Harmonic resist model for use in a lithographic apparatus and a device manufacturing method

Patent metadata

Field	Value
Publication number	US-8942463-B2
Application number	US-201414224534-A
Country	US
Kind code	B2
Filing date	Mar 25, 2014
Priority date	Nov 24, 2008
Publication date	Jan 27, 2015
Grant date	Jan 27, 2015

Abstract

A method for determining an image of a mask pattern in a resist coated on a substrate, the method including determining an aerial image of the mask pattern at substrate level; and convolving the aerial image with at least two orthogonal convolution kernels to determine a resist image that is representative of the mask pattern in the resist.

First claim

What is claimed is:

1. A method implemented by a computer processor for simulating a resist image, wherein the resist image comprises an image of a portion of a design layout to be lithographically projected onto a resist coated on a substrate, the method comprising:
determining an aerial image of the portion of the design layout at substrate level; and
transforming the aerial image into the resist image by convolving the aerial image with selected convolution kernels having both linear and bilinear terms.

2. The method of claim 1 , wherein the transforming step includes:
selecting the convolution kernels that form a complete basis, covering a vector space of all possible resist images.

3. The method of claim 1 , wherein the transforming step includes:
selecting the convolution kernels that form an orthogonal basis, wherein correlation between the selected convolution kernels is minimal.

4. The method of claim 3 , wherein the selected convolution kernels comprise solutions of a two-dimensional quantum harmonic oscillator.

5. The method of claim 4 , wherein the solutions are based on Laguerre and Whittaker functions that modulate Gaussian kernels and form the orthogonal basis.

6. The method of claim 1 , wherein the transforming step includes:
selecting the convolution kernels to preserve mirror symmetry of the resist image.

7. The method of claim 1 , wherein the transforming step further includes:
selecting the convolution kernels such that a pair of convolution kernels has rotationally-independent bilinear terms, thereby preserving rotational symmetry of the resist image.

8. The method of claim 1 , wherein the simulation of the resist image is based on an empirical model.

9. The method of claim 8 , wherein the bilinear terms in the convolution kernels conceptually approximate chemical reaction-diffusion equations in the empirical model.

10. A non-transitory computer program product having computer executable instructions for a computer processor to perform a method for simulating a resist image, wherein the resist image comprises an image of a portion of a design layout to be lithographically projected onto a resist coated on a substrate, the method comprising:
determining an aerial image of the portion of the design layout at substrate level; and
transforming the aerial image into the resist image by convolving the aerial image with selected convolution kernels having both linear and bilinear terms.

11. The computer program product of claim 10 , wherein the transforming step includes:
selecting the convolution kernels that form a complete basis, covering a vector space of all possible resist images.

12. The computer program product of claim 10 , wherein the transforming step includes:
selecting the convolution kernels that form an orthogonal basis, wherein correlation between the selected convolution kernels is minimal.

13. The computer program product of claim 12 , wherein the selected convolution kernels comprise solutions of a two-dimensional quantum harmonic oscillator.

14. The computer program product of claim 13 , wherein the solutions are based on Laguerre and Whittaker functions that modulate Gaussian kernels and form the orthogonal basis.

15. The computer program product of claim 10 , wherein the transforming step includes:
selecting the convolution kernels to preserve mirror and rotational symmetry of the resist image.

16. The computer program product of claim 15 , wherein the transforming step further includes:
selecting the convolution kernels such that a pair of convolution kernels has rotationally-independent bilinear terms, thereby preserving rotational symmetry of the resist image.

17. The computer program product of claim 10 , wherein the simulation of the resist image is based on an empirical model.

18. The computer program product of claim 17 , wherein the bilinear terms in the convolution kernels conceptually approximate chemical reaction-diffusion equations in the empirical model.

19. A method implemented by a computer processor for simulating an image of a portion of a design layout to be lithographically etched on a substrate, the method comprising:
determining an aerial image of the portion of the design layout at substrate level; and
transforming the aerial image into an etch image by convolving the aerial image with selected convolution kernels, having both linear and bilinear terms, wherein the etch image is representative of the image of the design layout lithographically etched on the substrate.

20. The method of claim 19 , wherein the transforming step includes:
selecting the convolution kernels that form a complete basis, covering a vector space of all possible etch images.

21. The method of claim 19 , wherein the transforming step includes:
selecting the convolution kernels that form an orthogonal basis, wherein correlation between the selected convolution kernels is minimal.

22. The method of claim 21 , wherein the selected convolution kernels comprise solutions of a two-dimensional quantum harmonic oscillator.

23. The method of claim 22 , wherein the solutions are based on Laguerre and Whittaker functions that modulate Gaussian kernels and form the orthogonal basis.

24. The method of claim 19 , wherein the transforming step includes:
selecting the convolution kernels to preserve mirror symmetry of the etch image.

25. The method of claim 19 , wherein the transforming step further includes:
selecting the convolution kernels such that a pair of convolution kernels has rotationally-independent bilinear terms, thereby preserving rotational symmetry of the etch image.

26. The method of claim 19 , wherein the simulation of the etch image is based on an empirical model.

Assignees

• Asml Netherlands Bv

Inventors

• Cao Yu
• Chen Luoqi
• Bruguier Antoine Jean
• Shao Wenjin

Classifications

• G03F7/705 Primary

  Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions · CPC title

• G06T7/0004

  Industrial image inspection · CPC title

• G06T3/0056 Primary

  Physics · mapped topic

• G03F7/70675

  Latent image, i.e. measuring the image of the exposed resist prior to development · CPC title

• G03F7/70666

  Aerial image, i.e. measuring the image of the patterned exposure light at the image plane of the projection system · CPC title