Analysis of problem in mathematical model for shadowed sputtering

A mathematical model for shadowed sputtering is an integral equation integral(Q2) db A(b, c) x (b + c, b) = Y(c), c is an element of Q(1) using compact supports Q(1), Q(2) of dimension 2 and exploiting a function of sputtered layer Y is an element of L-2(Q(1)), a source function X is an element of C(Q(2) x Q(1)) and a musk function A is an element of L-2(Q(1) x Q(2)) In frame of a given model there exist: three problems: a straight problem of predicting Y using given A and X; an auxiliary inverse problem of restoring X using experimentally given A an d Y; a main inverse problem of synthesis the shadowing mask parameters and a mas k function A using restored X and prescribed Y. Properties of integral operator of these problems let solving in a stable m anner both inverse problems. Besides the methods of their solving and their properties make it possible to approach a predicted function of a sputtere d layer with any given accuracy. (C) 2000 Published by Elsevier Science B.V . All rights reserved.