JP2000221659A - Light intensity calculating method for pattern - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a light intensity calculating method by which accurate calculation is realized and calculating speed is improved as a method for calculating the light intensity distribution of a mask by simulation. SOLUTION: This method includes a stage (S101) to make a table on the kernel ϕ and the characteristic value α of a stepper optical system, a stage (S102) to obtain a value Φ by extending the size L×L of the kernel to 2L×2L and setting it as a cyclic boundary and Fourier-transforming what is obtained by filling the extended part with 0, a stage (S103) to segment a pattern being a calculation object to the size of 2L×2L with a point P as center, a stage (S104) to divide the segmented pattern to a rectangle and a triangle so as to calculate the transmissivity as the sum F of the analysis Fourier of a cycle 2L, a stage (S105) to calculate a convolution integration I' by inversely Fourier- transforming the product of F and Φ, a stage (S106) to obtain the light intensity distribution I except the area of L/2 of the periphery of I' and stages (S107 and S108) to obtain the light intensity distribution of the pattern by moving the point P by L and repeating the respective stages.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a technique for exposing a mask pattern in a lithography process, and more particularly to a method for calculating the light intensity of a mask pattern on a wafer by simulation.

[0002]

2. Description of the Related Art In general, as a method of calculating a light intensity distribution in a lithography simulation, YCPat
i, T.Kailath, J.Opt.Soc.Am.A, vol.11, No.9, 1994
There is a calculation method disclosed in US Pat. This conventional method is shown in FIG.
This will be described with reference to the flowchart of FIG. Here, FIG.
It is assumed that the light intensity distribution on the wafer at the mask pattern MP schematically shown in FIG. Usually, the light intensity distribution I (x, y) on the wafer is determined by the transmittance f (x,
y) and a kernel φ (x,
y) and the eigenvalue α are calculated by the following (Equation 1). I (x, y) = Σα | (f * φ) (x, y) | ² (Equation 1) where (f * φ) (x, y) represents the convolution integral of f and φ.

Accordingly, first, the eigenvalue α and the kernel φ of (Equation 1) are calculated to create a table of the kernel φ (S
201). Next, a pattern included in a rectangular area having a size of L × L of the kernel is cut out from the entire mask pattern MP with the calculation point P set on the mask pattern MP as a center (S202). FIG. 4B is an enlarged view of the cut pattern. Then, if the cut pattern includes a diagonal pattern that is not rectangular,
As shown in FIG. 4C, the oblique pattern portion is replaced with a plurality of rectangular patterns by performing step approximation (S20).
3). Then, the above-described convolution integration is performed from the kernel table in step S201 to step S203.
The light intensity at the calculation point P is obtained as the sum of the table values (S2).
04). Then, as shown by arrows in FIG. 4A, the above-described steps S201 to S204 are calculated over the entire analysis area of the mask pattern while sequentially moving the calculation point P at a fine pitch (S205, S2).
06).

[0004]

In such a conventional light intensity calculation method, since the calculation is performed based on a rectangular pattern obtained by dividing a mask pattern, if a diagonal pattern exists, the diagonal pattern is calculated. It is necessary to calculate as a rectangular pattern approximated by stairs. Therefore, there is a problem in that the calculation accuracy is reduced due to an error due to bitmap conversion or the like in the approximated portion. In this case, it is conceivable to reduce the error due to approximation by increasing the number of divisions of the step approximation, but in that case, the number of processes in the convolution integration described above increases, and the calculation speed is extremely reduced. become.

[0005] An object of the present invention is to provide a light intensity calculation method which enables high-precision calculation while improving the calculation speed.

[0006]

The light intensity calculation method according to the present invention comprises a Fourier transform of a table in which the boundaries of the kernel of the stepper optical system are extended to be periodic boundaries, and the pattern is divided into rectangular and triangular pattern pieces. In addition, the light intensity distribution is obtained by performing convolution integration from the sum of the analysis Fourier of the transmittance of each divided pattern piece.

[0007] That is, the convolution integral of the above (Equation 1) is expressed by using the Fourier transform as follows from its definition. (F * φ) (x, y) = F ⁻¹ {F (f) F (φ)} (Equation 2) where F (f) is the Fourier transform of the transmittance f of the mask,
F (φ) represents the Fourier transform of the kernel function φ, and F ⁻¹ represents the inverse Fourier transform. That is, it can be seen that the convolution integral is obtained by performing an inverse Fourier transform on the product of F (f) and F (φ).

Further, the transmittance f of the mask of (Equation 2) is set to a plurality of rectangular and triangular mask pieces fi (i is 1 to
n). f = f1 + f2 +... + fn (Equation 3) At this time, when the Fourier transform of each mask piece is Fi, the Fourier transform of the mask fi is represented by a linear sum of the Fourier transform of each mask piece as follows. F = F1 + F2 +... + Fn (Equation 4) From this, the Fourier transform F of the transmittance f of the mask is obtained.
(F) can be obtained as the sum of Fourier transforms of a plurality of rectangular and triangular mask pieces based on (Equation 3) and (Equation 4).

Therefore, the sum of the Fourier transforms of a plurality of rectangular and triangular mask pieces can be used as F (f) in (Equation 2), and the Fourier transform Fi of the rectangular and triangular mask pieces fi is Since it can be calculated analytically, the use of this analytical solution eliminates the need for staircase approximation of diagonal patterns. Become.

[0010]

Next, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a flowchart showing the flow of this embodiment. Here, it is assumed that the light intensity distribution on the wafer at the mask pattern MP shown in FIG. 2A similar to that shown in FIG. 4A is calculated. First, a table of eigenvalues α and kernels φ is calculated as before (S101). Next, to satisfy the periodic boundary condition,
As shown in FIG. 2 (b), the boundary portion is extended vertically and horizontally by L / 2 with respect to the kernel size L to form a 2L × 2L region, and “0” is filled in the extended portion of this region. Is subjected to a Fourier transform, and this is defined as Φ (S10
2). Then, a point P is set on the mask pattern MP shown in FIG. 2A, and a pattern included in an area of 2L × 2L is cut out around the point P (S103). FIG.
(C) is a diagram of the cut-out pattern.

Next, the cut mask pattern is divided into a plurality of mask pieces. Here, since a diagonal pattern exists, as shown in FIG. 2C, the mask is divided into a plurality of rectangular and triangular mask pieces. Then, the transmittance f of the cut mask pattern is calculated based on (Equation 3).
It is expressed as the sum of the transmittances of the divided mask pieces, and the Fourier transform F thereof is expressed as a linear sum of the Fourier transform of each mask piece based on (Equation 4). As described above, since the Fourier transform Fi of the rectangular and triangular mask pieces fi can be calculated analytically, the Fourier transform F of the cut-out mask pattern is an analysis Fourier transform in which the period of each mask piece is 2L. (S104). Then, using Φ obtained in step S102 and F obtained in step S104, the convolution integration, that is, the inverse Fourier transform of F × Φ is performed from (Equation 2), and the value I of the inverse Fourier transform in a cycle of 2L is obtained. Is calculated (S105). Next, the light intensity distribution of the L × L rectangular area around the point P except for the data of the area of L / 2 expanded in step S102 around the convolution integral value I ′ obtained in step S105. I
Is obtained (S106).

As described above, the light intensity distribution I in the cut mask pattern MP can be obtained.
As shown by an arrow in (a), the point P is moved by L. Then, the light intensity distribution I of the next rectangular area L × L is similarly obtained by repeating steps S103 to S107 for the point P. Hereinafter, by performing this process on the entire analysis region of the mask pattern,
The light intensity distribution of the entire analysis area is calculated (S10
8).

[0013]

As described above, in the method for calculating the light intensity according to the present invention, the Fourier transform of the oblique pattern is analytically calculated. Since no error occurs due to the bitmap conversion of the shape, the calculation accuracy is increased. In addition, the processing for cutting out the pattern included in the kernel area from the entire mask pattern requires a longer processing time as the number of patterns is larger. In the conventional method, it is necessary to cut out the pattern every time one point is calculated. Since the region of L can be calculated at a time, the number of times of pattern cutting can be reduced, and the calculation speed is improved.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining a light intensity calculation method of the present invention.

FIG. 2 is a schematic diagram of a mask pattern for explaining a calculation method of the present invention.

FIG. 3 is a flowchart for explaining a conventional light intensity calculation method.

FIG. 4 is a schematic diagram of a mask pattern for explaining a calculation method of the present invention.

[Explanation of symbols]

 MP mask pattern

Claims (2)

[Claims] 1. A Fourier transform of a table in which a boundary of a kernel of a stepper optical system is extended to be a periodic boundary, a pattern is divided into rectangular and triangular pattern pieces, and an analysis Fourier analysis of transmittance of each of the divided pattern pieces is performed. A light intensity distribution obtained by performing convolution integration from the sum of 2. A kernel φ and an eigenvalue α of a stepper optical system.
Creating a table, and the size L of the kernel
× L to 2L × 2L to form a periodic boundary and obtain a value Φ obtained by performing a Fourier transform on the expanded portion padded with 0s.
A step of cutting out the cut out pattern into rectangles and triangles, and calculating the transmittance as a sum F of analytical Fourier with a period of 2 L;
Is inverse Fourier transformed to the convolution integral I '
And calculating the light intensity distribution I excluding the area of L / 2 around the I ′.
A method of calculating the light intensity distribution of the pattern by repeating the above steps while moving the light intensity distribution of the pattern.