] The memory 820 may include one or more computer-readable storage media, which may be non-transitory. The memory 820 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments, the non-transitory computer-readable storage media in the memory 820 are used to store a computer program configured to be executed by one or more processors (such as a GPU) to implement the above-described method for determining the electron beam lithography dose distribution.

[0209] Those skilled in the art will understand that Figure 8 The structure shown does not constitute a limitation on the computer device 800, and may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0210] This application also provides a computer-readable storage medium storing a computer program, which is loaded and executed by a processor to implement the method for determining the electron beam lithography dose distribution in any of the above implementations.

[0211] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. A processor of a computer device reads the computer program from the computer-readable storage medium and executes the computer program, causing the computer device to perform the electron beam lithography dose distribution determination method of any of the above implementations.

[0212] In some embodiments, the computer program product involved in the present application can be deployed and executed on a computer device, or on multiple computer devices located in one location, or on multiple computer devices distributed in multiple locations and interconnected through a communication network. Multiple computer devices distributed in multiple locations and interconnected through a communication network can form a blockchain system.

[0213] It should be noted that the data collection and processing in this application should strictly comply with the requirements of relevant national laws and regulations, obtain the informed consent or separate consent of the personal information subject, and carry out subsequent data use and processing within the scope of laws and regulations and the authorization of the personal information subject.

[0214] It should be understood that "multiple" as used herein refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. Furthermore, the step numbers described herein are merely illustrative of one possible execution order. In some other embodiments, the steps may not be executed in numerical order, such as two steps with different numbers being executed simultaneously, or two steps with different numbers being executed in the reverse order of the illustration. This application does not limit this.

[0215] All the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here. The above are only optional embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method of determining an e-beam lithography dose distribution, characterized in that, The method comprises: determining a first predicted imaging image based on a first dose distribution of electron beam lithography, the first predicted imaging image being an image obtained by simulating an electron beam lithography process based on the first dose distribution; iteratively updating the first dose distribution based on a difference between the first predicted imaging image and a first target imaging image, to obtain an updated first dose distribution, wherein the first target imaging image has a first resolution, and each element in the first dose distribution corresponds to a pixel in the first target imaging image; increasing the number of elements contained in the updated first dose distribution based on a second resolution, to obtain a second dose distribution, wherein the second resolution is greater than the first resolution; determining a second predicted imaging image based on the second dose distribution, the second predicted imaging image being an image obtained by simulating an electron beam lithography process based on the second dose distribution; iteratively updating the second dose distribution based on a difference between the second predicted imaging image and a second target imaging image, to obtain an updated second dose distribution, wherein the second target imaging image has the second resolution.

2. The method of claim 1, wherein, The method further comprises: interpolating the updated first dose distribution based on the second resolution, to obtain the second dose distribution.

3. The method of claim 2, wherein, The first dose distribution comprises electron beam doses on a plurality of first grids; The method further comprises: determining a plurality of second grids corresponding to a plurality of pixels on the second target imaging image based on the second resolution, wherein the size of each second grid is smaller than the size of each first grid, and the number of second grids is greater than the number of first grids; obtaining electron beam doses on the plurality of second grids based on the electron beam doses on the plurality of first grids; obtaining the second dose distribution based on the electron beam doses on the plurality of second grids.

4. The method of claim 3, wherein, The method further comprises: for each second grid in the plurality of second grids, determining an electron beam dose on the second grid as an electron beam dose on a first grid closest to the second grid.

5. The method of claim 2, wherein, The first dose distribution comprises electron beam doses on a plurality of first grids; The method further comprises: dividing each first grid into a plurality of second grids based on the second resolution; determining the electron beam doses on the first grids as electron beam doses on the plurality of second grids included in the first grids, respectively; obtaining the second dose distribution based on the electron beam doses on the plurality of second grids.

6. The method according to any one of claims 1 to 5, characterized in that, The first target imaging image comprises a target pattern region and a region other than the target pattern region; and the method further comprises: determine an initialized first dose distribution according to the first target imaging image; wherein, in a case that a first pixel in at least one pixel included in the first target imaging image belongs to the target pattern region, an electron beam dose value on a first grid corresponding to the first pixel in the initialized first dose distribution is a first numerical value; in a case that a first pixel in at least one pixel included in the first target imaging image does not belong to the target pattern region, an electron beam dose value on a first grid corresponding to the first pixel in the initialized first dose distribution is a second numerical value, the second numerical value being different from the first numerical value.

7. The method according to any one of claims 1 to 6, characterized in that, The number of times of iterative updating of the second dose distribution is less than the number of times of iterative updating of the first dose distribution.

8. The method according to any one of claims 1 to 7, characterized in that, The method further comprises: down-sampling the second target imaging image based on the first resolution to obtain the first target imaging image.

9. The method according to any one of claims 1 to 8, characterized in that, determine a first predicted imaging image based on the first dose distribution for electron beam lithography, comprising: obtaining the first predicted imaging image according to the first dose distribution by an electron beam lithography physical model, the electron beam lithography physical model being a physical model constructed based on a point spread function and a dose distribution, the point spread function being used to describe the propagation of an electron beam; or obtaining the first predicted imaging image according to the first dose distribution by an image prediction model, the image prediction model being a neural network model used to predict an imaging image based on a dose distribution.

10. The method of claim 9, wherein, The method further comprises: obtaining an energy deposition density distribution based on the point spread function and the first dose distribution, the energy deposition density distribution being used to indicate the energy deposition density of an electron beam at each position of photoresist; obtaining the first predicted imaging image according to the energy deposition density distribution by an activation function.

11. The method according to any one of claims 1 to 10, characterized in that, The method further comprises: determining a first imaging loss function based on the difference between the first predicted imaging image and the first target imaging image, the first imaging loss function being used to represent the difference between the first predicted imaging image and the first target imaging image; determining the gradient of the first imaging loss function with respect to the first dose distribution by using an automatic differentiation technique, the automatic differentiation technique being used to decompose and step-by-step differentiate the first imaging loss function to automatically calculate the gradient of the first imaging loss function with respect to the first dose distribution; iteratively updating the first dose distribution based on the gradient of the first imaging loss function with respect to the first dose distribution to obtain an updated first dose distribution.

12. The method of claim 11, wherein, The method further comprises: determining the gradient of the first imaging loss function with respect to the first dose distribution by using an automatic differentiation technique, the automatic differentiation technique being used to decompose and step-by-step differentiate the first imaging loss function to automatically calculate the gradient of the first imaging loss function with respect to the first dose distribution; In a case of updating the first dose distribution for a kth time, a first adjustment amount is determined according to a gradient of the first imaging loss function with respect to the first dose distribution and the first target imaging image, the first adjustment amount being an adjustment amount determined when the first dose distribution is updated for the kth time, k being a positive integer; The first dose distribution is updated based on the first adjustment amount to obtain an updated first dose distribution.

13. An apparatus for determining an e-beam lithography dose distribution, characterized in that The apparatus comprises: An image determination module configured to determine a first predicted imaging image based on a first dose distribution of electron beam lithography, the first predicted imaging image being an image obtained by simulating an electron beam lithography process based on the first dose distribution; A dose updating module configured to iteratively update the first dose distribution based on a difference between the first predicted imaging image and a first target imaging image to obtain an updated first dose distribution, wherein a resolution of the first target imaging image is a first resolution, and the first dose distribution is a matrix comprising a plurality of elements, each element in the first dose distribution corresponding to a pixel in the first target imaging image; An element increasing module configured to increase a number of elements comprised in the updated first dose distribution based on a second resolution to obtain a second dose distribution, the second resolution being greater than the first resolution; The image determination module is further configured to determine a second predicted imaging image based on the second dose distribution, the second predicted imaging image being an image obtained by simulating an electron beam lithography process based on the second dose distribution; The dose updating module is further configured to iteratively update the second dose distribution based on a difference between the second predicted imaging image and a second target imaging image to obtain an updated second dose distribution, a resolution of the second target imaging image being the second resolution.

14. A computer device, comprising: The computer device comprises a processor and a memory, the memory being configured to store a computer program, the computer program being loaded and executed by the processor to perform the method for determining a dose distribution of electron beam lithography according to any one of claims 1 to 12.

15. A computer-readable storage medium, characterized in that, The computer readable storage medium is configured to store a computer program, the computer program being configured to perform the method for determining a dose distribution of electron beam lithography according to any one of claims 1 to 12.

16. A computer program product, characterised in that, The computer program product comprises a computer program stored in a computer readable storage medium, a processor of a computer device reading the computer program from the computer readable storage medium, the processor executing the computer program to cause the computer device to perform the method for determining a dose distribution of electron beam lithography according to any one of claims 1 to 12.

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