CN112394615A - Extreme ultraviolet lithography light source mask optimization method - Google Patents
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- 238000000276 deep-ultraviolet lithography Methods 0.000 description 2
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Abstract
A mask optimization method for an extreme ultraviolet lithography light source adopts pixels to represent a light source and a mask pattern, calculates a photoresist image through a thick mask imaging model corrected by point pulses, takes a pattern error between the photoresist pattern and a target pattern as an evaluation function, and optimizes light source distribution and the mask pattern by adopting a particle swarm optimization (SLPSO) based on a social learning mechanism. The invention utilizes the extreme ultraviolet lithography thick mask imaging model to establish the evaluation function, and improves the accuracy of imaging calculation in the optimization process. In addition, the optimization efficiency and the optimization capability are effectively improved by utilizing the SLPSO algorithm, and the imaging quality is improved.
Description
Technical Field
The invention relates to the technical field of extreme ultraviolet lithography resolution enhancement, in particular to an extreme ultraviolet lithography light source mask optimization method.
Background
The extreme ultraviolet lithography (EUVL) technology is a lithography technology which is extremely important in the large-scale mass production manufacturing of chips with technology nodes of 7nm and below. Similar to deep ultraviolet lithography (DUVL), in extreme ultraviolet lithography, the diffraction effects of the mask cause a degradation in the quality of the lithographic image, and resolution enhancement techniques are therefore required. The light Source Mask Optimization (SMO) technique is an important resolution enhancement technique, and can improve the imaging quality and enlarge the process window by jointly optimizing the light source distribution and the mask pattern. The mask of several hundreds of nanometers makes EUV imaging calculation complicated, and furthermore, the reflective mask and optical system cause shadow effect and defocus effect peculiar to EUV lithography, which are problems to be considered when applying SMO technology to EUV.
Prior art 1 (see prior art 1, Ma X, Wang Z, Chen X, et al, gradient-Based Source Mask Optimization for Extreme Ultraviolet Lithography [ J ]. IEEE Transactions on Computational Imaging,2018,5(1):120-135.) proposes a gradient-Based Extreme Ultraviolet Lithography light Source Mask Optimization technique, which optimizes an objective function using a gradient descent method. However, in the technology, a kirchhoff thin mask model is still adopted in the process of deducing the analytical expression of the target function, and the EUV thick mask effect cannot be reflected. In addition, gradient-based SMO techniques are limited in their application as lithographic imaging models and photoresist models become increasingly complex and even impossible to interpret. Prior art 2 (see prior art 2, Lei Wang, Sikun Li, Xiangzhao Wang, Guanyong Yang, charging Yang, Pixed source optimization for optical lithography via partial simulation, J.Micro/Nanolith. MEMS MOEMS,2016,15(1),013506) and prior art 3 (see prior art 3, Lei Wang, Sikun Li, Xiangzhao Wang, charging Yang, Feng Tang, Pixel based mask optimization video partial simulation, Proc. SPIE 2016,9780:97801V) propose a Particle Swarm Optimization (PSO) based light source and mask optimization technique, which is different from the intelligent method, and is applicable to any prior lithography modeling, without the need for knowledge-based optimization of a prior art, and without the need for a priori knowledge of a lithographic objective model. The technology can be transferred and applied to EUV lithography easily, but when the sampling points of a light source and a mask are gradually increased, the optimization dimension is rapidly increased, and the optimization efficiency and the optimization capability of a PSO algorithm are greatly reduced. Furthermore, the EUV complex lithography imaging model also causes the optimization speed to be greatly reduced, so that an optimization algorithm with better performance needs to be adopted.
Disclosure of Invention
The invention aims to provide an extreme ultraviolet lithography light source mask optimization method, which is based on an EUV thick mask model and a vector imaging model, optimizes a light source and a mask pattern by utilizing an SLPSO algorithm and improves imaging quality.
The technical solution of the invention is as follows:
an extreme ultraviolet lithography light source mask optimization method mainly comprises the following steps:
the light source is characterized by a two-dimensional matrix S with the size of NS×NS，NSIs an odd number. Each element of the matrix represents a light source point, the value of the element is real number, the value of the element represents the intensity of the light source point, and the value range is [0,1 ]]. The position of the light source point in the matrix is denoted as S (m, n) and in frequency domain coordinates as S (f)s,gs) Wherein m is more than or equal to 1 and less than or equal to NS，1≤n≤NS， -1≤fs≤1，-1≤gsLess than or equal to 1. The incoherence and incoherence factors of the light source are expressed as sigmainAnd σoutIn order to ensure the symmetry of the light source, N which is the total number of the internal and external coherence factors in the first quadrant in the frequency domain coordinate system is selectedScThe individual light source points are coded and their intensity values are recorded as
The position in the matrix is recorded as
Mixing J and PSAs a code for the light source.
In the case of a lithographic imaging calculation,mixing J and PSDecoding into a complete light source matrix S: firstly resetting S to be a full 0 matrix, and then sequentially carrying out i is more than or equal to 1 and less than or equal to N on the ith light source point in the light source codeScFrom PSRead its position index (m)i,ni) Reading the intensity value J from JiSelecting the position S (m) in Si,ni)，S(NS+1-mi,ni)， S(mi,NS+1-ni)，S(NS+1-mi,NS+1-ni) Is set to have an element value of JiAnd finally obtaining the decoded complete light source matrix S.
The mask is characterized by a two-dimensional matrix M with the size of NM×NM，NMIs an odd number. Each element of the matrix represents a pixel of the mask pattern, the value of the element is 0 or 1, the element of 0 represents that the pixel is a background region, and the element of 1 represents that the pixel is a pattern region. The position of a mask pixel in the matrix is denoted M (p, q), where 1 ≦ p ≦ NM，1≤q≤NM. Will be the (N) th of the matrixM+1)/2 line and (N)MUsing +1)/2 columns as a reference, and selecting all matrix elements as pixels to be coded when the shape of the mask pattern is asymmetric; when the shape of the mask graph is symmetrical up and down, selecting elements of a first quadrant and a second quadrant as pixels to be coded; when the shape of the mask graph is symmetrical left and right, selecting elements of a first quadrant and a fourth quadrant as pixels to be coded; when the shape of the mask pattern is symmetrical up, down, left and right, the element of the first quadrant is selected as the pixel to be encoded. The number of pixels to be coded is recorded as NMcRecord their element values as
The position in the matrix is recorded as
Mixing T and PMAs the coding of the mask pattern.
When photoetching imaging calculation is carried out, T and P are addedMDecoding into a complete mask matrix M: first, M is reset to all 0Matrix, then sequentially for the jth pixel in the mask code, 1 ≦ j ≦ NMcFrom PMRead its position index (p)j,qj) Reading the intensity value T from TjSelecting M (p) as the position of M in accordance with the symmetry of the original mask patternj,qj) And its corresponding symmetric element, if TjGreater than a threshold value TmrIts element value is set to 1, otherwise its element value is set to 0, and finally the decoded complete mask matrix M is obtained.
initializing a light source matrix to S according to light source parametersinit(ii) a Initializing a mask matrix to M according to a mask patterninitWill MinitAs a matrix M of target patternstarget(ii) a Initializing a photoresist threshold trSensitivity of photoresist α, developing threshold t of photoresistrd. Initializing the normalized intensity I of the aerial imagenorm。
since the pattern on the silicon wafer is shifted due to the oblique incidence of the illumination light source on the mask in the extreme ultraviolet lithography, it is necessary to correct the shift of the pattern by setting the mask to be out of focus. Setting the mask defocusing amount as a parameter to be optimized, and taking the value as [ delta z [ ]min,Δzmax]Calculating photoresist images under different mask defocusing amounts by using a thick mask model and a vector imaging model according to real numbers in the range, taking Edge Placement Errors (EPE) of the photoresist images and a target image as evaluation functions, and optimizing by adopting a demarcation method to obtain the optimal mask defocusing amount delta zbestThe method comprises the following specific steps:
(1) initializing a maximum number of iterations NiterLower bound of variable zl＝ΔzminUpper bound of variable zr＝ΔzmaxIntermediate values z of the upper and lower bounds of the variablemid＝(zl+zr) /2, number of initialization iterations niter＝0。
(2) Will zl，zmidAnd zrInputting a thick mask model and vector imaging as mask defocus amounts, respectivelyThe model calculates the photoresist image and then calculates the corresponding evaluation function value fl，fmidAnd fr。
(3) Calculating a temporary variable ztemp＝(zl+zmid) And/2, inputting the mask defocus quantity into a thick mask model and a vector imaging model to calculate a photoresist image, and then calculating corresponding evaluation function values ftemp. If ftemp＞fmidLet zl＝ztempOn the contrary, z ismid＝ztemp。
(4) Calculating a temporary variable ztemp＝(zr+zmid) And/2, inputting the mask defocus quantity into a thick mask model and a vector imaging model to calculate a photoresist image, and then calculating corresponding evaluation function values ftemp. If ftemp＞fmidLet zr＝ztempOn the contrary, z ismid＝ztemp。
(5) Let n beiter＝niter+1, judgment of niter＝NiterWhether or not this is true. If not, the optimization is continued to (2). If yes, the procedure is terminated, and the optimal mask defocus amount Delta z is obtainedbest＝zmid。
calibration of absorber transmittance t for mask background region in thick mask model by rigorous electromagnetic field simulationaTransmittance t of absorption layer in pattern regionbAnd a dot pulse correction amount δ at the pattern boundary position, which are all complex numbers.
According to the incident angle theta of the central point of the illumination light sourceincAnd azimuth angle
Calculating the phase transmission factor phi of the incident light from the upper surface of the absorption layer to the middle position of the absorption layeraAnd a phase transmission factor phi of incident light from the middle position of the absorption layer to the lower surface of the absorption layerb。φaIs a complex number phibIs a complex matrix of size NO×NOIn which N isOFor diffraction orders of the mask in the x-directionOr the total number in the y-direction. Calculating the reflection matrix R of the multilayer film of the extreme ultraviolet lithography mask according to the equivalent film layer methodmlSize is NO×NO。
The optimal mask defocus amount Delta z obtained according to the step 3bestCalculating the mask defocus matrix phidSize is NO×NO。
(1) according to the initialized mask matrix MinitAn illumination cross-coefficient (ICC) matrix of the lithography imaging system is calculated from the thick mask model and the vector imaging model.
(2) And constructing an evaluation function for optimizing the light source. Calculating a normalized aerial image I according to the normalized intensity of the aerial image, the light source matrix and the ICC matrixAThen, calculating a photoresist image I through a Sigmoid photoresist modelR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
The photoresist pattern has a pass size of NM×NMThe binary matrix of 0 and 1 indicates that the element values have the same meaning as the element values of the mask matrix. The evaluation function FSO for light source optimization is expressed as
(3) Obtaining an initial light source code J according to the method in the step 1initThe method comprises the following steps of optimizing a light source through an SLPSO algorithm:
firstly, initializing the maximum iteration number NiterLet iteration number n iter0. Initializing particle swarm size MpopDetermining the particle dimension D according to the number of the coded light source pointspop＝NScSetting a social influence factor epsilon as kappa multiplied by Dpop/MpopWhere κ is a coefficient.
② setting the first particle position of the particle group as JinitThe positions of the rest particles are randomly generated. Particle position through a size and JinitThe same row vector characterization with dimension DpopAnd each dimension has a value of 0-1, and the random numbers are generated uniformly. The position of the ith particle is denoted as piAll particles having a position pass size of Mpop×DpopMatrix P ofpopAnd (4) showing. The velocity of each particle is characterized by a row vector of the same magnitude as the particle position, and the velocities of all particles are initialized to 0. The velocity of the ith particle is denoted viAll particles have a velocity passage size of Mpop×DpopMatrix V ofpopAnd (4) showing.
Calculating learning probability factor P for all particles in the particle swarmLThe learning probability factor of the ith particle can be expressed as
Fourthly, calculating the evaluation function value of all the particles in the particle group, wherein the evaluation function value of the ith particle is expressed as fi. Then, the evaluation function values are sorted in descending order, and the evaluation function values of all the particles are sorted into
And adjusting the speed of the particle swarm according to the corresponding sequence. The particle position at which the evaluation function value is minimum is defined as an optimum particle position pbest。
Calculating the average position of the particle swarm
M (M) after sortingpopThe particles are the optimal particles for the 1 st to M thpop-1 particle is updated in turn. For the ith particle (in this case 1 < i < M)pop-1) with a learning probability factor Pi L. Generating a random number p between 0 and 1rIf p isr＞Pi LIf the particle is not changed, the velocity and position of the particle are updated:
the j dimension v of the particle velocityi,jThe updating is as follows:
vi,j＝r1×vi,j+r2×(pk,j-pi,j)+r3×ε×(pmean,j-pi,j)，
wherein r is1，r2，r3Is a random real number between 0 and 1, and k is from i +1 to Mpop-1, random integer. p is a radical ofk,jDimension j, p, representing the position of the kth particlei,jDimension j, p, representing the position of the ith particlemean,jRepresents the j-th dimension of the mean position of the particle population.
The j dimension p of the particle positioni,jThe updating is as follows:
pi,j＝pi,j+vi,j。
sixthly, niter＝niter+1, judgment of niter＝NiterWhether or not this is true. If not, the optimization is continued to the fourth step. If yes, the procedure is terminated, and the optimal particle position p is outputbest。
To pbestDecoding according to the light source decoding method in the step 1 to obtain the optimal light source
(1) according to the optimized light source matrix
A cross-transmission coefficient (TCC) matrix of the lithography imaging system is calculated through a vector imaging model.
(2) An evaluation function for mask optimization is constructed. Calculating a mask diffraction spectrum matrix B with a size of N according to the mask matrix and the thick mask parametersO×NOThen combining the TCC matrix and the normalized intensity of the space image to calculate a normalized space image IAThen passing through a Sigmoid photoresist dieCalculating the photoresist image IR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
Evaluation function F for mask optimizationMOIs shown as
The specific process of calculating the mask diffraction spectrum matrix B in the process of constructing the evaluation function is as follows:
generating an absorption layer transmittance matrix:
initializing the absorption layer transmittance matrix TabsorberIs of size NM×NMLet the position of the pixel in the background area with 0 element in the mask matrix M be denoted as Pbg(P, q), the position of the pixel of the graphic region having the element 1 is denoted as Pft(P, q) the position of the boundary pixel of the pattern detected by the difference operator is expressed as Pedge(p, q). At TabsorberIn the matrix, the position is equal to PbgThe element value of (p, q) is set to taWill be equal to PftThe element value of (p, q) is set to tbWill be equal to PedgeThe element value of (p, q) is set to δ. Will TabsorberFourier transform is carried out, and N is selected by taking 0 level as a centerO×NORange as TabsorberFourier coefficient matrix B ofT。
Calculating a diffraction spectrum of the absorption layer after the first diffraction:
the diffraction spectrum of incident light propagating from the upper surface to the lower surface of the absorbing layer has a transit size NO×NOMatrix B ofabsorberExpressed, the calculation formula is:
Babsorber＝φa⊙BT⊙φb，
wherein |, indicates that the corresponding elements of the matrix are multiplied.
Calculating the diffraction spectrum after the reflection of the multilayer film:
light diffracted by the absorption layer passes through the multiple layersThe layer film is reflected, and the diffraction spectrum after reflection has a passing size of NO×NOMatrix B ofmlExpressed, the calculation formula is:
Bml＝Babsorber⊙Rml。
calculating the mask diffraction spectrum after the second diffraction of the absorption layer:
after the multilayer film is reflected, light in all directions is subjected to secondary diffraction through the absorption layer, and the light is mutually coherent and superposed to obtain a final mask diffraction spectrum B, wherein the calculation formula is as follows:
wherein
Representing a matrix convolution. Obtaining the optimal defocus amount Delta z of the mask according to optimizationbestAnd a mask defocus matrix phi obtained by pre-pressing calculation in advancedUpdating the mask diffraction spectrum:
B＝B⊙Φd。
(3) obtaining an initial mask code M according to the method in step 1initThe method comprises the following steps of optimizing a light source through an SLPSO algorithm: initializing a maximum number of iterations NiterLet iteration number n iter0. Initializing particle swarm size MpopDetermining the particle dimension D according to the number of the coded light source pointspop＝NMcSetting a social influence factor epsilon as kappa multiplied by Dpop/MpopWhere κ is a coefficient. Then, optimizing according to the methods from step (5) to step (3), in particular, setting the position of the first particle to be the initial mask code M when the position of the particle swarm is initializedinitOptimizing the output pbestDecoding according to the mask decoding method in the step 1 to obtain an optimal mask
Compared with the prior art, the invention has the following advantages:
1. the invention adopts the thick mask model and the vector imaging model to calculate the space image of the mask, has higher imaging simulation precision, can embody the thick mask effect, the shadow effect and the like inherently, and then improves the imaging quality through optimization without correcting the shadow effect of the optimized mask image.
2. The invention adopts the SLPSO algorithm as the optimization algorithm, and can effectively improve the optimization efficiency and the optimization capability by guiding the optimization direction by introducing a social learning mechanism.
Drawings
FIG. 1 is a schematic diagram showing the comparison of an initial light source, an initial mask, an optimized light source and an optimized mask adopted by the present invention.
FIG. 2 is a schematic diagram showing the comparison of the photoresist pattern in the initial state, the mask defocus state and the optimized state with the target pattern profile in the optimization process by using the method of the present invention.
FIG. 3 is a graph of the convergence of the merit function in the optimization process of the present invention.
Detailed Description
The present invention is further illustrated by the following examples, which should not be construed as limiting the scope of the invention.
The method comprises the following specific steps:
the light source is characterized by a two-dimensional matrix S with the size of NS×NS，NS51. Each element of the matrix represents a light source point, the value of the element is real number, the value of the element represents the intensity of the light source point, and the value range is [0,1 ]]. The position of the light source point in the matrix is denoted as S (m, n) and in frequency domain coordinates as S (f)s,gs) Wherein m is more than or equal to 1 and less than or equal to NS，1≤n≤NS， -1≤fs≤1，-1≤gsLess than or equal to 1. The incoherence and incoherence factors of the light source are expressed as sigmain0.4 and σout0.9, in order to ensure the symmetry of the light source, selecting the total N in the first quadrant and between the internal and external coherence factors in the frequency domain coordinate systemSc255 light source points are coded and their intensity values are recorded as
The position in the matrix is recorded as
Mixing J and PSAs a code for the light source.
When photoetching imaging calculation is carried out, J and P are calculatedSDecoding into a complete light source matrix S: firstly resetting S to be a full 0 matrix, and then sequentially carrying out i is more than or equal to 1 and less than or equal to N on the ith light source point in the light source codeScFrom PSRead its position index (m)i,ni) Reading the intensity value J from JiSelecting the position S (m) in Si,ni)，S(NS+1-mi,ni)， S(mi,NS+1-ni)，S(NS+1-mi,NS+1-ni) Is set to have an element value of JiAnd finally obtaining the decoded complete light source matrix S.
The mask pattern is shown in FIG. 2 with a periodicity of 130nm and a feature size CD of 18 nm. The mask is characterized by a two-dimensional matrix M with the size of NM×NM，NM65. Each element of the matrix represents a pixel of the mask pattern, the value of the element is 0 or 1, the element of 0 represents that the pixel is a background region, and the element of 1 represents that the pixel is a pattern region. The position of a mask pixel in the matrix is denoted M (p, q), where 1 ≦ p ≦ NM， 1≤q≤NM. Will be the (N) th of the matrixM+1)/2 line and (N)MUsing +1)/2 columns as a reference, and selecting all matrix elements as pixels to be coded when the shape of the mask pattern is asymmetric; when the shape of the mask graph is symmetrical up and down, selecting elements of a first quadrant and a second quadrant as pixels to be coded; when the shape of the mask graph is symmetrical left and right, selecting elements of a first quadrant and a fourth quadrant as pixels to be coded; when the shape of the mask pattern is symmetrical up, down, left and right, the element of the first quadrant is selected as the pixel to be encoded. Number of pixels to be encodedNumber is NMc，NMc1089, their element values are recorded as
The position in the matrix is recorded as
Mixing T and PMAs the coding of the mask pattern.
When photoetching imaging calculation is carried out, T and P are addedMDecoding into a complete mask matrix M: firstly, M is reset to be a full 0 matrix, and then j is more than or equal to 1 and less than or equal to N is sequentially carried out on the jth pixel in the mask codeMcFrom PMRead its position index (p)j,qj) Reading the intensity value T from TjSelecting M (p) as the position of M in accordance with the symmetry of the original mask patternj,qj) And its corresponding symmetric element, setting a threshold value Tmr0.5, if TjGreater than a threshold value TmrIts element value is set to 1, otherwise its element value is set to 0, and finally the decoded complete mask matrix M is obtained.
initializing a light source matrix to S according to light source parametersinit(ii) a Initializing a mask matrix to M according to a mask patterninitWill MinitAs a matrix M of target patternstarget(ii) a Initializing a photoresist threshold tr0.5, resist sensitivity α 200, resist development threshold trd. Initializing the normalized intensity I of the aerial imagenorm0.2541. The illumination wavelength of the lithography machine is λ 13.5nm, the light source polarization is y-direction polarization, the numerical aperture of the projection objective lens is NA 0.33, and the zoom magnification is Rreduction＝4。
since the pattern on the silicon wafer is shifted due to the oblique incidence of the illumination light source on the mask in the extreme ultraviolet lithography, it is necessary to correct the shift of the pattern by setting the mask to be out of focus. Setting mask defocus to be optimizedParameter, value of [ Delta z ]min,Δzmax]Real number in the range, Δ zmin＝0nm，Δz max200 nm. Calculating photoresist images under different mask defocusing amounts through a thick mask model and a vector imaging model, taking Edge Placement Errors (EPE) of a photoresist graph and a target graph as evaluation functions, and optimizing by adopting a demarcation method to obtain the optimal mask defocusing amount delta zbestThe method comprises the following specific steps:
(1) initializing a maximum number of iterations Niter20, lower bound of the variable zl＝ΔzminUpper bound of variable zr＝ΔzmaxIntermediate values z of the upper and lower bounds of the variablemid＝(zl+zr) /2, number of initialization iterations niter＝0。
(2) Will zl，zmidAnd zrRespectively inputting the mask defocusing amount into a thick mask model and a vector imaging model to calculate a photoresist image, and then calculating corresponding evaluation function values fl，fmidAnd fr。
(3) Calculating a temporary variable ztemp＝(zl+zmid) And/2, inputting the mask defocus quantity into a thick mask model and a vector imaging model to calculate a photoresist image, and then calculating corresponding evaluation function values ftemp. If ftemp＞fmidLet zl＝ztempOn the contrary, z ismid＝ztemp。
(4) Calculating a temporary variable ztemp＝(zr+zmid) And/2, inputting the mask defocus quantity into a thick mask model and a vector imaging model to calculate a photoresist image, and then calculating corresponding evaluation function values ftemp. If ftemp＞fmidLet zr＝ztempOn the contrary, z ismid＝ztemp。
(5) Let n beiter＝niter+1, judgment of niter＝NiterWhether or not this is true. If not, the optimization is continued to (2). If yes, the procedure is terminated, and the optimal mask defocus amount Delta z is obtainedbest＝zmid。
calibration of absorber transmittance t for mask background region in thick mask model by rigorous electromagnetic field simulationaTransmittance t of absorption layer in pattern regionbAnd a correction quantity delta of point pulse at the boundary position of the graph, which are respectively ta＝0.0762+0.2283j，tb＝0.397-0.918j，δ＝4.307+0.7426j。
Incident angle theta of central point of illumination light sourceincAt 6 deg. azimuth angle
Calculating the phase transmission factor phi of the incident light from the upper surface of the absorption layer to the middle position of the absorption layeraAnd a phase transmission factor phi of incident light from the middle position of the absorption layer to the lower surface of the absorption layerb。φaIs a complex number phibIs a complex matrix of size NO×NOIn which N isO31 is the total number of mask diffraction orders in either the x-direction or the y-direction. Calculating the reflection matrix R of the multilayer film of the extreme ultraviolet lithography mask according to the equivalent film layer methodmlSize is NO×NO。
The optimal mask defocus amount Delta z obtained according to the step 3bestCalculating the mask defocus matrix phidSize is NO×NO。
(1) according to the initialized mask matrix MinitAn illumination cross-coefficient (ICC) matrix of the lithography imaging system is calculated from the thick mask model and the vector imaging model.
(2) And constructing an evaluation function for optimizing the light source. Calculating a normalized aerial image I according to the normalized intensity of the aerial image, the light source matrix and the ICC matrixAThen, calculating a photoresist image I through a Sigmoid photoresist modelR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
Photoresist pattern passingSize NM×NMThe binary matrix of 0-1 indicates that the element values have the same meaning as the element values of the mask matrix. Evaluation function F for light source optimizationSOIs shown as
(3) Obtaining an initial light source code J according to the method in the step 1initThe method comprises the following steps of optimizing a light source through an SLPSO algorithm:
firstly, initializing the maximum iteration number NiterLet n be 200iter0. Initializing particle swarm size MpopDetermining the particle dimension D according to the number of the coded light source points (100)pop＝NSc255, setting a social influence factor epsilon as k x Dpop/MpopWherein κ ═ 0.01 is a coefficient.
② setting the first particle position of the particle group as JinitThe remaining particle positions are randomly generated. Particle position through a size and JinitThe same row vector characterization with dimension DpopAnd each dimension has a value of 0-1, and the random numbers are generated uniformly. The position of the ith particle is denoted as piAll particles having a position pass size of Mpop×DpopMatrix P ofpopAnd (4) showing. The velocity of each particle is characterized by a row vector of the same magnitude as the particle position, and the velocities of all particles are initialized to 0. The velocity of the ith particle is denoted viAll particles have a velocity passage size of Mpop×DpopMatrix V ofpopAnd (4) showing.
Calculating learning probability factor P for all particles in the particle swarmLThe learning probability factor of the ith particle can be expressed as
Fourthly, calculating the evaluation function value of all the particles in the particle group, wherein the evaluation function value of the ith particle is expressed as fi. However, the device is not suitable for use in a kitchenThen, the evaluation function values are sorted in descending order, and the evaluation function values of all the particles are sorted into
And adjusting the speed of the particle swarm according to the corresponding sequence. The particle position at which the evaluation function value is minimum is defined as an optimum particle position pbest。
Calculating the average position of the particle swarm
M (M) after sortingpopThe particles are the optimal particles for the 1 st to M thpop-1 particle is updated in turn. For the ith particle (in this case 1 < i < M)pop-1) with a learning probability factor Pi L. Generating a random number p between 0 and 1rIf p isr＞Pi LIf the particle is not changed, the velocity and position of the particle are updated:
the j dimension v of the particle velocityi,jThe updating is as follows:
vi,j＝r1×vi,j+r2×(pk,j-pi,j)+r3×ε×(pmean,j-pi,j)，
wherein r is1，r2，r3Is a random real number between 0 and 1, and k is from i +1 to Mpop-1, random integer. p is a radical ofk,jDimension j, p, representing the position of the kth particlei,jDimension j, p, representing the position of the ith particlemean,jRepresents the j-th dimension of the mean position of the particle population.
The j dimension p of the particle positioni,jThe updating is as follows:
pi,j＝pi,j+vi,j。
sixthly, niter＝niter+1, judgment of niter＝NiterWhether or not this is true. If not, the optimization is continued to the fourth step. If the above-mentioned conditions are met, the computer system can,terminating the procedure and outputting the optimal particle position pbest。
To pbestDecoding according to the light source decoding method in the step 1 to obtain the optimal light source
(1) according to the optimized light source matrix
A cross-transmission coefficient (TCC) matrix of the lithography imaging system is calculated through a vector imaging model.
(2) An evaluation function for mask optimization is constructed. Calculating a mask diffraction spectrum matrix B with a size of N according to the mask matrix and the thick mask parametersO×NOThen combining TCC matrix and the normalized intensity of the space image to calculate a normalized space image IAThen, calculating a photoresist image I through a Sigmoid photoresist modelR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
Evaluation function F for mask optimizationMOIs shown as
The specific process of calculating the mask diffraction spectrum matrix B in the process of constructing the evaluation function is as follows:
generating an absorption layer transmittance matrix:
initializing the absorption layer transmittance matrix TabsorberIs of size NM×NMLet the position of the pixel in the background area with 0 element in the mask matrix M be denoted as Pbg(P, q), the position of the pixel of the graphic region having the element 1 is denoted as Pft(P, q) the position of the boundary pixel of the pattern detected by the difference operator is expressed as Pedge(p, q). At TabsorberIn the matrix, the position is equal to PbgThe element value of (p, q) is set to taWill be equal to PftThe element value of (p, q) is set to tbWill be equal to PedgeThe element value of (p, q) is set to δ. Will TabsorberFourier transform is carried out, and N is selected by taking 0 level as a centerO×NORange as TabsorberFourier coefficient matrix B ofT。
Calculating a diffraction spectrum of the absorption layer after the first diffraction:
the diffraction spectrum of incident light propagating from the upper surface to the lower surface of the absorbing layer has a transit size NO×NOMatrix B ofabsorberExpressed, the calculation formula is:
Babsorber＝φa⊙BT⊙φb，
wherein |, indicates that the corresponding elements of the matrix are multiplied.
Calculating the diffraction spectrum after the reflection of the multilayer film:
the light diffracted by the absorption layer is reflected by the multilayer film, and the passing size of the diffraction spectrum after reflection is NO×NOMatrix B ofmlExpressed, the calculation formula is:
Bml＝Babsorber⊙Rml。
calculating the mask diffraction spectrum after the second diffraction of the absorption layer:
after the multilayer film is reflected, light in all directions is subjected to secondary diffraction through the absorption layer, and the light is mutually coherent and superposed to obtain a final mask diffraction spectrum B, wherein the calculation formula is as follows:
wherein
Representing a matrix convolution. Obtaining the optimal defocus amount Delta z of the mask according to optimizationbestAnd a mask defocus matrix phi obtained by pre-pressing calculation in advancedUpdating the mask diffraction spectrum:
B＝B⊙Φd。
(3) obtaining an initial mask code M according to the method in step 1initThe method comprises the following steps of optimizing a light source through an SLPSO algorithm: initializing a maximum number of iterations Niter400, let iteration number n iter0. Initializing particle swarm size MpopDetermining the particle dimension D according to the number of the coded light source points (100)pop＝NMc1089, the social influence factor epsilon is set to κ × Dpop/MpopWherein κ ═ 0.01 is a coefficient. Then, optimizing according to the methods from step (5) to step (3), in particular, setting the position of the first particle to be the initial mask code M when the position of the particle swarm is initializedinitOptimizing the output pbestDecoding according to the mask decoding method in the step 1 to obtain an optimal mask
In this example, the Pattern Error (PE) between the photoresist pattern and the target pattern before optimization was 603, and the Edge Placement Error (EPE) was 2.142 nm. After the light source mask is optimized by the method, the Pattern Error (PE) of the photoresist pattern and the target pattern is 35 and is reduced by 94.2 percent, and the Edge Placement Error (EPE) is 0.2037nm and is reduced by 90.49 percent. The entire optimization process takes 303.8 s. The method has the advantages of high optimization efficiency and high optimization speed.
The above description is only one specific embodiment of the present invention, and the embodiment is only used to illustrate the technical solution of the present invention and not to limit the present invention. The technical solutions available to those skilled in the art through logical analysis, reasoning or limited experiments according to the concepts of the present invention are all within the scope of the present invention.
Claims (2)
1. An extreme ultraviolet lithography light source mask optimization method is characterized by comprising the following steps:
step 1, encoding and decoding of light source and mask patterns:
(1) encoding and decoding of light sources
The light source is characterized by a two-dimensional matrix S with the size of NS×NS，NSEach element of the matrix represents a light source point, the value of the element is real number and represents the intensity of the light source point, and the value range is [0,1 ]](ii) a The position of the light source point in the matrix is denoted as S (m, n) and in frequency domain coordinates as S (f)s,gs) Wherein m is more than or equal to 1 and less than or equal to NS，1≤n≤NS，-1≤fs≤1，-1≤gs≤1；
The incoherence and incoherence factors of the light source are expressed as sigmainAnd σoutSelecting N in the first quadrant of the frequency domain coordinate system and between the internal and external coherence factorsScThe light source points are coded, and the intensity value is recorded as
The position in the matrix is recorded as
Mixing J and PSA code as a light source;
when photoetching imaging calculation is carried out, J and P are calculatedSAnd (3) decoding: firstly resetting a light source matrix S to be a full 0 matrix, and then sequentially carrying out i is more than or equal to 1 and less than or equal to N for the ith light source point in the light source codeScFrom PSRead its position index (m)i,ni) Reading the intensity value J from JiSelecting the position S (m) in Si,ni)，S(NS+1-mi,ni)，S(mi,NS+1-ni)，S(NS+1-mi,NS+1-ni) Is set to have an element value of JiFinally, obtaining a decoded complete light source matrix S;
(2) encoding and decoding of masks
The mask is characterized by a two-dimensional matrix M with the size of NM×NM，NMIs odd, each element of the matrix represents a pixel of the mask pattern, the value of the element is 0 or 1, the element is 0 representing that the pixel is a background area, the element is a background areaA value of 1 indicates that the pixel is a pattern region, and the position of the mask pixel in the matrix is represented as M (p, q), where 1. ltoreq. p.ltoreq.NM，1≤q≤NM；
Will be the (N) th of the matrixM+1)/2 line and (N)MUsing +1)/2 columns as a reference, and selecting all matrix elements as pixels to be coded when the shape of the mask pattern is asymmetric; when the shape of the mask graph is symmetrical up, down, left and right, the element of the first quadrant is selected as the pixel to be coded; when the shape of the mask graph is symmetrical up and down, selecting elements of a first quadrant and a second quadrant as pixels to be coded; when the shape of the mask graph is symmetrical left and right, selecting elements of a first quadrant and a fourth quadrant as pixels to be coded;
the number of pixels to be coded is recorded as NMcThe element value is recorded as
The position in the matrix is recorded as
Mixing T and PMA code as a mask pattern;
when photoetching imaging calculation is carried out, T and P are addedMDecoding into a complete mask matrix M: firstly resetting a mask matrix M to be a full 0 matrix, and then sequentially carrying out j is more than or equal to 1 and less than or equal to N on the jth pixel in the mask codeMcFrom PMRead its position index (p)j,qj) Reading the intensity value T from TjSelecting M (p) as the position of M in accordance with the symmetry of the original mask patternj,qj) And its corresponding symmetric element, if TjGreater than a threshold value TmrSetting the element value to 1, otherwise, setting the element value to 0, and finally obtaining a decoded complete mask matrix M;
step 2, initializing a light source matrix, a mask matrix and photoresist parameters:
initializing a light source matrix J according to light source parametersinitMask pattern initialization mask matrix MinitWill MinitAs a matrix M of target patternstargetInitializing the photoresist threshold trSensitivity of photoresist α, developing threshold t of photoresistrdInitializing the normalized intensity I of the aerial imagenorm；
Step 3, mask defocus optimization:
setting the mask defocusing amount as a parameter to be optimized, and taking the value as [ delta z [ ]min,Δzmax]Calculating photoresist images under different mask defocusing amounts by using a thick mask model and a vector imaging model according to real numbers in the range, taking Edge Placement Errors (EPE) of the photoresist images and a target image as evaluation functions, and optimizing by adopting a binary search method to obtain the optimal mask defocusing amount delta zbest；
Step 4, calculating the thick mask parameters:
calibration of absorber transmittance t for mask background region in thick mask model by rigorous electromagnetic field simulationaTransmittance t of absorption layer in pattern regionbAnd a point pulse correction δ at the pattern boundary position, all of which are complex;
according to the incident angle theta of the central point of the illumination light sourceincAnd azimuth angle
Calculating the phase transmission factor phi of the incident light from the upper surface of the absorption layer to the middle position of the absorption layeraAnd a phase transmission factor phi of incident light from the middle position of the absorption layer to the lower surface of the absorption layerb，φaIs a complex number phibIs a complex matrix of size NO×NOIn which N isOIs the total number of mask diffraction orders in the x-direction or y-direction;
calculating the reflection matrix R of the multilayer film of the extreme ultraviolet lithography mask according to the equivalent film layer methodmlSize is NO×NOAccording to the optimal mask defocus amount Delta z obtained in step 3bestCalculating the mask defocus matrix phidSize is NO×NO；
Step 5, optimizing a light source:
(1) according to the initialized mask matrix MinitThrough a thick mask dieThe type and vector imaging models calculate an Illumination Cross Coefficient (ICC) matrix of the photoetching imaging system;
(2) constructing an evaluation function of light source optimization: calculating a normalized aerial image I according to the normalized intensity of the aerial image, the light source matrix and the ICC matrixAThen, calculating a photoresist image I through a Sigmoid photoresist modelR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
The photoresist pattern has a pass size of NM×NMIs represented by a binary matrix of 0,1, the element values having the same meaning as those of the mask matrix, and the evaluation function F for light source optimizationSOIs shown as
(3) Carrying out light source coding according to the method in the step 1, and obtaining an optimal light source matrix through optimization of an SLPSO algorithm
Step 6, mask optimization:
(1) according to the optimized light source matrix
Calculating a cross transmission coefficient (TCC) matrix of the photoetching imaging system through a vector imaging model;
(2) constructing an evaluation function of mask optimization: calculating a mask diffraction spectrum matrix B of size N from the mask matrix and the thick mask parametersO×NOThen combining the TCC matrix and the normalized intensity of the space image to calculate a normalized space image IAThen, calculating a photoresist image I through a Sigmoid photoresist modelR＝1/(1+exp(-α*(IA-tr) ) is used in the process) and finally according to the photoresist development threshold t)rdCalculating the photoresist pattern
Evaluation function F for mask optimizationMOIs shown as
(3) Carrying out mask coding according to the method in the step 1, and obtaining an optimal mask matrix through optimization of an SLPSO algorithm
2. The euv lithography light source mask optimization method according to claim 1, wherein in the mask optimization process, a mask diffraction spectrum matrix B is calculated according to the mask matrix M and the thick mask parameters, specifically comprising the steps of:
step 1, generating an absorption layer transmittance matrix:
initializing the absorption layer transmittance matrix TabsorberIs of size NM×NMLet the position of the pixel in the background area with 0 element in the mask matrix M be denoted as Pbg(P, q), the position of the pixel of the graphic region having the element 1 is denoted as Pft(P, q) the position of the boundary pixel of the pattern detected by the difference operator is expressed as Pedge(p, q); at TabsorberIn the matrix, the position is equal to PbgThe element value of (p, q) is set to taWill be equal to PftThe element value of (p, q) is set to tbWill be equal to PedgeSetting the element value of (p, q) to delta, and setting TabsorberFourier transform is carried out, and N is selected by taking 0 level as a centerO×NORange as TabsorberFourier coefficient matrix B ofT；
Step 2, calculating a diffraction spectrum of the absorption layer after the first diffraction:
the diffraction spectrum of incident light propagating from the upper surface to the lower surface of the absorbing layer has a transit size NO×NOMatrix B ofabsorberExpressed by the formula of：
Babsorber＝φa⊙BT⊙φb，
Wherein [ ] indicates a multiplication of corresponding elements of the matrix;
step 3, calculating the diffraction spectrum after the reflection of the multilayer film:
the light diffracted by the absorption layer is reflected by the multilayer film, and the passing size of the diffraction spectrum after reflection is NO×NOMatrix B ofmlExpressed, the calculation formula is:
Bml＝Babsorber⊙Rml；
step 4, calculating a mask diffraction spectrum of the absorption layer after the second diffraction:
after the multilayer film is reflected, light in all directions is subjected to secondary diffraction through the absorption layer, and the light is mutually coherent and superposed to obtain a final mask diffraction spectrum B, wherein the calculation formula is as follows:
wherein
Representing a matrix convolution. Obtaining the optimal defocus amount Delta z of the mask according to optimizationbestAnd a mask defocus matrix phi obtained by pre-pressing calculation in advancedUpdating the mask diffraction spectrum:
B＝B⊙Φd。
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