Applied Materials, Inc.

Ulrich Hofmann

Richard E Crandall

Stephen A Rishton

Richard L Lozes

Volker Boegli

Weidong Wang

David Jeremy Copeland

A fast convolution method applicable to convolving a signal (indicative of an n-dimensional pattern, where n is greater than or equal to two) with a smooth kernel that can be approximated by a separated-spline kernel, and a system configured to perform such method using software or signal processing circuitry. Unlike Fourier-based convolution methods which require on the order of N log N arithmetic operations for a signal of length N, the method of the invention requires only on the order of N arithmetic operations to do so. Unlike wavelet-based convolution approximations (which typically also require more arithmetic operations than are required in accordance with the invention to convolve the same signal), the method of the invention is exact for convolution kernels which are spline kernels.

Method and apparatus for fast signal convolution using separated-spline kernel

A lithography method and apparatus which represent a substrate surface as gray level values and determine a shape data that specifies a shape and position of a flash field. The apparatus receives a pattern in a vector format, represents the substrate surface as a grid of pixels, and then represents each pixel as a gray level value specifying a proportion of the pixel that includes the pattern. Subsequently the apparatus constructs a matrix of a quadrant of four pixels and surrounding pixels, modifies the matrix so that three intermediate shapes corresponding to an exposed region of the quadrant may be provided, determines an intermediate shape data of the quadrant; and performs a reverse modification on the shape to determine the shape data that specifies a flash field.

Method and apparatus that determines charged particle beam shape codes

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Castro Valley, CA, United States of America

Ulrich Hofmann