HARMONIC RESIST MODEL FOR USE IN A LITHOGRAPHIC APPARATUS AND A DEVICE MANUFACTURING METHOD

• US 20100128969A1
• Filed: 11/24/2009
• Published: 05/27/2010
• Est. Priority Date: 11/24/2008
• Status: Active Grant

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: Brion Technologies Incorporated (ASML Holding NV)
• Inventors: CAO, Yu, CHEN, Luoqi, SHAO, Wenjin, Bruguier, Antoine Jean
• Granted Patent: US 8,447,095 B2
• Time in Patent Office: Days
• 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 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

convolving the aerial image with a number of orthogonal convolution kernels to determine a resist image that is representative of the mask pattern in the resist.

2. The method of claim 1, wherein convolution kernels are orthogonal solutions of a two dimensional quantum harmonic oscillator.

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

4. The method of claim 3, wherein the fitting coefficient are iteratively adjusted or solved using linear least square methods to reduce a difference between a critical dimension value of the resist image and a critical dimension target value.

5. The method of claim 4, wherein the fitting coefficients are iteratively adjusted using a Tikhonov-Wahba regression in order to regularize and stabilize the fitting.

6. The method of claim 1, further comprising converting the resist image into a critical dimension value;

comparing the critical dimension value with a target critical dimension value; and

adjusting fitting coefficients to reduce a difference between the critical dimension value and the target critical dimension value.

7. The method of claim 1, wherein the convolving includes convolving the aerial image with a plurality of orthogonal convolution kernels that form a complete basis.

8. The method of claim 1, wherein the aerial and resist images are two dimensional bitmaps.

9. The method of claim 8, wherein the convolving includes convolving each pixel of the two dimensional bitmap of the aerial image with a number of orthogonal convolution kernels to determine the two dimensional bitmap of the resist image.

10. The method of claim 1, wherein a model of the resist image 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.

11. The method of claim 10, wherein the first and second orthogonal convolution kernels are different.

12. The method of claim 1, wherein the aerial image corresponds to the image of the mask pattern projected on the substrate through a projection system.

13. The method of claim 1, wherein the convolving is carried out using FPGA or GPU-based hardware acceleration.

14. 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.

15. The method of claim 14, wherein the convolution kernels are orthogonal kernels.

16. The method of claim 15, wherein the convolution kernels are solutions of a two dimensional quantum harmonic oscillator.

17. The method of claim 14, wherein the resist image is represented by the following equation:

18. The method of claim 14, 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.

19. The method of claim 14, wherein the transforming is carried out using a FPGA hardware.

20. A computer 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

convolving the aerial image with at least two orthogonal convolution kernels to determine a resist image that is representative of the image of the mask pattern in the resist.

21. The computer product of claim 20, wherein the convolving is carried out using a FPGA hardware.

22. A computer 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.

23. The computer product of claim 22, wherein the transforming is carried out using FPGA or GPU-based hardware.