Browse Prior Art Database

Analytic Calculation of Chip Image Probabilities

IP.com Disclosure Number: IPCOM000099520D
Original Publication Date: 1990-Jan-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 3 page(s) / 67K

Publishing Venue

IBM

Related People

Rauch, SE III: AUTHOR

Abstract

Disclosed is a technique for the analytic calculation of chip image probabilities.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 52% of the total text.

Analytic Calculation of Chip Image Probabilities

       Disclosed is a technique for the analytic calculation of
chip image probabilities.

      Generally, the calculation of chip image probabilities (if more
than one image size or one edge-to-edge probability was required) was
performed using Monte Carlo simulation. Whereas this simulation tech-
nique has certain advantages, such as the ability to model complex
pro- blems, its drawbacks include poor accuracy in some cases (due to
its notoriously slow convergence), and the inability to calculate
very small probabilities in a reasonable time. An alternate approach
for problems of intermediate complexity involves their formulation in
terms of multivariate normal probability distributions.  This
analytic technique is presented here.

      The problem is to find the probability of a certain geometric
event in the chip image given the design layout, alignment order, and
the image and overlay tolerances.  An event is a set of possible
outcomes of the process.  An outcome may be represented by the vector
of all image and first-order center-line overlay errors which led to
it. This allows the introduction of the random variable (vector) E
which is this mapping of the sample space (the set of all possible
outcomes) to Rn (the space of all real vectors of dimension n), where
n is the number of image size and alignment errors of interest.

      Since all of the elements of E are assumed to be independent
normally distributed random variables,
    E N N(b,S...