Lithography model for 3D resist profile simulations

• US 9,235,662 B2
• Filed: 02/01/2013
• Issued: 01/12/2016
• Est. Priority Date: 02/03/2012
• Status: Active Grant

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: ASML Netherlands BV (ASML Holding NV)
• Inventors: Liu, Peng
• Primary Examiner(s): Thangavelu, Kandasamy
• Application Number:
  US13/757,472
• Publication Number:
  US 20130204594A1
• Time in Patent Office: 1,075 Days
• Field of Search: 703/13, 355/53, 355/30
• US Class Current: 1/1
• 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 7/70625 Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness
• 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: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30

Abstract

Described herein is a method for simulating a three-dimensional spatial intensity distribution of radiation formed within a resist layer on a substrate resulting from an incident radiation, the method comprising: calculating an incoherent sum of forward propagating radiation in the resist layer and backward propagating radiation in the resist layer; calculating an interference of the forward propagating radiation in the resist layer and the backward propagating radiation in the resist layer; and calculating the three-dimensional spatial intensity distribution of radiation from the incoherent sum and the interference.

Claims

1. A method for simulating a three-dimensional spatial intensity distribution of radiation formed within a resist layer on a substrate resulting from an incident radiation, the method comprising:

determining, using a computer system, an incoherent sum of forward propagating radiation in the resist layer and backward propagating radiation in the resist layer;

determining, using the computer system, an interference of the forward propagating radiation in the resist layer and the backward propagating radiation in the resist layer; and

determining, using the computer system, the three-dimensional spatial intensity distribution of radiation from the incoherent sum and the interference.

2. The method of claim 1, wherein the incoherent sum is free of a standing wave.

3. The method of claim 1, further comprising determining the interference by multiplying the incoherent sum and an interference factor, wherein the interference factor is a function of a depth into the resist layer.

4. The method of claim 3, wherein the interference factor is independent from a mask used in the lithographic projection apparatus to pattern the incident radiation.

5. The method of claim 1, wherein the interference factor is independent from directions of propagation of the forward propagating radiation and the backward propagating radiation.

6. The method of claim 1, wherein the forward propagating radiation and the backward propagating radiation form a standing wave.

7. The method of claim 1, further comprising approximating the incoherent sum by expanding the incoherent sum into a plurality of terms of a Taylor series of a depth into the resist layer.

8. The method of claim 7, wherein the incoherent sum is expanded to a quadratic term of the Taylor series of the depth into the resist layer.

9. The method of claim 1, wherein determining the incoherent sum comprises calculating a transmission cross coefficient (TCC).

10. The method of claim 9, wherein the TCC is calculated from a projection optics function.

11. The method of claim 10, wherein the projection optics function is a function of distortions of the incident radiation caused by the resist layer.

12. The method of claim 1, wherein determining the incoherent sum comprises calculating three transmission cross coefficients at at least three different depths into the resist layer.

13. The method of claim 1, further comprising computing a three-dimensional resist image formed within the resist layer from the three-dimensional spatial intensity distribution of radiation.

14. The method of claim 13, wherein computing a three-dimensional resist image comprises applying a blur and a threshold to the three-dimensional spatial intensity distribution of radiation and/or wherein computing a three-dimensional resist image comprises using a resist model.

15. The method of claim 14, wherein the resist model comprises calculating a three-dimensional spatial concentration of acid in the resist layer from the three-dimensional spatial intensity distribution of radiation.

16. The method of claim 13, wherein computing a three-dimensional resist image comprises calculating a three-dimensional concentration distribution of a chemical species.

17. The method of claim 16, wherein calculating the three-dimensional concentration distribution of the chemical species comprising comprises determining a diffusion of the chemical species from a two-dimensional concentration distribution of the chemical species at one or more planes in the resist layer.

18. The method of claim 1, wherein the substrate has features in or underlying the resist layer.

19. The method of claim 1, wherein the substrate is free of an anti-reflective coating.

20. A computer program product comprising a non-transitory computer readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of claim 1.

21. The method of claim 1, comprising:

producing a lithographic mask layout that compensates for a patterning defect indicated by the determined three-dimensional spatial intensity distribution of radiation.