# US 12,761,545 B2 · System for optimizing OPC lithography model parameters

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- Number: US 12,761,545 B2
- Document ID: US12761545B2
- Status: Granted
- Kind: B2
- Application number: 18/342,319
- Filed: 2023-06-27
- Published: 2024-06-06
- Granted: 2026-10-13
- Earliest claimed: 2022-12-05
- Assignees: Shanghai Huali Integrated Circuit Corporation
- Applicants: Shanghai Huali Integrated Circuit Corporation
- Inventors: Zhenbin Wang
- Web page: https://patentgrep.com/patent/US12761545B2

## CPC

- G03F 1/36: Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes
- G06F 30/398: Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM] (optical proximity correction [OPC] design processes G03F1/36)
- G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

The present application discloses a method for optimizing OPC lithography model parameters. Preliminary suboptimal parameter combinations in proximity to a plurality of local minima of a lens beam focus BF and defocus start DS are quickly found by means of a random direction search method; and then an optimal parameter combination of the lens beam focus BF and defocus start DS is finally obtained on the basis of the suboptimal parameter combinations by means of a precise search method. An optimal parameter solution can be found quickly by combining the random direction search method and the precise search method, without artificially configuring an initial search point. Moreover, the algorithm has a high convergence rate and strong robustness, and can quickly and precisely obtain parameters such as the lens beam focus BF and defocus start DS in modeling of an OPC lithography model.

## Claims

### Claim 1

A system for optimizing OPC lithography model parameters, comprises a parameter configuration module, a random direction method module, and a precise search method module; wherein
the parameter configuration module is used to configure an objective function J(u) of a lithography model, as well as a parameter constraint condition and a convergence condition;
the random direction method module finds preliminary suboptimal parameter combinations in proximity to a plurality of local minima of a lens beam focus BF and defocus start DS of the OPC lithography model by means of a random direction search method; and
the precise search method module obtains, by means of a precise search method, an optimal parameter combination of the lens beam focus BF and defocus start DS of the OPC lithography model on the basis of the suboptimal parameter combinations found by the random direction method module,
the objective function J(u) of the lithography model is:
J
⁢
(
u
)
=
1
2
⁢
n
⁢
∑
i
=
1
n
⁢
wt
i
*
[
T
⁡
(
x
i
,
y
i
,
BP
,
DS
)
-
CD
⁡
(
x
i
,
y
i
)
]
2
∑
I
=
1
n
⁢
wt
i
,
u
=
[
BF
,
DS
]
T
;
T(xi, yi, BF, DS) is a CD value estimated by means of an optical imaging model, CD(xi, yi) is a gauge calibration CD value obtained after exposure performed by an actual lithography system, Wti is a weight coefficient, the value of which is in positive correlation with the importance of the CD value, and n is the number of all feature patterns;
the parameter constraint condition of the objective function J(u) of the OPC lithography model comprises:
Gj(u)≤0,j∈I;
G1(u)=a1−BF,G2(u)=BF−b1; and
G3(u)=a2−DS,G4(u)=DS−b2;
a1 is a BF lower limit value, b1 is a BF upper limit value, a2 is a DS lower limit value, and b2 is a DS upper limit value, i.e., a1≤BF≤b1, and a2≤DS≤b2; a1, b1, a2, and b2 are determined by a lithography machine lens projection system and the thickness of a photoresist; and
the convergence condition of the objective function J(u) of the OPC lithography model comprises a random direction error ε1 and a precise search method error ε2, satisfying 0≤ε2<ε1<1.

### Claim 2 (depends on 1)

The system for optimizing OPC lithography model parameters according to claim 1, wherein
the random direction method module finds a feasible direction of a steepest descent in an objective function value on the basis of randomly generated feasible points and feasible directions of the lens beam focus BF and defocus start DS that satisfy the constraint condition, performs a line search to obtain a search step and thus obtain a next feasible point, then repeats the previous operation until a feasible point satisfying an error condition is finally found, and outputs the feasible point as a precise search initial feasible point to the precise search method module; and
the precise search method module converts the objective function of the lithography model into a sequential quadratic programming SQP objective function on the basis of the precise search initial feasible point, and solves the sequential quadratic programming SQP objective function according to the parameter constraint condition and the convergence condition, so as to obtain optimal lens beam focus BF parameter and defocus start DS parameter of the OPC lithography model.

### Claim 3 (depends on 2)

The system for optimizing OPC lithography model parameters according to claim 2, wherein
an operation process of the random direction method module comprises the following steps:
(1) configuring random direction method calculation precision ε1;
(2) randomly selecting a feasible point as a random initial point u0;
(3) generating k n-dimensional random unit vectors ej (j=1, 2, . . . , k), k being a positive integer;
(4) taking an experimental step a0, and calculating k random points uj;
(5) finding a feasible random points uL from the k random points, and generating a feasible search direction d, d=uL−u0;
(6) from the random initial point u0, performing iteration using the feasible search direction d and the experimental a0 until a new point u that satisfies all search conditions and has no descent in the objective function value is found; and
(7) if the convergence condition satisfies |J(uL)−J(u0)|<ε1, ending the iteration, or otherwise, assigning the value of uL to u0, i.e., u0←uL, and returning to step (2).

### Claim 4 (depends on 3)

The system for optimizing OPC lithography model parameters according to claim 3, wherein
a process of generating the random initial point u0 is:
first generating two pseudo random numbers q1 and q2 within an interval (0, 1),
BF0=a1+q1*(b1−a1),DS0=a2+q2*(b2−a2), and u0=[BF0,DS0]T.

### Claim 5 (depends on 3)

The system for optimizing OPC lithography model parameters according to claim 3, wherein
a method of generating the k n-dimensional random unit vectors ej in step (3) is:
obtaining the random unit vector ej on the basis of a pseudo random number rij generated within an interval (−1,1),
e
j
=
1
∑
i
=
1
n
⁢
(
r
i
j
)
2
[
r
1
j
r
2
j
…
r
n
j
]
.

### Claim 6 (depends on 3)

The system for optimizing OPC lithography model parameters according to claim 3, wherein
the precise search method module obtains, on the basis of a current iteration feasible point uk using an SQP algorithm, a feasible search direction dk and a corresponding Lagrange multiplier λj:
making:
∇
J
⁡
(
u
k
)
T
⁢
d
k
+
1
2
⁢
d
k
T
⁢
H
k
⁢
d
k
+
∑
j
∈
I
λ
j
⁢
∇
G
j
(
u
k
)
T
⁢
d
k
minimum, and
Gj(uk)+∇Gj(uk)Tdk≤0,j∈I;
wherein Hk is a second derivative matrix
∇
uu
2
L
⁡
(
u
k
,
λ
k
)
of a Lagrange function
L
⁡
(
u
,
λ
)
=
J
⁢
(
u
)
+
∑
j
∈
I
⁢
λ
j
⁢
G
j
(
u
)
with respect to u, a next iteration point is uk+1=uk+dk, and λj is a Lagrange constant.

### Claim 7 (depends on 6)

The system for optimizing OPC lithography model parameters according to claim 6, wherein the SQP algorithm used by the precise search method module comprises the following steps:
S0. providing an initial point u0 and an initial symmetrical positive definite matrix H0, k:=0;
S1. making
∇
J
⁢
(
u
k
)
T
⁢
d
k
+
1
2
⁢
dk
T
⁢
H
k
⁢
d
k
+
∑
j
∈
I
⁢
λ
j
⁢
∇
G
j
(
u
k
)
T
⁢
d
k
minimum at uk, Gj(uk)+∇Gj(uk)Tdk≤0, j∈I, and performing solution to obtain dk;
S2. uk+1=uk+μkdk, a step μk being obtained by a line search;
S3. correcting Hk to obtain Hk+1, such that Hk+1 is kept symmetrically positively definite; and
S4. k:=k+1, returning to step S1.

### Claim 8 (depends on 1)

The system for optimizing OPC lithography model parameters according to claim 1, further provided with:
an optimal parameter optimal solution output module;
the optimal parameter optimal solution output module being used to output a final optimal parameter combination of the lens beam focus BF and defocus start DS of the OPC lithography model.

### Claim 9 (depends on 8)

The system for optimizing OPC lithography model parameters according to claim 8, wherein
the optimal parameter optimal solution output module simultaneously outputs optimal parameter combinations of the lens beam focus BF and defocus start DS of the OPC lithography model with the values of the objective function J(u) sorted in an ascending order.