CN108693715A - Promote the multiple target light source and photomask optimization method of full filed optical patterning uniformity - Google Patents

Abstract

The present invention provides a multi-objective light source and mask optimization method for improving the uniformity of lithographic imaging in the whole field of view. Full-field polarization aberration information for the objective. Therefore, the optimized light source and mask obtained by the present invention are not only suitable for lithographic imaging of a specific field of view, but also suitable for lithographic imaging of a full field of view. For a large-field lithography objective lens with polarization aberration, the above effects help to improve the imaging uniformity of the full-field lithography and ensure the yield of the lithography process.

Description

Multi-target light source and mask optimization method to improve the imaging uniformity of full-field lithography

technical field

The invention relates to a multi-target light source and a mask optimization method for improving the uniformity of full-field lithography imaging, and belongs to the technical field of lithography resolution enhancement.

Background technique

Photolithography is a key technology in the field of VLSI manufacturing. At present, the operating wavelength of the mainstream deep ultraviolet lithography system in the industry is 193nm. As the lithography process node moves down to 45-14nm, the minimum linewidth of integrated circuits has been far smaller than the wavelength of the light source. At this time, the phenomenon of interference and diffraction of light waves is more significant, resulting in distortion, shift or resolution reduction of lithography imaging; therefore, the lithography system must adopt resolution enhancement technology to improve the resolution of lithography imaging and graphic fidelity , to ensure the yield of the photolithography process. Source mask optimization (SMO) is an important high-degree-of-freedom lithography resolution enhancement technology. By optimizing the light source intensity distribution and mask transmittance distribution, the amplitude of the mask diffraction spectrum and phase modulation, thereby improving the imaging quality of lithography.

At present, for the immersion projection lithography system with a large field of view, the polarization aberration corresponding to different field points of the lithography objective lens is different. Since polarization aberration is a key factor affecting vector light wave imaging, this difference will lead to uneven imaging of each area on the silicon wafer, resulting in a decrease in the yield of the lithography process.

The Chinese patent with the publication number CN 102269926B proposes a non-ideal lithography system based on the vector imaging model for the polarization aberration of the ultra-high numerical aperture (NA) lithography objective lens and the defocus error of the lithography system Optical proximity correction (OPC) method. This method takes into account the polarization aberration of the ultra-high NA lithography objective lens and the defocus error of the lithography system, and the optimized mask pattern is more suitable for the actual lithography process. However, this method ignores the difference in polarization aberration at different viewing points of the lithography objective lens, and it is difficult to take into account the uniformity of the lithography imaging of the whole field of view, which limits the further improvement of the lithography process yield.

The source of polarization aberration of lithography objective lens includes but not limited to: scattering of lens surface, film layer and crystal birefringence effect. All of the above factors will cause changes in the intensity, phase, and polarization state of imaging light waves, which in turn affect imaging resolution and fidelity. In addition, the polarization aberration corresponding to different field points of the lithography objective lens is also different. Therefore, a light source-mask optimization method that comprehensively considers the polarization aberration of each field of view of the lithography objective lens is needed to compensate the influence of polarization aberration on the lithography imaging performance and achieve uniform lithography imaging in the entire field of view.

Contents of the invention

The purpose of the present invention is to provide a multi-target light source-mask optimization method under the comprehensive consideration of the polarization aberration of each field of view of the lithography objective lens. An optimization objective function including the polarization aberration information of each field of view is designed, and the optimization objective function is used to obtain a relatively uniform lithographic imaging in the entire field of view with the optimized light source and mask.

Realize the technical solution of the present invention as follows:

The multi-target light source and mask optimization method for improving the uniformity of full-field photolithography imaging in the present invention is characterized in that it includes the following steps:

Step 1. Initialize the light source pattern and mask pattern;

Step 2. Construct the optimization objective function D:

Based on the polarization aberration PA _i corresponding to the ith field of view point of the lithography objective lens, determine the imaging fidelity function corresponding to the i-th field of view point Where i=1,2,...,n, n is the number of field points; is the pixel value of each pixel of the target pattern; Z(x, y, PA _i ) represents the photoresist imaging corresponding to the current light source pattern and mask pattern calculated by using the lithography imaging model considering the polarization aberration PA _i The pixel value of each pixel in ; the objective function D is constructed as the average value of the imaging fidelity function of each field of view of the lithography objective lens, that is

Step 3: Optimizing the light source and the mask based on the optimization objective function D.

Preferably, the specific process of the third step is:

Step 401, calculate the gradient matrix ▽D(Ω _s ) of the objective function D for the light source variable matrix Ω _s corresponding to the current light source pattern, and then obtain the approximate value of the gradient matrix Calculate the gradient matrix ▽D(Ω _M ) of the target function D for the mask variable matrix Ω _M corresponding to the current mask pattern; use the steepest descent method to update the light source variable matrix Ω _s as Obtain the light source pattern J corresponding to the current Ω _s ; use the steepest descent method to update the mask variable matrix Ω _M as in Optimizing the step size for the preset mask, obtaining the mask pattern M corresponding to the current Ω _M ; updating the binary mask pattern M _b corresponding to the current mask pattern M;

Step 402, calculate the value of the objective function D corresponding to the current light source pattern J and the binary mask pattern M _b ; when the value is less than a predetermined threshold or the number of times to update the light source variable matrix Ω _s and the mask variable matrix Ω _M reaches a predetermined upper limit value, enter step 403, otherwise return to step 401;

Step 403, terminating the optimization, and determining the current light source pattern J and the binary mask pattern _Mb as optimized light source patterns and mask patterns.

Preferably, the specific process of said step 1 is:

Step 301. Initialize the light source pattern J with a size of N _S × _NS , and initialize the mask pattern M with a target pattern with a size of N×N Wherein N _S and N are integers;

Step 302. Set the pixel value of the luminous area on the initial light source graph J to 1, and the pixel value of the non-luminous area to 0; set the light source variable matrix Ω _s with a size of N _S ×N _S : when J(x _s ,y _s )=1, When J(x _s ,y _s )=0, Where J(x _s , y _s ) represents the pixel value of the pixel point (x _s , y _s ) on the light source pattern; the transmittance of the light-transmitting area of the initial mask pattern M is set to 1, and the transmittance of the light-blocking area is set to 0; Set a mask variable matrix Ω _M with a size of N×N: when M(x,y)=1, When M(x,y)=0, Where M(x, y) represents the transmittance of each pixel point (x, y) on the mask pattern; let the initial binary mask pattern M _b =M.

Preferably, the polarization aberration PA _i is calculated under the premise of considering the effect of lens surface scattering, film layer and birefringence effect of crystal.

The present invention has following beneficial effects:

In the invention, the objective function is constructed as the average value of the graphic errors of the points in each field of view, so that the polarization aberration information of the whole field of view of the lithography objective lens is considered comprehensively in the optimization process. Therefore, the optimized light source and mask obtained by the present invention are not only suitable for lithographic imaging of a specific field of view, but also suitable for lithographic imaging of a full field of view. For a large-field lithography objective lens with polarization aberration, the above effects help to improve the imaging uniformity of the full-field lithography and ensure the yield of the lithography process.

Description of drawings

Fig. 1 is a flowchart of the optimization method of the present invention.

FIG. 2 is a flowchart of a multi-target light source-mask optimization method for a non-ideal photolithography system in this embodiment.

FIG. 3 is a schematic diagram of imaging in an initial light source, an initial mask and its corresponding photoresist.

Fig. 4 is a schematic diagram of optimized light source patterns, mask patterns and corresponding photoresist imaging using related technologies (CN 102269926 B, 2012.08.15).

FIG. 5 is a schematic diagram of the optimized light source pattern, mask pattern and corresponding photoresist imaging using the multi-target light source-mask optimization method proposed by the present invention.

FIG. 6 is a schematic diagram of a light source pattern and a mask pattern optimized for full field of view polarization aberration by using the multi-target light source-mask optimization method proposed by the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings.

Principle of the present invention: on the basis of the optimization method of the non-ideal lithography system OPC based on the Abbe vector imaging model, the present invention designs an optimization objective function that includes the polarization aberration information of each field of view point of the lithography objective lens at the same time, so that the optimization can be obtained The light source and mask can obtain better exposure effect in the whole field of view, which effectively improves the uniformity of photolithography imaging in the whole field of view.

As shown in Figure 1, a multi-target light source-mask optimization method to improve the uniformity of full-field lithography imaging, the specific process is:

Step 1. Initialize the light source pattern and mask pattern;

Step 2, constructing the optimization objective function D:

Let F be the imaging fidelity function, and consider the polarization aberration PA _i corresponding to the ith field of view point of the lithography objective lens, then in is the pixel value of each pixel of the target pattern, Z(x,y,PA _i ) means considering the polarization aberration PA _i , using the lithographic imaging model to calculate each pixel in the photoresist imaging corresponding to the current light source pattern and mask pattern The pixel value of ; the objective function D is constructed as the average value of the imaging fidelity function of each field of view of the lithography objective lens, that is

Step 3: Optimizing the light source and mask based on the objective function.

As shown in FIG. 2, this embodiment establishes a multi-target light source-mask optimization method for polarization aberration in the full field of view, and the specific steps are:

(1) Initialize the light source pattern J with a size of N _S × _NS , and initialize the mask pattern M with a target pattern with a size of N×N Where N _S and N are integers.

(2) Set the pixel value of the luminous area on the initial light source graph J to 1, and the pixel value of the non-luminous area to 0; set the light source variable matrix Ω _s with a size of N _S × _NS : when J(x _s , y _s )=1, When J(x _s ,y _s )=0, Where J(x _s , y _s ) represents the pixel value of each pixel point (x _s , y _s ) on the light source pattern; set the transmittance of the initial mask pattern M to 1 in the light-transmitting area, and 0 in the light-blocking area ;Set a mask variable matrix Ω _M with a size of N×N: when M(x,y)=1, When M(x,y)=0, Where M(x, y) represents the transmittance of each pixel point (x, y) on the mask pattern; let the initial binary mask pattern M _b =M.

(3) Construct and optimize the objective function D; let F be the imaging fidelity function, and consider the polarization aberration PA _i corresponding to the ith field of view point of the lithography objective lens, then in is the pixel value of each pixel of the target pattern, Z(x,y,PA _i ) means considering the polarization aberration PA _i , using the lithographic vector imaging model to calculate the imaged pixels in the photoresist corresponding to the current light source pattern and the mask pattern The pixel value of the point; the objective function D is constructed as the average value of the imaging fidelity function of each field of view of the lithography objective lens, namely

Referring to the prior art (CN 102269926B, 2012.08.15), in consideration of the polarization aberration of the lithography system, the spatial image corresponding to the current light source and the mask is calculated by using the Abbe vector imaging model as:

in, || means to take the modulus of each element in the matrix, and the final calculation result I is a scalar matrix with a size of N×N (if all the elements in a matrix are scalar, it is called a scalar matrix), which means that the current Aerial image intensity distribution corresponding to light source and mask. is the mask diffraction matrix corresponding to the light source point J(x _s ,ys), according to the Hopkins approximation, it is defined as the optical path from each point on the mask to the light source point J(x _s ,y _s ), namely :

Where NA represents the object-space numerical aperture of the projection system, and pixel represents the side length of each sub-region on the mask pattern.

Indicates convolution, ⊙ indicates that the elements corresponding to the two matrices are directly multiplied, Represents the inverse Fourier transform, n _w represents the refractive index of the immersion liquid at the image side of the photolithography system, R is the reduction magnification of the ideal projection system, generally 4; V′ _p consists of a vector matrix (if the elements in a matrix are vectors or matrices, is called a vector matrix) The p component of each element in ; here p represents the polarization direction of light, which reflects the vector characteristics of the imaging model, and PA represents the polarization aberration of the lithography system. According to the polarization theory of light, PA is generally a 2×2 complex matrix (Jones matrix). The specific calculation process of V' is described in detail in the prior art (CN 102269926 B, 2012.08.15), and will not be repeated here.

The sigmoid function is used to approximate the photolithography effect, where a represents the slope of the photoresist approximation model, and _tr represents the threshold of the photoresist approximation model. Therefore, the imaging in the photoresist corresponding to the light source pattern and the mask pattern is calculated according to the aerial image intensity I as:

According to the above calculation process, comprehensively considering the polarization aberration PA _i corresponding to each field of view point, calculating the imaging fidelity function of each field of view point and taking the arithmetic mean, the specific value of the objective function D can be obtained.

(4) Comprehensively consider the polarization aberration PA _i corresponding to each field of view point, under this condition, calculate the gradient matrix ▽D(Ω _s ) of the objective function D with respect to the light source variable matrix Ω _s , and convert each pixel point on the light source graph to The sum of the pixel values of J _sum is approximated as a given constant, and the approximate value of the gradient matrix is obtained Calculate the gradient matrix ▽D(Ω _M ) of the objective function D with respect to the mask variable matrix Ω _M . The gradient matrix ▽D(Ω _M ) is obtained by calculating the partial derivative of each element in the variable matrix Ω _M by the objective function D.

The polarization aberration considered in the present invention comes from factors such as scattering on the lens surface, film layer and crystal birefringence effect. The polarization aberration data used in the present invention can be obtained by tracing the multiple refraction and reflection of rays in the projection objective lens through CODE V software. In specific applications, the polarization aberration data of the lithography objective lens can also be obtained through actual measurement.

According to step (3), it can be seen that the gradient matrix gradient matrix References (J.Opt.Soc.Am.A, 2013, 30:112-123), give the specific forms of ▽F _i (Ω _S ) and ▽F _i (Ω _M ):

Among them, ^* means to take the conjugate operation, and ^o means to rotate the matrix by 180 degrees both horizontally and vertically. When calculating ▽F _i (Ω _S ) and ▽F _i (Ω _M ) corresponding to different field points, only Into different polarization aberration data.

Using the steepest descent method, update the light source variable matrix Ω _s as Obtain the light source graph J corresponding to the current Ω _s , Using the steepest descent method, update the mask variable matrix Ω _M as in To optimize the step size for the preset mask, obtain the mask pattern M corresponding to the current Ω _M , Update the binary mask pattern M _b corresponding to the current M, In general, t _m is taken as 0.5.

(5), calculate the value of the objective function D corresponding to the current light source pattern J and the binary mask pattern M _b ; when the value is less than the predetermined threshold δD or the number of times to update the light source variable matrix Ω _s and the mask variable matrix Ω _M reaches a predetermined value When the upper limit is K _SM , go to (6), otherwise return to (4).

(6) Terminate the optimization, and determine the current light source pattern J and the binary mask pattern _Mb as the optimized light source pattern and mask pattern.

Implementation example of the present invention:

Figure 3 is a schematic diagram of the position of the field of view of the lithography objective lens. The polarization aberration corresponding to each field of view is obtained by ray tracing through the optical design software CODE V. Generally, the polarization aberration value corresponding to the edge field point F11 is the largest, and the polarization aberration value corresponding to the central field point F3 is the smallest.

FIG. 4 is a schematic diagram of imaging in the initial light source, the initial mask and the corresponding photoresist. In FIG. 4 , 401 is an initial light source pattern, white represents a light-emitting part, and black represents a non-light-emitting part. 402 is the initial mask pattern, which is also the target pattern, white represents the light-transmitting area, black represents the light-blocking area, and its characteristic size is 45nm.

As shown in Fig. 5 , it is a schematic diagram of a light source pattern and a mask pattern optimized by using a related technology (CN102269926B, 2012.08.15) (abbreviated as method A) for the polarization aberration corresponding to the extreme field of view point F11. In FIG. 5 , 501 is the light source pattern optimized by method A; 502 is the mask pattern optimized by method A.

As shown in Figure 6, for the polarization aberration of the whole field of view (due to the symmetry, the polarization aberrations corresponding to 9 field points of F1～F3, F6～F8, F11～F13 are considered here), the method proposed by the present invention is adopted. Schematic diagram of optimized light source patterns and mask patterns by the multi-target light source-mask optimization method (abbreviated as method B below). In FIG. 6 , 601 is the light source pattern optimized by method A; 602 is the mask pattern optimized by method A.

Here, the pattern error is used to describe the photolithographic imaging quality. Under the hard threshold photoresist model, the pattern error can be considered to be approximately equal to the imaging fidelity. Table 1 shows the graphic error data of method A and method B imaging at different field of view points:

Table 1 Graphical error data corresponding to different methods at each field of view point

The data in Table 1 shows that for method A, the photolithographic imaging quality is higher at the extreme field of view point F11, and the photolithographic imaging effect is poorer at the central field of view point F3. This is because Method A only optimizes the polarization aberration corresponding to F11, and the optimization result is only applicable to F11 and its close field of view, not to F3 field of view which is far away from F11. For method B, since the polarization aberration information of 9 field of view points is considered in the optimization process, it is suitable for full-field lithographic imaging, that is, the image error of imaging at each field of view point is relatively average. Further, it can be calculated from the data in Table 1 that the average value of the graphic error of method A imaging at 9 field points is 690, the standard deviation is 103, and the PV value is 263; The mean value of the graphic error is 822, the standard deviation is 195, and the PV value is 503. The comparison of the above data shows that compared with the existing method A, the imaging quality of the method B proposed by the present invention is more uniform (standard deviation and PV value are all reduced) in the whole field of view, and the overall graphic error is also reduced, which is beneficial to The improvement of the yield rate of the photolithography process reflects the superiority of the present invention.

Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, for those skilled in the art, without departing from the principle of the present invention, some modifications, replacements and improvements can also be made, and these should also be regarded as belonging to the present invention. protection scope of the invention.

Claims (4)

1. A multi-objective light source-mask optimization method for improving full-field photoetching imaging uniformity is characterized by comprising the following steps:

step one, initializing a light source pattern and a mask pattern;

step two, constructing an optimized objective function D:

polarization aberration PA based on lithography objective ith view field point correspondence_iDetermining an imaging fidelity function for an ith field of view pointWherein i is 1,2, n, n is the number of field points;the pixel value of each pixel point of the target graph is taken; z (x, y, PA)_i) Presentation taking into account polarization aberrations PA_iUnder the condition of (1), calculating the pixel value of each pixel point in the photoresist imaging corresponding to the current light source pattern and the mask pattern by utilizing a photoetching imaging model; the objective function D is constructed as the average value of the imaging fidelity function of each field point of the lithography objective, i.e.

And thirdly, optimizing the light source and the mask based on the optimization objective function D.

2. The vector imaging model-based low-error-sensitivity multi-objective light source-mask optimization method according to claim 1, wherein the specific process of the third step is as follows:

step 401, calculating a light source variable matrix omega of the objective function D corresponding to the current light source graph_sD (Ω) gradient matrix_s) Then obtaining an approximation of the gradient matrixCalculating a mask variable matrix omega corresponding to the target function D to the current mask pattern_MD (Ω) gradient matrix_M) (ii) a Updating the light source variable matrix omega by using the steepest descent method_sIs composed ofObtaining a corresponding current omega_sLight source pattern J of (a); updating mask variable matrix omega by using steepest descent method_MIs composed ofWhereinObtaining the corresponding current omega for the preset mask optimization step length_MThe mask pattern M of (2); updating a binary mask pattern M corresponding to a current mask pattern M_b；

Step 402, calculating the current light source pattern J and the binary mask pattern M_bThe value of the corresponding objective function D; when the value is less than the predetermined threshold value or the light source variable matrix omega is updated_sAnd mask variable matrix omega_MWhen the number of times reaches a preset upper limit value, the step 403 is entered, otherwise, the step 401 is returned to;

step 403, terminating the optimization, and combining the current light source pattern J and the binary mask pattern M_bAnd determining the optimized light source pattern and mask pattern.

3. The method as claimed in claim 2, wherein the specific process of the first step is as follows:

step 301, initializing the light source to N_S×N_SThe mask pattern M is initialized to a target pattern of size N × NWherein N is_SAnd N is an integer;

step 302, setting the pixel value of a light-emitting area on the initial light source graph J as 1 and the pixel value of a non-light-emitting area as 0; set size to N_S×N_SLight source variable matrix omega_s: when J (x)_s,y_s) When the number is equal to 1, the alloy is put into a container,when J (x)_s,y_s) When the content is equal to 0, the content,wherein J (x)_s,y_s) Representing a pixel point (x) on the light source pattern_s,y_s) A pixel value of (a); setting the transmissivity of a light transmission area of the initial mask pattern M to be 1 and the transmissivity of a light blocking area to be 0; setting a mask variable matrix Ω of size N × N_M: when M (x, y) is 1,when M (x, y) is 0,wherein M (x, y) represents the transmittance of each pixel (x, y) on the mask pattern; let the initial binary mask pattern M_b＝M。

4. The method as claimed in claim 1, wherein the polarization aberration PA is a multi-objective light source-mask optimization method for improving the uniformity of full field lithography imaging_iCalculated under the premise of considering the influence of lens surface scattering and film and crystal birefringence effects.