Mask critical dimension compensation method based on piecewise polynomial nonlinear fitting

Abstract

The invention relates to mask manufacturing, in particular to a mask critical dimension compensation method based on piecewise polynomial nonlinear fitting, which comprises the following steps: designing hole layers with different hole diameters, performing photoetching to form hole layers of a whole plate, and calculating a CD deviation value corresponding to the hole layer with each hole diameter; presetting demarcation points, and dividing the different apertures into a plurality of intervals; dynamically adjusting the demarcation point by adopting a dynamic demarcation algorithm based on error gradient, and determining a plurality of final intervals; in each interval, determining an optimal order of a fitting polynomial corresponding to the interval by adopting an AIC criterion to obtain the fitting polynomial; determining an overlapping band between adjacent intervals, and performing linear weighting compensation on the overlapping band according to a fitting polynomial of the adjacent intervals to ensure smooth transition of a compensation value between the adjacent intervals; according to the technical scheme provided by the invention, the defect that the sizes of the pore layers with different pore sizes are difficult to adaptively compensate in the prior art can be effectively overcome.

Description

Technical Field

[0001] This invention relates to photomask manufacturing, and more specifically to a photomask critical dimension compensation method based on piecewise polynomial nonlinear fitting. Background Technology

[0002] The critical dimensional accuracy of the patterns in photomasks used in panel displays, especially the dimensional accuracy of different apertures, is crucial for the product precision of downstream panel customers. Due to the size differences between different aperture layers after photolithography, uneven wetting of the chemical solution during wet processing can lead to variations in the dimensional accuracy of the aperture layers. Summary of the Invention

[0003] (a) Technical problems to be solved

[0004] In view of the above-mentioned shortcomings of the prior art, the present invention provides a mask key size compensation method based on piecewise polynomial nonlinear fitting, which can effectively overcome the defect of the prior art that it is difficult to adaptively compensate for the size of the hole layer with different aperture sizes.

[0005] (II) Technical Solution

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A mask critical dimension compensation method based on piecewise polynomial nonlinear fitting includes the following steps:

[0008] S1. Design hole layers with different aperture sizes, and perform photolithography to form a complete plate of hole layers. Calculate the CD deviation value corresponding to each aperture size hole layer.

[0009] S2. Preset boundary points to divide different apertures into multiple intervals;

[0010] S3. A dynamic boundary algorithm based on error gradient is used to dynamically adjust the boundary points and determine the final multiple intervals.

[0011] S4. Within each interval, the AIC criterion is used to determine the optimal order of the corresponding fitting polynomial, thus obtaining the fitting polynomial.

[0012] S5. Determine the overlapping zone between adjacent intervals, and perform linear weighted compensation on the overlapping zone based on the fitting polynomial of the adjacent intervals to ensure that the compensation value transitions smoothly between adjacent intervals.

[0013] S6. For the target aperture, calculate the corresponding compensation value and compensate it into the GDS design file to form the compensated customer file.

[0014] Preferably, in S1, hole layers with different aperture sizes are designed, and photolithography is performed to form a complete plate of hole layers. The CD deviation value corresponding to each aperture layer is calculated, including:

[0015] S11. Design a layer of holes with different aperture sizes on the photomask;

[0016] S12. On a photolithography machine, a mass-production exposure dose is used to perform photolithography on a mask with mass-production resist type and resist thickness, and a mass-production wet process is used to form the hole layer of the entire mask.

[0017] S13. Under mass production testing conditions, use a dedicated CD measuring machine to measure the hole layers of each aperture size on the mask, and calculate the actual average CD value corresponding to each aperture size.

[0018] S14. Calculate the CD deviation value CD corresponding to the pore layer for each pore size. 偏差 :

[0019]

[0020] Among them, CD 设计 The CD design value is the pore size corresponding to a pore layer of a certain aperture.

[0021] Preferably, in S11, designing a layer of holes with different aperture sizes on the photomask includes:

[0022] A layer of pores with different aperture sizes was designed on the photomask, namely 0.75μm, 0.85μm, 0.95μm, ..., 5.75μm, 5.85μm, and 5.95μm, for a total of 53 sizes. Ten pores were designed for each aperture size, for a total of 530 pores.

[0023] Preferably, in S2, a preset dividing point is used to divide different apertures into multiple intervals, including:

[0024] Based on daily production experience, three dividing points are set: c1 = 1.5μm, c2 = 2.5μm, and c3 = 3.5μm, which divides the pore size into four intervals: 0.75μm to 1.5μm, 1.5μm to 2.5μm, 2.5μm to 3.5μm, and 3.5μm to 5.95μm.

[0025] Preferably, in S3, a dynamic boundary algorithm based on error gradient is used to dynamically adjust the boundary points and determine the final multiple intervals, including:

[0026] S31. Set the adjustment window size δ for dynamically adjusting the boundary point to ensure a smooth transition between adjacent interval models at the boundary point and avoid abrupt changes in the CD value after compensation.

[0027] S32, For the j-th boundary point c jj = 1, 2, ..., N, where N is the number of boundary points, in its neighborhood [c j -δ,c j Within +δ], the Savitzky-Golay filter is used to fit the polynomial of the CD deviation value with respect to the CD design value, and the second derivative is calculated;

[0028] S33, If the dividing point c j If the second derivative at point c is greater than a preset threshold, then for the boundary point c j Make fine adjustments to achieve the adjusted boundary point c. j If the second derivative at point ' is less than a preset threshold, otherwise the original boundary point c is maintained. j ;

[0029] S34. Repeat S32 to S33 until the second derivative at all boundary points is no greater than the preset threshold, and determine the final multiple intervals.

[0030] Preferably, in S4, within each interval, the optimal order of the fitting polynomial corresponding to the interval is determined using the AIC criterion to obtain the fitting polynomial, including:

[0031] S41. Based on the differences in the wetting and reaction degree of the developing and etching solutions on pores of different sizes, set the order m = 1, 2, ..., k, where k is the maximum order;

[0032] S42, for the l-th interval I l Let l = 1, 2, ..., M, M = N+1 be the interval quantity, and solve for the coefficient vector a = (a1, a2, ..., a k ) T To minimize the sum of squared residuals:

[0033]

[0034] Where, Δy i Let x be the i-th CD deviation value within the interval. i Let a be the i-th CD design value within the interval, i = 1, 2, ..., n, where n is the number of CD deviation values / CD design values ​​within the interval. m The coefficients are for order m;

[0035] S43. Calculate the squared residual σ 2 :

[0036]

[0037] in, Let be the i-th CD deviation value predicted by the model within the interval, and n be the number of CD deviation values ​​within the interval. The number of CD deviation values, CD design values, and CD deviation values ​​are equal.

[0038] S44. Calculate the AIC value for each order m. m :

[0039] AIC m =2(m+1)+nln(2πσ) 2 );

[0040] S45, Select the smallest AIC m The corresponding order m is used as the optimal order of the fitting polynomial for the interval, thus obtaining the fitting polynomial.

[0041] S46. Repeat S42 to S45 until the fitting polynomials for all intervals are obtained.

[0042] Preferably, in S5, the overlapping zone between adjacent intervals is determined, and linear weighted compensation is applied to the overlapping zone based on the fitted polynomial of the adjacent intervals to ensure a smooth transition of the compensation value between adjacent intervals, including:

[0043] S51. Based on the pore layers with different pore sizes, set the overlap band width w and determine the overlap band between adjacent intervals;

[0044] S52, for the j-th boundary point c j In its overlapping zone [c j -w,c j Within +w], calculate the weighting coefficients ω1 and ω2:

[0045]

[0046] Where x is the overlap band [c j -w,c j Any CD design value within +w];

[0047] S53, based on the j-th boundary point c j The fitting polynomial of adjacent intervals, for the overlapping band [c j -w,c j +w] performs linear weighted compensation to ensure a smooth transition of compensation values ​​between adjacent intervals:

[0048]

[0049] in, c is the j-th dividing point j The fitting polynomial for adjacent intervals, c is the j-th dividing point j The fitting polynomial of the overlapping zone;

[0050] S54. Repeat S52 to S53 until the fitting polynomials of the overlapping zones where all boundary points are located are obtained.

[0051] Preferably, in step S6, for the target aperture, the corresponding compensation value is calculated and compensated into the GDS design file to form a compensated customer file, including:

[0052] S61. For the target aperture, determine the fitting polynomial based on its interval and whether it is located within the overlapping zone of the interval, and use the fitting polynomial to calculate the corresponding compensation value.

[0053] S62. The calculated compensation value is applied to the GDS design file to form the compensated customer file, and then converted into a file that the lithography machine can recognize for mass production lithography.

[0054] (III) Beneficial Effects

[0055] Compared with existing technologies, the mask critical dimension compensation method based on piecewise polynomial nonlinear fitting provided by this invention has the following beneficial effects:

[0056] 1) By using segmented nonlinear compensation, the limitations of single compensation are avoided, and the size compensation accuracy for pore layers with different aperture sizes is effectively improved.

[0057] 2) A dynamic boundary algorithm based on error gradient is used to dynamically adjust the boundary point, which improves the sudden change in CD value after compensation caused by a fixed boundary point.

[0058] 3) Compared with the traditional fixed polynomial order selection, this invention uses the AIC criterion to determine the optimal order of the fitting polynomial for each interval, which can autonomously optimize the model complexity according to the data characteristics of each interval and avoid underfitting and overfitting.

[0059] 4) Linear weighted compensation is applied to the overlapping zone based on the fitting polynomial of adjacent intervals to effectively eliminate step jumps in the compensation amount;

[0060] 5) The technical solution of this invention can be effectively applied to photolithography of photomasks for high-specification AMOLED and LTPS. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0062] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0064] A mask critical dimension compensation method based on piecewise polynomial nonlinear fitting, such as Figure 1 As shown, S1, design aperture layers with different aperture sizes, and perform photolithography to form the aperture layers on the entire plate. Calculate the CD deviation value corresponding to each aperture layer size, specifically including:

[0065] S11. Design a layer of holes with different aperture sizes on the photomask;

[0066] S12. On a photolithography machine, a photolithography is performed on a mask with a mass production photoresist type and thickness using a mass production exposure dose, and a mass production wet process is used to form the hole layer of the entire mask.

[0067] S13. Under mass production testing conditions, use a dedicated CD measuring machine to measure the hole layers of each aperture size on the mask, and calculate the actual average CD value corresponding to each aperture size.

[0068] S14. Calculate the CD deviation value CD corresponding to the pore layer for each pore size. 偏差 :

[0069]

[0070] Among them, CD 设计 The CD design value is the pore size corresponding to a certain pore size.

[0071] Specifically, in the technical solution of this application, as a design scheme, S11 involves designing a layer of holes with different aperture sizes on the mask, including:

[0072] A layer of pores with different aperture sizes was designed on the photomask, namely 0.75μm, 0.85μm, 0.95μm, ..., 5.75μm, 5.85μm, and 5.95μm, for a total of 53 sizes. Ten pores were designed for each aperture size, for a total of 530 pores.

[0073] S2. Preset dividing points to divide different apertures into multiple intervals.

[0074] In this application's technical solution, as a design scheme, three dividing points c1 = 1.5μm, c2 = 2.5μm, and c3 = 3.5μm can be set based on daily production experience, that is, the pore size can be divided into four intervals: 0.75μm~1.5μm, 1.5μm~2.5μm, 2.5μm~3.5μm, and 3.5μm~5.95μm.

[0075] S3. A dynamic boundary algorithm based on error gradient is used to dynamically adjust the boundary points and determine the final multiple intervals, specifically including:

[0076] S31. Set the adjustment window size δ (δ = 0.3 μm) for dynamically adjusting the boundary point to ensure a smooth transition between adjacent interval models at the boundary point and avoid abrupt changes in the CD value after compensation.

[0077] S32, For the j-th boundary point c j j = 1, 2, ..., N, where N is the number of boundary points, in its neighborhood [c j -δ,c j Within +δ], the Savitzky-Golay filter is used to fit the polynomial of the CD deviation value with respect to the CD design value, and the second derivative is calculated;

[0078] S33, If the dividing point c j If the second derivative at point c is greater than a preset threshold, then for the boundary point c j Make fine adjustments to achieve the adjusted boundary point c. j If the second derivative at point ' is less than a preset threshold, otherwise the original boundary point c is maintained. j ;

[0079] S34. Repeat S32 to S33 until the second derivative at all boundary points is no greater than the preset threshold, and determine the final multiple intervals.

[0080] S4. Within each interval, the optimal order of the fitting polynomial is determined using the AIC criterion, resulting in the fitting polynomial, specifically including:

[0081] S41. Based on the differences in the wetting and reaction degree of the developing and etching solutions on pores of different sizes, set the order m = 1, 2, ..., k, where k is the maximum order;

[0082] S42, for the l-th interval I l Let l = 1, 2, ..., M, M = N+1 be the interval quantity, and solve for the coefficient vector a = (a1, a2, ..., a k ) T To minimize the sum of squared residuals:

[0083]

[0084] Where, Δy i Let x be the i-th CD deviation value within the interval. i Let a be the i-th CD design value within the interval, i = 1, 2, ..., n, where n is the number of CD deviation values / CD design values ​​within the interval. m The coefficients are for order m;

[0085] S43. Calculate the squared residual σ 2 :

[0086]

[0087] in, Let be the i-th CD deviation value predicted by the model within the interval, and n be the number of CD deviation values ​​within the interval. The number of CD deviation values, CD design values, and CD deviation values ​​are equal.

[0088] S44. Calculate the AIC value for each order m. m :

[0089] AIC m =2(m+1)+nln(2πσ) 2 );

[0090] S45, Select the smallest AIC m The corresponding order m is used as the optimal order of the fitting polynomial for the interval, thus obtaining the fitting polynomial.

[0091] S46. Repeat S42 to S45 until the fitting polynomials for all intervals are obtained.

[0092] S5. Determine the overlapping zone between adjacent intervals, and perform linear weighted compensation on the overlapping zone based on the fitted polynomial of the adjacent intervals to ensure a smooth transition of the compensation value between adjacent intervals. Specifically, this includes:

[0093] S51. Based on the pore layers with different pore sizes, set the overlap band width w (w = 0.2 μm) and determine the overlap band between adjacent intervals;

[0094] S52, for the j-th boundary point c j In its overlapping zone [c j -w,c j Within +w], calculate the weighting coefficients ω1 and ω2:

[0095]

[0096] Where x is the overlap band [c j -w,c j Any CD design value within +w];

[0097] S53, based on the j-th boundary point c j The fitting polynomial of adjacent intervals, for the overlapping band [c j -w,c j +w] performs linear weighted compensation to ensure a smooth transition of compensation values ​​between adjacent intervals:

[0098]

[0099] in, c is the j-th dividing point j The fitting polynomial for adjacent intervals, c is the j-th dividing point j The fitting polynomial of the overlapping zone;

[0100] S54. Repeat S52 to S53 until the fitting polynomials of the overlapping zones where all the boundary points are located are obtained.

[0101] S6. For the target aperture, calculate the corresponding compensation value and compensate it into the GDS design file to form the compensated customer file, which specifically includes:

[0102] S61. For the target aperture, determine the fitting polynomial based on its interval and whether it is located within the overlapping zone of the interval, and use the fitting polynomial to calculate the corresponding compensation value.

[0103] S62. The calculated compensation value is applied to the GDS design file to form the compensated customer file, and then converted into a file that the lithography machine can recognize for mass production lithography.

[0104] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for compensating critical dimensions of a mask based on piecewise polynomial nonlinear fitting, characterized in that: Includes the following steps: S1. Design hole layers with different aperture sizes, and perform photolithography to form a complete plate of hole layers. Calculate the CD deviation value corresponding to each aperture size hole layer. S2. Preset boundary points to divide different apertures into multiple intervals; S3. A dynamic boundary algorithm based on error gradient is used to dynamically adjust the boundary points and determine the final multiple intervals. S4. Within each interval, the AIC criterion is used to determine the optimal order of the corresponding fitting polynomial, thus obtaining the fitting polynomial. S5. Determine the overlapping zone between adjacent intervals, and perform linear weighted compensation on the overlapping zone based on the fitting polynomial of the adjacent intervals to ensure that the compensation value transitions smoothly between adjacent intervals. S6. For the target aperture, calculate the corresponding compensation value and compensate it into the GDS design file to form the compensated customer file.

2. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 1, characterized in that: In S1, aperture layers of different sizes are designed and photolithographically formed to create the entire plate of aperture layers. The CD deviation value corresponding to each aperture layer size is calculated, including: S11. Design a layer of holes with different aperture sizes on the photomask; S12. On a photolithography machine, a mass-production exposure dose is used to perform photolithography on a mask with mass-production resist type and resist thickness, and a mass-production wet process is used to form the hole layer of the entire mask. S13. Under mass production testing conditions, use a dedicated CD measuring machine to measure the hole layers of each aperture size on the mask, and calculate the actual average CD value corresponding to each aperture size. S14. Calculate the CD deviation value CD corresponding to the pore layer for each pore size. 偏差 : Among them, CD 设计 The CD design value is the pore size corresponding to a certain pore size.

3. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 2, characterized in that: In S11, different aperture layers with varying aperture sizes are designed on the photomask, including: A layer of pores with different aperture sizes was designed on the photomask, namely 0.75μm, 0.85μm, 0.95μm, ..., 5.75μm, 5.85μm, and 5.95μm, for a total of 53 sizes. Ten pores were designed for each aperture size, for a total of 530 pores.

4. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 3, characterized in that: S2 has preset dividing points that divide different apertures into multiple intervals, including: Based on daily production experience, three dividing points are set: c1 = 1.5μm, c2 = 2.5μm, and c3 = 3.5μm, which divides the pore size into four intervals: 0.75μm to 1.5μm, 1.5μm to 2.5μm, 2.5μm to 3.5μm, and 3.5μm to 5.95μm.

5. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 2, characterized in that: S3 employs a dynamic boundary algorithm based on error gradients to dynamically adjust the boundary points and determine multiple final intervals, including: S31. Set the adjustment window size δ for dynamically adjusting the boundary point to ensure a smooth transition between adjacent interval models at the boundary point and avoid abrupt changes in the CD value after compensation. S32, For the j-th boundary point c j j = 1, 2, ..., N, where N is the number of boundary points, in its neighborhood [c j -δ,c j Within +δ], the Savitzky-Golay filter is used to fit the polynomial of the CD deviation value with respect to the CD design value, and the second derivative is calculated; S33, If the dividing point c j If the second derivative at point c is greater than a preset threshold, then for the boundary point c j Make fine adjustments to achieve the adjusted boundary point c. j If the second derivative at point ' is less than a preset threshold, otherwise the original boundary point c is maintained. j ; S34. Repeat S32 to S33 until the second derivative at all boundary points is no greater than the preset threshold, and determine the final multiple intervals.

6. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 5, characterized in that: In S4, within each interval, the AIC criterion is used to determine the optimal order of the corresponding fitting polynomial, resulting in the fitting polynomial, including: S41. Based on the differences in the wetting and reaction degree of the developing and etching solutions on pores of different sizes, set the order m = 1, 2, ..., k, where k is the maximum order; S42, for the l-th interval I l Let l = 1, 2, ..., M, M = N+1 be the interval quantity, and solve for the coefficient vector a = (a1, a2, ..., a k ) T To minimize the sum of squared residuals: Where, Δy i Let x be the i-th CD deviation value within the interval. i Let a be the i-th CD design value within the interval, i = 1, 2, ..., n, where n is the number of CD deviation values / CD design values ​​within the interval. m The coefficients are for order m; S43. Calculate the squared residual σ 2 : in, Let be the i-th CD deviation value predicted by the model within the interval, and n be the number of CD deviation values ​​within the interval. The number of CD deviation values, CD design values, and CD deviation values ​​are equal. S44. Calculate the AIC value for each order m. m : AIC m =2(m+1)+nln(2πσ 2 ); S45, Select the smallest AIC m The corresponding order m is used as the optimal order of the fitting polynomial for the interval, thus obtaining the fitting polynomial; S46. Repeat S42 to S45 until the fitting polynomials for all intervals are obtained.

7. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 6, characterized in that: In S5, the overlapping zone between adjacent intervals is determined, and linear weighted compensation is applied to the overlapping zone based on the fitted polynomial of the adjacent intervals to ensure a smooth transition of the compensation value between adjacent intervals, including: S51. Based on the pore layers with different pore sizes, set the overlap band width w and determine the overlap band between adjacent intervals; S52, for the j-th boundary point c j In its overlapping zone [c j -w,c j Within +w], calculate the weighting coefficients ω1 and ω2: Where x is the overlap band [c j -w,c j Any CD design value within +w]; S53, based on the j-th boundary point c j The fitting polynomial of adjacent intervals, for the overlapping band [c j -w,c j +w] performs linear weighted compensation to ensure a smooth transition of compensation values ​​between adjacent intervals: in, c is the j-th dividing point j The fitting polynomial for adjacent intervals, c is the j-th dividing point j The fitting polynomial of the overlapping zone; S54. Repeat S52 to S53 until the fitting polynomials of the overlapping zones where all the boundary points are located are obtained.

8. The mask critical dimension compensation method based on piecewise polynomial nonlinear fitting according to claim 7, characterized in that: In S6, for the target aperture, the corresponding compensation value is calculated and compensated into the GDS design file, forming the compensated customer file, including: S61. For the target aperture, determine the fitting polynomial based on its interval and whether it is located within the overlapping zone of the interval, and use the fitting polynomial to calculate the corresponding compensation value. S62. The calculated compensation value is applied to the GDS design file to form the compensated customer file, and then converted into a file that the lithography machine can recognize for mass production lithography.

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