System and method for calculating aerial image of a spatial light modulator

• US 7,889,411 B2
• Filed: 05/22/2008
• Issued: 02/15/2011
• Est. Priority Date: 04/30/2004
• Status: Expired due to Fees

• Current Assignee: ASML Holding NV
• Original Assignee: ASML Holding NV
• Inventors: Latypov, Azat M.
• Primary Examiner(s): Ben; Loha
• Application Number:
  US12/125,844
• Publication Number:
  US 20080219562A1
• Time in Patent Office: 999 Days
• Field of Search: 359237-239, 359/290, 359/291, 359/298, 359/3, 359/11, 359/21, 359/24, 359/32, 359/33, 359/559, 359/573, 359/578, 356/458, 356/484, 356495-497, 356/509, 356/511, 356/512, 356/520, 382/190, 382/211, 365/216
• US Class Current: 359/237
• CPC Class Codes: G03F 7/70283 Mask effects on the imaging process
• CPC Class Codes: G03F 7/70291 Addressable masks, e.g. spatial light modulators [SLMs], digital micro-mirror devices [DMDs] or liquid crystal display [LCD] patterning devices
• CPC Class Codes: G03F 7/70441 Optical proximity correction [OPC]
• 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 7/70508 Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
• 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

Abstract

A method of calculating an aerial image of a spatial light modulator array includes calculating pair-wise interference between pixels of the spatial light modulator array; calculating effective graytones corresponding to modulation states of the pixels; and calculating the aerial image based on the pair-wise interference and the effective graytones. The graytones depend only on the modulation states of the pixels. The pair-wise interference depends only on position variables. The position variables are position in an image plane and position in a plane of a source of electromagnetic radiation. The pair-wise interference can be represented by a matrix of functions. The pair-wise interference can be represented by a four dimensional matrix. The effective graytones are approximated using sinc functions, or using polynomial functions.

Claims

1. A rasterization method for pixels of a spatial light modulator array, comprising:

pre-computing optical interferences between pixels of the spatial light modulator array in a partial coherent illumination; and

computing at least one of an aerial image and a derivative of the aerial image based on the pre-computed optical interferences, without performing a rasterization computaton that modifies pixel states of the pixels of the spatial light modulator array.

2. The method of claim 1, further comprising:

determining pixel states of the pixels of the spatial light modulator array based on computed aerial image or computed derivative of the aerial image to render a lithographically printed pattern in a maskless lithography system.

3. The method of claim 1, wherein computing the at least one of the aerial image and the derivative of the aerial image comprises:

pixelizing the spatial light modulator array and at least one derivative of the at least one aerial image with respect to pixel modulation parameters for calculating a partially coherent aerial image of the pixelized spatial light modulator array and the derivative of the aerial image with respect to the pixels states.

4. The method of claim 3, wherein pixelizing the spatial light modulator array and the at least one derivative of the at least one aerial image further comprises:

determining entries of a Pixel Interference Matrix (PIM); and

computing a quadratic function with known coefficients to compute the aerial image or the derivative of the aerial image in a vicinity of a given point based on the entries in the PIM corresponding to the pixels in a close proximity to the given point, wherein each entry of the PIM characterizes the optical interference between a respective pair of pixels.

5. The method of claim 1, wherein computing the at least one of the aerial image and the derivative of the aerial image comprises:

calculating pair-wise interference between the pixels of the spatial light modulator array.

6. The method of claim 5, wherein computing the at least one of the aerial image and the derivative of the aerial image further comprises:

calculating effective graytones corresponding to modulation states of the pixels.

7. The method of claim 6, wherein computing the at least one of the aerial image and the derivative of the aerial image further comprises:

calculating the at least one of the aerial image and the derivative of the aerial image based on the pair-wise interference and the effective graytones.

8. The method of claim 7, wherein the effective graytones depend only on the modulation states of the pixels.

9. The method of claim 7, wherein the pair-wise interference depends only on position variables.

10. The method of claim 9, wherein the position variables are position in an image plane and position in a plane of a source of electromagnetic radiation.

11. The method of claim 7, wherein the pair-wise interference is represented by a matrix of functions.

12. The method of claim 7, wherein the pair-wise interference is represented by a four dimensional matrix.

13. The method of claim 7, wherein the effective graytones are approximated using sinc functions.

14. The method of claim 7, wherein the effective graytones are approximated using polynomial functions.

15. A rasterization system for pixels of a spatial light modulator array, comprising:

means for pre-computing optical interferences between pixels of the spatial light modulator array in a partial coherent illumination; and

means for computing at least one of an aerial image and a derivative of the aerial image based on the pre-computed optical interferences, without performing a rasterization computation that modifies pixel states of the pixels of the spatial light modulator array.

16. The system of claim 15, further comprising:

means for determining pixel states of the pixels of the spatial light modulator array based on computed aerial image or computed derivative of the aerial image to render a lithographically printed pattern in a maskless lithography system.

17. The system of claim 15, wherein means for computing the at least one of the aerial image and the derivative of the aerial image comprises:

means for calculating pair-wise interference between the pixels of the spatial light modulator array;

means for calculating effective graytones corresponding to modulation states of the pixels; and

means for calculating the at least one of the aerial image and the at least one derivative based on the pair-wise interference and the effective graytones.

18. The system of claim 17, wherein the effective graytones depend only on the modulation states of the pixels.

19. The system of claim 17, wherein the pair-wise interference depends only on position variables.

20. The system of claim 17, wherein the pair-wise interference is represented by a matrix of functions in a four dimensional matrix, wherein the effective graytones are approximated using either sinc functions or polynomial functions.