Holographic photoetching mask design method based on alternate projection algorithm

Abstract

The invention provides a holographic photoetching mask design method based on an alternating projection algorithm, and the holographic photoetching resolution is improved. According to the method, a pixel representation mask is adopted, and finite series discretization is carried out on an amplitude matrix and a phase matrix corresponding to the mask in combination with mask manufacturing constraint conditions. In order to avoid stagnation in the optimization process, a step-by-step discretization strategy is adopted. And evaluating the imaging quality of the designed mask through a relative pattern error between the photoresist contour and the target pattern. According to the method, the alternative projection iterative algorithm and the advanced mask alignment photoetching technology are combined, different initial conditions are adopted according to mask types, and holographic photoetching mask design of any mask pattern can be effectively achieved.

Description

Technical Field

[0001] The invention relates to the technical field of holographic lithography, and in particular to a holographic lithography mask design method based on an alternating projection algorithm. Background Art

[0002] Projection lithography is the mainstream lithography technology in semiconductor manufacturing. Its principle is to scale and image the mask pattern onto the surface of the silicon wafer through the objective lens system, and then transfer the designed integrated circuit pattern to the silicon wafer through processes such as exposure, post-baking, development and etching. However, the projection lithography machine is limited by the complex projection objective lens system and high-precision alignment system, resulting in high equipment and maintenance costs. In contrast, mask alignment lithography is a mature and low-cost lithography technology with relatively simple equipment maintenance. Compared with the contact lithography mode, the proximity lithography mode avoids direct contact between the mask and the silicon wafer, thereby reducing mask contamination. Although mask alignment lithography is not the main choice for large-scale high-integration chip manufacturing, it still has broad application prospects in the field of large-area pattern manufacturing or customized chips. In order to manufacture smaller feature sizes, some resolution enhancement technologies in projection lithography can also be applied to mask alignment lithography. In particular, through the innovation of technologies such as illumination optics and photomasks, the application potential of mask alignment lithography has been further expanded.

[0003] Holographic lithography uses a holographic lithography mask to replace the traditional binary mask, which can apply additional phase modulation to the incident light field, thereby carrying more target pattern information and improving the mask alignment lithography resolution. Early holographic lithography masks were made by directly interfering the object light of the target mask with the reference light, and then recording the interference pattern in a photosensitive polymer. This technology is called total internal reflection (TIR) ​​holographic lithography mask technology (see prior art 1: Han WS, Carnal OH, Clube FS M. Method and apparatus for recording ahologram from a mask pattern by the use of total internal reflection holography and hologram manufactured by the method: US Patent 7,092,134 [P]. 2006-8-15.). TIR holographic lithography masks can control the phase by changing the refractive index of the mask material, so a continuous phase distribution can be achieved. In this way, lithography of non-periodic patterns with a lithography resolution below 250nm can be achieved. However, the chemical properties of the mask material of the TIR holographic lithography mask are unstable after multiple UV exposures, which limits its reliability in long-term use. Prior art 2 (Weichelt, T., et al. "Resolution enhancement for advanced mask aligner lithography using phase-shifting photomasks." Opticsexpress 22.13 (2014): 16310-16321.) uses the physical characteristics of the mask (such as etching depth) to regulate the phase, and uses the Gerchberg-Saxton (GS) algorithm to calculate the amplitude and phase distribution of the holographic lithography mask of the target pattern, thereby improving the service life of the mask. Non-periodic pattern lithography with a 2μm lithography resolution was achieved at a close spacing of 30μm. As the mask pattern becomes more complicated and the line width is further reduced, the existing design method based on the GS model has been difficult to meet the requirements of high-quality imaging. Summary of the invention

[0004] The purpose of the present invention is to provide a holographic lithography mask design method applicable to any mask pattern, which is used in holographic lithography technology and can improve the resolution of holographic lithography technology. The present invention is improved on the basis of the prior art, and the holographic lithography mask designed in theory can achieve approximately continuous amplitude distribution and phase distribution. However, considering the limitation of mask processing capacity, it is necessary to discretize the calculated mask amplitude value and phase value into limited grades. Therefore, it is necessary to adjust the design method to adapt to the mask manufacturing capacity.

[0005] The solution of the present invention is as follows:

[0006] A holographic lithography mask optimization design method based on an alternating projection algorithm is characterized in that it comprises the following steps:

[0007] Step 1. Define the mask surface and the silicon wafer surface. Set the complex amplitude distribution of the mask surface to be represented as the holographic lithography mask pattern distribution, and the complex amplitude distribution includes amplitude information and phase information. The silicon wafer surface is the spatial image plane, which is the spatial image of the complex amplitude distribution of the mask surface after coherent imaging or partial coherent imaging;

[0008] Step 2. Set the pixel size in the x-direction and y-direction to dx and dy respectively. Input the target mask pattern Mask target , and discretize it into a mask matrix of Nx×Ny according to the set pixel size dx and dy; each element in the matrix represents the transmittance of each point, where the value of the transparent part is 1 and the opaque part is 0;

[0009] Step 3. Define the signal area and noise area on the silicon wafer surface. The signal area is defined as the smallest rectangle covering the target mask pattern. Its size is generally the same as the input target mask pattern size and is set to Nx×Ny. With the signal area as the center, fill the background part around it. The initial amplitude of the background area is set to 0, and the filled part is the noise area. The signal area and the noise area together constitute the total calculation area. widx and widy are used to represent the ratio of the width of the unilateral extension of the noise area in the x-direction and y-direction to the width of the original target mask pattern. The size of the expanded calculation area is in Indicates rounding up. Usually widx = widy = 0.5, that is, the calculation area after expansion is twice the original area;

[0010] Step 4. Initialize the amplitude and phase of the silicon wafer surface. Since the alternating projection algorithm is used for optimization calculation, the selection of the initial value has an important influence on the optimization result. The method for initializing the amplitude and phase of the silicon wafer surface is as follows. First, the target mask pattern Mask targetAs the initial amplitude of the signal area, expand the noise area according to step 3 and set the amplitude value of the noise area to 0. The initial amplitude of the silicon wafer surface is represented by A0. Different initial phases are selected according to the type of input mask. The specific method is as follows:

[0011] (a) When the input mask is a symmetrical pattern: use quadratic phase distribution The spatial coordinates of the mask center are (0,0), k1 and k2 are the secondary phase parameters;

[0012] (b) When the input mask is an asymmetric pattern: a polygon-based partial alternating phase shift distribution is used. The mask pattern is mainly composed of polygons, so the input binary mask pattern is decomposed into independent and unconnected polygons, and numbered according to the following strategy: Starting from the upper left corner, all pixels are traversed from top to bottom and from left to right. When an unmarked pixel with a value of 1 (i.e., the light-transmitting part) is encountered, start looking for all pixels connected to the pixel and mark them as a polygon. Continue to look for the next unmarked pixel with a value of 1. Traverse all pixels until all polygons that constitute the mask pattern are marked. Then, a phase shift is introduced to the area represented by the odd-numbered or even-numbered polygons. The phase distribution obtained in this way is not necessarily a strict alternating phase shift distribution, but a phase shift of local adjacent polygons can be introduced.

[0013] The final initial complex amplitude distribution of the silicon wafer surface is expressed as E0 = A0exp(jφ0);

[0014] Step 5. Use the angular spectrum of plane waves (ASPW) algorithm to back-propagate the initial complex amplitude distribution E0 of the silicon wafer surface to the mask surface to obtain the complex amplitude distribution E mask ;

[0015] Step 6. E mask Apply mask manufacturing constraints. mask Decomposed into amplitude A mask With phase φ mask , where A mask is a value greater than 0, is a value in the range of 0 to 2π. A step-by-step discretization strategy is used to discretize the amplitude and phase of the mask surface into corresponding discrete levels. Theoretically, the amplitude can be divided into more sub-levels, but considering manufacturing limitations, the amplitude grading is set to two levels, that is, the discretized value is 0 or 1. The phase grading is set to n levels, that is, the discretized value is 0, 2π / n, 4π / n...2π-2π / n, and n is the number of phase grading levels. The step-by-step grading iteration parameter is set to m, that is, at least m iterations are required to discretize all the values ​​of the phase matrix and the amplitude matrix of the mask surface to corresponding levels. The amplitude and phase are discretized according to the following strategies:

[0016] (a) Discretization of amplitude: At the i-th iteration (i≤m), the amplitude A of the mask surface is first mask Divide by its mean A mean , so that the mean of the new amplitude distribution is 1. Then the amplitude A of the mask surface is calculated according to the following formula: mask Discretize:

[0017]

[0018] (b) Phase discretization: At the i-th iteration (i≤m), the phase of the mask surface is discretized according to the following formula: Discretize, where k represents the kth phase level, is the phase interval between adjacent phase levels:

[0019]

[0020] Update the amplitude A' after discretization mask With phase

[0021] Step 7. In the forward process of mask iterative calculation, we use a coherent light source to illuminate the mask. Combining the light source intensity distribution and phase distribution, update the mask surface complex amplitude distribution before forward propagation. Generally, uniform light incidence is used, so

[0022] Step 8. Use the ASPW algorithm to transform the mask surface complex amplitude distribution E' mask Propagate forward to the silicon wafer surface, and obtain the complex amplitude distribution E wafer ;

[0023] Step 9. Use the Sigmoid model to convert the spatial image of the silicon wafer surface into the photoresist profile. Set the imaging evaluation function D1:

[0024] D1 is the area error AER value of the photoresist profile in the signal area: Nsignal region is the total number of pixels in the signal area, ║*║2 represents the L-2 norm, z target is the photoresist profile of the target mask pattern, which is numerically equal to Mask target ;

[0025] Step 10. Set the threshold D of the imaging evaluation function D1 th With the maximum number of iterations i max When the AER value is lower than the threshold D th Or the number of iterations i is greater than the preset maximum number of iterations i max , the iteration ends, and the discretized mask amplitude A' in step 6 is output mask With phase If not satisfied, proceed to step 11;

[0026] Step 11. E wafer Apply the target light intensity constraint. Set the complex amplitude distribution E wafer Decomposed into amplitude A wafer With phase Update according to the following strategy:

[0027] (a) Update amplitude A' wafer : In this iteration, the amplitude distribution of the noise area calculated in the previous iteration is retained. The amplitude of the signal area is replaced by the target pattern amplitude A target Superposition with a uniform light field Δ. The new amplitude A' wafer It is composed of a linear combination of the amplitude of the noise region and the amplitude of the signal region. Where M is the mixing parameter, A target is the amplitude value of the target mask pattern, which is equal to Mask target , Δ is the amplitude of the uniform background light field added in the signal area;

[0028] (b) Update phase Keep the phase calculated in the previous iteration,

[0029] Update the silicon wafer surface complex amplitude distribution before back propagation:

[0030] Step 12. Use the ASPW algorithm to distribute the complex amplitude E' of the silicon wafer surface wafer Back propagates to the mask surface and obtains the complex amplitude distribution E of the mask surface mask , then return to step 6.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1. By introducing the noise region and retaining its information during calculation, it can carry more amplitude and phase information, significantly improving the modulation capability of the light field. By introducing the noise region and giving up control over the noise region, the imaging quality and contrast of the signal region are enhanced.

[0033] 2. When initializing the phase, a quadratic initial phase distribution is used for symmetrical target mask patterns, and a polygon-based partial alternating phase shift distribution is used for asymmetrical mask patterns, which can improve the imaging quality and the algorithm's optimization capability.

[0034] 3. The present invention realizes the optimal design of holographic lithography mask by integrating alternating projection algorithm, imposing target light intensity constraint, using Sigmoid model to predict photoresist profile, and flexible initial phase selection and iterative optimization strategy, which not only improves the fidelity and resolution of lithography pattern, but also enhances the manufacturability of mask, shortens the design cycle, and improves the overall performance of lithography technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The flowchart of the holographic lithography mask design method based on the alternating projection algorithm of the present invention is

[0036] Figure 2 The invention is used to design the target mask pattern of the synthetic holographic lithography mask and its spatial image under the conventional mask alignment lithography.

[0037] Figure 3 Schematic diagram of the signal area and the noise area in the present invention

[0038] Figure 4 The spatial image and the photoresist profile after exposure of the synthetic holographic lithography mask obtained by the present invention are

[0039] Figure 5 The spatial image and photoresist profile of the synthetic holographic lithography mask after exposure obtained by using existing technology DETAILED DESCRIPTION

[0040] In order to explain the present invention more clearly, the following will be described in detail with reference to specific examples. It should be noted that these examples are only used to illustrate the embodiments of the present invention and do not constitute a limitation on the scope of the present invention.

[0041] Figure 1 is a flow chart of a holographic lithography mask design method based on an alternating projection algorithm of the present invention, using a binary mask as a target mask pattern, such as Figure 2 (a) shows the minimum line width of 0.8 μm. The exposure wavelength of the mask alignment lithography is set to 365 nm, and the proximity distance is 50 μm. A circular light source with an illumination angle of 0.3° is used for illumination, and the obtained spatial image is as follows: Figure 2 As shown in (b), it can be seen that under this condition, traditional mask alignment lithography can no longer provide accurate imaging.

[0042] The following Figure 2 (a) The mask pattern shown is used for holographic lithography mask design:

[0043] Step 1. Define the mask plane and silicon wafer plane:

[0044] Mask plane: The plane where the holographic lithography mask is located. The complex amplitude distribution of the mask plane represents the distribution of the holographic lithography mask pattern.

[0045] Silicon wafer surface: The plane where the spatial image of the complex amplitude distribution of the mask surface is formed on the silicon wafer after exposure.

[0046] The complex amplitude distribution of the mask surface contains all the information used to form the desired silicon wafer pattern. When coherent light (such as laser) is irradiated onto the mask, the amplitude and phase of the light are modulated according to the pattern on the mask. The modulated light waves are propagated to the silicon wafer surface through an optical system (such as a projection lens) to form an aerial image.

[0047] In the iterative mask design process, coherent illumination is used to ensure the coherence of light waves on the mask surface. The ASPW algorithm (Angular Spectrum of Plane Waves) is used to describe the diffraction and propagation process of light, and the spatial image on the silicon wafer surface is calculated to evaluate the effectiveness of the mask design. If the spatial image does not match the expected target, the mask design can be adjusted and simulated again using the ASPW algorithm until a satisfactory result is achieved.

[0048] Step 2. Convert the target mask pattern into a pixelated mask matrix:

[0049] First, the pixel sizes of the mask matrix in the x-direction and the y-direction are set, which are denoted as dx and dy respectively. In this embodiment, the pixel sizes are 0.1 μm.

[0050] Next, enter the target mask graphic Mask target In this embodiment, the target mask pattern Mask target like Figure 2 As shown in (a), the target mask pattern size is 40μm×40μm.

[0051] Finally, according to the set pixel sizes dx and dy and the size of the target mask pattern, the target mask pattern is discretized into a 400×400 mask matrix, in which the value of the transparent part is 1 and the value of the opaque part is 0.

[0052] Step 3. Define the signal area and noise area of ​​the silicon wafer surface, such as Figure 3As shown:

[0053] Signal region: is defined as the smallest rectangle covering the target mask pattern, and its size is generally the same as the input target mask pattern size, which is set to Nx×Ny. In this embodiment, since the target mask pattern is discretized into a 400×400 mask matrix, the size of the signal region is also set to 400×400.

[0054] Noise region: The signal region is the center, and the surrounding area is filled with background. This region is used to simulate the noise and interference that may be generated during the photolithography process, such as diffraction and scattering of light, and imperfections in the optical system. The initial amplitude of the noise region is set to 0, indicating that there are no features of the target mask pattern in this region.

[0055] Calculation area: The signal area and the noise area together constitute the total calculation area. The size of this area depends on the size of the signal area and the width of the unilateral extension of the noise area. The parameters widx and widy are introduced to represent the ratio of the width of the unilateral extension of the noise area in the x-direction and y-direction to the width of the original target mask pattern. Usually, these two parameters are set to the same value, for example, widx = widy = 0.5, which means that the expanded calculation area is twice the original area. The size of the expanded calculation area is in In this embodiment, since the original area is 400×400, and widx=widy=0.5, the size of the expanded calculation area is 800×800 (ie, rounded up (400(1+2*0.5))).

[0056] Step 4. Initialize the silicon wafer amplitude matrix A0 and phase matrix φ0:

[0057] Initialization of silicon wafer surface amplitude: Set the target mask pattern Mask target As the initial amplitude of the signal area of ​​the silicon wafer surface, that is, the transparent part is also set to 1 in the initial amplitude of the silicon wafer surface, and the initial amplitude of the noise area is set to 0, that is, at the beginning of the optimization process, the noise area is considered to be completely opaque. The initial amplitude A0 of the silicon wafer surface is a matrix composed of these initial values ​​of the signal area and the noise area.

[0058] Initialization of silicon wafer phase: Select the appropriate initial phase based on the type of input mask (symmetric or asymmetric).

[0059] (a) When the input mask is a symmetrical pattern:

[0060] When the mask pattern is symmetrical, a quadratic phase distribution is used. The center of the mask is set as the coordinate origin (0,0), k1 and k2 are the secondary phase parameters. In this embodiment, k1 takes the value of -0.1 and k2 takes the value of -0.5, and the initial phase is obtained.

[0061] (b) When the input mask is an asymmetric pattern: polygon-based partial alternating phase shift distribution is used

[0062] First, the input binary mask pattern (a matrix consisting of 0s and 1s) is decomposed into independent and unconnected polygons. This is achieved by traversing all pixels and marking the connected transparent parts (pixels with a value of 1). Starting from the upper left corner, all pixels are traversed from top to bottom and from left to right. When an unmarked transparent pixel is encountered, all transparent pixels connected to the pixel are searched and marked as a polygon. After the polygon decomposition is completed, the next step is to number these polygons and introduce phase shifts to the areas represented by odd-numbered or even-numbered polygons. It should be noted that the phase distribution obtained in this way is not necessarily a strict alternating phase shift distribution (that is, the phase shift between each adjacent polygon is π), but a phase shift between local adjacent polygons can be introduced to optimize the light energy distribution and the quality of the lithography pattern.

[0063] Finally, the initial complex amplitude distribution E0 of the silicon wafer surface is calculated from the initial amplitude A0 and the initial phase φ0 through E0=A0exp(jφ0).

[0064] In this embodiment, the step-by-step iterative parameter m of the mask surface is set to 200, and the amplitude value is binary, that is, the discretized value is 0 or 1. The phase value is binary, that is, the discretized value is 0 or π. The maximum number of iterations is set to i max =300. During the iteration process, the target constraint parameters of the silicon wafer surface are set to M = 0.75, Δ 2 = 0.08. Parameter a in the photoresist model r and t r They are 200 and 0.26 respectively.

[0065] Step 5. Use the angular spectrum of plane waves (ASPW) algorithm to propagate the initial complex amplitude distribution E0 of the silicon wafer surface back to the mask surface to obtain the complex amplitude distribution E mask .

[0066] First, calculate the diffraction spectrum corresponding to the initial complex amplitude distribution E0 in Represents a two-dimensional Fourier transform.

[0067] Next, the frequency domain form H of the spatial filter function at the neighborhood spacing is calculated.

[0068] Then, back propagation is performed to obtain the diffraction spectrum of the mask surface Where . / is the matrix dot division operation.

[0069] Finally, a two-dimensional inverse Fourier transform is performed to obtain the complex amplitude distribution E of the mask surface. mask .

[0070] Step 6. Complex amplitude distribution E on the mask surface mask Apply mask manufacturing constraints:

[0071] First, the complex amplitude distribution E mask Decomposed into amplitude A mask and Phase The period of the phase value is set to 0 to 2π, indicating the phase delay of the light wave, and the amplitude A mask is a value greater than 0, indicating the intensity of the light wave;

[0072] Then, a step-by-step discretization operation is performed. Assuming that the current iteration number is i (i≤m), the mean value A of the amplitude of the mask surface is calculated. mean , and then the amplitude A of the mask surface mask Divide by A mean , so that the mean of the new amplitude distribution is 1. Then operate the mask matrix value according to the following formula to obtain A' mask :

[0073]

[0074] For the phase matrix, at the i-th iteration (i≤m), the following operation is performed to obtain

[0075]

[0076] When the iteration number i>m, update A' according to the strategy of i=m mask and

[0077] Step 7. In the forward process of mask iteration calculation, a coherent light source is used to illuminate the mask, and the influence of the light source intensity distribution and phase distribution on the complex amplitude distribution of the mask surface is considered to update the complex amplitude distribution E' of the mask surface. mask The specific formula is Among them, A source is the intensity distribution of the light source, is the phase distribution of the light source. In this embodiment, uniform light illumination is used, then

[0078] Step 8. Use the ASPW algorithm to convert the mask surface light field complex amplitude E'mask Propagate forward to the silicon wafer surface and obtain the complex amplitude distribution on the silicon wafer surface Where ⊙ represents the matrix dot multiplication operation; the relationship between the complex amplitude distribution on the silicon wafer surface (i.e., the spatial image information) and the complex amplitude distribution on the mask surface (i.e., the holographic lithography mask information) and the transfer function of the system is

[0079] Step 9. Use the Sigmoid model to calculate the photoresist profile on the silicon wafer surface

[0080] Computational imaging evaluation function D1: Where N signal region is the total number of pixels in the signal area, i.e. 400×400.

[0081] Step 10. The threshold of the imaging evaluation function D1 is set to D th =1e-2. If D1≤D th , or the number of iterations i>i max When the iteration is terminated, the synthetic holographic lithography mask pattern distribution E' in step 6 is output mask ; If the above requirements are not met, continue to step 11;

[0082] Step 11. Complex amplitude distribution E on the silicon wafer surface wafer The target light intensity constraint is imposed by adjusting E wafer The amplitude and phase of the light intensity distribution formed on the silicon wafer surface are closer to the target pattern. Specifically:

[0083] The complex amplitude distribution E of the silicon wafer surface wafer Decomposed into amplitude A wafer With phase

[0084] (a) Update amplitude A' wafer : In this iteration, the amplitude distribution of the noise area calculated in the previous iteration is retained. The amplitude of the signal area is replaced by the target pattern amplitude A target Superposition with a uniform light field Δ. The new amplitude A' wafer It is composed of a linear combination of the amplitude of the noise region and the amplitude of the signal region. Where M is the mixing parameter, A target is the amplitude value of the target mask pattern, which is equal to Mask target , Δ is the amplitude of the uniform background light field added in the signal area;

[0085] (b) Update phase Keep the phase calculated in the previous iteration,

[0086] Update the silicon wafer surface complex amplitude distribution before back propagation,

[0087] Step 12. Use the ASPW algorithm to distribute the complex amplitude E' of the silicon wafer surface wafer Back propagates to the mask surface and obtains the complex amplitude distribution E mask , then return to step 6.

[0088] In this example, a circular light source with an illumination angle of 0.3° is used for exposure. The spatial image and the photoresist profile of the synthetic holographic lithography mask after exposure are obtained by using the design of the present invention. Figure 4 As shown in the figure, the obtained photoresist profile is continuous and clear. After optimization, the AER value of the photoresist pattern and the target pattern is 0.984%. For comparison, the existing synthetic holographic lithography mask technology based on the GS algorithm is used for comparison. The aerial image and photoresist profile obtained after exposure are shown in the figure. Figure 5 As shown, it can be seen that there are discontinuities and gaps in the partial profile of the photoresist. The AER value obtained by the GS algorithm is 3.29%. In this example, the AER value of the photoresist of the present invention is reduced by 70.1% compared with the prior art, showing a better optimization effect.

[0089] The above result is one of the better examples of the effect of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A holographic lithography mask optimization design method based on an alternating projection algorithm, characterized in that: The following steps are involved: Step 1: Define the mask surface and silicon wafer surface: The complex amplitude distribution of the mask surface is set to represent the distribution of the holographic lithography mask pattern, and the complex amplitude distribution includes amplitude information and phase information; The silicon wafer surface is the aerial image plane, which is the aerial image of the complex amplitude distribution of the mask surface after coherent imaging or partial coherent imaging; Step 2: Convert the target mask pattern into a pixelated mask matrix: Set the pixel size of the mask matrix in the x-direction and y-direction to dx and dy respectively, and input the target mask graphic Mask target , and discretize it into a mask matrix of Nx×Ny according to the set pixel size dx and dy, and each element in the mask matrix represents the transmittance of each point, where the value of the transparent part is 1 and the opaque part is 0; Step 3: Define the signal area and noise area of ​​the silicon wafer: The signal area is the smallest rectangle covering the target mask pattern, and its size is set to Nx×Ny. The signal area is the center, and the background part is filled around it as the noise area; The signal area and the noise area together constitute the total calculation area, which is in represents rounding up, widx and widy represent the ratio of the width of the unilateral extension of the noise area in the x-direction and y-direction to the width of the target mask pattern, respectively; Step 4: Initialize the amplitude and phase of the silicon wafer surface: The target mask shape Mask target As the initial amplitude A0 of the signal area, the amplitude value of the noise area is set to 0; Select different initial phases according to the type of input mask For symmetric patterns, quadratic phase distribution is used, and for asymmetric patterns, polygon-based partial alternating phase shift distribution is used. The final initial complex amplitude distribution of the silicon wafer surface is obtained. Step 5: Use the ASPW algorithm to back-propagate the initial complex amplitude distribution E0 of the silicon wafer surface to the mask surface to obtain the complex amplitude distribution E mask ; Step 6: Complex amplitude distribution E on the mask surface mask Apply mask manufacturing constraints and decompose into amplitude A mask With phase And discretized to corresponding discrete levels respectively; wherein, the amplitude grading is two-level, that is, the value after discretization is 0 or 1; the phase grading is n-level, that is, the value after discretization is 0, 2π / n, 4π / n...2π-2π / n, n is the number of phase grading levels; a step-by-step discretization strategy is adopted for iteration until all values ​​of the phase matrix and the amplitude matrix of the mask surface are discretized to corresponding levels; Step 7: Use a coherent light source to illuminate the mask, combine the light source intensity distribution and phase distribution, and update the mask surface complex amplitude distribution before forward propagation Step 8: Use the ASPW algorithm to convert the mask surface light field complex amplitude E' mask Propagate forward to the silicon wafer surface, and obtain the complex amplitude distribution E on the silicon wafer surface wafer ; Step 9: Use the Sigmoid model to convert the aerial image of the silicon wafer surface into a photoresist profile, and set the imaging evaluation function D1 to quantify the difference between the photoresist profile and the target mask pattern; Step 10: Set the threshold D of the imaging evaluation function D1 th With the maximum number of iterations i max ; When the AER value is lower than the threshold D th Or the number of iterations is greater than the preset maximum number of iterations i max When , the iteration terminates and the discretized mask amplitude A' is output mask With phase Otherwise, go to step 11; Step 11: Calculate the complex amplitude distribution E of the silicon wafer surface wafer Apply the target light intensity constraint and update the amplitude A' of the silicon wafer surface wafer With phase Update the silicon wafer surface complex amplitude distribution E' before back propagation wafer ; Step 12: Use the ASPW algorithm to distribute the complex amplitude E' of the silicon wafer surface wafer Back propagates to the mask surface and obtains the new mask surface complex amplitude distribution E mask , return to step 6.

2. The holographic lithography mask optimization design method based on the alternating projection algorithm according to claim 1, characterized in that: The step 4: adopting polygon-based partial alternating phase shift distribution for asymmetric graphics, specifically includes: decomposing the input binary mask graphics into unconnected polygons; and numbering them in order from top to bottom and from left to right; and introducing phase shift to the odd-numbered or even-numbered polygonal regions.

3. The holographic lithography mask optimization design method based on the alternating projection algorithm according to claim 1, characterized in that: Step 5: Use the ASPW algorithm to reversely propagate the initial complex amplitude distribution E0 of the silicon wafer surface to the mask surface to obtain the complex amplitude distribution E mask , specifically including: Step 5.1 Calculate the diffraction spectrum corresponding to the initial complex amplitude distribution E0 in represents the two-dimensional Fourier transform; Step 5.2 calculates the frequency domain form H of the spatial filter function at the adjacent spacing; Step 5.3 Calculate the diffraction spectrum of the mask surface The formula is as follows: Step 5.4 Diffraction spectrum of the mask surface Perform a two-dimensional inverse Fourier transform to obtain the complex amplitude distribution E of the mask surface mask .

4. The holographic lithography mask optimization design method based on the alternating projection algorithm according to claim 1, characterized in that: In step 6, the amplitude is discretized by first discretizing the amplitude A of the mask surface in each iteration. mask Divide by its mean A mean , so that the mean of the new amplitude distribution is 1, and then discretization is performed according to the preset discretization rule; the phase discretization is to discretize the phase of the mask surface according to the preset discretization rule and the phase grading number n Discretization processing is performed.

5. The holographic lithography mask optimization design method based on the alternating projection algorithm according to claim 1, characterized in that: The imaging evaluation function D1 in step 9 is the area error AER value of the photoresist profile in the signal area, and the formula is as follows: Where N signalregion is the total number of pixels in the signal area, ║*║2 represents the L-2 norm, z target is the photoresist profile of the target mask pattern, which is numerically equal to Mask target .

6. The holographic lithography mask optimization design method based on the alternating projection algorithm according to claim 1, characterized in that: In step 11, the amplitude A' of the silicon wafer surface is updated. wafer With phase The formula is as follows: Where M is a mixing parameter, and its value range is adjusted according to actual needs to control the linear combination ratio of the amplitude of the signal area and the noise area; A target The amplitude value of the target mask pattern, which is equal to Mask target ; Δ is the amplitude of the uniform background light field added in the signal area; The phase calculated in the previous iteration.

Images