Optimized generation method and equipment of amplitude type holographic mask and application

Abstract

The invention belongs to the related technical field of semiconductor photoetching technology, and discloses an amplitude type holographic mask optimization generation method and equipment and application, and the method comprises the following steps: (1) determining a system loss function based on a to-be-generated target pattern, initial to-be-optimized parameter distribution of an optimization system and an imaging method of the optimization system, carrying out gradient solution on the system loss function through a gradient descent method or a conjugate gradient method, and carrying out parameter updating on the to-be-optimized parameter through a gradient obtained through solution so as to obtain an optimal optimization parameter; and (2) converting the optimal optimization parameter into a binary amplitude holographic mask through parameter transformation. The precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to semiconductor lithography, and more specifically, relates to an optimized generation method, device and application of an amplitude holographic mask. Background Art

[0002] The semiconductor industry is an important pillar of the economy, driving the modern technological revolution and global digital transformation, and supporting the continuous development of technologies such as artificial intelligence, autonomous driving, and Internet of Everything. As the core technology in the field of micro-nano manufacturing, the development level of lithography technology directly determines the process accuracy and integration density of semiconductor devices. As the current mainstream lithography technology, projection lithography is facing numerous challenges with the continuous development of lithography technology nodes: limited by the characteristics of projection, the imaging result is greatly affected by mask defects, and expensive mask maintenance costs are required; complex projection lens groups are needed, and the design, processing, and installation costs are high. Holographic lithography can effectively avoid the above problems. Holographic masks are less sensitive to defects, and holographic lithography systems are simpler and do not require complex projection lens groups.

[0003] As an important device in the holographic lithography system, current research on holographic mask generation methods mostly uses a spatial light modulator to load the mask based on the phase modulation mode. However, this scheme is limited by the spatial bandwidth area of the spatial light modulator, and the modulation accuracy is limited. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement requirements of the prior art, the present invention provides an optimized generation method, device and application of an amplitude holographic mask, aiming to solve the problem of low accuracy caused by the limitation of the spatial bandwidth area of the spatial light modulator in the existing holographic mask generation method.

[0005] To achieve the above object, according to one aspect of the present invention, an optimized generation method of an amplitude holographic mask is provided. The method includes the following steps:

[0006] (1) Determine the system loss function based on the target pattern to be generated, the initial parameter distribution to be optimized of the optimization system, and the imaging method of the optimization system, and perform gradient solution on the system loss function by the gradient descent method or the conjugate gradient method. Update the parameters to be optimized with the obtained gradient to obtain the optimal optimization parameters;

[0007] (2) Convert the optimal optimization parameters into a binary amplitude holographic mask through parameter transformation.

[0008] Further, the parameter transformation is divided into two steps: first, the optimal optimization parameters need to be mapped to the interval [0,1], and then the mapped parameters are binarized so that the parameter distribution is only 0 and 1. At this time, the parameters are converted into a binary amplitude holographic mask.

[0009] Further, the initial parameter distribution to be optimized is an arbitrary random distribution or an interference hologram calculated according to the holographic principle.

[0010] Further, the expression of the system loss function is:

[0011] C = ∑{T[S(α)] - I t} n

[0012] where α is the parameter to be optimized for the optimization system, S(α) represents the parameter transformation of the parameter to be optimized to convert the parameter to be optimized into a mask distribution, T[S(α)] represents the light field distribution after the imaging propagation of the mask pattern, and I t is the selected target pattern distribution, and n is the exponent of the system loss function.

[0013] Further, the gradient of the system loss function is solved by the gradient descent method or the conjugate gradient method. The parameter to be optimized is updated according to the obtained gradient, and it is judged whether the updated parameter meets the imaging requirements or reaches the maximum number of iterations. If it meets, the optimized parameter, that is, the best optimized parameter, is output; if it does not meet, the parameter is continuously iteratively updated.

[0014] Further, the gradient of the loss function is solved by the gradient descent method, and the number of iterations is 150 times. The corresponding expression of the gradient descent method is:

[0015]

[0016] In each iteration process, the parameter to be optimized is updated according to the obtained gradient information, that is:

[0017] α = α - step * g

[0018] where step is the step size of gradient optimization.

[0019] The present invention also provides a lithography method. The lithography method uses the above-mentioned optimization generation method of the amplitude holographic mask to generate a binary holographic mask, and then loads the obtained binary amplitude holographic mask onto the amplitude mask template to modulate the light field. The modulated reconstruction light is incident on the binary amplitude holographic mask for imaging, and then the obtained image is used for etching.

[0020] Further, the light field after mask modulation is imaged and propagated by Fraunhofer diffraction propagation.

[0021] The present invention also provides an optimization generation system for an amplitude holographic mask. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the optimization generation method for the amplitude holographic mask as described above.

[0022] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the optimization generation method for the amplitude holographic mask as described above or the lithography method as described above.

[0023] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the optimization generation method, device and application of the amplitude holographic mask provided by the present invention mainly have the following beneficial effects:

[0024] 1. The present invention converts the optimal optimization parameters into a binary amplitude holographic mask through parameter transformation, that is, a parameter transformation method is introduced to perform parameter transformation on the mask. By parameter transformation, the mask to be optimized is converted into parameters to be optimized, which can ensure that the optimized parameters are distributed in [0, 1], and then a mask distribution is obtained. This method can convert the original restricted, discrete, and non-linear optimization problem into an unrestricted, continuous, and linear optimization problem, greatly reducing the complexity of the calculation process, accelerating the calculation speed, and reducing the processing difficulty of the mask, thereby improving the accuracy.

[0025] 2. When calculating the amplitude holographic mask, the gradient descent method or the conjugate gradient method is used to perform cyclic iterative optimization on the mask. Compared with the iterative Fourier algorithm (such as the Gerchberg-Saxton algorithm) in the existing phase mask solution, the gradient method has stronger directivity, faster calculation speed, and better convergence.

[0026] 3. Different loss function exponents n can be designed in the loss function setting to obtain different optimization effects according to different application scenarios and different target patterns.

[0027] 4. The optimization generation method of the present invention is based on an amplitude holographic mask. Compared with the existing method based on a phase spatial light modulator, when the amplitude holographic mask modulates the light field, different-sized and -precision mask plates can be freely processed according to requirements, getting rid of the limitations of the specific resolution and pixel size of the spatial light modulator, having a higher spatial bandwidth product, so more complex patterns can be generated, and higher imaging resolution can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of an optimization generation method for an amplitude holographic mask provided by the present invention;

[0029] Figure 2 is a schematic diagram of the structure to be generated constructed in the preferred embodiment of the present invention;

[0030] Figure 3 is a distribution diagram of the initial parameters to be optimized constructed in the preferred embodiment of the present invention;

[0031] Figure 4 is a schematic diagram of the light field propagation imaging model constructed in the preferred embodiment of the present invention;

[0032] Figure 5 is a schematic diagram of the amplitude holographic mask constructed in the preferred embodiment of the present invention;

[0033] Figure 6 is a reconstruction result diagram of the amplitude holographic mask constructed in the preferred embodiment of the present invention. Detailed implementation manners

[0034] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0035] The present invention provides an optimization generation method for an amplitude holographic mask, and the method can be applied to fields such as holographic lithography, holographic display, and beam shaping. Please refer to Figure 1 , the method mainly includes the following steps:

[0036] Step 1, determine the system loss function based on the target pattern to be generated, the initial parameter distribution to be optimized of the optimization system, and the imaging method of the optimization system, and perform gradient solution on the system loss function by the gradient descent method or the conjugate gradient method, and update the parameters to be optimized through the obtained gradient to obtain the optimal optimization parameters.

[0037] Select the target pattern to be generated and give the initial parameter distribution to be optimized of the optimization system. Among them, the initial parameter distribution to be optimized can be any random distribution or an interference hologram calculated according to the holographic principle. The expression of the interference hologram is:

[0038] H(x,y) = (O(x,y) + R(x,y)) · (O(x,y) + R(x,y)) *

[0039] where O(x,y) is the object light wave related to the target pattern, and R(x,y) is the reference light wave for holographic recording.

[0040] In one embodiment, as Figure 2 shown, the pattern to be generated selected in this preferred example is a two-dimensional grating structure. As Figure 3 shown, the selected initial distribution of parameters to be optimized is a random distribution, and the parameter values are arbitrarily distributed.

[0041] The expression of the system loss function is:

[0042] C = ∑{T[S(α)] - I t} n

[0043] where α is the parameter to be optimized for the optimization system, S(α) represents the parameter transformation of the parameter to be optimized to convert the parameter to be optimized into a mask distribution, T[S(α)] represents the light field distribution after imaging propagation of the mask pattern, I t is the selected target pattern distribution, and n is the exponent of the system loss function.

[0044] The gradient of the system loss function is solved by the gradient descent method or the conjugate gradient method. The parameter to be optimized is updated according to the obtained gradient, and it is judged whether the updated parameter meets the imaging requirements or reaches the maximum number of iterations. If it meets the requirements, the optimized parameter, that is, the optimal optimized parameter, is output; if it does not meet the requirements, the parameter is continuously iteratively updated.

[0045] In one embodiment, the exponent n of the loss function is 2. The exponent n determines the sensitivity of the model to the prediction error and the penalty method: when n = 1, it is the absolute value loss, and the penalty for the error is linearly related to the error size, and the sensitivity to outliers is low; when n = 2, it is the square loss, and the penalty for the error is quadratic with the error size, and it is sensitive to large errors; when n > 2 (such as n = 3, 4), it is the high-order loss, and the penalty of the function for large errors increases exponentially, and in extreme cases, it may over-focus on outliers; when n < 1 (such as n = 0.5), it is the sublinear loss, which is more sensitive to small errors but has a weak penalty for large errors, which may lead to slow convergence of the model.

[0046] In a specific embodiment, the gradient of the loss function is solved by the gradient descent method, and the number of iterations is 150 times. The corresponding expression of the gradient descent method is:

[0047]

[0048] In each iteration process, the parameter to be optimized is updated according to the obtained gradient information, that is:

[0049] α = α - step * g

[0050] where step is the step size of gradient optimization, and the step size can be selected according to the actual situation.

[0051] In an example of the present invention, during the iteration process, it is necessary to make a judgment after each parameter update. If the reconstructed light field meets the target requirements after the parameter update or the number of iterations is greater than 150 times, the optimized parameters are output. If the above requirements are not met, the iterative optimization continues until the conditions are satisfied.

[0052] Step two: Convert the optimal optimization parameters into a binary amplitude holographic mask through parameter transformation.

[0053] The parameter transformation is divided into two steps: First, it is necessary to map the optimal optimization parameters into the interval [0, 1], and then perform binarization processing on the mapped parameters so that the parameter distribution is only 0 and 1. At this time, the parameters are converted into a mask, and the mask distribution is as Figure 5 shown, and the mask information can be loaded; among them, the reconstruction result of the amplitude holographic mask is as Figure 6 shown.

[0054] The present invention also provides a lithography method. The lithography method uses the above-mentioned optimization generation method of the amplitude-type holographic mask to generate a binary holographic mask, and then loads the obtained binary amplitude holographic mask onto the amplitude mask template to modulate the light field. The modulated reconstructed light is incident on the binary amplitude holographic mask for imaging, and then the obtained image is used for etching.

[0055] In one embodiment, the light field after mask modulation is imaged and propagated by Fraunhofer diffraction propagation. The imaging process is as Figure 4 shown. The mask is located at the front focal plane of the lens, and the image plane is located at the rear focal plane of the lens. The plane wave is incident on the mask and is modulated by the mask and then converged by the lens to form an image.

[0056] Specifically, in this example, the wavelength of the incident reconstructed light is 405 nm, the focal length of the lens is 18 mm, and the mask transmittance distribution is M = S(α). Then, the calculation of the image plane light field distribution can be converted to:

[0057] U(u, v) = A · FFT(M)

[0058] In the formula, the FFT operation is the fast Fourier transform.

[0059] The amplitude mask template can be a digital micromirror device or an amplitude-type modulated spatial light modulator or a common transmissive chromium layer mask. In this example, a transmissive chromium layer mask is used to load the information. The mask unit size is 1 μm, the mask substrate material is light-transmitting silica, and the surface pattern material is opaque chromium layer. The mask is processed according to the calculated mask distribution, and after processing, the mask can be used to modulate the light field.

[0060] In an example of the present invention, a plane wave incident mask scheme is adopted. After the light field is incident on the mask, it propagates through free space to the lens, and the lens collects the information and converges the image on the image plane.

[0061] The present invention also provides an optimization generation system for an amplitude holographic mask. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the optimization generation method for the amplitude holographic mask as described above.

[0062] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the optimization generation method for the amplitude holographic mask or the lithography method as described above.

[0063] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing and generating an amplitude type holographic mask, characterized in that: The method comprises the following steps: (1) determining a system loss function based on a target pattern to be generated, an initial parameter distribution of the optimization system to be optimized, and an imaging method of the optimization system, and performing a gradient solution on the system loss function by a gradient descent method or a conjugate gradient method, and updating the parameters to be optimized by using the gradient obtained by the solution to obtain the optimal optimization parameters; (2) The best optimized parameters are converted into a binary amplitude holographic mask through parameter transformation.

2. The method for optimizing and generating an amplitude type holographic mask according to claim 1, wherein: The parameter transformation is divided into two steps: first, the best optimization parameters need to be mapped to the interval [0,1], and then the mapped parameters are binarized so that the parameter distribution is only 0 and 1. At this time, the parameters are converted into a binary amplitude holographic mask.

3. The method for optimizing and generating an amplitude type holographic mask according to claim 1, wherein: The initial parameter distribution to be optimized is an arbitrary random distribution or an interference hologram calculated according to the holographic principle.

4. The method for optimizing and generating an amplitude type holographic mask according to claim 1, wherein: The expression of the system loss function is: C=∑{T[S(α)]-I t } n Where α is the parameter to be optimized of the optimization system, S(α) represents the parameter transformation of the parameter to be optimized to convert the parameter to be optimized into the mask distribution, T[S(α)] represents the light field distribution after the mask pattern is imaged and propagated, I t is the selected target pattern distribution, and n is the exponent of the system loss function.

5. The method for optimizing and generating an amplitude type holographic mask according to claim 1, wherein: The gradient of the system loss function is solved by the gradient descent method or the conjugate gradient method. The parameters to be optimized are updated by the gradient obtained, and it is judged whether the updated parameters meet the imaging requirements or whether the maximum number of iterations has been reached. If so, the optimization parameters, i.e., the best optimization parameters, are output; if not, the optimization parameters are continued to be iteratively updated.

6. The method for optimizing and generating an amplitude type holographic mask according to claim 1, wherein: The gradient descent method is used to solve the gradient of the loss function. The expression corresponding to the gradient descent method is: In each iteration, the parameters to be optimized are updated according to the obtained gradient information, namely: α=α-step*g Where step is the step size of gradient optimization.

7. A photolithography method, characterized in that: The photolithography method adopts the optimized generation method of the amplitude-type holographic mask described in any one of claims 1 to 6 to generate a binary holographic mask, and then loads the obtained binary amplitude holographic mask into the amplitude mask plate to modulate the light field, uses the modulated reconstructed light to incident on the binary amplitude holographic mask for imaging, and then uses the obtained image for etching.

8. The photolithography method according to claim 7, wherein: The light field modulated by the mask is imaged and propagated using Fraunhofer diffraction propagation.

9. An optimized generation system for an amplitude type holographic mask, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the method for optimizing and generating an amplitude-type holographic mask according to any one of claims 1 to 6 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the optimized generation method of the amplitude-type holographic mask described in any one of claims 1-6 or the lithography method described in any one of claims 7-8.

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