Method for constructing three-dimensional simulation etching model

Abstract

A method for constructing a three-dimensional simulation etching model includes: etching samples for multiple lithographic design patterns using multiple preset etching durations to obtain corresponding etching contours; measuring the dimensions of each etching contour and determining the etching depth of each lithographic design pattern at multiple measurement positions under each etching duration; determining the etching probability of each measurement position using a two-dimensional simulation etching model for each etching duration; fitting the etching depth to determine a fitting function based on the etching duration and the etching probability of each measurement position; and constructing the three-dimensional simulation etching model based on the fitting function. This invention can improve the simulation value of simulation results and expand the applicability of simulation results.

Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing technology, and in particular to a method for constructing a three-dimensional simulation etching 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 using photolithography based on a designed mask pattern to obtain a mask pattern layer. Then, using chemical, physical, or a combination of chemical and physical methods, the portion of the thin film layer not masked by the patterned mask layer is selectively removed, resulting in a pattern on the thin film that is completely identical to the patterned mask layer.

[0003] Since etching is irreversible, it is essential to simulate the etching profile before actual etching. Specifically, the etching process, whether dry or wet, is a complex phenomenon influenced by multiple factors, such as the shape and density of the mask pattern, the diffusion of the etchant, 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 transfer the mask pattern is a crucial step in creating semiconductor devices that meet performance requirements.

[0004] Several models have been proposed in the existing technology to simulate and analyze the actual etching process. However, due to the high complexity of simulation, there is currently no highly accurate three-dimensional simulation etching model. Summary of the Invention

[0005] The technical problem solved by this invention is to provide a method for constructing a three-dimensional simulation etching model, which can improve the simulation value of the simulation results and expand the applicability of the simulation results.

[0006] To address the aforementioned technical problems, this invention provides a method for constructing a three-dimensional simulation etching model, comprising: etching samples using multiple preset etching durations for multiple lithographic design patterns to obtain corresponding etching contours; measuring the dimensions of each etching contour and determining the etching depth of each lithographic design pattern at multiple measurement positions under each etching duration; determining the etching probability of each measurement position using a two-dimensional simulation etching model for each etching duration; fitting the etching depth to determine a fitting function based on the etching duration and the etching probability of each measurement position; and constructing the three-dimensional simulation etching model based on the fitting function.

[0007] Optionally, the etching depth is fitted based on the etching duration and the etching probability at each measurement location. The fitting function is determined by: for each etching duration, using interpolation to determine the etching probability and etching depth at multiple preset target simulation locations to obtain multiple interpolated data sets, wherein each interpolated data set includes the etching duration, the interpolated etching depth, and the interpolated etching probability; using the etching duration and the etching probability as elements, the interpolated data sets are used to determine the fitting parameters of the binary fitting function for the etching depth.

[0008] Optionally, determining the etching probability and etching depth of multiple preset target simulation locations using interpolation includes: for each etching duration, interpolating the etching depth of at least a portion of the measurement locations to determine the interpolated etching depth of each preset target simulation location; interpolating the etching probability of at least a portion of the measurement locations to determine the interpolated etching probability of each preset target simulation location; and associating the interpolated etching depth and interpolated etching probability of locations with the same target simulation location to obtain the interpolated data set.

[0009] Optionally, the following bivariate fitting polynomial formula is used, with the etching duration and the etching probability as elements, and the interpolation data set is used to determine the fitting parameters of the bivariate fitting function for the etching depth:

[0010] z(x,y,N t )=z0+a1×d(x,y,N t )+a2×d(x,y,N t ) 2 +…+a c ×d(x,y,N t ) c +b1×N t +b2×N t 2 +…+b c ×N t c

[0011] Where z(x,y,N) t A binary fitting function d(x,y,N) is used to represent the etching depth. t ) is used to represent the etching time N t The etching probability at the simulated target position (x, y), where c is a positive integer and a1 to a2 are given. c b1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth; wherein, the number of interpolation data sets is greater than or equal to the number of fitting parameters.

[0012] Optionally, constructing the three-dimensional simulation etching model based on the fitting function includes:

[0013]

[0014] Where z(x,y,N) t ) is used to represent the etching time N t The etching depth at the simulated target position (x,y), d(x,y,N) t ) is used to represent the etching time N t The etching probability at the simulated target position (x,y), D0(N) t ) is used to represent the etching time N t The etching probability threshold below.

[0015] Optionally, the method for constructing the three-dimensional simulation etching model further includes: using the etching duration to be simulated and the two-dimensional simulation etching model to determine the etching probability of the coordinates to be simulated; substituting the etching probability of one or more of the simulation coordinates and the etching duration to be simulated into the three-dimensional simulation etching model to obtain the simulation value of the etching depth of each simulation coordinate.

[0016] Optionally, the etching probability and the etching duration to be simulated for one or more of the simulation coordinates are substituted into the three-dimensional simulation etching model to obtain the simulated value of the etching depth for each simulation coordinate, including: z(x r ,y r ,t r )=z0+a1×d(x r ,y r ,t r )+a2×d(x r ,y r ,t r ) 2 +…+a c ×d(x r ,y r ,t r ) c +b1×t r +B2×tr 2 +…+b c ×t r c

[0017] Where z(x) r ,y r ,t r ) is a bivariate fitting function used to represent the etching depth, d(x) r ,y r ,t r ) is used to represent the etching time t to be simulated. r The coordinates to be simulated below (x) r ,y r The etching probability of ), where c is a positive integer, and a1 to a2. c b1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth.

[0018] Optionally, before determining the etching probability of each measurement position using a two-dimensional simulation etching model for each etching duration, the method for constructing the three-dimensional simulation etching model further includes: determining an implicit fitting incremental iterative model based on an initial probability convolution model, the size of the lithographic design pattern, and the etching deviation size, and forming an etching probability convolution model based on the implicit fitting incremental iterative model; for each etching duration, substituting the size of the lithographic design pattern and the etching deviation size into the etching probability convolution model to determine the values ​​of each simulation parameter in the simulation parameter group of the two-dimensional simulation etching model; wherein, the initial probability convolution model is constructed based on a single-core or multi-core composite Gaussian kernel function.

[0019] Optionally, the initial etching probability convolution model is:

[0020]

[0021] 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, which is any simulation position other than the target simulation position during 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; exp represents an exponential function with the natural constant e as the base; K(xx′,yy′) is used to represent the composite Gaussian kernel function, σ h The equivalent characteristic distance of each Gaussian kernel, nh t represents the normalized weighting coefficient of each Gaussian kernel; h and t are positive integers, and 1 ≤ h ≤ t.

[0022] Optionally, determining the implicit fitting incremental iterative model based on the initial probabilistic convolution model, the size of the lithographic design pattern, and the etching deviation size includes: determining an analytical equation set corresponding to each lithographic design pattern based on the size of the lithographic design pattern and the etching deviation size, wherein the analytical equation set includes an etching probability threshold; performing several incremental iterations based on the initial probabilistic convolution model and the analytical equation set to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iterative model; wherein the simulation parameter set of the implicit fitting incremental iterative model includes the equivalent feature distance, the normalized weight coefficient, and the etching probability threshold.

[0023] Optionally, the set of analytical equations corresponding to the i-th lithographic design pattern is:

[0024]

[0025] Where, n h σ is the normalized weighting coefficient corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function. h The equivalent feature distance corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function is given by erf, which represents the error function, and D0 is the etching probability threshold; Wx i and Wy i For the length and width of the i-th lithographic pattern, Wx i ′ and Wy i ′ represents the length and width of the etching profile obtained by the i-th lithographic design pattern under the current etching parameter values; The length deviation Sx corresponding to the i-th group i The calculated length deviation, where, Sy corresponds to the width deviation of the i-th group. i The calculated width deviation, where, t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

[0026] Optionally, based on the initial probabilistic convolution model and the analytical equation set, several incremental iterations are performed to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iterative model. This includes: designating one of the etching probability threshold, the normalized weight coefficients of each Gaussian kernel, and the equivalent feature distance of each Gaussian kernel as a specified parameter with a preset fixed value; and forming a parameter set {P} with all parameters except the specified parameter. Based on the specified parameter, an implicit fitting process is performed on the analytical equation set to obtain the following implicit fitting incremental iterative model:

[0027]

[0028] Where, p j and p k Each of these can be any parameter in the parameter group {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 p represents the parameter corresponding to the (l-1)th iteration in several incremental iterations. j j, k, and l are all positive integers, 1 ≤ j ≤ 2t, v is the number of the analytical equations, and v ≥ 2t, i is used to represent the i-th analytical equation, 1 ≤ i ≤ v; in the first incremental iteration process, l = 1, and the parameter... The value is a preset value, which is substituted into the analytical equation system to obtain the calculated length deviation. The value, and the calculated width deviation The value is then substituted into the implicitly fitted incremental iterative model to obtain the corresponding increment. The value and parameters The value; 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 system of analytical equations are used to obtain the calculated 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 positive integer and M≥1, and the parameters obtained from the Mth incremental iteration process are... The value is taken as: the value of the parameter other than the specified parameter among the etching probability threshold D0, the normalized weight coefficient of t Gaussian kernels, and the equivalent feature distance of t Gaussian kernels.

[0029] Optionally, the preset fixed value of the specified parameter is 1.

[0030] Optionally, the preset percentage is selected from 0.5% to 2%.

[0031] Optionally, the etching probability convolution model formed based on the implicitly fitted incremental iterative model is:

[0032]

[0033] Where (x′, y′) are the two-dimensional coordinates of the associated simulation position, which is any simulation position other than the target simulation position during convolution, n h ′ represents the normalized weighting coefficient n h The value of σ h ′ is the equivalent feature distance σ h The value of .

[0034] Optionally, at least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and are arranged along the dimensional direction of the width Wy; and / or, at least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and have the same spacing in the dimensional direction of the width Wy.

[0035] Optionally, for multiple photolithographic design patterns, the sample is etched using multiple preset etching durations to obtain corresponding etching profiles, including: forming a photoresist layer on the surface of the sample; patterning the photoresist layer according to the photolithographic design pattern, forming a mask layer on the sample surface that exposes a portion of the sample surface; etching the sample using the mask layer as a mask to form corresponding etching grooves within the sample; wherein the boundary line of the etching groove on the sample surface serves as the etching profile.

[0036] Compared with the prior art, the technical solution of the embodiments of the present invention has the following beneficial effects:

[0037] In this embodiment of the invention, after obtaining the etching profile of the sample using multiple preset etching durations, the etching depth of multiple measurement positions under each etching duration is determined by measurement. Then, a two-dimensional simulation etching model is used to obtain two-dimensional simulation results (i.e., the etching probability of each measurement position). By fitting the etching depth, a three-dimensional simulation etching model containing the three-dimensional parameter of etching depth can be constructed. The obtained simulation results have higher simulation value. Furthermore, since the fitting is based on the etching duration, the obtained three-dimensional simulation model can also reflect the dynamic simulation results that change over time. Compared with static simulation results, the applicability of the simulation results can be further expanded.

[0038] Furthermore, for each etching duration, interpolation is used to determine the etching probability and etching depth at multiple preset target simulation locations, resulting in multiple interpolated data sets. Each interpolated data set includes the etching duration, interpolated etching depth, and interpolated etching probability. Using the etching duration and etching probability as elements, the interpolated data sets are used to determine the fitting parameters of the binary fitting function for the etching depth. This approach allows for the acquisition of untested data portions through interpolation calculations, leading to a more complete correspondence and improving the accuracy of the interpolated data sets used for fitting, thereby further enhancing the accuracy of the 3D etching simulation model.

[0039] Furthermore, when the number of interpolation data sets is greater than or equal to the number of fitting parameters, the interpolation data sets are used to determine each fitting parameter of the binary fitting function for the etching depth. By using appropriate formulas to perform polynomial fitting, a continuous fitting function can be extracted from the discrete simulation parameter values. Moreover, the accuracy of the continuous fitting parameters increases with the increase of the number of interpolation data sets, thereby obtaining a more accurate three-dimensional etching simulation model.

[0040] Furthermore, based on the fitted function, by comparing d(x,y,N) t ) and D0(N t The contour lines are divided into simulated etching contours, simulated etched areas, and simulated unetched areas. Based on the optimized fitting parameters calculated in the previous steps, a high-precision three-dimensional simulated etching model can be constructed.

[0041] Furthermore, the etching probability of the coordinates to be simulated is determined by using the etching duration to be simulated and the two-dimensional simulation etching model. The etching probability of one or more of the simulation coordinates and the etching duration to be simulated are substituted into the three-dimensional simulation etching model to obtain the simulation value of the etching depth of each simulation coordinate. Thus, the high-precision three-dimensional simulation etching model constructed in this embodiment of the invention can be used to obtain high-precision simulation etching results for different etching durations to be simulated.

[0042] Furthermore, an implicit fitting incremental iterative model is determined based on the initial probabilistic convolution model, the size of the lithographic design pattern, and the etching deviation size, and the etching probabilistic convolution model is formed based on the implicit fitting incremental iterative model. Using the above scheme, a high-precision two-dimensional simulation etching model can be constructed. Based on this, since a lithographic design pattern is provided, and the lithographic design pattern is subjected to etching simulation processing through the two-dimensional simulation etching model to obtain the simulated etching contour data of the lithographic design pattern, high-precision etching simulation is performed to obtain high-precision simulated etching contour data. Therefore, the deviation generated by etching can be accurately predicted, and accurate adjustment of the designed mask pattern can be achieved.

[0043] Furthermore, by determining the set of analytical equations corresponding to each lithographic design pattern, several incremental iterations are performed to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iterative model. Since the set of analytical equations is determined by the size of the lithographic design pattern and the measured etching deviation size, and the number of analytical equations is greater than or equal to the number of simulation parameters, optimized simulation parameter values ​​can be obtained after iterative processing. Substituting these values ​​into the implicit fitting incremental iterative model yields an optimized etching probability convolution model, which is used to construct the simulated etching model.

[0044] Furthermore, among the etching probability threshold, the normalized weight coefficient of each Gaussian kernel, and the equivalent feature distance of each Gaussian kernel, one is designated as a specified parameter with a preset fixed value. The parameters other than the specified parameter are grouped into a parameter group {P}. In each iteration, the value of the specified parameter (the preset fixed value) and the parameter... Substitute the values ​​of each of the v analytical equations into the solution to calculate the length deviation. Values ​​and calculated width deviations The value of is then substituted back into the implicitly fitted incremental iterative model to obtain . The parameters in parameter group {P} (Increment corresponding to incremental iteration processing) The value of the parameter (and thus the value of the parameter set {P} from the previous round) is used to obtain the parameter. The value of .

[0045] Furthermore, in the simulated etching model constructed based on the updated etching probability convolution model, by comparing the contour lines of d(x,y) and D0, it is divided into simulated etching contour, simulated etched region, and simulated unetched region. Based on the optimized simulation parameters calculated in the aforementioned steps, a high-precision two-dimensional simulated etching model can be constructed. Attached Figure Description

[0046] Figure 1This is a flowchart of a method for constructing a three-dimensional simulation etching model according to an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of a photolithographic design pattern in an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram of an etching profile based on multiple etching durations in an embodiment of the present invention;

[0049] Figure 4 This is a top view and a cross-sectional structural diagram of an etched groove according to an embodiment of the present invention;

[0050] Figure 5 This is a schematic diagram of another photolithographic design pattern in an embodiment of the present invention;

[0051] Figure 6 yes Figure 1 A flowchart of a specific implementation of step S14;

[0052] Figure 7 yes Figure 6 A flowchart of a specific implementation of step S61;

[0053] Figure 8 This is a partial flowchart of another method for constructing a three-dimensional simulation etching model in an embodiment of the present invention;

[0054] Figure 9 This is a flowchart of a method for constructing a two-dimensional simulation etching model according to an embodiment of the present invention;

[0055] Figure 10 yes Figure 9 A flowchart of a specific implementation of step S91;

[0056] Figure 11 yes Figure 9 A flowchart of a specific implementation of step S92. Detailed Implementation

[0057] As mentioned earlier, some simulation etching models have been proposed in the existing technology to simulate and analyze the actual etching process. However, due to the high complexity of the simulation, there is currently no highly accurate three-dimensional simulation etching model.

[0058] Specifically, in existing technologies, physical simulation of the etching process is very difficult, and the accuracy of the simulation is poor, with two-dimensional simulation etching models being the main approach.

[0059] An attempt is made to address the diffusion field problem of surface reactions and moving boundaries during etching using a complex mathematical model employing perturbation techniques. However, due to mathematical complexity, this model can only handle simple cases such as semi-infinite interfaces or circular holes. Furthermore, the model employs the assumption of static liquid flow, which differs significantly from industrial realities.

[0060] In an empirical model based on pattern density (PD), an approximate solution is used to simplify the model and calibrate the model parameters. As a result, the model parameters obtained by this model cannot reach the global optimum, which leads to poor computational accuracy and poor accuracy of the etching simulation model.

[0061] The inventors of this invention have discovered through research that the two existing simulation etching models are both two-dimensional and static simulation etching models, which do not involve the etching depth, a three-dimensional parameter perpendicular to the etched plane, and thus the applicability of the obtained simulation results is limited.

[0062] In this embodiment of the invention, after obtaining the etching profile of the sample using multiple preset etching durations, the etching depth of multiple measurement positions under each etching duration is determined by measurement. Then, a two-dimensional simulation etching model is used to obtain two-dimensional simulation results (i.e., the etching probability of each measurement position). By fitting the etching depth, a three-dimensional simulation etching model containing the three-dimensional parameter of etching depth can be constructed. The obtained simulation results have higher simulation value. Furthermore, since the fitting is based on the etching duration, the obtained three-dimensional simulation model can also reflect the dynamic simulation results that change over time. Compared with static simulation results, the applicability of the simulation results can be further expanded.

[0063] 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.

[0064] Reference Figure 1 , Figure 1 This is a flowchart of a method for constructing a three-dimensional simulation etching model according to an embodiment of the present invention. The method for constructing the three-dimensional simulation etching model may include steps S11 to S15:

[0065] Step S11: For multiple photolithography design patterns, the sample is etched using multiple preset etching durations to obtain the corresponding etching contours.

[0066] Step S12: Measure the dimensions of each etching profile and determine the etching depth of each lithographic design pattern at multiple measurement locations under each etching duration;

[0067] Step S13: For each etching duration, a two-dimensional simulation etching model is used to determine the etching probability at each measurement location;

[0068] Step S14: Based on the etching duration and the etching probability at each measurement position, fit the etching depth to determine the fitting function;

[0069] Step S15: Construct the three-dimensional simulation etching model based on the fitting function.

[0070] In the specific implementation of step S11, the multiple lithographic design patterns provided can have different sizes. Taking a rectangular lithographic design pattern as an example, the lithographic design pattern can have different lengths and / or different widths.

[0071] Reference Figure 2 , Figure 2 This is a schematic diagram of a photolithographic design pattern in an embodiment of the present invention.

[0072] Figure 2 A plurality of rectangular photolithographic design patterns 100 are schematically represented. The dimensions of any photolithographic design pattern 100 include: the length Wx and the width Wy of the first photolithographic design pattern 100.

[0073] Furthermore, at least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and are arranged along the dimensional direction of the width Wy; and / or, at least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and have the same spacing in the dimensional direction of the width Wy.

[0074] In a non-limiting embodiment, multiple first lithographic design patterns 100 having the same length Wx can be arranged along a width Wy direction, each having a different width Wy. Furthermore, the multiple lithographic design patterns 100 having the same length Wx and arranged along the width Wy direction can have the same spacing in the width Wy direction. This further improves the rationality of the size and arrangement of the lithographic design patterns 100, thereby better enhancing the reliability of the sample data.

[0075] In another non-limiting embodiment, the lithographic design pattern may include multiple lithographic design patterns with the same width Wy and different lengths Wx, or it may include multiple lithographic design patterns with different widths Wy and different lengths Wx.

[0076] In practice, etching time is a parameter of the etching process. Generally speaking, the longer the etching time, the larger the size of the etching profile and the deeper the etching depth.

[0077] Reference Figure 3, Figure 3 This is a schematic diagram of an etching profile based on multiple etching durations in an embodiment of the present invention.

[0078] like Figure 3 As shown, for the same set of photolithographic design patterns 100, multiple sets of etching contours can be obtained by using multiple preset etching durations to etch the sample.

[0079] Taking an etching duration of 3 as an example, 3 etching profiles can be obtained: etching profile 201 based on the first etching duration, etching profile 211 based on the second etching duration, and etching profile 221 based on the third etching duration. Among them, the first etching duration < the second etching duration < the third etching duration.

[0080] As shown in the figure, for the same set of photolithography design patterns, the etching contour 201 is generally smaller in size, while the etching contour 203 is generally larger in size.

[0081] Reference Figure 4 , Figure 4 This is a top view and a cross-sectional structural diagram of an etched groove according to an embodiment of the present invention.

[0082] For ease of explanation and understanding, Figure 4 The first etching profile of etching profile 201 is shown only schematically.

[0083] Specifically, for multiple photolithographic design patterns, the step of etching the sample using multiple preset etching durations to obtain the corresponding etching contours may include: forming a photoresist layer (not shown) on the surface of the sample 300; patterning the photoresist layer according to the photolithographic design pattern 100, and forming a mask layer 301 that exposes a portion of the sample surface on the surface of the sample 300; etching the sample using the mask layer 301 as a mask, and forming corresponding etching grooves 302 in the sample 300; wherein the boundary line of the etching grooves 302 on the sample surface serves as the etching contour 201.

[0084] Different etching depths may be obtained at different measurement positions. For example, the etching depth d1 is measured at a measurement position close to the center of the photolithographic design pattern, and the etching depth d2 is measured at a measurement position close to the center of the photolithographic design pattern. d1 and d2 may not be equal, and d1 may be greater than d2.

[0085] The mask layer 301 can be obtained by patterning the photoresist layer through processes such as exposure and development.

[0086] Specifically, after the etched groove 302 is formed, the mask layer 301 can be removed to facilitate subsequent measurement of the etched groove 302 and obtain the dimensions of the corresponding etched contour 201.

[0087] It should be noted that, just as the etched grooves 302 correspond to the etched contours 201, the multiple etched grooves and multiple etched contours have a one-to-one correspondence.

[0088] Combined with reference Figure 1 and Figure 4 In the specific implementation of step S12, the dimensions of each etching profile are measured, and the etching depth of each photolithographic design pattern at multiple measurement positions under each etching duration is determined.

[0089] Specifically, the dimensions of the etching profile can be used to represent the size of the etching profile, in order to Figure 2 Taking a rectangular lithographic design pattern as an example, the dimensions of the etching profile can include both length and width. If the lithographic design pattern is a polygon, the dimensions of the etching profile can include the length of each side.

[0090] Furthermore, based on the dimensions of each etching profile, the etching deviation size of each lithographic design pattern at each etching duration can be determined.

[0091] Furthermore, the etching deviation dimensions of each lithographic design pattern at each etching duration can include length deviation and width deviation.

[0092] Specifically, the length deviation of the i-th group Among them, Wx i ′ is the length Wx′ of the i-th etch profile (e.g., etch profile 201), Wx i Wx is the length of the i-th lithographic design pattern (e.g., lithographic design pattern 100), where i is a positive integer.

[0093] Specifically, the width deviation of the i-th group Among them, Wy i ′ is the width Wy′ of the i-th etch profile (e.g., etch profile 201), Wy i Wy is the width of the i-th lithographic design pattern (e.g., lithographic design pattern 100).

[0094] Reference Figure 5 , Figure 5 This is a schematic diagram of another photolithographic design pattern in an embodiment of the present invention.

[0095] Specifically, multiple photolithographic design patterns 500 arranged in an array can be provided. The photolithographic design patterns 500 are regular hexagons, and the multiple photolithographic design patterns 500 are arranged in a honeycomb array.

[0096] It should be noted that, Figure 5The image only schematically illustrates one set of lithographic design patterns 500. In actual implementation, multiple lithographic design pattern groups can be set up, with the lithographic design patterns in different lithographic design pattern groups having the same shape but different dimensions (such as different side lengths).

[0097] The lithographic design pattern can also be a circle or other polygons.

[0098] In one specific embodiment of the present invention, the spacing between the lithographic design patterns in different lithographic design pattern groups can be different.

[0099] In this embodiment of the invention, by employing photolithographic design patterns with more shapes and more arrangements, the accuracy of the three-dimensional simulation etching model can be further improved based on richer detection data.

[0100] Continue to refer to Figure 1 In the specific implementation of step S13, for each etching duration, a two-dimensional simulation etching model is used to determine the etching probability of each measurement position.

[0101] Specifically, the two-dimensional simulation etching model can be a conventional simulation etching model, or it can be a two-dimensional simulation etching model obtained based on a construction method disclosed in the embodiments of this application (see below for details), which is used to determine the etching probability of each measurement position, that is, to obtain the simulation results of whether the measurement position is etched or not, so that subsequent fitting processing can be performed based on the simulation results, and a three-dimensional simulation etching model can be constructed.

[0102] In the specific implementation of step S14, the etching depth is fitted according to the etching duration and the etching probability at each measurement position to determine the fitting function.

[0103] In practice, interpolation can be performed on the data to be fitted during the fitting process.

[0104] Reference Figure 6 , Figure 6 yes Figure 1 A flowchart of a specific implementation of step S14 is provided. The step of fitting the etching depth to determine the fitting function based on the etching duration and the etching probability at each measurement location may include steps S61 to S62, which are described below.

[0105] In step S61, for each etching duration, the etching probability and etching depth of multiple preset target simulation positions are determined by interpolation to obtain multiple interpolation data sets, wherein each interpolation data set includes etching duration, interpolated etching depth and interpolated etching probability.

[0106] Specifically, interpolation, also known as interpolation, involves adding a continuous function to discrete data so that the continuous curve passes through all given discrete data points. Interpolation is an important method for approximating discrete functions; it allows us to estimate the approximate value of a function at other points by considering the function's values ​​at a finite number of points.

[0107] In this embodiment of the invention, the untested data portion can be obtained by calculating interpolated data, thereby obtaining a more complete correspondence.

[0108] Reference Figure 7 , Figure 7 yes Figure 6 A flowchart of a specific implementation of step S61 is provided. The step of determining the etching probability and etching depth of multiple preset target simulation positions using interpolation may include steps S71 to S73, which are described below.

[0109] In step S71, for each etching duration, the etching depth of at least a portion of the measurement locations is interpolated to determine the interpolated etching depth of each preset target simulation location.

[0110] It should be noted that actual testing is subject to measurement limits and deviations. Furthermore, simulation results are limited by the minimum resolution of the equipment, making it difficult to ensure that all important locations can be detected. For example, when testing the central area of ​​a lithographic design pattern, the preset target simulation position may be the center point of the lithographic design pattern (such as the center of a polygon or the center of a circle). The actual detection position may be offset from the center point. Through interpolation, the interpolated etching depth of the preset target simulation position can be determined.

[0111] In step S72, the etching probabilities of at least a portion of the measurement locations are interpolated to determine the interpolated etching probabilities of each preset target simulation location.

[0112] Specifically, by interpolating some or all of the etching probabilities, interpolated data of the interpolated etching probabilities at a preset target simulation location can also be determined under measurement constraints.

[0113] In step S73, the interpolation etching depth and interpolation etching probability with the same target simulation position are associated to obtain the interpolation data set.

[0114] Referring to Table 1, which is an exemplary interpolation data set in an embodiment of the present invention.

[0115] Table 1

[0116]

[0117] As shown in Table 1, t1, t2 to t E This is used to represent the etching duration. Taking an example where each interpolation data group contains z sets of data, and each set of data contains etching duration t, interpolation etching probability d, and interpolation etching depth z.

[0118] Among them, the interpolated etching probability d can be used to represent the interpolated data of the etching probability at a specific position (x,y).

[0119] Continue to refer to Figure 6 In step S62, using the etching duration and the etching probability as elements, the interpolation data set is used to determine the various fitting parameters of the binary fitting function for the etching depth.

[0120] In one specific embodiment of the present invention, a polynomial fitting formula can be used for fitting. Taking univariate fitting as an example, the polynomial fitting formula can be expressed as follows:

[0121] F(q)=a c ×q c +a c-1 ×q c-1 +…+a1×q+a0

[0122] Where F(q) represents the polynomial fitting function of the selected simulation parameters, q represents the univariate fitting parameters, c is a positive integer, and a0 to a100 are the ranges from 0 to 100. c These are phenomenological parameters.

[0123] In another specific embodiment of the present invention, a quadratic fitting formula can also be used for bivariate fitting. Taking univariate fitting as an example, the quadratic fitting formula can be expressed as follows:

[0124] F(q) = a² × q 2 +a1×q+a0

[0125] Where F(q) represents the fitting function of the selected simulation parameters, q represents the univariate fitting parameter, c is a positive integer, and a0 to a2 are phenomenological parameters.

[0126] Furthermore, the following bivariate fitting polynomial formula can be used, with the etching duration and the etching probability as elements, to determine the various fitting parameters of the bivariate fitting function for the etching depth using the interpolation data set:

[0127] z(x,y,N t )=z0+a1×d(x,y,N t )+a2×d(x,y,N t ) 2 +…+a c×d(x,y,N t ) c +b1×N t +b2×N t 2 +…+b c ×N t c

[0128] Where z(x,y,N) t A binary fitting function d(x,y,N) is used to represent the etching depth. t ) is used to represent the etching time N t The etching probability at the simulated target position (x, y), where c is a positive integer and a1 to a2 are given. c b1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth; wherein, the number of interpolation data sets is greater than or equal to the number of fitting parameters.

[0129] In this embodiment of the invention, for each etching duration, interpolation is used to determine the etching probability and etching depth of multiple preset target simulation locations, resulting in multiple interpolated data sets. Then, using the etching duration and the etching probability as elements, the interpolated data sets are used to determine the fitting parameters of the binary fitting function for the etching depth. By employing this scheme, untested data portions can be obtained through interpolation data calculation, thereby obtaining a more complete correspondence, improving the accuracy of the interpolated data sets used for fitting, and further improving the accuracy of the three-dimensional etching simulation model.

[0130] In this embodiment of the invention, when the number of interpolation data sets is greater than or equal to the number of fitting parameters, the interpolation data sets are used to determine each fitting parameter of the binary fitting function of the etching depth. By using appropriate formulas to perform polynomial fitting, a continuous fitting function can be extracted from the discrete simulation parameter values. Moreover, the accuracy of the continuous fitting parameters increases with the increase of the number of interpolation data sets, thereby obtaining a more accurate three-dimensional etching simulation model.

[0131] Continue to refer to Figure 1 In the specific implementation of step 15, the three-dimensional simulation etching model is constructed based on the fitting function.

[0132] Specifically, by comparing the obtained fitting function with a preset etching probability threshold, it can be divided into simulated etching contour, simulated etched region, and simulated unetched region. In other words, the etching probability threshold is used to characterize the critical etching probability.

[0133] More specifically, by comparing the obtained fitting function with a preset etching probability threshold, the simulated etching profile can be determined. Then, for the area within the simulated etching profile, it is determined that it can be etched, and the fitting function is used to determine the simulated etching depth. For the area on and outside the simulated etching profile, it is determined that it will not be etched, and 0 is used to represent the simulated etching depth.

[0134] Furthermore, the step of constructing the three-dimensional simulation etching model based on the fitting function may include:

[0135]

[0136] Where z(x,y,N) t ) is used to represent the etching time N t The etching depth at the simulated target position (x,y), d(x,y,N) t ) is used to represent the etching time N t The etching probability at the simulated target position (x,y), D0(N) t ) is used to represent the etching time N t The etching probability threshold below.

[0137] In this embodiment of the invention, based on the fitting function, by comparing d(x,y,N) t ) and D0(N t The contour lines are divided into simulated etching contours, simulated etched areas, and simulated unetched areas. Based on the optimized fitting parameters calculated in the previous steps, a high-precision three-dimensional simulated etching model can be constructed.

[0138] Furthermore, after constructing the three-dimensional simulation etching model, the simulation value of the etching depth of one or more coordinates to be simulated can be determined based on the three-dimensional simulation etching model.

[0139] Reference Figure 8 , Figure 8 This is a partial flowchart of another method for constructing a three-dimensional simulation etching model according to an embodiment of the present invention. The other method for constructing a three-dimensional simulation etching model may include steps S81 to S82, which are described below.

[0140] In step S81, the etching probability of the coordinates to be simulated is determined using the etching duration to be simulated and the two-dimensional simulation etching model.

[0141] In step S82, the etching probability of one or more of the simulation coordinates and the etching duration to be simulated are substituted into the three-dimensional simulation etching model to obtain the simulation value of the etching depth of each simulation coordinate.

[0142] Furthermore, the step of substituting the etching probability and the etching duration to be simulated for one or more of the simulation coordinates into the three-dimensional simulation etching model to obtain the simulation value of the etching depth for each simulation coordinate may include:

[0143] z(x r ,y r ,t r )=z0+a1×d(x r ,y r ,t r )+a2×d(x r ,y r ,t r ) 2 +…+a c ×d(x r ,y r ,t r ) c +b1×t r +b2×t r 2 +…+b c ×t r c

[0144] Where z(x) r ,y r ,t r ) is a bivariate fitting function used to represent the etching depth, d(x) r ,y r ,t r ) is used to represent the etching time t to be simulated. r The coordinates to be simulated below (x) r ,y r The etching probability of ), where c is a positive integer, and a1 to a2. c b1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth.

[0145] In this embodiment of the invention, the etching probability of the coordinates to be simulated is determined by using the etching duration to be simulated and the two-dimensional simulation etching model; the etching probability of one or more of the simulation coordinates and the etching duration to be simulated are substituted into the three-dimensional simulation etching model to obtain the simulation value of the etching depth of each simulation coordinate. Thus, the high-precision three-dimensional simulation etching model constructed in this embodiment of the invention can be used to obtain high-precision simulation etching results for different etching durations to be simulated.

[0146] In this embodiment of the invention, after obtaining the etching profile of the sample using multiple preset etching durations, the etching depth of multiple measurement positions under each etching duration is determined by measurement. Then, a two-dimensional simulation etching model is used to obtain two-dimensional simulation results (i.e., the etching probability of each measurement position). By fitting the etching depth, a three-dimensional simulation etching model containing the three-dimensional parameter of etching depth can be constructed. The obtained simulation results have higher simulation value. Furthermore, since the fitting is based on the etching duration, the obtained three-dimensional simulation model can also reflect the dynamic simulation results that change over time. Compared with static simulation results, the applicability of the simulation results can be further expanded.

[0147] It should be noted that, in the specific implementation of the step of determining the etching probability of each measurement position using a two-dimensional simulation etching model, the following two-dimensional simulation etching model can also be used to determine the etching probability with high accuracy.

[0148] Reference Figure 9 , Figure 9 This is a flowchart illustrating a method for constructing a two-dimensional simulation etching model according to an embodiment of the present invention. The method for constructing the two-dimensional simulation etching model may include steps S91 to S92 and can be used for... Figure 1 Before step S13 is shown.

[0149] Step S91: Determine the implicit fitting incremental iteration model based on the initial probabilistic convolution model, the size of the lithographic design pattern, and the etching deviation size, and form an etching probabilistic convolution model based on the implicit fitting incremental iteration model; wherein, the initial probabilistic convolution model is constructed based on a single-kernel or multi-kernel composite Gaussian kernel function;

[0150] Step S92: For each etching duration, substitute the size of the lithographic design pattern and the etching deviation size into the etching probability convolution model to determine the values ​​of each simulation parameter in the simulation parameter group of the two-dimensional simulation etching model.

[0151] In the specific implementation of step S91, an initial etching probability convolution model can be determined first, which can be a phenomenological model.

[0152] Furthermore, the initial etching probability convolution model can be:

[0153]

[0154] 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;

[0155] K(xx′,yy′) is used to represent the composite Gaussian kernel function, σ h The equivalent characteristic distance of each Gaussian kernel, n h These are the normalized weighting coefficients for each Gaussian kernel.

[0156] t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

[0157] In practice, the etching results (such as the deviations caused by etching) of the photolithographic design pattern can be predicted by using the mask pattern to be simulated.

[0158] The mask pattern to be simulated may include: a preset etched area and a non-etched area.

[0159] The preset etching area can be the area that is desired to be etched during the actual etching process, and the preset non-etchable area can be the area that is desired not to be etched during the actual etching process. That is, in the mask pattern to be simulated, the non-etchable area is the area outside the etching area.

[0160] It should be noted that the boundary between the preset etched area and the non-etched area is the critical position (boundary) of the area that is to be etched during the actual etching process, which belongs to the etched area.

[0161] The d(x,y) represents the etching probability at the target simulation location. Specifically, the etching probability d(x,y) can characterize the probability that the material at the target simulation location 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.

[0162] The etching probability threshold D0 can characterize the critical etching probability. Specifically, 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.

[0163] More specifically, during the etching simulation process, when the etching probability d(x,y) of the target simulation position (x,y) is equal to the etching probability threshold D0, it indicates that the target simulation position (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 profile.

[0164] M(x′,y′) is the binary image function of the associated simulation position.

[0165] As a non-limiting example, based on the mask pattern to be simulated during etching simulation, when any associated simulation position is within a preset etching region, the binary image function M(x′,y′) of the any 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 any associated simulation position is 0.

[0166] It is important to understand that, since different types of photoresists have different material properties during exposure and development, the pre-defined etching area in the simulation mask may be a light-transmitting area or an opaque area, depending on the type of photoresist.

[0167] Specifically, for positive photoresist, the pre-defined etching area in the mask pattern to be simulated is designed as a transparent area. 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 as opaque, M(x′,y′) is assigned a value of 0.

[0168] Specifically, for the case of negative photoresist, the pre-defined etching area in the mask pattern to be simulated is designed as an opaque area. Therefore, when the associated simulation position (x′,y′) is located within the opaque area, M(x′,y′) is assigned a value of 1, and when the associated simulation position (x′,y′) is located within the other areas designed as transparent, M(x′,y′) is assigned a value of 0.

[0169] K(xx′,yy′) is the kernel function, and exp represents an exponential function with the natural constant e as the base.

[0170] 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.

[0171] Furthermore, t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

[0172] 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.

[0173] 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.

[0174] 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.

[0175] It should be noted 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, the number of parameter sets increases (i.e., the number of kernels t increases), and the complexity and accuracy of the subsequent etching probability convolution model formed based on the initial etching probability convolution model are both improved. Consequently, the amount of data computation is greater when using the etching probability convolution model for etching simulation.

[0176] 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.

[0177] By using the initial etching probability convolution model in this embodiment of the invention, the etching probability at each position can be determined, which is beneficial for quantifying the etching situation at each position based on the etching probability in subsequent steps and obtaining simulation values, thereby improving the simulation accuracy.

[0178] Reference Figure 10 , Figure 10 yes Figure 9 A flowchart of a specific implementation of step S91. The step of determining the implicit fitting incremental iterative model based on the initial probability convolution model, the size of the lithographic design pattern, and the etching deviation size may include:

[0179] Step S101: Based on the size of the lithographic design pattern and the etching deviation size, determine the analytical equation set corresponding to each lithographic design pattern, wherein the analytical solution equation set includes an etching probability threshold.

[0180] Step S102: Based on the initial probabilistic convolution model and the analytical equation set, perform several incremental iterations to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iteration model, wherein the simulation parameter set of the implicit fitting incremental iteration model includes the equivalent feature distance, the normalized weight coefficient, and the etching probability threshold.

[0181] In the specific implementation of step S101, the analytical equation set corresponding to the i-th lithographic design pattern can be determined based on the size of the i-th lithographic design pattern and its corresponding i-th etching deviation size.

[0182] The analytical equations corresponding to the i-th lithographic design pattern are as follows:

[0183]

[0184] Where, n h σ is the normalized weighting coefficient corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function. h The equivalent feature distance corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function is erf, which represents the error function, and D0 is the etching probability threshold.

[0185] Wx i and Wy i For the length and width of the i-th lithographic pattern, Wx i ′ and Wy i ′ represents the length and width of the etching profile obtained by the i-th lithographic design pattern under the current etching parameter values;

[0186] The length deviation Sx corresponding to the i-th group i The calculated length deviation, where, Sy corresponds to the width deviation of the i-th group. i The calculated width deviation, where,

[0187] t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

[0188] Specifically, based on the initial etching probability convolution model and the dimensions of the v lithographic design patterns, an analytical equation set corresponding to each lithographic design pattern is obtained, and each set of simulation parameters corresponds to one or more of the analytical equation sets.

[0189] In other words, based on the initial etching probability convolution model and the dimensions of the v lithographic design patterns, a set of v analytical equations can be obtained.

[0190] Here, erf can represent the error function. It can be the length deviation Sx corresponding to the i-th group. i The calculated length deviation, It can be the width deviation Sy corresponding to the i-th group i The calculated width deviation. and This can be intermediate calculation data during the process of performing several incremental iterations based on the implicitly fitted incremental iterative model.

[0191] In this embodiment of the invention, by determining the set of analytical equations corresponding to each lithographic design pattern, several incremental iterations are performed to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iteration model. Since the set of analytical equations is determined by the size of the lithographic design pattern and the measured etching deviation size, and the number of analytical equations is greater than or equal to the number of simulation parameters, optimized simulation parameter values ​​can be obtained after iterative processing. Substituting these values ​​into the implicit fitting incremental iteration model yields an optimized etching probability convolution model, which is used to construct the simulated etching model.

[0192] Reference Figure 11 , Figure 11 yes Figure 9 A flowchart of a specific implementation of step S92. The step of performing several incremental iterations based on the initial probabilistic convolution model and the analytical equation set to obtain the simulation parameter values ​​of the implicitly fitted incremental iterative model may include steps S111 to S112, which are described below.

[0193] Step S111: Among the etching probability threshold, the normalized weight coefficient of each Gaussian kernel, and the equivalent feature distance of each Gaussian kernel, designate one of them as a specified parameter with a preset fixed value, and form a parameter group {P} with the parameters other than the specified parameter.

[0194] Specifically, taking t=2 as an example, the simulation parameter set may include: normalized weight coefficient n1, equivalent feature distance σ1, normalized weight coefficient n2, equivalent feature distance σ2, and etching probability threshold D0.

[0195] It is understandable that as the number of kernels increases, when t = 3, 4..., in addition to the simulation parameters mentioned above, the simulation parameter set may also include: normalized weight coefficients n3, n4... and equivalent feature distances σ3, σ4... For ease of understanding, the following explanation will use t = 2 as an example.

[0196] 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 into a parameter group {P}.

[0197] 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 into a parameter set {P}. In this case, the parameter set {P} can be {D0, σ1, n2, σ2}.

[0198] First, set any one of the normalized weight coefficients and equivalent feature distances in the t-group parameter set to a preset fixed value. Then, solve for the values ​​of 2t unknowns, including the etching probability threshold D0, to obtain the simulation parameter values ​​of the simulation parameter set.

[0199] Furthermore, the preset fixed value of the specified parameter can be 1.

[0200] Specifically, there is a 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. More specifically, a high-accuracy etching probability convolution model can be formed simply 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.

[0201] Based on this, the value of the specified parameter can be used as a benchmark to determine that other parameters are multiples of the specified parameter. As a non-restrictive example, the preset fixed value of the specified parameter can be set to 1 to reduce the computational complexity and amount of calculation.

[0202] In the specific implementation of step S112, implicit fitting processing is performed on the analytical equation system based on the specified parameters to obtain the following implicit fitting incremental iterative model:

[0203]

[0204] Where, p j and p k Each of these can be any parameter in the parameter group {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 p represents the parameter corresponding to the (l-1)th iteration in several incremental iterations. j j, k, and l are all positive integers, 1 ≤ j ≤ 2t, v is the number of the analytical equation system, and v ≥ 2t, i is used to represent the i-th analytical equation, 1 ≤ i ≤ v;

[0205] During the first incremental iteration, l = 1, and the parameter... The value is a preset value, which is substituted into the analytical equation system to obtain the calculated length deviation. The value, and the calculated width deviation The value is then substituted into the implicitly fitted incremental iterative model to obtain the corresponding increment. The value and parameters The value;

[0206] 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 system of analytical equations are used to obtain the calculated length deviation. The value, and the calculated width deviation The value of the parameter when l = 1. The value is the preset value;

[0207] The calculated 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;

[0208] 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 positive integer and M≥1, and the parameters obtained from the Mth incremental iteration process are... The value is taken as: the value of the parameter other than the specified parameter among the etching probability threshold D0, the normalized weight coefficient of t Gaussian kernels, and the equivalent feature distance of t Gaussian kernels.

[0209] In practical implementation, several incremental iterations can be performed based on the analytical equations in step S111 and the implicit fitting incremental iterative model in step S112. In each iteration, the values ​​of the specified parameters (preset fixed values) and the parameters are... Substitute the values ​​of each of the v analytical equations into the solution to calculate the length deviation. Values ​​and calculated width deviations The value of is then substituted back into the implicitly fitted incremental iterative model to obtain . The parameters in parameter group {P} (Increment corresponding to incremental iteration processing) (value).

[0210] based on It can be seen that the implicit fitting incremental iterative model actually contains 2t implicit equations.

[0211] It should be noted that by setting v≥2t, a sufficient number of lithographic design patterns and etching grooves formed based on the lithographic design patterns can be ensured to provide enough sample data to solve for the values ​​of the 2t unknowns.

[0212] It is understandable 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.

[0213] 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 This will be explained. It should be noted that the parameter p... j and parameter p k The selected parameters can be the same or different.

[0214] 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.

[0215] In this embodiment, the least squares method can be used to implicitly fit the set of analytical equations v based on the specified parameters to obtain the implicitly fitted incremental iterative model.

[0216] After obtaining the implicitly fitted incremental iterative model, the step of performing several incremental iterations based on the initial probabilistic convolution model and the analytical equation set to obtain the simulation parameter values ​​of the simulation parameter set of the implicitly fitted incremental iterative model may further include the l-th incremental iteration process and obtaining the increment corresponding to the l-th incremental iteration process. Values, calculation parameters The steps include setting the value and terminating the incremental iteration process.

[0217] Specifically, in the first incremental iteration process, l = 1, and the parameter... The value is a preset value, which is substituted into the analytical equation system to obtain the calculated length deviation. The value, and the calculated width deviation The value is then substituted into the implicitly fitted incremental iterative model to obtain the corresponding increment. Values ​​and parameters The value of .

[0218] Where, when l = 1, the parameter The value can be a preset value.

[0219] Taking the parameter set {P} = {D0, σ1, n2, σ2} as an example, since 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.

[0220] Specifically, the value of the specified parameter (a preset fixed value) and the parameter can be specified. Substitute the values ​​of each of the v analytical equations into the calculation length deviation when l = 1. Values ​​and calculated width deviations 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 of .

[0221] Furthermore, during the first incremental iteration, the computation length deviation was obtained. After obtaining the value, the length deviation can be calculated. 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 of .

[0222] Next, the l-th incremental iteration is performed.

[0223] Specifically, 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 system of analytical equations are used to obtain the calculated length deviation. The value, and the calculated width deviation The value of .

[0224] Specifically, taking the second incremental iteration (l=2) as an example: the values ​​of the specified parameters, and the parameters (obtained during the first incremental iteration) can be used. Substitute the values ​​of each of the v analytical equations into the calculation length deviation when l = 2. Values ​​and calculated width deviations 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 of the parameter when l=1, thus based on the parameter. The value of l is used to calculate the parameters when l = 2. The value of .

[0225] 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 of , and the calculation parameters The value of .

[0226] Then, the calculated 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 .

[0227] 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 .

[0228] Finally, the incremental iteration process can be terminated under appropriate conditions.

[0229] Specifically, the increment obtained from the Mth incremental iteration can be considered as... When all values ​​are within a preset percentage, the incremental iteration process is terminated, where M is a positive integer and M≥1, and the parameters obtained from the Mth incremental iteration process are... The value is taken as: the value of the parameter other than the specified parameter among the etching probability threshold D0, the normalized weight coefficient of t Gaussian kernels, and the equivalent feature distance of t Gaussian kernels.

[0230] 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.

[0231] It should be noted that the parameters obtained in the Mth incremental iteration process The value can be the value of each parameter in the parameter set {P} obtained from the Mth incremental iteration.

[0232] Continuing with the example of t=2, and specifying the normalized weight coefficient n1 as a parameter with a preset fixed value, and the parameter set {P}={D0, σ1, n2, σ2}, the parameters obtained from the Mth incremental iteration process can be... 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.

[0233] Furthermore, the preset percentage can be selected from 0.7% to 2%.

[0234] As a non-limiting example, the preset percentage could be 1%, thereby ensuring that the increment obtained during the Mth incremental iteration is... It also converges relatively well.

[0235] Then, the specified parameters and the parameters obtained from the Mth incremental iteration can be processed. Substituting the value into the initial etching probability convolution model, we form the etching probability convolution model:

[0236]

[0237] Where (x′, y′) are the two-dimensional coordinates of the associated simulation position, which is any simulation position other than the target simulation position during convolution, 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 the parameter value from the parameter itself.

[0238] In this embodiment of the invention, in the etching probability convolution model formed according to the implicit fitting incremental iterative model, by comparing the contour lines of d(x,y) and D0, the model is divided into simulated etching contour, simulated etched region, and simulated unetched region. Based on the optimized simulation parameters calculated in the aforementioned steps, a high-precision two-dimensional simulated etching model can be constructed.

[0239] In this embodiment of the invention, among the etching probability threshold, the normalized weight coefficient of each Gaussian kernel, and the equivalent feature distance of each Gaussian kernel, one is designated as a specified parameter with a preset fixed value. Furthermore, the parameters other than the specified parameter are grouped into a parameter group {P}. In each iteration, the value of the specified parameter (the preset fixed value) and the parameter... Substitute the values ​​of each of the v analytical equations into the solution to calculate the length deviation. Values ​​and calculated width deviations The value of is then substituted back into the implicitly fitted incremental iterative model to obtain . The parameters in parameter group {P} (Increment corresponding to incremental iteration processing) The value of is then combined with the value of the parameter set {P} from the previous round to obtain the parameter. The value of .

[0240] In this embodiment of the invention, an initial probabilistic convolution model is constructed based on a single-core or multi-core composite Gaussian kernel function. Compared with the existing models mentioned above, such as mathematical models based on perturbation techniques or empirical models based on graph density, the two-dimensional simulation etching model constructed in this embodiment of the invention can provide higher simulation accuracy, thereby providing a better foundation for the subsequent construction of a three-dimensional simulation etching model.

[0241] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article indicates that the preceding and following related objects have an "or" relationship.

[0242] In the embodiments of this application, "multiple" refers to two or more.

[0243] The descriptions of "first," "second," etc., appearing in the embodiments of this application are for illustrative purposes and to distinguish the objects being described. They have no order and do not indicate any special limitation on the number of devices in the embodiments of this application, nor do they constitute any limitation on the embodiments of this application.

[0244] 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 a three-dimensional simulation etching model, characterized in that, include: For multiple lithographic design patterns, multiple preset etching durations are used to etch the sample to obtain the corresponding etching contours; Measure the dimensions of each etching profile and determine the etching depth of each lithographic design pattern at multiple measurement locations under various etching durations; For each etching duration, a two-dimensional simulation etching model is used to determine the etching probability at each measurement location; Based on the etching duration and the etching probability at each measurement location, the etching depth is fitted to determine the fitting function; Based on the fitting function, the three-dimensional simulation etching model is constructed; The step of constructing the three-dimensional simulation etching model based on the fitting function includes: in, Used to indicate the etching duration Lower target simulation position The etching depth, Used to indicate the etching duration Lower target simulation position The etching probability, Used to indicate the etching duration The etching probability threshold is set below, where c is a positive integer. a 1 to a c , b 1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth; Before determining the etching probability at each measurement location using a two-dimensional simulation etching model for each etching duration, the method further includes: The implicit fitting incremental iterative model is determined based on the initial probabilistic convolution model, the size of the lithographic design pattern, and the etching deviation size, and the etching probabilistic convolution model is formed based on the implicit fitting incremental iterative model. For each etching duration, the size of the lithographic design pattern and the etching deviation size are substituted into the etching probability convolution model to determine the values ​​of each simulation parameter in the simulation parameter group of the two-dimensional simulation etching model. The initial probabilistic convolution model is constructed based on a single-kernel or multi-kernel composite Gaussian kernel function; The initial probabilistic 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 two-dimensional coordinates of the associated simulation position, where the associated simulation position is any simulation position other than the target simulation position during convolution, M( ) 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) = 1; ) = 0; exp represents an exponential function with the natural constant e as its base; Used to represent the composite Gaussian kernel function. The equivalent characteristic distance of each Gaussian kernel, n h These are the normalized weighting coefficients for each Gaussian kernel; t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

2. The method for constructing a three-dimensional simulation etching model according to claim 1, characterized in that, Based on the etching duration and the etching probability at each measurement location, the etching depth is fitted, and the fitting function is determined by: For each etching duration, interpolation is used to determine the etching probability and etching depth of multiple preset target simulation locations to obtain multiple interpolation data sets. Each interpolation data set includes etching duration, interpolation etching depth, and interpolation etching probability. Using the etching duration and the etching probability as elements, the various fitting parameters of the binary fitting function for the etching depth are determined using the interpolation data set.

3. The method for constructing a three-dimensional simulation etching model according to claim 2, characterized in that, The method of determining the etching probability and etching depth of multiple preset target simulation locations using interpolation includes: For each etching duration, the etching depth at at least a portion of the measurement locations is interpolated to determine the interpolated etching depth at each preset target simulation location; Interpolation processing is performed on the etching probabilities of at least a portion of the measurement locations to determine the interpolated etching probabilities of each preset target simulation location; The interpolated etching depth and interpolated etching probability with the same target simulation position are correlated to obtain the interpolated data set.

4. The method for constructing a three-dimensional simulation etching model according to claim 2, characterized in that, The following bivariate fitting polynomial formula is used, with the etching duration and the etching probability as variables, and the interpolation data set is used to determine the various fitting parameters of the bivariate fitting function for the etching depth: ， in, A binary fitting function used to represent the etching depth. Used to indicate the etching duration Lower target simulation position The etching probability, where c is a positive integer. a 1 to a c , b 1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth; The number of interpolated data sets is greater than or equal to the number of fitting parameters.

5. The method for constructing a three-dimensional simulation etching model according to claim 1, characterized in that, Also includes: The etching probability of the coordinates to be simulated is determined by using the etching duration to be simulated and the two-dimensional simulation etching model. The etching probability and the etching duration to be simulated for one or more of the simulation coordinates are substituted into the three-dimensional simulation etching model to obtain the simulation value of the etching depth for each simulation coordinate.

6. The method for constructing a three-dimensional simulation etching model according to claim 5, characterized in that, Substituting the etching probability and the etching duration to be simulated for one or more of the simulation coordinates into the three-dimensional simulation etching model, the simulated values ​​of the etching depth for each simulation coordinate are obtained, including: ， in, A binary fitting function used to represent the etching depth. Used to indicate the duration of the simulated etching. The coordinates to be simulated The etching probability, c It is a positive integer. a 1 to a c , b 1 to b c For each fitting parameter, z0 is used to represent the preset initial value of the etching depth.

7. The method for constructing a three-dimensional simulation etching model according to claim 1, characterized in that, The step of determining the implicit fitting incremental iterative model based on the initial probability convolution model, the size of the lithographic design pattern, and the etching deviation size includes: Based on the size of the lithographic design pattern and the etching deviation size, a set of analytical equations corresponding to each lithographic design pattern is determined, wherein the set of analytical equations includes an etching probability threshold. Based on the initial probabilistic convolution model and the analytical equation set, incremental iteration processing is performed to obtain the simulation parameter values ​​of the simulation parameter set of the implicit fitting incremental iteration model. The simulation parameter set of the implicit fitting incremental iterative model includes the equivalent feature distance, the normalized weight coefficient, and the etching probability threshold.

8. The method for constructing a three-dimensional simulation etching model according to claim 7, characterized in that, The system of analytical equations corresponding to the i-th lithographic design pattern is: ， in, These are the normalized weighting coefficients corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function. The equivalent feature distance corresponding to the h-th Gaussian kernel of the composite Gaussian kernel function is erf, which represents the error function, and D0 is the etching probability threshold. and Design the length and width of the i-th lithographic pattern. and The length and width of the etching profile obtained for the i-th lithographic design pattern under the current etching parameter values; It corresponds to the length deviation of the i-th group. The calculated length deviation, where, ; It corresponds to the width deviation of the i-th group. The calculated width deviation, where, ; t is the number of kernels in the composite Gaussian kernel function, h and t are positive integers, and 1≤h≤t.

9. The method for constructing a three-dimensional simulation etching model according to claim 8, characterized in that, Based on the initial probabilistic convolution model and the analytical equation set, incremental iteration is performed to obtain the simulation parameter values ​​of the implicitly fitted incremental iteration model, including: Among the etching probability threshold, the normalized weight coefficient of each Gaussian kernel, and the equivalent feature distance of each Gaussian kernel, one of them is designated as a specified parameter with a preset fixed value, and the parameters other than the specified parameter are grouped into parameter group {P}. Based on the specified parameters, an implicit fitting process is performed on the analytical equation system to obtain the following implicit fitting incremental iterative model: in, and The parameter groups are respectively { Any parameter in} , , and The incremental iteration process is respectively the first... l The parameters corresponding to the next incremental iteration are processed. ,parameter Calculate the length deviation and calculate width deviation , For the incremental iterative process, the first... l The parameter corresponding to -1. j, k, l All are positive integers, 1≤j≤2t, v is the number of the analytical equation system, and v≥2t, i is used to represent the i-th analytical equation, 1≤i≤v; During the first incremental iteration process l =1, parameter ~ The value is a preset value, which is substituted into the analytical equation system to obtain the calculated length deviation. ~ The value, and the calculated width deviation ~ The value is then substituted into the implicitly fitted incremental iterative model to obtain the corresponding increment. ~ The value and parameters ~ The value; 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 system of analytical equations are used to obtain the calculated length deviation. ~ The value, and the calculated width deviation ~ The value when l When =1, the parameter ~ The value is the preset value; The calculated length deviation ~ 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 by the Mth incremental iteration ~ The incremental iteration process terminates when all values ​​are within a preset percentage, where M is a positive integer and M ≥ 0. l Furthermore, the parameters obtained from the Mth incremental iteration process... ~ The value is taken as: the value of the parameter other than the specified parameter among the etching probability threshold D0, the normalized weight coefficient of t Gaussian kernels, and the equivalent feature distance of t Gaussian kernels.

10. The method for constructing a three-dimensional simulation etching model according to claim 9, characterized in that, The preset fixed value of the specified parameter is 1.

11. The method for constructing a three-dimensional simulation etching model according to claim 9, characterized in that, The preset percentage is selected from 0.5% to 2%.

12. The method for constructing a three-dimensional simulation etching model according to claim 9, characterized in that, The etching probability convolution model formed based on the implicit fitting incremental iterative model is as follows: in, The coordinates are two-dimensional coordinates of the associated simulation position, which is any simulation position other than the target simulation position during convolution. Normalized weighting coefficients The value, Equivalent feature distance The value of .

13. The method for constructing a three-dimensional simulation etching model according to claim 1, characterized in that, At least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and are arranged along the dimensional direction of the width Wy; And / or, At least a portion of the plurality of photolithographic design patterns have the same length Wx and different widths Wy, and have the same spacing in the dimensional direction of the width Wy.

14. The method for constructing a three-dimensional simulation etching model according to claim 1, characterized in that, For multiple lithographic design patterns, multiple preset etching durations are used to etch the samples to obtain the corresponding etching contours, including: A photoresist layer is formed on the surface of the sample; Based on the photolithography design pattern, the photoresist layer is patterned to form a mask layer on the sample surface that exposes a portion of the sample surface; Using the mask layer as a mask, an etched sample is formed, and corresponding etched grooves are formed within the sample. The boundary line of the etched groove on the sample surface serves as the etched profile.

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