CN102289156B - Optimization method for NA-Sigma configuration of photoetching machine - Google Patents

Abstract

The invention provides a method for optimizing the NA-Sigma configuration of a lithography machine; the specific process is: select a point with the maximum lithography focal depth in two optimization directions set in advance; when the selected point does not meet the conditions, calculate a new Optimize the direction, and obtain the point corresponding to the maximum lithographic focal depth in the new optimized direction, and further judge whether the obtained point satisfies the condition; if not, update the selected optimized direction until the obtained maximum lithography The point of depth of focus satisfies the condition. By adopting the present invention, the optimum NA-Sigma configuration can be quickly and effectively optimized to obtain the maximum focal depth of lithography and high precision.

Description

An optimization method for NA-Sigma configuration of lithography machine

technical field

The invention relates to an optimization method for configuring the numerical aperture of a projection objective lens of a lithography machine and the coherence factor (NA-Sigma) of an illumination system, and belongs to the field of collaborative optimization design of parameters of a lithography machine.

Background technique

At present, large-scale integrated circuits are generally manufactured by photolithography systems. The lithography system is mainly divided into five parts: light source, illumination system, mask, projection system and wafer. The light emitted by the light source is incident on the mask after being shaped by the lighting system, and the opening of the mask is partially transparent; after passing through the mask, the light is incident on the wafer coated with photoresist through the projection system, so that the mask pattern is copied on the wafer .

Depth of focus in lithography is one of the main parameters for evaluating the performance of a lithography system, which is defined as: within a certain exposure latitude (exposure dose variation range), and the mask pattern replicated on the wafer satisfies a certain pattern size error, Under the constraints of pattern sidewall angle and photoresist loss, the maximum defocus amount that can be achieved. The larger the lithographic depth of focus, the better the lithographic performance.

In the lithography system, NA and Sigma are important factors affecting the depth of focus in lithography. Among them, NA is directly proportional to the lithographic resolution, and its square is inversely proportional to the lithographic focal depth. Therefore, in order to achieve good lithographic resolution and large lithographic focal depth, an organic configuration between NA and Sigma is necessary.

At present, there have been a lot of research on the reasonable NA-Sigma configuration under different conditions (Li Yanqiu et al., Research on the Effect of Optical Parameter Configuration on ArF Lithography Performance [J]. Special Equipment for Electronic Industry, 2004, 33(4): 36-39 .). The above research is mainly to determine the NA-Sigma configuration by traversing the simulation method, that is, traversing the combination of all values in the NA and Sigma ranges, and obtaining the relationship between NA-Sigma and the focal depth of lithography, and then selecting the maximum light. NA-Sigma configuration with engraved depth of focus. However, this method often needs to traverse all possible values in the range of NA and Sigma, which requires a large amount of calculation and low precision, making it difficult to find the optimal NA-Sigma configuration.

Contents of the invention

The object of the present invention is to provide a method for optimizing the NA-Sigma configuration of a lithography machine; the method can quickly and effectively optimize the NA-Sigma configuration with the maximum lithography focal depth.

Realize the technical scheme of the present invention as follows:

A method for optimizing the NA-Sigma configuration of a photolithography machine, the specific steps are:

Step 101, given the initial point NA and the value of Sigma, set it as (NA, σ) ^{(1, 0)} , determine two initial linearly independent directions d ^{(1, 1)} and d ^{(1, 2)} , set Search precision ε, let k=1;

Step 102, start from (NA, σ) ^{(k, 0)} , search along the direction d ^{(k, 1)} , and obtain the point (NA, σ) ^{(k, 1)} with the maximum lithographic focal depth in this direction , where if the values of the lithographic depth of focus corresponding to all points in this direction are equal, then choose a point as the point (NA, σ) ^{(k, 1)} of the maximum lithographic focal depth; from (NA, σ) ^{(k , 1)} , search along the direction d ^{(k, 2)} , and get the point (NA, σ) ^{(k, 2)} with the maximum lithographic focal depth in this direction, where if all points in this direction correspond to the lithographic When the values of the depth of focus are all equal, then choose a point as the point (NA, σ) ^{(k, 2)} of the maximum depth of focus for lithography;

Step 103, if ||(NA, σ) ^{(k, 2)} -(NA, σ) ^{(k, 0)} ||≤ε, then set (NA, σ)=(NA, σ) ^{(k, 2)} , enter step 109, where || || is a modulo operation; otherwise, enter step 104;

Step 104, calculate the new search direction d ^{(k, 3)} = (NA, σ) ^{(k, 2)} - (NA, σ) ^{(k, 0)} ; starting from (NA, σ) ^{(k, 0)} , Carry out search along direction d ^{(k, 3)} , obtain the point (NA, σ) ^{(k, 3)} with maximum lithography focal depth on this direction;

Step 105, if ||(NA, σ) ^{(k, 3)} -(NA, σ) ^{(k, 2)} ||≤ε, then set (NA, σ)=(NA, σ) ^{(k, 3)} , go to step 109; otherwise go to step 106;

Step 106, when {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1))} }≥{f((NA, σ) ^{(k, 1)} )-f ((NA, σ) ^{(k, 2)} )}, let m=1; when {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1)} )} <{f((NA,σ) ^(k,1) )-f((NA,σ) ^(k,2)) }, let m=2; where f((NA,σ) ^(p,q) ) represents the focal depth of lithography corresponding to the point (NA, σ) ^{(p, q)} ;

Step 107, command $\mathrm{\&lambda;}=\frac{\left|\right|{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,3)}-{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,0)}\left|\right|}{\left|\right|{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,2)}-{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,0)}\left|\right|},$

则进入步骤108；否则，从(NA，σ)^(k，1)、(NA，σ)^(k，2)以及(NA，σ)^(k，3)中选取具有最大光刻焦深的点，令k加1，并将所选取的点作为初始点(NA，σ)^(k，0)，令此时搜索方向d^(k，1)和d^(k，2)为原搜索方向d^(k-1，1)和d^(k-1，2)，返回步骤102；like

Then go to step 108; otherwise, select the point with the maximum lithography focal depth from (NA, σ) ^{(k, 1)} , (NA, σ) ^{(k, 2)} and (NA, σ) ^{(k, 3)} , add 1 to k, and take the selected point as the initial point (NA, σ) ^{(k, 0)} , let the search directions d ^{(k, 1)} and d ^{(k, 2)} be the original search directions d ^{( k-1, 1)} and d ^{(k-1, 2)} , return to step 102;

Step 108, replace the search direction: when m=1, then d ^{(k+1, 1)} = d ^{(k, 2)} , d ^{(k+1, 2)} = d ^{(k, 3)} ; when m = 2, this time d ^{(k+1, 1)} = d ^{(k, 1)} , d ^{(k+1, 2)} = d ^{(k, 3)} ; let k add 1, let the initial point (NA, σ) ^{(k, 0)} is the original initial point (NA, σ) ^{(k-1, 0)} , and return to step 102;

Step 109 , output the value of NA-Sigma (NA, σ) and the optimal lithography focal depth f((NA, σ)), and the optimization ends.

In step 102 of the present invention, when searching along the direction d ^{(k, 1)} the value of the lithographic focal depth corresponding to all points is equal to the lithographic focal depth of the initial point in this search direction, then let (NA, σ) ^{(k, 1)} is equal to (NA, σ) ^{(k, 0)} ; when searching along the direction d ^{(k, 2)} , the values of the lithography focal depths corresponding to all points are equal to the light at the initial point of this search direction When engraving the depth of focus, let (NA, σ) ^{(k, 2)} be equal to (NA, σ) ^{(k, 1)} .

In the present invention, the direction d ^{(1, 1)} is along the [0, 1] direction, and the direction d ^{(1, 2)} is along the [1, 0] direction.

Beneficial effect

The present invention selects two optimization directions, and optimizes the optimization directions under constraint conditions, and finally obtains the optimization direction with a larger lithographic focal depth gradient; therefore, the present invention can be quickly and effectively optimized to obtain the optimal NA -Sigma configuration, to get the largest focal depth of lithography, and have higher precision.

Description of drawings

FIG. 1 is a flowchart of an optimization method for NA-Sigma configuration of a photolithography machine.

Fig. 2 is a schematic diagram of the coherence factor of the lighting system of the lithography machine.

Fig. 3 is a relationship diagram of NA-Sigma configuration and lithography focal depth.

Detailed ways

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

Fig. 1 is the flowchart of the optimization method of photolithography machine NA-Sigma configuration of the present invention, and its specific steps are:

Step 101, according to the type of the lighting system and projection system of the lithography machine, the values of the initial points NA and Sigma are given, set (NA, σ) ^{(1, 0)} , (σ is the initial value of Sigma), and two initial points are determined Linearly independent directions d ^{(1, 1)} , d ^{(1, 2)} , determine the search accuracy ε>0, where ε can be determined according to the accuracy of NA and Sigma, for example, when the required NA and Sigma accuracy requirements are relatively When it is high, the precision factor ε can be set smaller; let k=1. As shown in Figure 3, in the present embodiment, horizontal direction and vertical direction establish coordinate axis, and wherein horizontal direction represents NA, and vertical direction represents Sigma; Make initial direction d ^(1,1) be along [0,1] direction, The direction d ^{(1, 2)} is along the [1, 0] direction.

Step 102, starting from (NA, σ) ^{(k, 0)} , search along the direction d ^{(k, 1)} that is, along the [0, 1] (vertical) direction, wherein the search is performed according to the set vertical The vertical search step is carried out, that is, keeping NA unchanged, gradually changing σ according to the set vertical search step, and obtaining the point (NA, σ) with the maximum lithographic focal depth in the vertical direction within the range of σ ^{(k, 1)} , where, if the lithographic depth of focus values corresponding to all points in the vertical direction are equal, then choose a point as the maximum lithographic focal depth point (NA, σ) ^{(k, 1)} . The preferred setting of the present invention is: if the lithographic focal depths corresponding to all points searched in the vertical direction are equal, then (NA, σ) ^{(k, 1)} is equal to (NA, σ) ^{(k ,0)} .

Starting from (NA, σ) ^{(k, 1)} , along the direction d ^{(k, 2)} is to search along the [1, 0] (horizontal) direction, wherein the search is based on the set horizontal search step Proceeding, even if σ is constant, gradually change NA according to the set horizontal search step size, and obtain the point (NA, σ) ^{(k, 2)} with the maximum lithography focal depth in the horizontal direction within the range of NA, Among them, if the values of lithographic focal depth corresponding to all points in the horizontal direction are equal, then select a point as the maximum lithographic focal depth point (NA, σ) ^{(k, 2)} . The preferred setting of the present invention is: if the lithographic focal depths corresponding to all points searched in the horizontal direction are all equal, then (NA, σ) ^{(k, 2)} is equal to (NA, σ) ^{(k, 1)} . In this implementation, preferably, the horizontal search step size is equal to the vertical search step size.

Step 103. Determine the distance between the point (NA, σ) ( ^{k, 2)} corresponding to the maximum lithographic focal depth in the direction d ^{(k, 2)} and the given initial point (NA, σ) ^{(k, 0)} , if ||(NA, σ) ^{(k, 2)} -(NA, σ) ^{(k, 0)} ||≤ε, then set (NA, σ) = (NA, σ) ^{(k, 2)} and enter Step 109, where || || is a modulo operation; otherwise, go to step 104.

Step 104, calculate the new search direction d ^{(k, 3)} = (NA, σ) ^{(k, 2)} - (NA, σ) ^{(k, 0)} ; starting from (NA, σ) ^{(k, 0)} , Search along the direction d ^{(k, 3)} , wherein the search is within the range of σ and NA, according to the set step size, to obtain the point (NA, σ) ^{(k, 3)} .

Step 105, judging the point (NA, σ) corresponding to the maximum depth of focus of lithography in direction d ^{(k, 3) and} the point (NA, σ ^{) corresponding to the maximum depth of focus of lithography in direction d (k, 2} ) σ) the size of the distance between ^{(k, 2)} , if ||(NA, σ) ^{(k, 3)} -(NA, σ) ^{(k, 2)} ||≤ε, then let (NA, σ)= (NA, σ) ^{(k, 3)} , go to step 109; otherwise go to step 106.

Step 106, judge {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1)} )} and {f((NA, σ) ^{(k, 1)} )-f ((NA, σ) ^{(k, 2)} )}, where f((NA, σ) ^{(p, q)} ) represents the focal depth of lithography corresponding to the point (NA, σ) ^{(p, q)} ;

When {f((NA,σ) ^(k,0) )-f((NA,σ) ^(k,1) )}≥{f((NA,σ) ^(k,1) )-f((NA , σ) ^{(k, 2)} )}, it indicates that the variation of the focal depth of lithography along the direction d ^{(k, 1)} is relatively large at this time, and m=1 at this time;

When {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1)} )}<{f((NA, σ) ^{(k, 1)} )-f((NA , σ) ^{(k, 2)} )}, it indicates that the variation of the focal depth of lithography along the direction d ^{(k, 2)} is small at this time, and m=2 at this time.

通过λ判断当前搜索方向d^(k，1)和d^(k，2)与新的搜索方向d^(k，3)的线性无关性，根据判断的结果确定是否需要用新的搜索方向替换当前搜索方向d^(k，1)和d^(k，2)；判断的过程如下：Step 107, command

Judging the linear independence between the current search direction d ^{(k, 1)} and d ^{(k, 2)} and the new search direction d ^{(k, 3)} by λ, and determining whether to replace the current search direction with a new search direction according to the result of the judgment Direction d ^{(k, 1)} and d ^{(k, 2)} ; the process of judging is as follows:

like Then it shows that the new search direction d ^{(k, 3)} has better linear independence with one of the current two search directions at this time, and now enters step 108, and replaces the original search direction with the new search direction; otherwise , select the point with the maximum lithographic focal depth from (NA, σ) ^{(k, 1)} , (NA, σ) ^{(k, 2)} and (NA, σ) ^{(k, 3)} , let k add 1, And take the selected point as the initial point (NA, σ) ^{(k, 0)} , let the search directions d ^{(k, 1)} and d ^{(k, 2)} at this time be the original search direction d ^{(k-1, 1)} and d ^{(k-1, 2)} , return to step 102.

Step 108, replace the search direction:

When m is equal to 1, d ^{(k+1, 1)} = d ^{(k, 2)} at this time, d ^{(k+1, 2)} = d ^{(k, 3)} ; guarantee that the two search directions determined at this time are linear irrelevant, and with the continuation of the iterations, the degree to which the search direction is close to the conjugate gradually increases.

When m is equal to 2, this order d ^{(k+1, 1)} = d ^{(k, 1)} , d ^{(k+1, 2)} = d ^{(k, 3)} ; guarantee that the two search directions determined at this time are linear irrelevant, and with the continuation of the iterations, the degree to which the search direction is close to the conjugate gradually increases.

Add 1 to k, let the initial point (NA, σ) ^{(k, 0)} be the original initial point (NA, σ) ^{(k-1, 0)} , and return to step 102 .

Step 109 , output the value of NA-Sigma (NA, σ) and the corresponding optimal lithography focal depth f((NA, σ)), and the optimization ends.

Implementation example of the present invention:

The optimization process of the present invention will be described below by taking the optimization of the NA-Sigma configuration of a 45nm node photolithography machine as an example.

For dense lines at 45nm nodes, immersion lithography is used, the refractive index of the immersion liquid is 1.44, the numerical aperture of the projection objective lens is adjustable within [1, 1.35], the exposure wavelength is 193nm, and resolution enhancement technology is used to improve its resolution and increase Large depth of focus for lithography, attenuated phase-shift mask for the mask type, and ring lighting for the illumination method. In order to improve the resolution and ensure the yield, the ring width of the ring illumination method is selected as 0.15, that is, the outer coherence factor and the inner The difference between the coherence factors is 0.15 (Δσ=σ _out −σ _in =0.15), as shown in FIG. 2 . In order to further increase the focal depth of lithography, the linearly polarized light with the same direction as the line is used in the lithography simulation. For such a lithography configuration, the search range of the external coherence factor is [0.15, 1], the search accuracy of NA and Sigma is 0.001, the initial NA-Sigma configuration is (1.1, 0.8), and the initial search direction is [0, 1 ;1,0]. Next, the best NA-Sigma configuration is determined by the method of the present invention, so as to obtain the maximum focal depth of lithography.

FIG. 3 is a graph showing the relationship between the NA-Sigma configuration and the focal depth of lithography under the above conditions obtained by traversing the simulation method. It can be seen from Figure 3 that NA and Sigma can only obtain the lithographic focal depth in a small part of the area. To obtain the NA-Sigma configuration to achieve the maximum lithographic focal depth, it is necessary to accurately traverse the simulation within the range of NA and Sigma This diagram. Accurately traversing the simulated graph takes 17 hours.

The following table shows the iterative search process of the present invention. From the iterative process, the focal depth of lithography at the initial point NA-Sigma configuration (1.1, 0.8) is 0, and after searching along the [0, 1] direction, no Depth of focus in lithography, return to point (1.1, 0.8), and then search along the direction of [1, 0], you can get the maximum depth of focus in lithography at point (1.3496, 0.8) 0.15442μm, and then along the path from the initial point (1.1 , 0.8) and (1.3496, 0.8) in the direction of the line (0.2496, 0.8) to search, still get the maximum focal depth of 0.15442μm at the point (1.3496, 0.8), judging that it does not meet the conditions for the end of optimization, start the first Two rounds of search. The second round of search starts from the point (1.3496, 0.8), and searches along the [0, 1] direction first, and obtains the maximum lithographic focal depth of 0.38657 μm at the point (1.3496, 0.90184), and then along the [1, 0] Direction search, it can be obtained that the maximum lithographic focal depth at point (1.3004, 0.90184) is 0.46063 μm, and then along the direction of the line between the initial point (1.3496, 0.8) and (1.3004, 0.90184) (-0.0492, 0.1447 ) to search, and the maximum lithographic focal depth of 0.52215 μm is obtained at the point (1.2797, 0.9447), which does not meet the conditions for the end of optimization, and the third round of search starts; it goes on and on until the convergence conditions are met, and finally obtains At the point (1.2214, 0.97017), there is a maximum lithographic focal depth of 0.62192 μm, and the search is over. This invention takes 8 minutes, as shown in Table 1:

Table 1 selects and adopts the number of times of the present invention's search iteration

NA Sigma DOF(μm) First round of search 1.1 0.8 0 1.3496 0.8 0.15442 1.3496 0.8 0.15442 Second round of search 1.3496 0.90184 0.38657 1.3004 0.90184 0.46063

1.2797 0.9447 0.52215 The third round of search 1.2797 0.9447 0.52215 1.2518 0.9447 0.55768 1.2518 0.9447 0.55768 Fourth round of search 1.2518 0.9546 0.56742 1.2369 0.9546 0.58217 1.2214 0.96493 0.61567 Fifth round of search 1.2214 0.97017 0.62192 1.2214 0.97017 0.62192 1.2214 0.97017 0.62192

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 premise of the present invention, some modifications, replacements and improvements can also be made, and these are also considered to belong to the present invention scope of protection.

Claims (3)

1. an optimization method for photoetching machine NA-Sigma configuration, described NA is projection objective lens numerical aperture, and described Sigma is illumination system coherence factor, it is characterized in that, concrete steps are: Step 101, given the initial point NA and the value of Sigma, set it as (NA, σ) ^{(1, 0)} , determine two initial linearly independent directions d ^{(1, 1} ) and d ^{(1, 2)} , set Search precision ε, let k=1; Step 102, start from (NA, σ) ^{(k, 0)} , search along the direction d ^{(k, 1)} , and obtain the point (NA, σ) ^{(k, 1)} with the maximum lithographic focal depth in this direction , where if the values of the lithographic depth of focus corresponding to all points in this direction are equal, then choose a point as the point (NA, σ) ^{(k, 1)} of the maximum lithographic focal depth; from (NA, σ) ^{(k , 1)} , search along the direction d ^{(k, 2)} , and get the point (NA, σ) ^{(k, 2)} with the maximum lithographic focal depth in this direction, where if all points in this direction correspond to the lithographic When the values of the depth of focus are all equal, then choose a point as the point (NA, σ) ^{(k, 2)} of the maximum depth of focus for lithography; Step 103, if ||(NA, σ) ^{(k, 2)} -(NA, σ) ^{(k, 0)} ||≤ε, then let (NA, σ)=(NA, σ) ^{(k, 2)} , enter step 109, where |||| is a modulo operation; otherwise, enter step 104; Step 104, calculate the new search direction d ^{(k, 3)} = (NA, σ) ^{(k, 2)} - (NA, σ) ^{(k, 0)} ; starting from (NA, σ) ^{(k, 0)} , Carry out search along direction d ^{(k, 3)} , obtain the point (NA, σ) ^{(k, 3)} with maximum lithography focal depth on this direction; Step 105, if ||(NA, σ) ^{(k, 3)} -(NA, σ) ^{(k, 2)} ||≤ε, then let (NA, σ)=(NA, σ) ^{(k, 3)} , go to step 109; otherwise go to step 106; Step 106, when {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1)} )}≥{f((NA, σ) ^{(k, 1)} )-f ((NA, σ) ^{(k, 2)} )}, let m=1; when {f((NA, σ) ^{(k, 0)} )-f((NA, σ) ^{(k, 1)} )} <{f((NA,σ) ^(k,1) )-f((NA,σ) ^(k,2) )}, let m=2; where f((NA,σ) ^(p,q) ) represents the focal depth of lithography corresponding to the point (NA, σ) ^{(p, q)} ; Step 107, command $\mathrm{\&lambda;}=\frac{\left|\right|{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,3)}-{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,0)}\left|\right|}{\left|\right|{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,2)}-{(\mathrm{NA},\mathrm{\&sigma;})}^{(k,0)}\left|\right|}$ like

Then go to step 108; otherwise, select the point with the maximum lithography focal depth from (NA, σ) ^{(k, 1)} , (NA, σ) ^{(k, 2)} and (NA, σ) ^{(k, 3)} , add 1 to k, and take the selected point as the initial point (NA, σ) ^{(k, 0)} , let the search directions d ^{(k, 1)} and d ^{(k, 2)} be the original search directions d ^{( k-1, 1)} and d ^{(k-1, 2)} , return to step 102; Step 108, replace the search direction: when m=1, then order d ^{(k+1, 1)} = d ^{(k, 2)} , d ^{(k+1, 2)} = d ^{(k, 3)} ; when m = 2, this time d ^{(k+1, 1)} = d ^{(k, 1)} , d ^{(k+1, 2)} = d ^{(k, 3)} ; let k add 1, let the initial point (NA, σ) ^{(k, 0)} is the original initial point (NA, σ) ^{(k-1, 0)} , and return to step 102; Step 109 , output the value of NA-Sigma (NA, σ) and the optimal lithography focal depth f((NA, σ)), and the optimization ends. 2. The optimization method according to claim 1, characterized in that, in the step 102, when searching along the direction d ^{(k, 1),} the values of the photolithography focal depths corresponding to all points are equal to the initial search direction When the lithographic focal depth of a point is set, (NA, σ) ^{(k, 1)} is equal to (NA, σ) ^{(k, 0)} ; when the lithography corresponding to all points is searched along the direction d ^{(k, 2)} When the focal depth values are all equal to the photolithographic focal depth of the initial point in this search direction, then make (NA, σ) ^{(k, 2)} equal to (NA, σ) ^{(k, 1)} . 3. optimization method according to claim 1, is characterized in that, described direction d ^(1,1) is along [0,1] direction, and described direction d ^(1,2) is along [1,0] direction.

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