Method for constructing etching simulation model

Abstract

A method for constructing an etching simulation model, comprising: obtaining a two-dimensional etching simulation model; providing a plurality of first lithography pattern groups, each including a plurality of first lithography design patterns arranged in an array, the first lithography design patterns of different first lithography pattern groups having different sizes; etching a sample based on the plurality of first lithography pattern groups to form a plurality of first sample groups; detecting the plurality of first sample groups to obtain a plurality of detection data corresponding to a plurality of detection positions, including position data and etching depth of the detection positions; obtaining a plurality of specified simulation data corresponding to a plurality of specified target simulation positions based on the plurality of first lithography pattern groups, the two-dimensional etching simulation model, and the plurality of detection positions; and constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data, and the two-dimensional etching simulation model. Thus, the two-dimensional etching profile and the three-dimensional etching topography are simultaneously simulated.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit manufacturing, and in particular to a method for constructing an etching simulation model. Background Technology

[0002] As the semiconductor industry shrinks in size, the number of transistors on integrated circuit devices is constantly increasing, leading to ever-higher requirements for the precision of integrated circuit manufacturing. In the integrated circuit manufacturing process, semiconductor devices typically require etching. Semiconductor devices are three-dimensional geometric structures composed of multiple layers of materials, mainly including a substrate, deposited thin films, and photoresist on the surface. Etching semiconductor devices involves first exposing the photoresist to a designed mask pattern using photolithography to obtain the mask pattern layer. Then, unwanted materials are selectively removed from the surface of the deposited thin film using chemical or physical methods to transfer the designed mask pattern.

[0003] The etching process, whether dry or wet, involves a complex interplay of multiple factors, including the shape and density of the mask pattern, the diffusion of the etching material, the flow of the etchant, interface delamination, and chemical reactions. Accurately predicting etching deviations and determining whether unwanted material can be removed during etching to facilitate the transfer of the mask pattern is a crucial step in creating semiconductor devices that meet performance requirements. To predict deviations in the designed mask pattern during actual etching and to adjust the pattern before etching, existing technologies have proposed several models for simulating and analyzing the etching process. For example, one existing technology employs a complex mathematical model using perturbation techniques to address the diffusion field issues related to surface reactions and moving boundaries during etching. Another example is an empirical model based on pattern density, which, due to its complexity, uses approximate solutions to simplify the model and calibrate its parameters.

[0004] Compared to dry etching, which is anisotropic, wet etching is usually isotropic. Consequently, the sidewalls of the grooves formed by wet etching are prone to tilting.

[0005] However, the simulation models proposed by the aforementioned existing technologies can usually only simulate two-dimensional etching contours, and cannot simultaneously simulate three-dimensional etching profiles, resulting in an inability to accurately predict etching deviations in structures formed by wet etching. Summary of the Invention

[0006] The technical problem solved by this invention is to provide a method for constructing an etching simulation model, so as to construct a three-dimensional etching simulation model to simultaneously simulate the two-dimensional etching contour and the three-dimensional etching morphology.

[0007] To address the aforementioned technical problems, the present invention provides a method for constructing an etching simulation model, comprising: acquiring a two-dimensional etching simulation model; providing a plurality of first lithographic pattern groups, each first lithographic pattern group including multiple first lithographic design patterns arranged in an array, and the sizes of the first lithographic design patterns in different first lithographic pattern groups being different; etching samples based on the plurality of first lithographic pattern groups to form corresponding plurality of first sample groups, each first sample group including multiple first etching grooves; detecting the plurality of first sample groups to acquire a plurality of detection data corresponding to a plurality of detection positions, the detection data including position data and etching depth of the detection positions; acquiring a plurality of specified simulation data corresponding to a plurality of specified target simulation positions based on the plurality of first lithographic pattern groups, the two-dimensional etching simulation model, and the plurality of detection positions, the specified target simulation positions being target simulation positions corresponding to the detection positions, the specified simulation data including position data and etching probability of the specified target simulation positions; and constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data, and the two-dimensional etching simulation model.

[0008] Optionally, the two-dimensional etching simulation model includes the value D′0 of the etching probability threshold D0; the method for constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data, and the two-dimensional etching simulation model includes: interpolating the plurality of detection data corresponding to the plurality of detection positions to obtain a plurality of interpolated detection positions, and interpolated position data and interpolated etching depth of each interpolated detection position; interpolating the plurality of specified simulation data corresponding to the plurality of specified target simulation positions to obtain a plurality of interpolated specified target simulation positions having the same interpolated position data as the plurality of interpolated detection positions, and so on. The interpolation etching probability is specified for each target simulation position; the interpolation etching depth and interpolation etching probability with the same interpolation position data are associated to obtain several interpolation data sets; the several interpolation data sets are fitted to obtain the etching depth fitting model z(x,y)=G[d(x,y)] between the simulation etching depth z and the etching probability d(x,y) at the target simulation position, where G represents the functional relationship between z(x,y) and d(x,y); based on the etching depth fitting model z(x,y)=G[d(x,y)] and the two-dimensional etching simulation model, a three-dimensional etching simulation model is constructed:

[0009]

[0010] Optionally, the method for obtaining the two-dimensional etching simulation model includes: providing an initial etching probability convolution model containing t sets of parameters, each parameter set including the corresponding equivalent feature distance and normalized weight coefficients, where t is a natural number; providing v rectangular second lithographic design patterns, each second lithographic design pattern having a different size, where v is a natural number and v≥2t; etching the sample based on the v second lithographic design patterns to form corresponding v second etching grooves; measuring the v second etching grooves to obtain the dimensions of the corresponding v second etching contours; and based on the dimensions of the v second lithographic design patterns and the v... The dimensions of the second etching contour are used to obtain the corresponding v sets of etching deviation dimensions. Based on the initial etching probability convolution model, the dimensions of the v second lithographic design patterns, and the v sets of etching deviation dimensions, an implicit fitting incremental iterative model is obtained. According to the implicit fitting incremental iterative model, several incremental iterations are performed to obtain the value of the etching probability threshold and the value of the t sets of parameters. The value of the t sets of parameters is substituted into the initial etching probability convolution model to form an etching probability convolution model. Based on the etching probability convolution model and the value of the etching probability threshold, a two-dimensional etching simulation model is constructed.

[0011] Optionally, the method for obtaining the implicit fitting incremental iterative model based on the initial etching probability convolution model, the dimensions of v second lithographic design patterns, and v sets of etching deviation dimensions includes: obtaining an analytical solution equation set corresponding to each second lithographic design pattern based on the initial etching probability convolution model and the dimensions of v second lithographic design patterns, wherein the analytical solution equation set includes an etching probability threshold; and performing implicit fitting processing based on the v sets of etching deviation dimensions and the v analytical solution equation sets corresponding to the v second lithographic design patterns to obtain the implicit fitting incremental iterative model.

[0012] Optionally, in the v second lithographic design patterns, the size of any second lithographic design pattern includes the length Wx and width Wy of the second lithographic design pattern; in the v second etching profiles, the size of any second etching profile includes the length Wx′ and width Wy′ of the second etching profile; in the v groups of etching deviation dimensions, any group of etching deviation dimensions includes length deviation and width deviation, and the length deviation of the i-th group... Width deviation of group i The Wx i ′ is the length Wx′ of the i-th second etched profile, wherein Wx i The length Wx of the i-th second lithographic design pattern, wherein Wy i ′ is the width Wy′ of the i-th second etch profile, wherein Wy iWy is the width of the i-th second lithographic design pattern, where i is a natural number and i ≤ v.

[0013] Optionally, among the v second lithographic design patterns, there are multiple second lithographic design patterns with the same length Wx and arranged along the width Wy dimension direction. The multiple first lithographic design patterns with the same length Wx and arranged along the width Wy dimension direction have different widths Wy, and the multiple second lithographic design patterns with the same length Wx and arranged along the width Wy dimension direction have the same spacing in the width Wy dimension direction.

[0014] Optionally, based on the initial etching probability convolution model and the dimensions of the v second lithography design patterns, an analytical solution equation set corresponding to each second lithography design pattern is obtained, and each set of parameters corresponds to more than one set of analytical solution equations, wherein the analytical solution equation set corresponding to the i-th second lithography design pattern is:

[0015]

[0016] h is a natural number, and h ≤ t, n h It is the normalized weight coefficient in the h-th parameter group, where σ is... h It is the equivalent feature distance in the h-th parameter group, where erf represents the error function, and D0 is the etching probability threshold. The length deviation Sx corresponding to the i-th group i The calculated length deviation, the Sy corresponds to the width deviation of the i-th group. i The calculated width deviation.

[0017] Optionally, the method for obtaining the implicit fitting incremental iterative model by implicitly fitting the v sets of analytical solution equations corresponding to the v sets of etching deviation dimensions and the v second lithography design patterns includes: specifying the etching probability threshold D0, any normalized weight coefficient in the t sets of parameters, or any equivalent feature distance in the t sets of parameters as a specified parameter with a preset fixed value; and forming a parameter set {P} by combining the parameters other than the specified parameter in the etching probability threshold D0, each normalized weight coefficient in the t sets of parameters, and each equivalent feature distance in the t sets of parameters; performing implicit fitting on the v sets of analytical solution equations based on the specified parameter to obtain the implicit fitting incremental iterative model, wherein the implicit fitting incremental iterative model is:

[0018]

[0019] Where j, k, and l are all natural numbers, where j ≤ 2t, and pj and p k Each of the parameters is any parameter in the parameter set {P}. and The parameters p are respectively the parameters corresponding to the l-th incremental iteration process in the several incremental iteration processes. j Parameter p k Calculate the length deviation and calculate width deviation The parameter p is the parameter p corresponding to the (l-1)th iteration in the several incremental iterations described above. i The method for obtaining the etching probability threshold and the values ​​of the t sets of parameters by performing several incremental iterations based on the implicitly fitted incremental iterative model includes: during the l-th incremental iteration, based on the parameters obtained in the (l-1)-th incremental iteration... The value of the specified parameter, and the v analytical solution equations are used to obtain the computational length deviation. The value, and the calculated width deviation The value of the parameter when l = 1. The value is a preset value; the calculated length deviation is... The value, and the calculated width deviation Substituting the value into the implicitly fitted incremental iterative model, we obtain the increment corresponding to the l-th incremental iteration. The value and parameters The value; the increment obtained in the Mth incremental iteration. When all values ​​are within a preset percentage, the incremental iteration process is terminated, where M is a natural number and M≥1, and the parameters obtained from the Mth incremental iteration process are... The value is taken as: the value of the parameters other than the specified parameter in the etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the equivalent feature distances in the t sets of parameters.

[0020] Optionally, the preset fixed value of the specified parameter is 1.

[0021] Optionally, the preset percentage is 1%.

[0022] Optionally, the initial etching probability convolution model is:

[0023]

[0024] Where (x,y) are the two-dimensional coordinates of the target simulation position, d(x,y) is the etching probability of the target simulation position, (x′,y′) are the two-dimensional coordinates of the associated simulation position, the associated simulation position is any simulation position other than the target simulation position when performing convolution, M(x′,y′) is the binary image function of the associated simulation position, when any associated simulation position is within the preset etching region, the binary image function M(x′,y′) = 1, when any associated simulation position is outside the preset etching region, the binary image function M(x′,y′) = 0, and exp represents an exponential function with the natural constant e as the base.

[0025] Optionally, the method of substituting the values ​​of the t sets of parameters into the initial etching probability convolution model to form the etching probability convolution model includes: based on the specified parameters and the values ​​of each parameter in the parameter set {P} obtained by the Mth incremental iteration, substituting the values ​​of each equivalent feature distance and each normalized weight coefficient into the initial etching probability convolution model to form the etching probability convolution model.

[0026]

[0027] Where, n h ′ represents the normalized weighting coefficient n h The value of σ h ′ is the equivalent feature distance σ h The value of .

[0028] Optionally, the two-dimensional etching simulation model constructed based on the etching probability convolution model and the value D0′ of the etching probability threshold D0 includes:

[0029]

[0030] Optionally, the method of etching the sample based on v second photolithographic design patterns to form v corresponding second etched grooves includes: forming a first photoresist layer on the sample surface; patterning the first photoresist layer according to v second photolithographic design patterns to form a first mask layer on the sample surface that exposes a portion of the sample surface; and etching the sample using the first mask layer as a mask to form v corresponding second etched grooves within the sample.

[0031] Optionally, the method for detecting several first sample groups and obtaining several detection data corresponding to several detection positions includes: detecting each first sample group according to several preset intervals, obtaining several sets of detection data corresponding to several preset intervals, each set of detection data including a set of several detection data corresponding to several detection positions arranged along a straight line, and the maximum detection interval between the several detection positions arranged along the straight line is equal to the corresponding preset interval.

[0032] Optionally, the method of detecting several first sample groups and obtaining several detection data corresponding to several detection positions further includes: detecting each first sample group according to several preset intervals, obtaining the several sets of detection data including several specified detection data groups, wherein several detection positions corresponding to each specified detection data group are arranged along a straight line passing through the center position of the first sample group.

[0033] Optionally, a method for obtaining several specified simulation data corresponding to several specified target simulation positions based on several first lithography pattern groups, a two-dimensional etching simulation model, and several detection positions includes: inputting several first lithography pattern groups into the two-dimensional etching simulation model, obtaining simulation result data corresponding to the several first lithography pattern groups, wherein the simulation result data includes a two-dimensional simulation etching contour pattern, and position data and etching probability of any target simulation position in the two-dimensional simulation etching contour pattern; determining several sets of several specified target simulation positions arranged along a straight line in the two-dimensional simulation etching contour pattern according to several preset spacings and several sets of several detection positions arranged along a straight line, and obtaining specified simulation data corresponding to each specified target simulation position, wherein the maximum detection spacing between the several specified target simulation positions arranged along a straight line is equal to the corresponding preset spacing.

[0034] Optionally, the location data of the detection location includes the two-dimensional coordinates x of the detection location. E and y E Furthermore, several location data points in any detection data set have the same x-coordinate. E or coordinate y E The location data of the specified target simulation location includes the two-dimensional coordinates x of the specified target simulation location. S and y S Furthermore, any set of several specified target simulation positions arranged along a straight line have the same x-coordinate. S or coordinate y S .

[0035] Compared with the prior art, the technical solution of the embodiments of the present invention has the following beneficial effects:

[0036] The method for constructing an etching simulation model provided by the technical solution of the present invention includes: acquiring a two-dimensional etching simulation model; providing a plurality of first lithographic pattern groups, each first lithographic pattern group including a plurality of first lithographic design patterns arranged in an array, and the size of the first lithographic design patterns in different first lithographic pattern groups is different; etching a sample based on the plurality of first lithographic pattern groups to form a plurality of corresponding first sample groups, each first sample group including a plurality of first etching grooves; detecting the plurality of first sample groups to acquire a plurality of detection data corresponding to a plurality of detection positions, the detection data including the position data and etching depth of the detection positions; acquiring a plurality of specified simulation data corresponding to a plurality of specified target simulation positions based on the plurality of first lithographic pattern groups, the two-dimensional etching simulation model and the plurality of detection positions, the specified target simulation positions being the target simulation positions corresponding to the detection positions, the specified simulation data including the position data and etching probability of the specified target simulation positions; and constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data and the two-dimensional etching simulation model. Therefore, the constructed three-dimensional etching simulation model can simultaneously simulate the two-dimensional etching profile and the three-dimensional etching morphology, thereby accurately predicting the etching deviation of the structure formed by wet etching. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating a method for constructing an etching simulation model according to an embodiment of the present invention;

[0038] Figure 2 This is a flowchart illustrating step S1000 in one embodiment of the present invention;

[0039] Figure 3 This is a schematic diagram of the structure of the second photolithographic design pattern in one embodiment of the present invention;

[0040] Figure 4 This is a top view of the second etched groove in one embodiment of the present invention;

[0041] Figure 5 yes Figure 4 A schematic diagram of the cross-sectional structure along the central direction A1-A2;

[0042] Figure 6 This is a schematic diagram of the second etching profile in one embodiment of the present invention;

[0043] Figure 7 This is a schematic diagram of the etching deviation size in one embodiment of the present invention;

[0044] Figure 8 This is a flowchart illustrating step S1600 in one embodiment of the present invention;

[0045] Figure 9This is a flowchart illustrating step S1620 in one embodiment of the present invention;

[0046] Figure 10 This is a flowchart illustrating step S1700 in one embodiment of the present invention;

[0047] Figure 11 This is a schematic diagram of the structure of the first photolithographic pattern group in one embodiment of the present invention;

[0048] Figure 12 This is a top view of the structure of the first sample group in one embodiment of the present invention;

[0049] Figure 13 yes Figure 12 A schematic diagram of the cross-sectional structure along the B1-B2 direction;

[0050] Figure 14 yes Figure 12 The first sample group of images;

[0051] Figure 15 This is a flowchart illustrating step S5000 in one embodiment of the present invention;

[0052] Figure 16 This is a flowchart illustrating step S6000 in one embodiment of the present invention. Detailed Implementation

[0053] As described in the background section, existing simulation models can typically only simulate two-dimensional etching profiles, but cannot simultaneously simulate three-dimensional etching morphology, resulting in an inability to accurately predict etching deviations in structures formed by wet etching.

[0054] To address the aforementioned technical problems, the present invention provides a method for constructing an etching simulation model, comprising: acquiring a two-dimensional etching simulation model; providing a plurality of first lithographic pattern groups, each first lithographic pattern group including multiple first lithographic design patterns arranged in an array, and the sizes of the first lithographic design patterns in different first lithographic pattern groups being different; etching samples based on the plurality of first lithographic pattern groups to form corresponding plurality of first sample groups, each first sample group including multiple first etching grooves; detecting the plurality of first sample groups to acquire a plurality of detection data corresponding to a plurality of detection positions, the detection data including position data and etching depth of the detection positions; acquiring a plurality of specified simulation data corresponding to a plurality of specified target simulation positions based on the plurality of first lithographic pattern groups, the two-dimensional etching simulation model, and the plurality of detection positions, the specified target simulation positions being target simulation positions corresponding to the detection positions, the specified simulation data including position data and etching probability of the specified target simulation positions; and constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data, and the two-dimensional etching simulation model. The constructed three-dimensional etching simulation model can simultaneously simulate the two-dimensional etching profile and the three-dimensional etching morphology, thereby accurately predicting the etching deviation of the structure formed by wet etching.

[0055] To make the above-mentioned objectives, features and beneficial effects of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0056] Figure 1 This is a flowchart illustrating a method for constructing an etching simulation model according to an embodiment of the present invention.

[0057] Please refer to Figure 1 The method for constructing the etching simulation model includes:

[0058] Step S1000: Obtain the two-dimensional etching simulation model;

[0059] Step S2000: Provide a plurality of first photolithography pattern groups, each first photolithography pattern group including a plurality of first photolithography design patterns arranged in an array, and the size of the first photolithography design patterns in different first photolithography pattern groups is different;

[0060] Step S3000: The sample is etched based on several first photolithography pattern groups to form several corresponding first sample groups, each first sample group including multiple first etched grooves;

[0061] Step S4000: Detect several first sample groups and obtain several detection data corresponding to several detection positions. The detection data includes the position data and etching depth of the detection positions.

[0062] Step S5000: Based on several first lithography pattern groups, a two-dimensional etching simulation model, and several detection positions, obtain several specified simulation data corresponding to several specified target simulation positions. The specified target simulation position is the target simulation position corresponding to the detection position. The specified simulation data includes the position data and etching probability of the specified target simulation position.

[0063] Step S6000: Construct a three-dimensional etching simulation model based on several detection data, several specified simulation data, and a two-dimensional etching simulation model.

[0064] Compared to dry etching, wet etching is usually an isotropic etching process. Therefore, wet etching not only focuses on the contour formed after etching, but also on the profile formed after etching, such as the inclination of the sidewalls of the holes.

[0065] The method for constructing the etching simulation model includes: obtaining a two-dimensional etching simulation model based on an etching probability convolution model; providing several first lithographic pattern groups, each first lithographic pattern group including multiple first lithographic design patterns arranged in an array, and the sizes of the first lithographic design patterns in different first lithographic pattern groups are different; etching samples based on several first lithographic pattern groups to form several corresponding first sample groups, each first sample group including multiple first etching grooves; detecting several first sample groups to obtain several detection data corresponding to several detection positions, the detection data including the position data and etching depth of the detection position; obtaining several specified simulation data corresponding to several specified target simulation positions based on several first lithographic pattern groups, the two-dimensional etching simulation model and several detection positions, the specified target simulation positions being the target simulation positions corresponding to the detection positions, the specified simulation data including the position data and etching probability of the specified target simulation positions; and constructing a three-dimensional etching simulation model based on several detection data, several specified simulation data and the two-dimensional etching simulation model. Therefore, by linking the detection data of the first sample group with the two-dimensional etching simulation model, a three-dimensional etching simulation model is constructed. This not only achieves accurate etching contour simulation but also accurate etching morphology simulation, meeting the simulation requirements of wet etching processes. Thus, the constructed three-dimensional etching simulation model simultaneously simulates both the two-dimensional etching contour and the three-dimensional etching morphology, accurately predicting etching deviations in the structure formed by wet etching.

[0066] In this embodiment, a two-dimensional etching simulation model is obtained based on the etching probability convolution model.

[0067] In some other embodiments, empirical models based on pattern density proposed in the prior art may also be used as the two-dimensional etching simulation model.

[0068] Specifically, please refer to Figure 2 , Figure 2 This is a flowchart illustrating step S1000 in one embodiment of the present invention. The method for obtaining the two-dimensional etching simulation model in step S1000 includes:

[0069] Step S1100: Provide an initial etching probability convolution model containing t sets of parameters, where each set of parameters includes the corresponding equivalent feature distance and normalized weight coefficients, and t is a natural number;

[0070] Step S1200: Provide v rectangular second lithographic design patterns, each second lithographic design pattern having a different size, where v is a natural number and v≥2t;

[0071] Step S1300: Based on v second photolithographic design patterns, the sample is etched to form v corresponding second etched grooves;

[0072] Step S1400: Measure v second etched grooves to obtain the dimensions of the corresponding v second etched contours;

[0073] Step S1500: Based on the dimensions of v second photolithographic design patterns and v second etching contours, obtain the corresponding v sets of etching deviation dimensions;

[0074] Step S1600: Based on the initial etching probability convolution model, the dimensions of v second lithography design patterns, and v sets of etching deviation dimensions, obtain the implicit fitting incremental iterative model.

[0075] Step S1700: Based on the implicit fitting incremental iterative model, perform several incremental iterations to obtain the value of the etching probability threshold and the value of the t set of parameters.

[0076] Step S1800: Substitute the values ​​of the t sets of parameters into the initial etching probability convolution model to form an etching probability convolution model;

[0077] Step S1900: Based on the etching probability convolution model and the value of the etching probability threshold, construct a two-dimensional etching simulation model.

[0078] Typically, for empirical models based on graphic density, due to the complexity of the model, approximate solutions are used to simplify the model and calibrate the model parameters. Therefore, the model parameters obtained by this model cannot reach the global optimum, which affects the computational accuracy of the model and consequently affects the simulation accuracy of the 3D etching simulation model built based on this model.

[0079] In this embodiment, the method for constructing the etching simulation model includes: providing an initial etching probability convolutional model containing t sets of parameters, where each parameter set includes a corresponding equivalent feature distance and a normalized weight coefficient, and t is a natural number; providing v rectangular second lithographic design patterns, each second lithographic design pattern having a different size, where v is a natural number and v≥2t; etching the sample based on the v second lithographic design patterns to form corresponding v second etching grooves; measuring the v second etching grooves to obtain the dimensions of the corresponding v second etching contours; obtaining the corresponding v sets of etching deviation dimensions based on the dimensions of the v second lithographic design patterns and the dimensions of the v second etching contours; obtaining an implicit fitting incremental iterative model based on the initial etching probability convolutional model, the dimensions of the v second lithographic design patterns, and the v sets of etching deviation dimensions; and performing several incremental iterations based on the implicit fitting incremental iterative model to obtain the value of the etching probability threshold and the value of the t sets of parameters. Therefore, globally optimal parameter values ​​(the etching probability threshold and the parameter values ​​of the t sets of parameters are simultaneously ideal) can be obtained. Thus, by substituting the values ​​of the t sets of parameters into the initial etching probability convolution model, an etching probability convolution model can be formed. Furthermore, based on the etching probability convolution model and the value of the etching probability threshold, a more accurate two-dimensional etching simulation model can be constructed, thereby achieving the construction of a more accurate three-dimensional etching simulation model.

[0080] Specifically, the initial etching probability convolution model is a phenomenological model.

[0081] In this embodiment, the initial etching probability convolution model is:

[0082]

[0083] Based on the mask pattern input during etching simulation, (x,y) are the two-dimensional coordinates of the target simulation position, and (x′,y′) are the two-dimensional coordinates of the associated simulation position, which is any simulation position other than the target simulation position when performing convolution.

[0084] The mask pattern includes: a preset etched area and a non-etched area.

[0085] In this context, the preset etching area is the area that is desired to be etched during the actual etching process, while the preset non-etchable area is the area that is desired not to be etched during the actual etching process. That is, in the mask pattern, the preset non-etchable area is the area outside the preset etching area.

[0086] It should be noted that the boundary between the preset etching area and the preset non-etching area is the critical position (boundary) of the area to be etched during the actual etching process, which belongs to the preset etching area.

[0087] The d(x,y) is the etching probability of the target simulation position.

[0088] Specifically, the etching probability d(x,y) represents the probability that the material at the target simulation position with two-dimensional coordinates (x,y) will be etched due to the complex coupling phenomena of the structure (shape and density, etc.) of the nearby mask, the diffusion of the etching material, the flow of the etchant, and chemical reactions.

[0089] The etching probability threshold D0 represents the critical etching probability.

[0090] That is, by comparing the etching probability d(x,y) of the target simulation position (x,y) with the etching probability threshold D0, it can be determined whether the target simulation position (x,y) has been etched.

[0091] Specifically, during the etching simulation, when the etching probability d(x,y) of the target simulation location (x,y) is equal to the etching probability threshold D0, it indicates that the target simulation location (x,y) is at the boundary (critical position) between the simulated etched area and the unetched area. Correspondingly, the contour line of d(x,y) and the etching probability threshold D0 is the simulated etching contour.

[0092] M(x′,y′) is the binary image function of the associated simulation position.

[0093] Based on the mask pattern input during etching simulation, when any associated simulation position is within the preset etching region, the binary image function M(x′,y′) of the associated simulation position is 1, and when any associated simulation position is outside the preset etching region, the binary image function M(x′,y′) of the associated simulation position is 0.

[0094] It is important to understand that, since different types of photoresists have different material properties during exposure and development, the pre-defined etching areas in the photomask pattern can be either light-transmitting or opaque areas, depending on the type of photoresist.

[0095] Specifically, for positive photoresist, the pre-defined etching areas in the mask pattern are designed to be transparent. Therefore, when the associated simulation position (x′,y′) is located within the transparent area, M(x′,y′) is assigned a value of 1, and when the associated simulation position (x′,y′) is located within the remaining areas designed to be opaque, M(x′,y′) is assigned a value of 0.

[0096] Specifically, for negative photoresist, the pre-defined etching areas in the mask pattern are designed to be opaque. Therefore, when the associated simulation position (x′,y′) is located within the opaque area, M(x′,y′) is assigned a value of 1; when the associated simulation position (x′,y′) is located within the remaining areas designed to be transparent, M(x′,y′) is assigned a value of 0.

[0097] K(xx′,yy′) is the kernel function, and exp represents an exponential function with the natural constant e as the base.

[0098] In this embodiment, K(xx′,yy′) is a linear superposition of two-dimensional Gaussian functions, and the monotonically decreasing nature of K(xx′,yy′) indicates that during the etching process, the influence of the associated simulation position (x′,y′) on the target simulation position (x,y) decreases as the distance between them decreases.

[0099] Furthermore, h is a natural number, and h ≤ t.

[0100] Based on this, the n h It is the normalized weight coefficient in the h-th parameter group within the t-th parameter group, and σ h It is the equivalent feature distance in the h-th parameter group of the t-group parameter group.

[0101] The equivalent feature distance characterization refers to the feature scale that generates etching interaction between the associated simulation position (x′,y′) and the target simulation position (x,y) due to the influence of complex phenomena such as the structure of the mask (shape and density, etc.), the diffusion of etching material, the flow of etchant, and chemical reactions.

[0102] It should be noted that in the initial etching probability convolution model, the values ​​of each normalized weight coefficient and each equivalent feature distance in the t sets of parameters are unknowns to be obtained.

[0103] It is important to understand that as the number of expanded terms in the kernel function K(xx′,yy′) increases, the complexity of the initial etching probability convolution model increases, as does the number of parameter sets (i.e., the increase of t). At the same time, the complexity and accuracy of the subsequent etching probability convolution model formed based on the initial etching probability convolution model both improve. Consequently, the amount of data computation is greater during etching simulation using the etching probability convolution model.

[0104] Furthermore, the values ​​of the etching probability threshold D0, the normalized weight coefficients in the t parameter groups, and the equivalent feature distances are correlated, and the value of the etching probability threshold D0 is also an unknown to be obtained.

[0105] Please refer to Figure 3 , Figure 3 This is a schematic diagram of the structure of the second photolithographic design pattern in one embodiment of the present invention. For step S1200, v rectangular second photolithographic design patterns 100 are provided. The size of each second photolithographic design pattern 100 is different, v is a natural number, and v≥2t.

[0106] It should be noted that, for ease of understanding, Figure 2 The diagram schematically illustrates multiple second lithographic design patterns 100.

[0107] In this embodiment, the dimensions of any one of the v second lithographic design patterns 100 include: the length Wx and the width Wy of the any one second lithographic design pattern 100.

[0108] In this embodiment, the v second lithographic design patterns 100 include multiple second lithographic design patterns 100 having the same length Wx and arranged along the width Wy dimensional direction. The multiple second lithographic design patterns 100 having the same length Wx and arranged along the width Wy dimensional direction each have a different width Wy, and the multiple second lithographic design patterns 100 having the same length Wx and arranged along the width Wy dimensional direction have the same spacing. Therefore, the rationality of the size and arrangement of the v second lithographic design patterns 100 is further improved, thereby better enhancing the reliability of the sample data.

[0109] In some other embodiments, the v second lithographic design patterns include multiple second lithographic design patterns having the same width Wy and different lengths Wx, or the v second lithographic design patterns include multiple second lithographic design patterns having different widths Wy and different lengths Wx.

[0110] It should be noted that, based on the method for obtaining the value of the etching probability threshold D0 and the value of the t sets of parameters, which will be explained later, the etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the proportional relationship between the equivalent feature distances in the t sets of parameters can be obtained.

[0111] Based on this, it is necessary to preset fixed values ​​for any one of the etching probability threshold D0, the normalized weight coefficients in the t-group parameter set, and the equivalent feature distances in the t-group parameter set, to determine the numerical values ​​of the etching probability threshold D0, the normalized weight coefficients in the t-group parameter set, and the equivalent feature distances in the t-group parameter set. That is, after presetting fixed values ​​for any one of the normalized weight coefficients in the t-group parameter set and the equivalent feature distances in the t-group parameter set, it is necessary to solve for the remaining 2t unknowns to obtain a set of fixed values ​​for the etching probability threshold D0 and the t-group parameter set.

[0112] Therefore, by using v≥2t, it can be ensured that there is a sufficient number of second lithographic design patterns 100 and second etched grooves formed based on the second lithographic design patterns 100, so as to provide sufficient sample data to solve for the values ​​of the 2t unknowns.

[0113] It should be understood that as v increases, the number of samples used to solve for the values ​​of the 2t unknowns increases, and correspondingly, the accuracy of the obtained etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the values ​​of the equivalent feature distances in the t sets of parameters is further improved.

[0114] Furthermore, it should be understood that by ensuring the proportional relationship between the etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the equivalent feature distances in the t sets of parameters, a more accurate and precise etching probability convolution model can be formed.

[0115] Please refer to Figure 4 and Figure 5 , Figure 4 This is a top view schematic diagram of the second etched groove in one embodiment of the present invention. Figure 5 yes Figure 4 A cross-sectional structural diagram along the direction A1-A2. For step S1300, the sample 110 is etched based on v second photolithographic design patterns 100 to form corresponding v second etched grooves 120.

[0116] In this embodiment, the method of etching a sample based on v second photolithographic design patterns 100 to form v corresponding second etched grooves 120 includes: forming a first photoresist layer (not shown) on the surface of a sample 110; patterning the first photoresist layer according to the v second photolithographic design patterns 100, and forming a first mask layer 130 on the surface of the sample 110 that exposes a portion of the surface of the sample 110; etching the sample 110 using the first mask layer 130 as a mask to form v corresponding second etched grooves 120 within the sample 110.

[0117] For ease of explanation and understanding, Figure 4 and Figure 5 Only one second etched groove 120 is schematically shown, and, Figure 4 The first mask layer 130 is not shown in the figure.

[0118] In this embodiment, the first photoresist layer is patterned through processes such as exposure and development.

[0119] In this embodiment, after forming the corresponding v second etched grooves 120, the first mask layer 130 is removed to facilitate subsequent measurement of the v second etched grooves and to obtain the dimensions of the corresponding v second etched contours.

[0120] Please refer to Figure 6 , Figure 6 This is a schematic diagram of the second etching profile in one embodiment of the present invention. In step S1400, v second etching grooves 120 are measured to obtain the dimensions of the corresponding v second etching profiles 121.

[0121] For ease of explanation and understanding, Figure 6 Only one second etched profile 121 is schematically shown.

[0122] It should be understood that there is a one-to-one correspondence between the v second etched grooves 120 and the v second etched contours 121. Specifically, any second etched contour 121 is the etched contour of the second etched groove 120 corresponding to the given second etched contour 121.

[0123] In the dimensions of the v second etching profiles 121, the dimensions of any second etching profile 121 include: the length Wx′ and the width Wy′ of the any second etching profile 121.

[0124] Please refer to Figure 7 , Figure 7 This is a schematic diagram of etching deviation dimensions in one embodiment of the present invention. For step S1500, based on the dimensions of v second photolithographic design patterns 100 and v second etching contours 121, the corresponding v sets of etching deviation dimensions are obtained.

[0125] In this embodiment, any group of etching deviation dimensions in group v includes length deviation and width deviation.

[0126] Specifically, the length deviation of the i-th group Among them, Wx i ′ is the length Wx′ of the i-th second etched profile, Wx i Wx is the length of the i-th second lithographic design pattern.

[0127] Specifically, the width deviation of the i-th group Among them, Wy i ′ is the width Wy′ of the i-th second etched profile, Wy i Wy is the width of the i-th second lithographic design pattern.

[0128] The i is a natural number, and i ≤ v.

[0129] For ease of explanation and understanding, Figure 7 Only one set of etching deviation dimensions is schematically shown.

[0130] Please refer to Figure 8 , Figure 8 This is a flowchart illustrating step S1600 in one embodiment of the present invention. For step S1600, the method for obtaining the implicit fitting incremental iterative model based on the initial etching probability convolution model, the dimensions of v second lithographic design patterns, and v sets of etching deviation dimensions includes:

[0131] Step S1610: Based on the initial etching probability convolution model and the dimensions of v second lithography design patterns, obtain an analytical solution equation set corresponding to each second lithography design pattern, wherein the analytical solution equation set includes an etching probability threshold D0.

[0132] Step S1620: Based on the etching deviation dimensions of group v and the set of v analytical solution equations corresponding to the second lithography design patterns, perform implicit fitting processing to obtain the implicit fitting incremental iterative model.

[0133] In this embodiment, for step S1610, further, based on the initial etching probability convolution model and the dimensions of v second lithography design patterns, an analytical solution equation set corresponding to each second lithography design pattern is obtained, and each set of parameters corresponds to one or more sets of analytical solution equations.

[0134] In other words, based on the initial etching probability convolution model and the dimensions of the v second lithography design patterns, a total of v analytical solution equations were obtained.

[0135] The analytical solution equations corresponding to the i-th second lithographic design pattern are as follows:

[0136]

[0137] The erf represents the error function. The length deviation Sx corresponding to the i-th group i The calculated length deviation, the Sy corresponds to the width deviation of the i-th group. i The calculated width deviation.

[0138] Specifically, the and stated This refers to the intermediate calculation data during the process of performing several incremental iterations based on the implicitly fitted incremental iterative model in step S1700.

[0139] In this embodiment, please refer to Figure 9 , Figure 9 This is a flowchart illustrating step S1620 in one embodiment of the present invention. For step S1620, based on the v sets of etching deviation dimensions and the v sets of analytical equations corresponding to the v second lithography design patterns, an implicit fitting process is performed to obtain the implicit fitting incremental iterative model. The method includes:

[0140] Step S1621: Specify the etching probability threshold D0, any normalized weight coefficient in the t-group parameter set, or any equivalent feature distance in the t-group parameter set as a specified parameter with a preset fixed value; and form a parameter set {P} by combining the etching probability threshold D0, each normalized weight coefficient in the t-group parameter set, and each equivalent feature distance in the t-group parameter set other than the specified parameter.

[0141] Step S1622: Perform implicit fitting processing on the set of analytical solution equations in group v based on the specified parameters to obtain the implicit fitting incremental iterative model.

[0142] To facilitate understanding, step S1621 will be explained using t=2 as an example.

[0143] Specifically, when t=2, the t-group of parameters includes: normalized weight coefficient n1, equivalent feature distance σ1, normalized weight coefficient n2, and equivalent feature distance σ2.

[0144] Accordingly, in step S1621, the etching probability threshold D0, normalized weight coefficient n1, equivalent feature distance σ1, normalized weight coefficient n2, or equivalent feature distance σ2 are specified parameters with preset fixed values. Furthermore, the parameters other than the specified parameters among the etching probability threshold D0, normalized weight coefficient n1, equivalent feature distance σ1, normalized weight coefficient n2, and equivalent feature distance σ2 are combined to form a parameter set {P}.

[0145] For example, when the normalized weight coefficient n1 is specified as a parameter with a preset fixed value, the etching probability threshold D0, the equivalent feature distance σ1, the normalized weight coefficient n2, and the equivalent feature distance σ2 are combined to form the parameter set {P}.

[0146] That is, the parameter set at this time is {P} = {D0, σ1, n2, σ2}.

[0147] Preferably, the preset fixed value of the specified parameter is 1.

[0148] In this embodiment, the implicit fitting incremental iterative model in step S1622 is:

[0149]

[0150] Where j, k, and l are all natural numbers, where j ≤ 2t, and p j and p k Each of the parameters is any parameter in the parameter set {P}. and The parameters p are respectively the parameters corresponding to the l-th incremental iteration process in the several incremental iteration processes. j Parameter p k Calculate the length deviation and calculate width deviation The parameter p is the parameter p corresponding to the (l-1)th iteration in the several incremental iterations described above. j .

[0151] It is important to understand that, based on It can be seen that the implicit fitting incremental iterative model actually contains 2t implicit equations.

[0152] To facilitate understanding, let's continue with the example of t=2 and parameter set {P}={D0, σ1, n2, σ2}, and examine the parameter p. j and parameter p k Please provide an explanation.

[0153] Specifically, in any implicit equation of the implicitly fitted incremental iterative model, p j It can be the etching probability threshold D0, the equivalent feature distance σ1, the normalized weight coefficient n2, or the equivalent feature distance σ2, p k It can be the etching probability threshold D0, the equivalent feature distance σ1, the normalized weight coefficient n2, or the equivalent feature distance σ2.

[0154] In this embodiment, the least squares method is used to implicitly fit the set of analytical solution equations in group v to obtain the implicitly fitted incremental iterative model.

[0155] Please refer to Figure 10 , Figure 10 This is a flowchart illustrating step S1700 in one embodiment of the present invention. For step S1700, the method for obtaining the value of the etching probability threshold and the values ​​of the t sets of parameters by performing several incremental iterations based on the implicit fitting incremental iterative model includes:

[0156] Step S1710: During the l-th incremental iteration, the parameters obtained in the (l-1)-th incremental iteration are used... The value of the specified parameter, and the v analytical solution equations are used to obtain the computational length deviation. The value, and the calculated width deviation The value of the parameter when l = 1. The value is the preset value;

[0157] Step S1720, calculate the length deviation The value, and the calculated width deviation Substituting the value into the implicitly fitted incremental iterative model, we obtain the increment corresponding to the l-th incremental iteration. The value and parameters The value of .

[0158] It should be noted that when obtaining the calculation length deviation... After obtaining the value, the length deviation can be calculated. The value, and the calculated length deviation The value is used to obtain the corresponding partial derivative component. The value of the partial derivative component, and the value of the partial derivative component. Substitute the value into the implicitly fitted incremental iterative model to obtain the increment corresponding to the l-th incremental iteration. The value and parameters The value of .

[0159] For ease of understanding, steps S1710 to S1720 will be explained with t=2, the normalized weight coefficient n1 being a specified parameter with a preset fixed value, and the parameter set {P}={D0, σ1, n2, σ2}, taking l=1 and l=2 as examples respectively.

[0160] It is important to understand that, due to the parameter p j Let p1 be any parameter in the parameter set {P}, therefore, the parameters p1 to p2 are... 2t That is: etching probability threshold D0, equivalent feature distance σ1, normalized weight coefficient n2, and equivalent feature distance σ2.

[0161] When l = 1, the parameter The value is the preset value.

[0162] Based on this, the first incremental iteration is performed (l=1): the value of the specified parameter (preset fixed value) and the parameter are... Substitute the values ​​of each of the v analytical equations into the calculation length deviation when l = 1. Value and calculated width deviation The value; the calculated length deviation when l=1 The value, and the calculated width deviation Substitute the value into the implicitly fitted incremental iterative model to obtain the increment corresponding to the first incremental iteration. The value and parameters The value of .

[0163] Furthermore, during the first incremental iteration, the computation length deviation was obtained. After determining the value, calculate the length deviation. The value, and the preset calculation length deviation. The value of the partial derivative component when l=1 is obtained. The value, and the calculated length deviation when l=1. The value, and the calculated width deviation While substituting the value into the implicitly fitted incremental iterative model, the partial derivative component when l=1 is also... Substitute the value into the implicitly fitted incremental iterative model to obtain the increment corresponding to the first incremental iteration. The value and parameters The value of .

[0164] Next, a second incremental iteration is performed (l=2): the values ​​of the specified parameters and the parameters (based on those obtained during the first incremental iteration) are used. Substitute the values ​​of each of the v analytical equations into the calculation length deviation when l = 2. Value and calculated width deviation The value; the calculated length deviation when l=2 The value, and the calculated width deviation Substitute the value into the implicitly fitted incremental iterative model to obtain the increment corresponding to the second incremental iteration. The value and parameters The value of .

[0165] Furthermore, during the second incremental iteration, the computation length deviation was obtained. After determining the value, calculate the length deviation. The value, and the calculated length deviation The value of the partial derivative component when l=2 is obtained. The value, and the calculated length deviation when l=2. The value, and the calculated width deviation While substituting the value into the implicitly fitted incremental iterative model, the partial derivative component when l=2 is also included. Substitute the value into the implicitly fitted incremental iterative model to obtain the increment corresponding to the second incremental iteration. The value and parameters The value of .

[0166] Please continue to refer to this. Figure 10 Regarding step S1700, the method of obtaining the value of the etching probability threshold and the value of the t-group parameter set by performing several incremental iterations based on the implicit fitting incremental iteration model further includes: step S1730, when the incremental value obtained by the M-th incremental iteration is... When all values ​​are within a preset percentage, the incremental iteration process is terminated, where M is a natural number and M≥1, and the parameters obtained from the Mth incremental iteration process are... The value is taken as: the value of the parameters other than the specified parameter in the etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the equivalent feature distances in the t sets of parameters.

[0167] Specifically, when the increment obtained in the Mth incremental iteration is... When all values ​​are within a preset percentage, it represents the increment at the Mth incremental iteration. Simultaneous convergence occurs, at which point the parameters obtained from the Mth incremental iteration process are... The values ​​of the etch probability threshold D0, the values ​​of the normalized weight coefficients in the t parameter groups, and the values ​​of the equivalent feature distances in the t parameter groups are obtained as the globally optimal parameter values.

[0168] It is important to understand that the parameters obtained in the Mth incremental iteration process... The value of is the value of each parameter in the parameter set {P} obtained by the Mth incremental iteration.

[0169] For ease of understanding, we will take t=2 as an example, and specify the normalized weight coefficient n1 as a specified parameter with a preset fixed value, and the parameter set {P}={D0, σ1, n2, σ2} as an example.

[0170] When t = 2, and the specified normalized weight coefficient n1 is a specified parameter with a preset fixed value, and the parameter set {P} = {D0, σ1, n2, σ2}, according to step S1730, the parameters obtained by the Mth incremental iteration process are... The values ​​are respectively used as: the etching probability threshold D0, the equivalent feature distance σ1, the normalized weight coefficient n2, and the equivalent feature distance σ2.

[0171] Preferably, the preset percentage is 1%. This ensures that the increment obtained in the Mth incremental iteration is... It also converges relatively well.

[0172] Please continue to refer to this. Figure 2 Regarding step S1800, the method for substituting the values ​​of the t sets of parameters into the initial etching probability convolution model to form the etching probability convolution model includes:

[0173] Based on the specified parameters and the values ​​of each parameter in the parameter set {P} obtained from the Mth incremental iteration, the values ​​of each equivalent feature distance and each normalized weight coefficient are substituted into the initial etching probability convolution model to form the etching probability convolution model:

[0174]

[0175] Where, n h ′ represents the normalized weighting coefficient n h The value of σ h ′ is the equivalent feature distance σ h The value is used to distinguish between parameters and their values.

[0176] Please continue to refer to this. Figure 2 Regarding step S1900, the two-dimensional etching simulation model constructed based on the etching probability convolution model and the value D0′ of the etching probability threshold D0 includes:

[0177]

[0178] Therefore, by inputting the mask pattern into the two-dimensional etching simulation model and performing etching simulation, the simulated etching contour corresponding to the mask pattern can be accurately simulated.

[0179] Please refer to Figure 11 , Figure 11 This is a schematic diagram of the structure of the first photolithographic pattern group in one embodiment of the present invention. For step S2000, a plurality of first photolithographic pattern groups 200 are provided. Each first photolithographic pattern group 200 includes a plurality of first photolithographic design patterns 210 arranged in an array. Furthermore, the size of the first photolithographic design patterns 210 of different first photolithographic pattern groups 200 is different.

[0180] It should be noted that, Figure 11 Only one first lithographic pattern group 200 is schematically shown in the figure.

[0181] In this embodiment, the first photolithographic design pattern 210 is a regular hexagon, and the multiple first photolithographic design patterns 210 in the first photolithographic pattern group 200 are arranged in a honeycomb array.

[0182] In some other embodiments, the first lithographic design pattern may be a circle or other polygons.

[0183] In this embodiment, the side lengths of the first lithographic design patterns 210 of different first lithographic pattern groups 200 are different.

[0184] In some other embodiments, the spacing between adjacent first lithographic design patterns is different in different first lithographic pattern groups.

[0185] Please refer to Figures 12 to 14 , Figure 12 This is a top view of the first sample group in one embodiment of the present invention. Figure 13 yes Figure 12 A schematic diagram of the cross-sectional structure along the B1-B2 direction. Figure 14 yes Figure 12 For the first sample group image, in step S3000, the sample 300 is etched based on several first photolithography pattern groups 200 to form several corresponding first sample groups 310, each first sample group 310 including multiple first etched grooves 311.

[0186] In this embodiment, the method of etching a sample 300 based on a plurality of first photolithographic pattern groups 200 to form a plurality of first sample groups 310 includes: forming a second photoresist layer (not shown) on the surface of the sample 300; patterning the second photoresist layer according to the plurality of first photolithographic pattern groups 200, and forming a second mask layer 320 on the surface of the sample 300 that exposes a portion of the surface of the sample 300; etching the sample 300 using the second mask layer 320 as a mask to form a plurality of first sample groups 310 within the sample 300, each first sample group 310 including a plurality of first etching grooves 311.

[0187] For ease of explanation and understanding, Figure 12 Only one first sample group 310 is schematically represented in the text, and, Figure 12 The second mask layer 320 is not shown in the figure.

[0188] In this embodiment, the second photoresist layer is patterned through processes such as exposure and development.

[0189] Preferably, a wet etching process is used, with the second mask layer 320 as the mask for etching the sample 300.

[0190] Preferably, multiple first lithographic pattern groups 200 are provided, and multiple first sample groups 310 are formed to further improve the accuracy of the three-dimensional etching simulation model based on more detection data.

[0191] In this embodiment, after forming a number of first sample groups 310 within the sample 300, the second mask layer 220 is removed to facilitate subsequent detection of the number of first sample groups 310 and acquisition of several detection data corresponding to several detection positions.

[0192] Please continue to refer to this. Figure 12 and Figure 13 In step S4000, several first sample groups 310 are detected to obtain several detection data corresponding to several detection positions 331. The detection data includes the position data and etching depth of the detection positions 331.

[0193] It should be noted that, Figure 12 The image only schematically shows multiple detection locations 331.

[0194] In this embodiment, the position data of the detection position 331 includes the two-dimensional coordinates x of the detection position 331. E and y E .

[0195] Specifically, the detection data corresponding to any detection position 331 includes: the two-dimensional coordinates x of any detection position 331. E and y E and the etching depth z at any detection position 331 E .

[0196] In this embodiment, the method for detecting multiple first sample groups 310 and obtaining several detection data corresponding to several detection positions 331 includes: detecting each first sample group 310 according to several preset intervals, and obtaining several sets of detection data corresponding to several preset intervals.

[0197] Each set of detection data includes a set of detection data corresponding to a number of detection positions 331 arranged along a straight line, and the maximum detection distance H between the number of detection positions 331 arranged along the straight line is equal to the corresponding preset distance.

[0198] Accordingly, since the several detection positions 331 in each group of detection data are arranged along a straight line, the several position data in any group of detection data have the same coordinate x. E or coordinate y E .

[0199] In addition, a set of several detection positions 331 arranged in a straight line correspond to a preset spacing.

[0200] In this embodiment, the several detection positions 331 arranged along a straight line in each group correspond to the same preset spacing.

[0201] In some other embodiments, at least two of the several detection positions arranged in a straight line may correspond to different preset intervals.

[0202] In this embodiment, each first sample group 310 is detected at the same preset interval, and based on each first sample group 310, several detection data corresponding to two sets of detection positions 331 arranged along orthogonal straight lines are obtained.

[0203] In some other embodiments, one or more sets of detection data corresponding to several detection positions arranged in a straight line can also be obtained based on each first sample group.

[0204] It should be noted that those skilled in the art can determine the two-dimensional coordinate x according to the actual situation. E and y E The position of the corresponding origin point.

[0205] Preferably, several detection positions 331 corresponding to each specified detection data group are located along the center position 332 passing through the first sample group 310 (e.g., ...). Figure 12 The linear arrangement (as shown in the diagram). That is, the center position 332 of the first sample group 310 is taken as the two-dimensional coordinate x. E and y E The origin of the coordinate system. Therefore, the etching depth z of the detection position 331 in the middle region of the first sample group 310 can be detected more accurately. E This improves the stability and reliability of the detection data set, thereby further enhancing the accuracy of the three-dimensional etching simulation model.

[0206] Please refer to Figure 15 , Figure 15 This is a flowchart illustrating step S5000 in one embodiment of the present invention. For step S5000, the method for obtaining several specified simulation data corresponding to several specified target simulation positions based on several first lithographic pattern groups, a two-dimensional etching simulation model, and several detection positions includes:

[0207] Step S5100: Input several first lithography pattern groups into the two-dimensional etching simulation model, and obtain simulation result data corresponding to several first lithography pattern groups. The simulation result data includes a two-dimensional simulation etching contour pattern, as well as the position data and etching probability of any target simulation position in the two-dimensional simulation etching contour pattern.

[0208] Step S5200: Based on several preset spacings and several sets of detection positions arranged along a straight line, determine several sets of specified target simulation positions arranged along a straight line in the two-dimensional simulation etching contour pattern, and obtain the specified simulation data corresponding to each specified target simulation position.

[0209] Specifically, the designated target simulation position is the target simulation position corresponding to the detection position 331, and the designated simulation data includes the position data and etching probability of the designated target simulation position.

[0210] The location data of the specified target simulation location includes: the two-dimensional coordinates x of the specified target simulation location. S and y S .

[0211] Accordingly, the specified simulation data includes: the two-dimensional coordinates x of the specified target simulation location. S and y S and the etching probability d(x) at the specified target simulation location. S y S ).

[0212] In this embodiment, a set of detection positions 331 arranged along a straight line corresponds to a set of designated target simulation positions arranged along a straight line. Correspondingly, any set of designated target simulation positions arranged along a straight line has the same two-dimensional coordinate x. S or coordinate y S .

[0213] Furthermore, in this embodiment, the maximum detection spacing between the plurality of designated target simulation positions arranged along a straight line is equal to the corresponding preset spacing. That is, a group of designated target simulation positions arranged along a straight line corresponds to the same preset spacing as a corresponding group of detection positions 331 arranged along a straight line.

[0214] It is important to understand that, due to the limitations and deviations inherent in actual testing processes, and the constraints of the equipment's minimum resolution, the determined simulated target position in the two-dimensional simulated etching profile pattern is difficult to perfectly align with the corresponding detection position 331. In other words, the simulated target position tends to deviate from the corresponding detection position 331. For example, the two-dimensional coordinates of detection position 331 are (3.01, 5.05), while the two-dimensional coordinates of the corresponding simulated target position are (3, 5).

[0215] In this embodiment, by making the maximum detection spacing between the specified target simulation positions arranged along the straight line equal to the corresponding preset spacing, the correlation and correspondence between the corresponding set of specified target simulation positions arranged along the straight line and the set of detection positions 331 arranged along the straight line are better improved as a whole, thereby further improving the accuracy of the three-dimensional etching simulation model.

[0216] Please refer to Figure 16 , Figure 16 This is a flowchart illustrating step S6000 in one embodiment of the present invention. Regarding step S6000, the method for constructing a three-dimensional etching simulation model based on the plurality of detection data, the plurality of specified simulation data, and the two-dimensional etching simulation model includes:

[0217] Step S6100: Interpolate the detection data corresponding to the detection positions to obtain the interpolated detection positions, the interpolated position data and the interpolated etching depth of each interpolated detection position.

[0218] Step S6200: Perform interpolation processing on several specified simulation data corresponding to several specified target simulation positions to obtain several interpolated specified target simulation positions that have the same interpolation position data as several interpolated detection positions, and the interpolation etching probability of each interpolated specified target simulation position.

[0219] Step S6300: Associate the interpolation etching depth and interpolation etching probability with data at the same interpolation position to obtain several interpolation data sets;

[0220] Step S6400: Fit several interpolated data sets to obtain the etching depth fitting model z(x,y)=G[d(x,y)] between the simulated etching depth z and the etching probability d(x,y) at the target simulation position, where G represents the functional relationship between z(x,y) and d(x,y);

[0221] Step S6500: Based on the etching depth fitting model z(x,y)=G[d(x,y)] and the two-dimensional etching simulation model, construct a three-dimensional etching simulation model:

[0222]

[0223] Therefore, by inputting the mask pattern into the three-dimensional etching simulation model and performing etching simulation, the simulated etching contour and etching simulation morphology corresponding to the mask pattern can be accurately simulated, that is, three-dimensional etching simulation is performed.

[0224] In step S6100 of this embodiment, interpolation processing is performed on several detection data corresponding to several detection positions to calculate the interpolation position data and the interpolation etching depth z of the interpolated detection positions. EX The interpolation position data is the two-dimensional coordinate x of the interpolation detection position. EX and y EX .

[0225] In step S6200 of this embodiment, by interpolating several specified simulation data corresponding to several specified target simulation positions, several interpolated specified target simulation positions with the same interpolated position data as several interpolated detection positions are calculated, as well as the interpolation etching probability d(x) of each interpolated specified target simulation position. SX y SX ).

[0226] Based on this, through step S6300, several sets of interpolation data are formed, each set of interpolation data including: the associated interpolation etching depth zEX and interpolation etching probability d(x) SX y SX ).

[0227] To facilitate understanding and explanation, we will take the example of obtaining the interpolation position data and interpolation etching depth of two interpolation detection positions based on the detection data of a set of detection positions 331 (including 3 detection positions 331).

[0228] Specifically, the set of detection positions 331 includes three detection positions, and the detection data corresponding to the three detection positions are as follows: two-dimensional coordinates (x... E 1, y E 1) and etching depth z E 1. Two-dimensional coordinates (x E 2, y E 2) and etching depth z E 2. Two-dimensional coordinates (x) E 3, y E 3) and etching depth z E 3.

[0229] By interpolating the detection data corresponding to the three detection locations, the two-dimensional coordinates (x, y) of the interpolated detection locations are calculated. EX 1, y EX 1) and interpolation etching depth z EX 1. Two-dimensional coordinates (x EX 2, y EX 2) and interpolation etching depth z EX 2.

[0230] Based on this, we will continue the explanation using a set of corresponding simulated target locations as an example.

[0231] Specifically, the set of corresponding designated target simulation positions includes three designated target simulation positions corresponding to three detection positions, and the designated simulation data corresponding to the three designated target simulation positions are as follows: two-dimensional coordinates x S 1 and y S 1 and etching probability d(x) S 1, y S 1) Two-dimensional coordinates x S 2 and y S 2 and etching probability d(x) S 2, y S 2) Two-dimensional coordinates x S 3 and y S 3 and etching probability d(x) S 3, y S 3).

[0232] By interpolating the specified simulation data corresponding to the three specified target simulation locations, the two-dimensional coordinates (x, y, z) are calculated. SX 1, y SX 1) and the corresponding interpolation etching probability d(x) SX 1, y SX 1) Two-dimensional coordinates (x) SX 2, y SX 2) and the corresponding interpolation etching probability d(x) SX 2, y SX 2), where x SX 1 = x EX 1, y SX 1 = y EX 1,x SX 2 = x EX 2, y SX 2 = y EX 2.

[0233] Next, by associating the interpolation etch depth and interpolation etch probability of data with the same interpolation position, several sets of interpolated data are obtained. That is: associating the interpolation etch probability d(x) SX 1, y SX 1) with interpolation etching depth z EX 1. Correlation interpolation etching probability d(x) SX 2, y SX 2) with interpolation etching depth z EX 2. This forms two sets of interpolated data corresponding to two two-dimensional coordinates.

[0234] In this embodiment, by interpolating several detection data corresponding to several detection locations to obtain several interpolated detection locations, as well as interpolated position data and interpolated etching depth of each interpolated detection location, and by interpolating several specified simulation data corresponding to several specified target simulation locations to obtain several interpolated specified target simulation locations with the same interpolated position data as several interpolated detection locations, as well as interpolated etching probabilities of each interpolated specified target simulation location, and by associating the interpolated etching depth and interpolated etching probability with the same interpolated position data, several interpolated data sets are obtained. Therefore, the accuracy of the interpolated data sets used for fitting is improved, thereby further improving the accuracy of the three-dimensional etching simulation model.

[0235] Specifically, for step S6100, interpolation processing can be performed on several detection data corresponding to several detection positions based on quadratic spline interpolation.

[0236] Specifically, for step S6200, interpolation processing can be performed on several specified simulation data corresponding to several specified target simulation positions based on quadratic spline interpolation.

[0237] Specifically, for step S6400, based on polynomial fitting, several interpolated data sets can be fitted to obtain the etching depth fitting model z(x,y)=G[d(x,y)] between the simulated etching depth z and the etching probability d(x,y) at the target simulation position.

[0238] In some other embodiments, steps S6100 and S6200 are not executed. Instead, the etching probabilities and etching depths with corresponding relationships are directly associated to form several data sets. The several data sets are then fitted to obtain an etching depth fitting model z(x,y)=G[d(x,y)] between the simulated etching depth z at the target simulation position and the etching probability d(x,y).

[0239] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A method for constructing an etching simulation model, characterized in that, include: Obtain a two-dimensional etching simulation model; A plurality of first photolithographic pattern groups are provided, each first photolithographic pattern group including a plurality of first photolithographic design patterns arranged in an array, and the size of the first photolithographic design patterns in different first photolithographic pattern groups is different; The sample is etched based on several first photolithography pattern groups to form several corresponding first sample groups, each first sample group including multiple first etched grooves; Several first sample groups are tested to obtain several detection data corresponding to several detection positions. The detection data includes the location data and etching depth of the detection positions. Based on several first lithography pattern groups, a two-dimensional etching simulation model, and several detection positions, several specified simulation data corresponding to several specified target simulation positions are obtained. The specified target simulation positions are target simulation positions corresponding to the detection positions, and the specified simulation data include the position data and etching probability of the specified target simulation positions. Based on several detection data, several specified simulation data, and a two-dimensional etching simulation model, a three-dimensional etching simulation model is constructed. The two-dimensional etching simulation model includes the value of the etching probability threshold D0. ; The method for constructing a three-dimensional etching simulation model based on the aforementioned detection data, the aforementioned specified simulation data, and the two-dimensional etching simulation model includes: Interpolation processing is performed on several detection data corresponding to several detection positions to obtain several interpolated detection positions, as well as the interpolated position data and interpolation etching depth of each interpolated detection position; Interpolation processing is performed on several specified simulation data corresponding to several specified target simulation positions to obtain several interpolated specified target simulation positions with the same interpolated position data as several interpolated detection positions, and the interpolation etching probability of each interpolated specified target simulation position; By associating the interpolation etching depth and interpolation etching probability of data with the same interpolation position, several interpolation data sets can be obtained. By fitting several sets of interpolated data, the simulated etching depth z and etching probability d at the target simulation location are obtained. The etching depth fitting model z() between ) ) = G[d( ], G represents the z ( ) and d ( The functional relationship between them; According to the etching depth fitting model z ( ) = G[d( Based on the two-dimensional etching simulation model, a three-dimensional etching simulation model is constructed: 。 2. The method for constructing the etching simulation model as described in claim 1, characterized in that, Methods for obtaining two-dimensional etching simulation models include: An initial etching probability convolutional model is provided, which includes t sets of parameters, each set of parameters including the corresponding equivalent feature distance and normalized weight coefficients, where t is a natural number; Provide v rectangular second lithographic design patterns, each second lithographic design pattern having a different size, where v is a natural number and v≥2t; Based on v second photolithographic design patterns, the sample is etched to form v corresponding second etched grooves; Measure v second etched grooves to obtain the dimensions of the corresponding v second etched profiles; Based on the dimensions of v second lithographic design patterns and v second etching contours, obtain the corresponding v sets of etching deviation dimensions; Based on the initial etching probability convolution model, the dimensions of v second lithography design patterns, and v sets of etching deviation dimensions, an implicit fitting incremental iterative model is obtained; Based on the implicit fitting incremental iterative model, several incremental iterations are performed to obtain the value of the etching probability threshold and the value of the t-group parameter set. Substitute the values ​​of the t sets of parameters into the initial etching probability convolution model to form the etching probability convolution model; A two-dimensional etching simulation model is constructed based on the etching probability convolution model and the etching probability threshold value.

3. The method for constructing the etching simulation model as described in claim 2, characterized in that, The method for obtaining the implicit fitting incremental iterative model based on the initial etching probability convolution model, the dimensions of v second lithographic design patterns, and v sets of etching deviation dimensions includes: Based on the initial etching probability convolution model and the dimensions of v second lithography design patterns, obtain a set of analytical solution equations corresponding to each second lithography design pattern, wherein the set of analytical solution equations includes an etching probability threshold. Based on the etching deviation dimensions of group v and the set of v analytical solution equations corresponding to the second lithography design patterns, implicit fitting processing is performed to obtain the implicit fitting incremental iterative model.

4. The method for constructing the etching simulation model as described in claim 3, characterized in that, In the v second lithographic design patterns, the size of any second lithographic design pattern includes the length Wx and the width Wy of the any second lithographic design pattern; In the dimensions of the v second etching profiles, the dimension of any second etching profile includes: the length of the any second etching profile. and width ; In the etching deviation dimensions described in group v, any group of etching deviation dimensions includes length deviation and width deviation, and the length deviation of the i-th group... Width deviation of group i The It is the length of the i-th second etched profile. The It is the length of the i-th second lithographic design pattern. The It is the width of the i-th second etch profile. The Wy is the width of the i-th second lithographic design pattern, where i is a natural number and i ≤ v.

5. The method for constructing the etching simulation model as described in claim 4, characterized in that, The v second lithographic design patterns include multiple second lithographic design patterns with the same length Wx and arranged along the dimensional direction of width Wy. The multiple first lithographic design patterns with the same length Wx and arranged along the dimensional direction of width Wy have different widths Wy. Furthermore, the multiple second lithographic design patterns with the same length Wx and arranged along the dimensional direction of width Wy have the same spacing in the dimensional direction of width Wy.

6. The method for constructing the etching simulation model as described in claim 4, characterized in that, Based on the initial etching probability convolution model and the dimensions of the v second lithography design patterns, an analytical solution equation set corresponding to each second lithography design pattern is obtained. Furthermore, each parameter set corresponds to one or more of the analytical solution equation sets. The analytical solution equation set corresponding to the i-th second lithography design pattern is as follows: ， h is a natural number, and h ≤ t. These are the normalized weight coefficients in the h-th parameter group. It is the equivalent feature distance in the h-th parameter group, where erf represents the error function, and D0 is the etching probability threshold. It corresponds to the length deviation of the i-th group. The calculated length deviation, the It corresponds to the width deviation of the i-th group. The calculated width deviation.

7. The method for constructing the etching simulation model as described in claim 6, characterized in that, The method for obtaining the implicit fitting incremental iterative model based on the v sets of etching deviation dimensions and the v sets of analytical solution equations corresponding to the v second lithography design patterns includes: The etching probability threshold D0, any normalized weight coefficient in the t-group parameter set, or any equivalent feature distance in the t-group parameter set are specified as parameters with preset fixed values. Furthermore, the etching probability threshold D0, each normalized weight coefficient in the t-group parameter set, and all parameters other than the specified parameter in each equivalent feature distance of the t-group parameter set are combined to form a parameter set {. }; Based on the specified parameters, an implicit fitting process is performed on the set of analytical solution equations in group v to obtain the implicit fitting incremental iterative model, and the implicit fitting incremental iterative model is as follows: The j, k, l All are natural numbers, where j ≤ 2t, and the... and The parameter set { Any parameter in}, the , , and In the incremental iteration process described above, the first... l The parameters corresponding to the next incremental iteration are processed. ,parameter Calculate the length deviation and calculate width deviation , In the incremental iteration process described above, the first... l The parameter corresponding to -1 ; The method for obtaining the etching probability threshold and the values ​​of the t sets of parameters by performing several incremental iterations based on the implicitly fitted incremental iterative model includes: During the first l During the incremental iteration, according to the... l Parameters obtained in -1 incremental iterations ~ The value of the specified parameter, and the v analytical solution equations are used to obtain the computational length deviation. ~ The value, and the calculated width deviation ~ The value when l When =1, the parameter ~ The value is a preset value; the calculated length deviation is... ~ The value, and the calculated width deviation ~ Substituting the value into the implicitly fitted incremental iterative model, we obtain the first... l The increment corresponding to the next incremental iteration processing ~ The value and parameters ~ The value; the increment obtained in the Mth incremental iteration. ~ The incremental iteration process terminates when all values ​​are within a preset percentage, where M is a natural number and M ≥ 0. l Furthermore, the parameters obtained from the Mth incremental iteration process... ~ The value is taken as: the value of the parameters other than the specified parameter in the etching probability threshold D0, the normalized weight coefficients in the t sets of parameters, and the equivalent feature distances in the t sets of parameters.

8. The method for constructing the etching simulation model as described in claim 7, characterized in that, The preset fixed value of the specified parameter is 1.

9. The method for constructing the etching simulation model as described in claim 7, characterized in that, The preset percentage is 1%.

10. The method for constructing the etching simulation model as described in claim 7, characterized in that, The initial etching probability convolution model is: ， in, Let d be the two-dimensional coordinates of the target simulation location. ) represents the etching probability at the target simulation location. The M( ) represents the two-dimensional coordinates of the associated simulation position, which is any simulation position other than the target simulation position during convolution. ) is a binary image function for the associated simulation location. When any associated simulation location is within a preset etching region, the binary image function M( for any associated simulation location) is... ) = 1, when any associated simulation position is outside the preset etching area, the binary image function M( of any associated simulation position) is 1. =0, where exp represents an exponential function with the natural constant e as the base.

11. The method for constructing the etching simulation model as described in claim 10, characterized in that, The method for substituting the values ​​of the t sets of parameters into the initial etching probability convolution model to form the etching probability convolution model includes: The parameter set obtained based on the specified parameters and the Mth incremental iteration process { The values ​​of each parameter in the equation are substituted into the values ​​of each equivalent feature distance and each normalized weight coefficient, and then into the initial etching probability convolution model to form the etching probability convolution model: ， in, Normalized weighting coefficients The value, Equivalent feature distance The value of .

12. The method for constructing the etching simulation model as described in claim 11, characterized in that, Based on the etching probability convolution model and the value of the etching probability threshold D0 The constructed two-dimensional etching simulation model includes: 。 13. The method for constructing the etching simulation model as described in claim 2, characterized in that, The method for etching a sample based on v second photolithographic design patterns to form v corresponding second etched grooves includes: forming a first photoresist layer on the sample surface; patterning the first photoresist layer according to v second photolithographic design patterns to form a first mask layer on the sample surface that exposes a portion of the sample surface; and etching the sample using the first mask layer as a mask to form v corresponding second etched grooves within the sample.

14. The method for constructing an etching simulation model as described in any one of claims 1 to 13, characterized in that, The method for detecting several first sample groups and obtaining several detection data corresponding to several detection positions includes: detecting each first sample group according to several preset intervals, obtaining several sets of detection data corresponding to several preset intervals, each set of detection data including several detection data corresponding to several detection positions arranged along a straight line, and the maximum detection interval between the several detection positions arranged along the straight line is equal to the corresponding preset interval.

15. The method for constructing the etching simulation model as described in claim 14, characterized in that, The method of detecting several first sample groups and obtaining several detection data corresponding to several detection positions further includes: detecting each first sample group according to several preset intervals, obtaining the several sets of detection data including several specified detection data groups, wherein several detection positions corresponding to each specified detection data group are arranged along a straight line passing through the center position of the first sample group.

16. The method for constructing the etching simulation model as described in claim 14, characterized in that, A method for obtaining specified simulation data corresponding to specified target simulation positions based on several first lithographic pattern groups, a two-dimensional etching simulation model, and several detection positions includes: Several first lithographic pattern groups are input into the two-dimensional etching simulation model to obtain simulation result data corresponding to the several first lithographic pattern groups. The simulation result data includes a two-dimensional simulation etching contour pattern, as well as the position data and etching probability of any target simulation position in the two-dimensional simulation etching contour pattern. Based on several preset intervals and several sets of detection positions arranged along a straight line, several sets of specified target simulation positions arranged along a straight line are determined in the two-dimensional simulation etching contour pattern, and specified simulation data corresponding to each specified target simulation position is obtained. Furthermore, the maximum detection interval between the several specified target simulation positions arranged along the straight line is equal to the corresponding preset interval.

17. The method for constructing the etching simulation model as described in claim 15, characterized in that, The position data of the detection positions comprises two-dimensional coordinates x E and y E of the detection positions, and several position data in any detection data set have the same coordinate x E or coordinate y E ; The location data of the specified target simulation location includes the two-dimensional coordinates x of the specified target simulation location. S and y S Furthermore, any set of several specified target simulation positions arranged along a straight line have the same x-coordinate. S or coordinate y S .

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