Optical proximity correction mask optimization method to reduce mask complexity

Abstract

The present invention belongs to the field of chip manufacturing, and proposes an optical proximity correction mask optimization method that can reduce the complexity of the mask. The method proposes a new loss function for optical proximity correction that can resist deviation. In addition to considering the influence of printing errors and process deviation loops, an item representing the deviation between the mask and the target image is introduced to standardize the geometric features of the mask. By adding restrictions to the solution space, a better balance is achieved between the image generation quality and complexity of the mask; the process deviation modeling is optimized, and the generated mask can more effectively resist the process deviation. The chip manufacturing mask is optimized so that the pattern after lithography has higher fidelity.

Description

Technical Field

[0001] The invention belongs to the field of chip manufacturing and relates to an optical proximity correction mask optimization method capable of reducing mask complexity. Background Art

[0002] As the feature size of integrated circuit processes continues to decrease, existing manufacturing technologies face great challenges. Since the size of circuit patterns and the wavelength of the light source used in the lithography process are similar, interference effects will inevitably occur, resulting in distortion of the lithography patterns, which in turn affects the integrated circuit manufacturing capacity. The application of resolution enhancement technology is a key step in improving production capacity. Optical proximity correction is the most core resolution enhancement technology. During the optical proximity correction process, the pattern on the mask to be processed will be adjusted to compensate for the influence of optical scattering. The first type is the design rule-based method, which is characterized by simple application and fast speed, and can handle simple designs well. However, the design rules for large-scale designs at advanced technology nodes are growing exponentially, so the quality of mask optimization based on design rule methods is limited. The other is the model-based method, which has a huge solution space, so it is very time-consuming to get a high-quality result. As the complexity of circuit design increases, the above design rule-based and model-based methods will face problems of efficiency or output quality. Therefore, analytical methods have become a new trend. The classic inverse lithography technology makes corrections based on the intensity of each pixel, and finally determines whether the window at each coordinate on the mask is open by setting up a threshold function. The mask produced by this pixel-level method has an irregular shape, which makes the production of the mask more difficult. If the geometric shape of the mask is simply constrained by geometric rules, the solution space that can be optimized will be greatly compressed, and the quality of the printed image will be greatly reduced. Summary of the invention

[0003] In order to overcome the problems existing in the prior art, the present invention is fundamentally different from the traditional inverse lithography technology of pixel-level correction. The inverse lithography technology with the level set algorithm as the core extracts the boundary line of the mask, and uses the overall contraction, expansion, separation and merging of the boundary line to represent the changes in the mask image. In each cycle, by comparing the deviation between the actual output graphics and the target graphics, the optimization and iteration of the mask are reversely guided. Since the object of the optimization process is a continuous graphic contour, the graphics it produces are more regular. In the actual operation process, by marking various places on the plane, it is possible to distinguish whether the place belongs to the inside or outside of the mask graphic. The chip manufacturing mask is optimized using numerical optimization and gradient descent methods, so that the pattern after lithography has higher fidelity.

[0004] 1) Lithography model and inverse lithography technology modeling

[0005] According to the forward lithography model, a printed pattern is obtained based on a given mask. This includes two steps: the lithography projection model and the photoresist model. The lithography projection model can be described as an operation between the lithography core and the mask. The photoresist model determines the actual printed shape by judging whether the intensity of the transmitted light exceeds the threshold.

[0006] 2) Precise margin error

[0007] The distortion of the printed graphics is continuous, and the distorted part of the graphics only contains convexities or concavities. A large number of detection points are inserted on the contour line of the target pattern, and the vertical distance between the target contour at the detection point and the actual printed image is calculated (perpendicular to the target contour line). If the sum of the errors exceeds a threshold, then an edge placement error (EPE) violation is considered to have occurred at this measurement point.

[0008] The EPE value of the printed image is the total number of detection points with precise margin errors on the image. The EPE error function is the EPE loss function.

[0009] 3) Process deviation modeling

[0010] When process deviation occurs, the printed graphics are minimally affected by disturbances. Such disturbances can be measured by the process variation band (PVBand); based on this idea, a PVBand loss function is added to the commonly used optimization objective of minimizing the printed graphics error in the hope of achieving the purpose of collaborative optimization, so the optimization objective can be expressed as.

[0011] The expressions involved in the modeling process are all continuous differentiable functions, so the general gradient-based first-order algorithm can still be used to iteratively solve them.

[0012] 4) Add constraints on mask complexity

[0013] Under normal circumstances, after multiple iterations of inverse lithography, in order to make the final printed graphics generated by the mask as close to the target graphics as possible, the mask itself will undergo multiple local minor modifications. The result is that the geometric features of the mask are too complex, full of various tiny burrs and isolated stains, which makes the production of the mask very difficult. However, if the mask image is too simple, the generated printed image will be too different from the target image. In order to balance the printing accuracy and mask complexity, a geometric complexity loss function is added to the optimization function. On the basis that the mask can generate high-quality printed images, the optimal solution whose geometric features are more similar to the regular target graphics is found; plus the optimization function of this item, the loss function is finally optimized.

[0014] The specific technical solutions are as follows:

[0015] An optical proximity correction mask optimization method that can reduce mask complexity includes the following steps:

[0016] Step 1: Input target image Z t , lithography core h1,…,h k and the corresponding weight coefficients μ1,…,μ k ;

[0017] Step 2, initialization;

[0018] Step 2.1, the mask is initialized to the same size as the target image Z t The same shape, and calculate the initial level set function φ0, calculate the geometric gradient of φ0

[0019] Step 2.2, after lithography simulation, the initial loss function F0 is obtained, and the initial loss function gradient G0 is calculated;

[0020] F=αF epe +βF pvb +γF geo

[0021] Among them, F is the optimization loss function, α, β, and γ are the weights of the EPE loss function, PVBand loss function, and geometric complexity loss function respectively; F is initialized to F0;

[0022]

[0023] P epe =∑EPE violations

[0024] Among them, F epe is the EPE loss function, (x, y) is the point on the mask plane, D is the vertical distance between the target contour measurement point and the printed image contour, and th EPE is the EPE meter error threshold;

[0025]

[0026] Among them, F pvb is the PVBand loss function, Z k is the printed image generated under the kth condition, Z t is the target graph, N p is the number of different lithography conditions considered;

[0027] Step 2.3, calculate the initial boundary evolution speed

[0028] Step 3, enter the i-th loop:

[0029] Step 3.1 Calculate the boundary evolution time step Δt i ;

[0030] Step 3.2 Calculate the change in the level set function: Δφ i (x,y)=(v i +λ v v i-1 )Δt i ;

[0031] Step 3.3 Update the level set function: φ i (x,y)=φ i-1 (x,y)+Δφ i (x,y);

[0032] Step 3.4 Each point on the plane is calculated according to φ i The sign of (x, y) determines the value of the mask matrix; if it is a positive number, the mask matrix value is 1, which means it is inside the mask, otherwise it is 0, which means it is outside the mask;

[0033] Step 3.5: Perform lithography simulation on the updated mask to obtain the printed images generated under the optimal conditions and the maximum deviation conditions, evaluate them and obtain the new loss function value F. i , update the loss function gradient G i ;

[0034] Step 3.6 Calculate the new boundary evolution velocity v i ;

[0035] Step 3.7 is used to judge that if the maximum absolute value of the velocity of each point on the plane is less than the set threshold, it is considered that convergence is complete and the mask M is output. * Otherwise, return to step 3.1 and proceed to the next cycle.

[0036] Further, the level set function φ(x,y);

[0037] In the level set method, the plane is divided into three regions by the boundary of the figure: interior, exterior, and boundary line; the level set function is the central function that characterizes the geometric information of the plane:

[0038]

[0039] Where d(x,y) is the Euclidean distance from the point (x,y) on the plane to the boundary;

[0040] The boundary of the graph evolves according to the designed algorithm to reduce the loss function as expected. The boundary evolution rate function v is composed of the gradient of the loss function G and the geometric gradient of the level set function Decide:

[0041] in

[0042] The iteration of the level set function depends on the boundary evolution velocity v and the time step Δt, which is determined by the conjugate gradient descent method:

[0043] Δφ=(v(x,y)+λ v v f (x,y))Δt

[0044] where v f is the evolution speed of the last iteration process, λ v The calculation of depends on the type of conjugate gradient method. In this invention, the traditional Polak-Ribiere-Polyak conjugate gradient method is used.

[0045] In the final mask plane, whether a mask is generated at each position depends on the sign of the level set function at that point. If it is negative, it means that the point is inside the mask, and if it is positive, it means that the point is outside the mask.

[0046] Furthermore, the piecewise Euler time step algorithm is used to set the step parameter λ t ,Time step calculation:

[0047]

[0048] Where σ is a parameter between 0 and 1, which is used to control the numerical change of evolution update.

[0049] Furthermore, the gradient calculation of the loss function with respect to the mask information proves:

[0050]

[0051]

[0052] where h k and μ k is the lithography core and the corresponding weight coefficient, Yes k The conjugate transpose of .

[0053] Furthermore, in the above step 3.5, the optimal condition is that the lens imaging point is exactly at the receiving plane and the exposure dose is also standardized to 1; the maximum deviation condition is the maximum deviation range set according to the optimal condition.

[0054] The beneficial effect of the present invention is that a new loss function for optical proximity correction that can resist deviation is proposed. In addition to considering the influence of printing error and process deviation ring, an item representing the deviation between the mask and the target image is introduced to standardize the geometric features of the mask. The invention has the following characteristics:

[0055] 1. Achieve a better balance between the quality and complexity of mask image generation by adding restrictions to the solution space;

[0056] 2. Realize the lithography acceleration model with high algorithm efficiency;

[0057] 3. Modeling and optimization of process deviations are carried out to produce masks that can more effectively combat process deviations;

[0058] 4. Ability to support expansion of other optimization objectives. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the target mask.

[0060] Figure 2 Schematic diagram for comparison of photolithography simulation effects. (a) is a traditional mask, and (b) is a mask optimized by the present invention. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is described in detail with reference to the accompanying drawings and specific embodiments.

[0062] An optical proximity correction mask optimization method that can reduce mask complexity includes the following steps:

[0063] Step 1: Input target image Z t ,like Figure 1 As shown, the photolithography cores h1,…,h k and the corresponding weight coefficients μ1,…,μ k ;

[0064] Step 2, initialization;

[0065] Step 2.1, the mask is initialized to the same size as the target image Z t The same shape, and calculate the initial level set function φ0, calculate the geometric gradient of φ0

[0066] Step 2.2, after lithography simulation, the initial loss function F0 is obtained, and the initial loss function gradient G0 is calculated;

[0067] F=αF epe +βF pvb +γF geo

[0068] Among them, F is the optimization loss function, α, β, and γ are the weights of the EPE loss function, PVBand loss function, and geometric complexity loss function respectively; F is initialized to F0; EPE =15nm.

[0069]

[0070] F epe =∑EPE violations

[0071] Among them, F epe is the EPE loss function, (x, y) is the point on the mask plane, D is the vertical distance between the target contour measurement point and the printed image contour, and th EPE is the EPE meter error threshold;

[0072]

[0073] Among them, F pvb is the PVBand loss function, Z k is the printed image generated under the kth condition, Z t is the target graph, N p is the number of different lithography conditions considered;

[0074] Step 2.3, calculate the initial boundary evolution speed

[0075] Step 3, enter the i-th loop:

[0076] Step 3.1 Calculate the boundary evolution time step Δt i ;

[0077] Step 3.2 Calculate the change in the level set function: Δφ i (x,y)=(v i +λ v v i-1 )Δt i ;

[0078] Step 3.3 Update the level set function: φ i (x,y)=φ i-1 (x,y)+Δφ i (x,y);

[0079] Step 3.4 Each point on the plane is calculated according to φ i The sign of (x, y) determines the value of the mask matrix; if it is a positive number, the mask matrix value is 1, which means it is inside the mask, otherwise it is 0, which means it is outside the mask;

[0080] Step 3.5: Perform lithography simulation on the updated mask to obtain the printed image generated under the optimal conditions and the maximum deviation conditions. The optimal conditions are: the lens imaging point is exactly at the receiving plane, and the exposure dose is also standardized to 1; and the maximum deviation of the lens imaging plane allowed in this embodiment from the receiving plane is plus or minus 25nm, and the exposure dose range is 0.98 to 1.02; evaluate and obtain a new loss function value F i , update the loss function gradient Gi ;

[0081] Step 3.6 Calculate the new boundary evolution velocity v i ;

[0082] Step 3.7 is used to judge that if the maximum absolute value of the velocity of each point on the plane is less than the set threshold, the threshold is 0.015, then it is considered that convergence is complete and the mask M is output. * Otherwise, return to step 3.1 and proceed to the next cycle.

[0083] The lithography kernel function and image evaluation module used in this embodiment are provided by the public ICCAD 2013 CAD competition organizing committee (Banerjee S, Li Z, Nassif S R. ICCAD-2013 CAD contest in mask optimization and benchmark suite [C] / / 2013 IEEE / ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 2013: 271-274.).

[0084] pass Figure 2 As shown, the mask obtained by the optimization method of the present invention is closer to the target mask and has a clearer boundary.

Claims

1. An optical proximity correction mask optimization method capable of reducing mask complexity, characterized in that: The steps include: Step 1: Input target image Z t , lithography core h1,…,h k and the corresponding weight coefficients μ1,…,μ k ; Step 2, initialization; Step 2.1, the mask is initialized to the same size as the target image Z t The same shape, and calculate the initial level set function φ0, calculate the geometric gradient of φ0 Step 2.2, after lithography simulation, the initial loss function F0 is obtained, and the initial loss function gradient G0 is calculated; F=αF epe +βF pvb +γF geo Among them, F is the optimization loss function, α, β, and γ are the weights of the EPE loss function, PVBand loss function, and geometric complexity loss function respectively; F is initialized to F0; F epe =∑EPE violations Among them, F epe is the EPE loss function, (x, y) is the point on the mask plane, D is the vertical distance between the target contour measurement point and the printed image contour, and th EPE is the EPE meter error threshold; Among them, F pvb is the PVBand loss function, Z k is the printed image generated under the kth condition, Z t is the target graph, N p is the number of different lithography conditions considered; Step 2.3, calculate the initial boundary evolution speed Step 3, enter the i-th loop: Step 3.1 Calculate the boundary evolution time step Δt i ; Step 3.2 Calculate the change in the level set function: Δφ i (x,y)=(v i +λ v v i-1 )Δt i ; Step 3.3 Update the level set function: φ i (x,y)=φ i-1 (x,y)+Δφ i (x,y); Step 3.4 Each point on the plane is calculated according to φ i The sign of (x, y) determines the value of the mask matrix; if it is a positive number, the mask matrix value is 1, which means it is inside the mask, otherwise it is 0, which means it is outside the mask; Step 3.5: Perform lithography simulation on the updated mask to obtain the printed images generated under the optimal conditions and the maximum deviation conditions. The optimal condition is that the lens imaging point is exactly at the receiving plane, and the exposure dose is also standardized to 1; the maximum deviation condition is that the lens imaging plane can deviate from the receiving plane by a maximum of plus or minus 25nm, and the exposure dose range is 0.98 to 1.02; evaluate and obtain a new loss function value F i , update the loss function gradient G i ; Step 3.6 Calculate the new boundary evolution velocity v i ; Step 3.7 is used to judge that if the maximum absolute value of the velocity of each point on the plane is less than the set threshold, it is considered that convergence is complete and the mask M is output. * Otherwise, return to step 3.1 and proceed to the next cycle.

2. The optical proximity correction mask optimization method capable of reducing mask complexity according to claim 1, characterized in that: Level set function φ(x,y) In the level set method, the plane is divided into three regions by the boundary of the figure: interior, exterior, and boundary line; the level set function is the central function that characterizes the geometric information of the plane: Where d(x,y) is the Euclidean distance from the point (x,y) on the plane to the boundary; The boundary evolution rate function v is composed of the gradient of the loss function G and the geometric gradient of the level set function Decide: in The iteration of the level set function depends on the boundary evolution velocity v and the time step Δt, which is determined by the conjugate gradient descent method: Δφ=(v(x,y)+λ v v f (x,y))Δt where v f is the evolution speed of the last iteration process, λ v The calculation of depends on the type of conjugate gradient method.

3. The optical proximity correction mask optimization method capable of reducing mask complexity according to claim 2, characterized in that: Step 3.1 Calculate the boundary evolution time step Δt i ; The piecewise Euler time step algorithm is used, and the step parameter λ is set t ,Time step calculation: Where σ is a parameter between 0 and 1, which is used to control the numerical change of evolution update.

4. The optical proximity correction mask optimization method capable of reducing mask complexity according to claim 2, characterized in that: Proof of optimizing the gradient calculation of the loss function for mask information: where h k and μ k is the lithography core and the corresponding weight coefficient, Yes k The conjugate transpose of .

5. The optical proximity correction mask optimization method capable of reducing mask complexity according to claim 1, characterized in that: In step 3.5, the optimal condition is that the lens imaging point is exactly at the receiving plane and the exposure dose is also standardized to 1; the maximum deviation condition is the maximum deviation range set according to the optimal condition.

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