Lithographic mask functions to model the incident angles of a partially coherent illumination

• US 10,656,528 B1
• Filed: 01/02/2019
• Issued: 05/19/2020
• Est. Priority Date: 10/05/2018
• Status: Active Grant

• Current Assignee: Synopsys Incorporated
• Original Assignee: Synopsys Incorporated
• Inventors: Liu, Peng
• Primary Examiner(s): Gordon, Steven Whitesell
• Application Number:
  US16/238,444
• Time in Patent Office: 503 Days
• 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 1/76 Patterning of masks by imaging
• CPC Class Codes: G03F 7/70091 Illumination settings, i.e. intensity distribution in the pupil plane or angular distribution in the field plane; On-axis or off-axis settings, e.g. annular, dipole or quadrupole settings; Partial coherence control, i.e. sigma or numerical aperture [NA]
• CPC Class Codes: G03F 7/70158 Diffractive optical elements
• CPC Class Codes: G03F 7/705 Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions

Abstract

In the embodiments disclosed herein, an approach based on a mask function M is disclosed. This approach meets the requirement of the Hopkins model and at the same time incorporates the incident angle effects of a given partially coherent illumination. The new mask function M is referred to as a partially coherent mask function (PCMF). In the embodiments disclosed herein, the incident angle effects of individual source points of a given partially coherent illumination are removed from the mask function M and incorporated into a source function G. As a result, use of the partially coherent mask function M does not require an integration over individual plane waves in the illumination, as would be the case with a rigorous mask function M. Therefore, the Hopkins model can be used with partially coherent mask function M and at the same time capture the incident angle effects.

Claims

1. A method implemented on a computer system, the computer system executing instructions to effect the method for approximating the effect of a lithographic mask on illumination produced by a partially coherent source, the method comprising:

pre-calculating a source function G that is the same for different mask layouts and accounts for partial coherence of the illumination, wherein the source function G integrates effects of individual planes waves in the illumination;

representing the mask layout using a partially coherent mask function M that is specific for the illumination and calculated as a function of the source function G; and

using the partially coherent mask function M to calculate the effect of the mask on the illumination, wherein the calculation using the partially coherent mask function M does not integrate over individual plane waves in the illumination.

2. The computer-implemented method of claim 1 further comprising:

revising the mask layout based on the calculated effect of the mask on the illumination; and

using the revised mask layout in a process to design and manufacture the lithographic mask.

3. The computer-implemented method of claim 1 wherein the partially coherent mask function M is used to calculate a full-chip lithography simulation.

4. The computer-implemented method of claim 1 further comprising:

calculating partially coherent mask functions M for different types of mask primitives;

wherein representing the mask layout comprises decomposing the mask layout into the mask primitives; and

calculating the effect of the mask on the illumination comprises, based on the decomposition, using the partially coherent mask functions M for the mask primitives to calculate the effect of the mask on the illumination.

5. The computer-implemented method of claim 4 further comprising:

storing the partially coherent mask functions M for the different types of mask primitives in a lookup table, wherein calculating the effect of the mask comprises retrieving the stored partially coherent mask functions M from the lookup table.

6. The computer-implemented method of claim 4 wherein partially coherent mask functions M are calculated for mask primitives that include edges, corners, edge-edge pairs, and corner-corner pairs.

7. The computer-implemented method of claim 1 further comprising:

based on the calculated effect of the mask on the illumination, predicting an aerial image produced by the mask.

8. The computer-implemented method of claim 1 wherein the source function G also include spatial frequency filter effects of an entrance pupil for projection optics that are downstream of the mask.

9. The computer-implemented method of claim 1 wherein the partially coherent mask function M is independent of projection optics that are downstream of the mask.

10. The computer-implemented method of claim 1 wherein a rigorous imaging model is based on a sum of terms that include a rigorous mask function M and the sum is over individual plane waves;

and the partially coherent mask function M approximates the rigorous imaging model by pulling the mask function M outside the sum.

11. The computer-implemented method of claim 1 wherein the partially coherent mask function M take the tensor form

12. The computer-implemented method of claim 11 wherein the components M1 of the partially coherent mask function M are defined by

M1*_γ

α

({right arrow over (k)}₁)M1<sub>γ

β</sub>

({right arrow over (k)}₂)G<sub>α

,β</sub>

({right arrow over (k)}₁,{right arrow over (k)}₂)=H<sub>α

,β

,γ</sub>

({right arrow over (k)}₁,{right arrow over (k)}₂)

G<sub>α

,β</sub>

({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

_sQ({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,α

E_s,β

H<sub>α

,β

,γ</sub>

({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

_sM*<sub>γ

α</sub>

({right arrow over (k)}₁,s)M<sub>γ

β</sub>

({right arrow over (k)}₂,s)Q({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,α

E_s,β

where M is a rigorous mask function based on a rigorous imaging model;

E is an incident plane wave polarization from the illumination;

k represents a Fourier frequency;

superscript * indicates complex conjugate;

subscripts α

, β

, γ

denote x or y polarization;

the summation Σ

_s is over individual incident plane waves; and

Q represents spatial frequency filter effects of an entrance pupil for projection optics that is downstream of the mask.

13. The computer-implemented method of claim 1 wherein the partially coherent mask function M allows for differences in x and y polarizations and also allows for cross-polarization effects between x and y polarizations.

14. The computer-implemented method of claim 1 wherein the partially coherent mask function M take the tensor form

15. The computer-implemented method of claim 14 wherein the components M2 of the partially coherent mask function M are defined by

M2*_γ

γ

({right arrow over (k)}₁)M2<sub>γ

γ</sub>

({right arrow over (k)}₂)G_γ

({right arrow over (k)}₁,{right arrow over (k)}₂)=H_γ

({right arrow over (k)}₁,{right arrow over (k)}₂)

G_γ

({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

_sQ({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,γ

E_s,γ

H_γ

({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

<sub>α

,β

,s</sub>M*<sub>γ

α</sub>

({right arrow over (k)}₁,s)M<sub>γ

β</sub>

({right arrow over (k)}₂,s)Q({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,α

E_s,β

where M is a rigorous mask function based on a rigorous imaging model;

E is an incident plane wave polarization from the illumination;

k represents a Fourier frequency;

superscript * indicates complex conjugate;

subscripts α

, β

, γ

denote x or y polarization;

the summation Σ

<sub>α

,β

,s</sub> is over individual incident plane waves and polarizations α

, β

; and

Q represents spatial frequency filter effects of an entrance pupil for projection optics that is downstream of the mask.

16. The computer-implemented method of claim 1 wherein the partially coherent mask function M does not allow for cross-polarization effects between x and y polarizations but does allow for differences in x and y polarizations.

17. The computer-implemented method of claim 1 wherein the partially coherent mask function M take the tensor form

18. The computer-implemented method of claim 17 wherein the component M3 of the partially coherent mask function M is defined by

M3*({right arrow over (k)}₁)M3({right arrow over (k)}₂)G({right arrow over (k)}₁,{right arrow over (k)}₂)=H({right arrow over (k)}₁,{right arrow over (k)}₂)

G({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

<sub>γ

,s</sub>Q({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,γ

E_s,γ

H({right arrow over (k)}₁,{right arrow over (k)}₂)=Σ

<sub>γ

,α

,β

,s</sub>M*<sub>γ

α</sub>

({right arrow over (k)}₁,s)M<sub>γ

β</sub>

({right arrow over (k)}₂,s)Q({right arrow over (k)}₁,{right arrow over (k)}₂,{right arrow over (k)}_s)E*_s,α

E_s,β

where M is a rigorous mask function based on a rigorous imaging model;

E is an incident plane wave polarization from the illumination;

k represents a Fourier frequency;

superscript * indicates complex conjugate;

subscripts α

, β

, γ

denote x or y polarization;

the summation Σ

<sub>γ

,α

,β

,s</sub> is over individual incident plane waves and polarizations α

, β

, γ

; and

Q represents spatial frequency filter effects of an entrance pupil for projection optics that is downstream of the mask.

19. The computer-implemented method of claim 1 wherein the partially coherent mask function M does not allow for differences in x and y polarizations or for cross-polarization effects between x and y polarizations.

20. An EDA tool for approximating the effect of a lithographic mask on illumination produced by a partially coherent source, comprising:

a data store that stores a design for the lithographic mask, and that further stores pre-calculated partially coherent mask functions M for different types of mask primitives;

wherein the partially coherent mask functions M are specific for the illumination and calculated as a function of a source function G, and the source function G is the same for different mask primitives and accounts for partial coherence of the illumination and integrates effects of individual planes waves in the illumination;

a computer system in communication with the data store, the computer system configured to;

decompose the mask layout into the mask primitives; and

based on the decomposition, use pre-calculated partially coherent mask functions M for the mask primitives to calculate the effect of the mask on the illumination, wherein the calculations using the partially coherent mask functions M does not integrate over individual plane waves in the illumination.