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

• US 8,682,059 B2
• Filed: 05/17/2013
• Issued: 03/25/2014
• Est. Priority Date: 11/24/2008
• Status: Active Grant

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: ASML Netherlands BV (ASML Holding NV)
• Inventors: Cao, Yu, Chen, Luoqi, Bruguier, Antoine Jean, Shao, Wenjin
• Primary Examiner(s): NGUYEN, SANG H
• Application Number:
  US13/896,805
• Publication Number:
  US 20130251237A1
• Time in Patent Office: 312 Days
• Field of Search: 382/144, 382/141, 382/145, 382/149, 716/4, 716/19, 716/20, 716/21, 703/2, 703/5, 703/13, 430/5, 430/30
• US Class Current: 382/144
• CPC Class Codes: G03F 7/705 Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
• CPC Class Codes: G03F 7/70666 Aerial image, i.e. measuring the image of the patterned exposure light at the image plane of the projection system
• CPC Class Codes: G03F 7/70675 Latent image, i.e. measuring the image of the exposed resist prior to development
• CPC Class Codes: G06T 3/10 Selection of transformation methods according to the characteristics of the input images
• CPC Class Codes: G06T 7/0004 Industrial image inspection

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.

Claims

1. A method implemented by a computer processor for determining an image of a mask pattern in a resist coated on a substrate, the method comprising:

determining, by the computer processor, an aerial image of the mask pattern at substrate level; and

transforming, by the computer processor, the aerial image into a resist image that is representative of the image of the mask pattern in the resist, the aerial image being transformed into the resist image using a model that includes at least two convolution kernels, the transforming including convolving the aerial image with the at least two convolution kernels, wherein the at least two convolution kernels are selected such that the transformation of the aerial image into the resist image has the properties of rotational and mirror symmetry conservation.

2. The method of claim 1, wherein the convolution kernels are orthogonal kernels.

3. The method of claim 2, wherein the convolution kernels are solutions of a two dimensional quantum harmonic oscillator.

4. The method of claim 1, wherein the resist image is represented by the following equation:

5. The method of claim 1, wherein the model includes a bilinear term that is the product between a first term and a second term, the first term corresponding to the convolution of the aerial image with a first orthogonal convolution kernel and the second term corresponding to the convolution of the aerial image with a second orthogonal convolution kernel.

6. The method of claim 1, wherein the computer processor comprises FPGA hardware.

7. The method of claim 1, wherein the computer processor comprises GPU-based hardware.

8. A non-transitory computer program product having machine executable instructions, the instructions being executable by a machine to perform a method for determining an image of a mask pattern in a resist coated on a substrate, the method comprising:

determining an aerial image of the mask pattern at substrate level; and

transforming the aerial image into a resist image that is representative of the image of the mask pattern in the resist, the aerial image being transformed into the resist image using a model that includes at least two convolution kernels, the transforming including convolving the aerial image with the at least two convolution kernels, wherein the at least two convolution kernels are selected such that the transformation of the aerial image into the resist image has the properties of rotational and mirror symmetry conservation.

9. The computer program product of claim 8, wherein the convolution kernels are orthogonal kernels.

10. The computer program product of claim 9, wherein the convolution kernels are solutions of a two dimensional quantum harmonic oscillator.

11. The computer program product of claim 8, wherein the resist image is represented by the following equation:

12. The computer program product of claim 8, wherein the model includes a bilinear term that is the product between a first term and a second term, the first term corresponding to the convolution of the aerial image with a first orthogonal convolution kernel and the second term corresponding to the convolution of the aerial image with a second orthogonal convolution kernel.

13. The computer program product of claim 8, wherein the transforming is carried out using a FPGA hardware.

14. The computer program product of claim 8, wherein the transforming is carried out using GPU-based hardware.