Method of modeling a mask having patterns with arbitrary angles

• US 10,466,586 B2
• Filed: 08/02/2017
• Issued: 11/05/2019
• Est. Priority Date: 11/29/2016
• Status: Active Grant

• Current Assignee: Taiwan Semiconductor Manufacturing Company Limited
• Original Assignee: Taiwan Semiconductor Manufacturing Company Limited
• Inventors: Lai, Chien-Jen, Zhou, Xin, Peng, Danping
• Primary Examiner(s): Tat, Binh C
• Application Number:
  US15/666,775
• Publication Number:
  US 20180149967A1
• Time in Patent Office: 825 Days
• Field of Search: 716 50- 56
• CPC Class Codes: G03F 1/36 Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes
• CPC Class Codes: G03F 1/70 Adapting basic layout or design of masks to lithographic process requirements, e.g., second iteration correction of mask patterns for imaging
• CPC Class Codes: G03F 7/70283 Mask effects on the imaging process
• CPC Class Codes: G03F 7/70441 Optical proximity correction [OPC]
• CPC Class Codes: G03F 7/705 Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions

Abstract

A mask layout containing a non-Manhattan pattern is received. The received mask layout is processed. An edge of the non-Manhattan pattern is identified. A plurality of two-dimensional kernels is generated based on a set of processed pre-selected mask layout samples. The two-dimensional kernels each have a respective rotational symmetry. The two-dimensional kernels are applied to the edge of the non-Manhattan pattern to obtain a correction field for the non-Manhattan pattern. A thin mask model is applied to the non-Manhattan pattern. The thin mask model contains a binary modeling of the non-Manhattan pattern. A near field of the non-Manhattan pattern is determined by applying the correction field to the non-Manhattan pattern having the thin mask model applied thereon. An optical model is applied to the near field to obtain an aerial image on a wafer. A resist model is applied to the aerial image to obtain a final resist image on the wafer.

Claims

1. A method, comprising:

receiving a mask layout;

generating a two-dimensional kernel based on a set of pre-selected mask layout samples;

applying the two-dimensional kernel to the mask layout to obtain a correction field for the mask layout, wherein the applying the two-dimensional kernel includes;

building an orientation map for the mask layout, the orientation map including an orientation angle φ

for each edge segment of an edge of the mask layout, and

applying the two-dimensional kernel to the edge according to the orientation map;

determining a near field of the mask layout based at least in part on the correction field;

evaluating a simulated device layout based on the near field of the mask layout against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

2. The method of claim 1, wherein the mask layout contains a non-Manhattan pattern, and wherein the generating, the applying the two-dimensional kernel to the mask layout, the determining, and the evaluating are performed using the non-Manhattan pattern with a mask design system that is configured to manipulate an integrated circuit design layout according to a variety of design rules, wherein the variety of design rules includes the design rule.

3. The method of claim 1, wherein the two-dimensional kernel is described using polar coordinates.

4. The method of claim 2, wherein the building the orientation map for the mask layout includes identifying the edge by taking a gradient of the non-Manhattan pattern;

and building the orientation map by determining the orientation angle φ

of each edge segment according to a normal vector of the edge segment.

5. The method of claim 4, wherein the applying the two-dimensional kernel according to the orientation map includes rotating the two-dimensional kernel according to the orientation angle for the edge segment;

and applying the rotated two-dimensional kernel to the edge segment.

6. The method of claim 1, further comprising:

processing the mask layout, wherein the two-dimensional kernel is applied to the processed mask layout.

7. The method of claim 1, further comprising:

applying a thin mask model to the mask layout, and wherein the near field is determined as a function of the correction field of the mask layout having the thin mask model applied thereon.

8. The method of claim 1, wherein the generating the two-dimensional kernel includes generating the two-dimensional kernel f(r, θ

) as a function of a radial coordinate r and an angular coordinate θ

, and as a sum of a plurality of components including at least h₀ (r) and h₁ (r) e^iθ

, and

wherein the applying the two-dimensional kernel includes, for each edge segment having the orientation angle φ

, applying a rotated two-dimensional kernel, the rotated two-dimensional kernel including the two-dimensional kernel f (r, θ

) convolved with a function of the orientation angle φ and

including at least h₀ (r) and h₁ (r) e^iθ

e<sup>−

iφ</sup>

.

9. The method of claim 1, wherein the generating further includes:

building a set of orientation maps, each associated with one sample of the set of pre-selected mask layout sample;

applying a thin mask model to a first sample of the set of pre-selected mask layout samples to obtain a thin mask near field;

computing a rigorous near field of the first sample;

computing a difference between the rigorous near field and the thin mask near field; and

regressing the difference against the set of orientation maps.

10. A method, comprising:

receiving a mask layout, the mask layout containing a non-Manhattan pattern;

processing the mask layout;

generating a two-dimensional kernel based on a set of processed pre-selected mask layout samples, wherein the two-dimensional kernels each have a respective rotational symmetry;

applying the two-dimensional kernel to an edge segment of the non-Manhattan pattern having an orientation angle φ

to obtain a correction field for the non-Manhattan pattern represented by a modified kernel, wherein the modified kernel includes e<sup>−

iφ</sup>

; and

determining a near field of the non-Manhattan pattern based at least in part on the correction field;

obtaining a final resist image of the non-Manhattan pattern based on the near field;

evaluating the final resist image against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

11. The method of claim 10, wherein the applying the two-dimensional kernel comprises identifying the edge segment of the non-Manhattan pattern by taking a gradient of the non-Manhattan pattern and identifying the orientation angle φ

according to a normal vector of the edge segment.

12. The method of claim 10, wherein the processing the mask layout comprises performing rasterization or anti-aliasing filtering to the mask layout.

13. The method of claim 10, further comprising:

applying a thin mask model to the mask layout, the thin mask model containing a binary modeling of the non-Manhattan pattern, wherein the near field is determined by combining the correction field and the mask layout having the thin mask model applied thereon.

14. The method of claim 10, wherein the two-dimensional kernel includes components each having a rotational symmetry, wherein the generating includes building a pattern edge by taking a gradient of each of the set of processed pre-selected mask layout samples, and building an orientation map using a normal vector of a segment of the pattern edge.

15. The method of claim 14, wherein each of the components is a function independent of the normal vector.

16. The method of claim 10, wherein the two-dimensional kernel includes components h₀ (r) and h₁ (r) e^iθ

, wherein r is a radial coordinate, and θ

is an angular coordinate, and wherein the correction field includes h₀ (r) and h₁ (r) e^iθ

e<sup>−

iθ</sup>

.

17. A method, comprising:

generating a two-dimensional kernel, wherein the generating includes;

receiving a processed pre-selected mark layout sample having a first non-Manhattan pattern;

identifying a first set of edges of the first non-Manhattan pattern and an orientation angle for each of the first set;

generating the two-dimensional kernel as a first function independent of the orientation angle for the each of the first set;

receiving a mask layout, the mask layout containing a second non-Manhattan pattern;

processing the mask layout;

identifying a second set of edges of the second non-Manhattan pattern and an orientation angle for each of the second set;

applying the two-dimensional kernel to each of the second set by convolving the two-dimensional kernel with a second function of the orientation angle for the each of the second set to obtain a correction field for the second non-Manhattan pattern;

applying a thin mask model to the second non-Manhattan pattern, the thin mask model containing a binary modeling of the second non-Manhattan pattern;

determining a near field of the second non-Manhattan pattern by applying the correction field to the second non-Manhattan pattern having the thin mask model applied thereon;

applying an optical model to the near field to obtain an aerial image on a wafer;

applying a resist model to the aerial image to obtain a final resist image on the wafer;

evaluating the final resist image against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

18. The method of claim 17, wherein the first function includes a plurality of components, each having a respective rotational symmetry and each being independent of the orientation angle for the each of the first set.

19. The method of claim 17, wherein the two-dimensional kernel includes components h₀ (r) and h₁ (r) e^iθ

, wherein r is a radial coordinate, and θ

is an angular coordinate, and wherein the correction field includes h₀ (r) and h₁ (r) e^iθ

e<sup>−

iφ</sup>

.

20. The method of claim 17,

wherein the generating the two-dimensional kernel as the first function includes generating components h₀ (r) and h₁ (r) e^iθ

, r being a radial coordinate, and θ

being an angular coordinate, and

wherein the applying the two-dimensional kernel includes, for each edge segment having an orientation angle φ

, applying a rotated two-dimensional kernel, the rotated two-dimensional kernel includes h₀ (r) and h₁ (r) e^iθ

e<sup>−

iφ</sup>

.