Method for determining illumination intensity distribution of light source and mask pattern of photo-etching process

A technology of light intensity and photolithography technology, which is applied in the field of integrated circuit manufacturing, can solve the problems of long calculation time and unsatisfactory effect, and achieve the effects of shortened calculation time, good effect and good optimization effect

Inactive Publication Date: 2011-08-31
TSINGHUA UNIV
2 Cites 19 Cited by

AI-Extracted Technical Summary

Problems solved by technology

Method (8), the calculation takes a l...
the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
View more

Abstract

The invention relates to a method for determining the illumination intensity distribution of a light source and a mask pattern of a photo-etching process and belongs to the technical field of manufacturing of an integrated circuit. The method comprises the following steps of: determining the initial shape and initial illumination intensity of the light source, and representing the initial shape and the initial illumination intensity by matrixes; determining an initial pattern of a mask, and representing the initial pattern of the mask by a pixel matrix; adding two compensation items and establishing a target function by using imaging accuracy and focal depth in photo-etching process as a basic optimization target; calculating and normalizing the illumination intensity distribution after the mask pattern is subjected to action of a photo-etching system; repeating the calculation step until a condition of convergence is met; obtaining a light source matrix and calculating an imaging nucleus of the photo-etching system and coefficients of the imaging nucleus; calculating an illumination intensity distribution matrix; calculating a pattern which is etched on a silicon wafer and representing the pattern by the matrix; calculating the gradient of the target function on the matrix; updating the matrix; and repeating the calculation step until the condition of convergence is met. The method for optimizing the light source and the mask of the photo-etching process has the advantages of short time and good optimization effect.

Application Domain

Technology Topic

Computational physicsMatrix representation +7

Image

  • Method for determining illumination intensity distribution of light source and mask pattern of photo-etching process
  • Method for determining illumination intensity distribution of light source and mask pattern of photo-etching process
  • Method for determining illumination intensity distribution of light source and mask pattern of photo-etching process

Examples

  • Experimental program(1)

Example Embodiment

[0046] The embodiments of the present invention will be described in detail below in conjunction with the drawings.
[0047] figure 1 It is a flow chart of the method for optimizing the light source of the photolithography process of the present invention. Such as figure 1 As shown, the method for determining the light intensity distribution of the light source in the lithography process of the present invention includes the following steps:
[0048] (1) Use the matrix Γ to represent the initial light intensity distribution of the determined light source;
[0049] According to the traditional light sources used in the lithography process in the current integrated circuit manufacturing, such as circular and annular light sources, determine the initial light intensity distribution of a light source, and use a matrix Γ to represent the light source. Each element in the matrix Γ is respectively Corresponding to a pixel at a corresponding position in the light source, the element value of the element in the matrix Γ corresponds to the light intensity of the pixel; in this embodiment, the element of the pixel in the matrix Γ that is lit in the light source (that is, the element in the light source Elements in the matrix Γ corresponding to pixels with a light intensity value greater than 0) are limited to a circle with the center of the matrix Γ as the center and a radius of σ, where σ is the partial coherence factor of the lithography system;
[0050] (2) Normalize the matrix Γ to obtain the matrix γ;
[0051] The method of normalizing the matrix Γ is to obtain the maximum light intensity value Γmax that the lithography system (mainly refers to the lens group) can bear, and divide each element value in the matrix Γ by Γmax to obtain a new matrix γ To represent the light source, that is, the range of the element values ​​of the elements of the matrix γ is limited to the closed interval [0, 1];
[0052] (3) Use formula (1) to transform the matrix γ into a matrix θ;
[0053] Since the matrix γ representing the light source obtained in the step (2) is bounded, it is difficult to perform optimization calculations; according to formula (1), the matrix γ is converted into an unbounded matrix θ to optimize The process went smoothly;
[0054] θ=arccos(2γ-1) (1)
[0055] (4) Use the pixel matrix m to represent the initial mask pattern;
[0056] The process of obtaining the initial mask pattern is: the customer who needs to tape out the layout to the chip foundry; then the foundry processes the layout into the mask pattern required by the lithography system, which can be obtained from the foundry The mask pattern is used as the initial mask pattern; according to the type of the mask, the mask pattern is represented by a pixel matrix m, and the elements of the matrix m correspond to those in the mask pattern Pixel, the element value of each element corresponds to the light transmission characteristic of the pixel; use M m And N m Respectively represent the number of rows and columns of matrix m; determine M m And N m , The scale of matrix m, first determine the size of a pixel (the pixel is a square, and the side length is generally 1/k of the minimum feature size of the mask pattern, and k can be an integer between 3-10), and then Divide the width of the mask graphic by the side length of the pixel to get M m , Divide the length of the mask graphic by the side length of the pixel to get N m The reticle can choose a binary mask, the light-transmitting points of the binary mask are represented by 1 in the matrix m, and the opaque points of the binary mask are represented by 0 in the matrix m; the mask can also be all The phase shift mask, the opaque point of the full phase shift mask is represented by 0 in the matrix m, and the transparent point without phase shift of the full phase shift mask is in the matrix m It is represented by 1, and the light transmission point of the full phase shift mask whose phase is shifted by 180° is represented by -1 in the matrix m.
[0057] (5) Using formula (2) to transform the matrix m into a matrix φ;
[0058] Since the matrix m representing the mask pattern obtained in the step (4) is bounded, it is difficult to perform optimization calculations; according to formula (2), the matrix γ is converted into an unbounded matrix φ, So that the optimization process can proceed smoothly;
[0059] φ=arccos(2m-1) (2)
[0060] (6) Determine the imaging accuracy and focal depth of the mask pattern in the photolithography process, and calculate the pixels of the pattern carved on the silicon wafer to be on the focal plane or deviate from the focal plane. The sum of squares of errors between points, the two sums of squares are respectively multiplied by the given weight coefficient α 1 , Α 2 After the addition, plus two compensation terms, it is used as the objective function. One of them is the light source shape complexity compensation item, and the other is the mask dispersion compensation item;
[0061] The weight coefficient α of the sum of the squares of the error between the pixel points of the pattern engraved on the silicon wafer and the pixel points of the ideal pattern when they are located on the focal plane and deviated from the focal plane 1 , Α 2 Generally taken in the open interval (0, 1), the values ​​of the two weighting coefficients can be weighed according to actual needs. If you want to improve the focal depth, the coefficient of the sum of squares obtained in the case of deviating from the focal plane should be greater than that of the focal plane. The coefficient of the sum of squares obtained in the case of a plane; if one wants to improve the imaging accuracy, the opposite approach is adopted. The method of calculating the pattern carved on the silicon wafer in this embodiment adopts the calculation process in steps (6) and (7).
[0062] The calculation method of the light source shape complexity compensation term is: move all elements of the matrix γ forward with zero padding and move one bit to form a matrix γ 1 、Move backward by zero to form a matrix γ 2 , Move one bit to the left to form a matrix γ 3 , Move one bit to the right with zero padding to form a matrix γ 4 , Move one bit forward with zero padding and then move one bit with zero padding to the left to form a matrix γ 5 , Move one bit forward with zero padding and then move one bit with zero padding to the right to form a matrix γ 6 、Move one bit backward to zero and then one bit to the left to form a matrix γ 7 、Move one bit backward to zero and then one bit to the right to form a matrix γ 8 , Calculate γ and γ separately 1 To | 8 The sum of the squares of the errors between the pixels, add these 8 sums of squares, and then multiply by the given weight coefficient β 1 It is the value of the light source shape complexity compensation term. The weight coefficient β 1 Take 0.001.
[0063] The calculation method of the mask discreteness compensation term is: multiply each element of matrix m by π, and then calculate its sine value to obtain a new matrix R, and add each element of matrix R to the sum , And then multiplied by the given weight coefficient β 2 It is the value of the compensation term of the mask dispersion. The weight coefficient β 2 Take 0.001.
[0064] (7) Calculate the light intensity distribution imaged by the mask pattern after the photolithography system acts, and the light intensity distribution is calculated by using the Abbe imaging model; use a matrix I whose scale is consistent with the matrix m for the light intensity distribution , And normalize the matrix I;
[0065] In this embodiment, the light intensity distribution of the mask pattern imaged in step (7) is calculated by the Abbe imaging model after the action of the photolithography system, and is represented by a matrix I with the same scale as m, and then the matrix I Perform normalization, and the normalized Abbe imaging model is given by formula (3):
[0066] I ( i , j ) = X a = 1 M S X b = 1 N S γ ( a , b ) | | ( k a , b ⊗ m ) ( i , j ) | | 2 X a = 1 M S X b = 1 N S γ ( a , b ) X x = 1 X 2 X y = 1 Y 2 | | k a , b ( x , y ) | | 2 - - - ( 3 )
[0067] Where (i, j) and (a, b) are the labels of the elements of the matrix I and the matrix γ, M s And N s Are the number of rows and columns of matrix γ, M s And N s Generally set equal, generally between 20-100, the larger the value, the finer the light source, k a, b Is the pupil function of the pixel corresponding to the element at (a, b) in the matrix γ, X 2 And Y 2 Is the pupil function k a, b The number of rows and columns (X 2 Can be taken as M m Half of Y 2 Can be taken as N m Half of ), (x, y) is the pupil function k a, b The label, symbol of the element Represents the convolution operation; in order to facilitate the calculation, formula (4) gives the matrix I operation form of formula (3) as follows:
[0068] I 1 D = Q γ 1 D S 1 D T γ 1 D - - - ( 4 )
[0069] Among them, the subscript 1D represents the column vector form, the superscript T represents the transpose; Q is a row number M m ×N m , The number of columns is M s ×N s The matrix of formula (3) is calculated as follows: calculate in order Put the obtained matrix into a column of the matrix Q in order; matrix S 1D Store each one in turn The number of elements is equal to the number of elements of the matrix γ; in the entire optimization process, Q and S 1D It only needs to be calculated once and can be reused in the future; for convenience, use V to represent S 1D T γ 1D The calculation result.
[0070] (8) Simulate the photoresist effect to calculate the pattern carved on the silicon wafer, and use the matrix z to represent the pattern carved on the silicon wafer;
[0071] This step needs to simulate the effect of photoresist. Generally, the effect of photoresist can be represented by a cutoff function, that is, a threshold is set. When the light intensity exceeds the threshold, it can be carved on the silicon wafer. When it is lower than the threshold , It cannot be engraved, but because the cutoff function is not continuous, it is not conducive to the optimization calculation. Therefore, this embodiment uses the sigmoid function to approximate the cutoff effect of the photoresist, that is, the process of obtaining the final engraved pattern from the light intensity Given by formula (5):
[0072] z ( i , j ) = 1 1 + e - a ( I ( i , j ) - t r ) - - - ( 5 )
[0073] In the formula: z is the matrix representing the figure carved out on the silicon wafer, i, j are any elements in the matrix z, a is a constant of the sigmoid function, generally taken between 50-200, t r Is the threshold value of the photoresist (you can find the photoresist data used), the elements of the matrix z correspond to the pixels in the carved pattern, and the element values ​​of the elements of the matrix z correspond to the corresponding pixel points Whether to expose (exposure is 1, non-exposure is 0).
[0074] (9) Calculate the gradient of the objective function to the matrix θ using the matrices z, I, m and θ F(θ);
[0075] Using formula (6), it is possible to directly calculate the sum of squared errors between the pixel points of the graphics carved on the silicon wafer and the pixels of the ideal graphics when they are located on the focal plane or deviated from the focal plane. Matrix θ gradient F 0 (θ);
[0076] ▿ F 0 ( θ ) = α nom ▿ R nom ( θ ) + α off ▿ R off ( θ ) - - - ( 6 )
[0077] Where the gradient F 0 (θ) is given in the form of a matrix (according to the general habit, bold characters represent vectors or matrices, and later this kind of symbolic representation is given in matrix form), R nom (θ) represents the gradient of the square of the error between the pixel points of the pattern engraved on the silicon wafer and the pixel points of the ideal pattern to the matrix θ when it is located on the focal plane, R off (θ) represents the gradient of the square of the error between the pixel points of the pattern engraved on the silicon wafer and the pixel points of the ideal pattern when deviating from the focal plane, α nom Is the weight coefficient in the case of the focal plane, α nom Is the weight coefficient in the case of deviating from the focal plane. The gradient R nom (θ) and R off (θ) can be calculated by formula (7):
[0078]
[0079]
[0080] In the formula, the symbol "ο" represents the multiplication of matrix or vector elements, and the subscript 1D→2D represents that the calculated column vector is arranged line by line and converted into a matrix in the order. Need to pay attention to R nom (θ), when formula (7) is used, the matrices z and I used are both calculated in the case of the focal plane; and for R off (θ), when formula (7) is used, the matrices z and I used are calculated when deviating from the focal plane.
[0081] The gradient of the light source complexity compensation term to the matrix θ R C (θ), can be calculated by formula (8):
[0082]
[0083]
[0084]
[0085]
[0086] Where, S ZF For zero padding shift operation function, function S ZF The first parameter indicates that the zero padding shift operation is required, and the second parameter indicates the direction vector of the movement, e x And e y Is the unit vector in the positive direction of x and y.
[0087] Calculate the above F 0 (θ) and R C (θ), the gradient of the objective function to the matrix θ F(θ) can be calculated by formula (9):
[0088] ▿ F ( θ ) = ▿ F 0 ( θ ) + β 1 ▿ R C ( θ ) - - - ( 9 )
[0089] Where: β 1 Is the coefficient of the light source complexity compensation term.
[0090] (10) Use formula Update the matrix θ, where s 1 Represents the step size, and its value can be 0.001, 0.01 or 0.1 to ensure that the optimization converges as soon as possible and avoid falling into local minima as the principle of selection, n represents the number of iterations;
[0091] (11) Repeat steps (7) to (10) until the first convergence condition is met, and the matrix γ is obtained; the conditions considered in the optimization process to have been converged can choose one of the following conditions:
[0092] (1) Reach the predetermined maximum number of iterations, and the range of the maximum number of iterations is 500-1000;
[0093] (2) The objective function is already smaller than a predetermined ideal value (usually between 0-10);
[0094] (3) Predetermine a step value X (usually between 10-20) and an acceptable minimum objective function decrement ε (generally less than or equal to 0.001), and the decrease of the objective function for consecutive X steps is less than ε situation.
[0095] (12) Using the matrix γ, the calculation of the lithography system is used to obtain the imaging core of the lithography system (see the description of step (13), and the mask matrix m is used for convolution in the SOCS model To calculate the light intensity distribution matrix) and its coefficients;
[0096] The method of calculating the imaging nucleus of the lithography system and its coefficients in the present invention can generally be calculated by the known open source software LAVA.
[0097] (13) Using the imaging core and coefficients of the lithography system, calculate the light intensity distribution imaged by the mask pattern after the photolithography system acts, and the light intensity distribution is calculated by using the SOCS imaging model; the light intensity The distribution is represented by a matrix I whose scale is consistent with the matrix m, and the matrix I is normalized;
[0098] In this embodiment, the light intensity distribution of the mask pattern imaged by the photolithography system in step (13) is calculated by using the SOCS imaging model and represented by a matrix I with the same scale as m, and then the matrix I Perform normalization, and the normalized SOCS imaging model is given by equation (10):
[0099] I ( i , j ) = X l = 1 P μ l | | ( H l ⊗ m ) ( i , j ) | | 2 X l = 1 P μ l X x = 1 X 1 X y = 1 Y 1 | | H l ( x , y ) | | 2 - - - ( 10 )
[0100] Where H 1 Is the imaging core of the lithography system described in step (12) and is in matrix form, μ 1 Is the coefficient of the imaging nuclei of the lithography system in the step (12), and P is the number of imaging nuclei of the lithography system. X 1 , Y 1 Is the imaging core matrix H of the lithography system 1 The number of rows and columns. Use U for It only needs to be calculated once for one iteration.
[0101] (14) In the same step (8), simulate the photoresist effect to calculate the pattern carved on the silicon wafer, and use the matrix z to represent the pattern carved on the silicon wafer;
[0102] (15) Calculate the gradient of the objective function to the matrix φ using the imaging core and coefficients of the lithography system and the matrices z, I, m, and φ F(φ);
[0103] Using formula (11), it is possible to directly calculate the sum of squares of errors between the pixel points of the graphics carved on the silicon wafer and the pixels of the ideal graphics when they are located on the focal plane or deviated from the focal plane. Matrix gradient F 0 (φ);
[0104] ▿ F 0 ( Φ ) = α nom ▿ R nom ( Φ ) + α off ▿ R off ( Φ ) - - - ( 11 )
[0105] among them, R nom (φ) represents the gradient of the square of the error between the pixel points of the pattern engraved on the silicon wafer and the pixel points of the ideal pattern to the matrix φ when it is located on the focal plane, R off (φ) represents the gradient of the square of the error between the pixel points of the pattern engraved on the silicon wafer and the pixel points of the ideal pattern when deviating from the focal plane, α nom Is the weight coefficient in the case of the focal plane, α nom Is the weight coefficient in the case of deviating from the focal plane. The gradient R nom (φ) and R off (φ) can be calculated by formula (12):
[0106]
[0107] Where z * Is the matrix form of the ideal mask pattern, Means H 1 Take the conjugate and rotate the matrix obtained by 180 degrees. Re represents a function that takes the real part in parentheses. for R nom (φ), when formula (12) is used, the matrices z and H used 1 Are calculated in the focal plane; and for R off (φ), when formula (12) is used, the matrices z and H used 1 They are all calculated when they deviate from the focal plane.
[0108] The gradient of the mask dispersion compensation term to the matrix φ R D (φ), can be calculated by formula (13):
[0109]
[0110] Calculate the above F 0 (φ) and R D (φ), the gradient of the objective function to the matrix φ F(φ) can be calculated by formula (14):
[0111] ▿ F ( Φ ) = ▿ F 0 ( Φ ) + β 2 ▿ R D ( Φ ) - - - ( 14 )
[0112] Where: β 2 Is the coefficient of the reticle dispersion compensation term.
[0113] (16) Use formula Update the matrix φ, where s 2 The representative step value can be selected as 0.005, 0.05 or 0.5 to ensure that the optimization converges as soon as possible and avoid falling into local minima as the principle of selection, k represents the number of iterations;
[0114] (17) Repeat steps (13) to (16) until the first convergence condition is met, and the matrix φ is obtained;
[0115] The optimization process is regarded as a condition that has converged, and one of the following conditions can be selected:
[0116] (1) Reach the predetermined maximum number of iterations, and the range of the maximum number of iterations is 500-1000;
[0117] (2) The objective function is smaller than a predetermined ideal value, and the ideal value ranges from 0-10;
[0118] (3) Predetermine a step value X (usually between 10-20) and an acceptable minimum objective function decrement ε (generally less than or equal to 0.001), and the decrease of the objective function for consecutive X steps is less than ε situation.
[0119] (18) Repeat steps (7) to (17) until the second convergence condition is met;
[0120] The optimization process is regarded as a condition that has converged, and one of the following conditions can be selected:
[0121] (1) The predetermined maximum number of repetitions is reached, and the value range of the maximum number of repetitions is 10-20;
[0122] (2) The objective function is less than a predetermined ideal value, and the ideal value ranges from 0-10;
[0123] (3) Repeating the steps (7) to (17) once, the reduction of the objective function brought about is less than 1% of the value of the objective function brought about by the previous repetition.
[0124] (19) According to the obtained matrices θ and φ, the matrix γ representing the light source and the matrix m representing the mask pattern are obtained, and the optimized light source and mask are made according to this result.
[0125] The above embodiments are only exemplary embodiments of the present invention and are not used to limit the present invention. The protection scope of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within the essence and protection scope of the present invention, and such modifications or equivalent substitutions should also be regarded as falling within the protection scope of the present invention.
the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

PUM

no PUM

Description & Claims & Application Information

We can also present the details of the Description, Claims and Application information to help users get a comprehensive understanding of the technical details of the patent, such as background art, summary of invention, brief description of drawings, description of embodiments, and other original content. On the other hand, users can also determine the specific scope of protection of the technology through the list of claims; as well as understand the changes in the life cycle of the technology with the presentation of the patent timeline. Login to view more.
the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

Similar technology patents

Methods for treating hcv

InactiveUS20130273005A1Good effect很少和不太严重的副作用BiocideDipeptide ingredientsHenipavirus InfectionsRegimen
Owner:GILEAD PHARMASSET LLC

Device and process for heating III-V wafers, and annealed III-V semiconductor single crystal wafer

ActiveUS20070012242A1Good effectHigh heat conductivityFrom gel stateFrom solid stateDislocationEngineering
Owner:FREIBERGER COMPOUND MATERIALS

Musculo-skeletal implant having a bioactive gradient

ActiveUS20060045903A1Good effectEnhances chemotactic propertyPharmaceutical delivery mechanismLigamentsActive agentMusculoskeletal implant
Owner:DEPUY SPINE INC (US)

Classification and recommendation of technical efficacy words

  • Reduce computing time
  • Good effect

Hyperlipemia therapeutic agent

ActiveUS20050187292A1Good effectBiocideMetabolism disorderEPA - Eicosapentaenoic acidHyperlipidemia
Owner:KOWA CO LTD +1
Who we serve
  • R&D Engineer
  • R&D Manager
  • IP Professional
Why Eureka
  • Industry Leading Data Capabilities
  • Powerful AI technology
  • Patent DNA Extraction
Social media
Try Eureka
PatSnap group products