Grid-based resist simulation

Abstract

A grid-based resist simulator predicts how a wafer coated with one or more resist layers will develop when exposed with a mask pattern. Image intensity values are calculated at a grid of points on the wafer, and the image intensity points are analyzed with a resist simulator that produces a resist surface function. A threshold contour of the resist surface function defines how the mask pattern will print on a wafer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:

FIG. 1 illustrates a conventional method of simulating how a pattern on a mask will be printed on a wafer using a known variable threshold resist simulator;

FIG. 2 illustrates a method of simulating how a pattern on a mask will be printed on a wafer using a grid-based resist simulator in accordance with one embodiment of the present invention;

FIG. 2A illustrates a mask layout and its corresponding aerial image and the resist surface function generated in accordance with one embodiment of the present invention;

FIG. 3 illustrates a resist simulating process in accordance with one embodiment of the present invention;

FIG. 4 illustrates smoothed and sharp neutralizations;

FIG. 5 illustrates three Gaussian-Laguerre polynomials;

FIG. 6 illustrates a seventh Gaussian-Laguerre polynomial;

FIG. 7 illustrates the interaction radius on the Gaussian-Laguerre polynomial;

FIG. 8 illustrates a gauge placed between adjacent features and corresponding measured image intensities;

FIG. 9 illustrates modeling layers used in accordance with an embodiment of the present invention;

FIG. 10 illustrates a search technique for finding a maximum image intensity;

FIG. 11 illustrates a relationship between minimum image intensity and maximum base concentration;

FIG. 12 illustrates image intensity versus a Nyquist sampling grid;

FIG. 13 illustrates image intensity versus upsampling on a Nyquist grid;

FIG. 14 illustrates image intensity versus further upsampling on a Nyquist grid;

FIG. 15 illustrates image intensity versus upsampling using a Fast Fourier Transform;

FIG. 16 illustrates image intensity versus different techniques for calculating slope;

FIG. 17 illustrates image intensity versus curvature calculations;

FIG. 18 illustrates image intensity versus squaring of an upsample;

FIG. 19 illustrates image intensity versus the square root of an upsample; and

FIG. 20 illustrates a flow chart for improving speed in a resist simulator in accordance with one embodiment of the present invention.

Claims

1. A method of simulating how a target mask pattern will be printed on a wafer that is coated with a resist material, comprising: receiving a number of image intensity values that are calculated on a grid of sample points on a wafer when the wafer is exposed with the mask pattern;supplying the image intensity values to a resist simulator that determines a resist surface function;selecting a single threshold contour value for the resist surface function; anddefining the boundaries of how the mask pattern will be printed on the wafer from the contours of the resist surface function at the selected threshold.

2. The method of claim 1, wherein the resist simulator calculates the resist surface function by: summing the products of a number of coefficients and modeling terms, wherein each modeling term is defined by

3. The method of claim 2, wherein Gs,p is selected from the set of Gaussian functions.

4. The method of claim 2, wherein Gs,p is selected from the set of Gauss-Laguerre polynomials.

5. A computer-readable media including a set of instructions that when executed cause a computer system to perform a method of simulating how a mask pattern will be printed on a wafer that is coated with a resist material, by: receiving a number of image intensity values that are calculated on a grid of sample points on a wafer when the wafer is exposed with the mask pattern;supplying the image intensity values to a resist simulator that determines a resist surface function;selecting a single threshold contour value from the resist surface function; anddefining the boundaries of how the mask pattern will be printed on the wafer from the contours of the resist surface function at the selected threshold.

6. A method of determining a number of coefficients for use in a resist simulator that calculates the image intensity required to develop a resist material at a grid of points on a wafer, comprising: obtaining a number of measurements of features where a resist is exposed on a test wafer;

7. The method of claim 6 further comprising requiring the function ciM(x, y) to have a non-zero derivative at each of the measurement points.

8. A computer-readable media including a set of instructions that when executed cause a computer system to perform a method of determining a number of coefficients for use in a resist simulator that calculates the image intensity required to develop a resist material at a grid of points on a wafer, comprising: obtaining a number of measurements of features where a resist is exposed on a test wafer;