Analysis of problem in mathematical model for shadowed sputtering Original Research Article

A mathematical model for shadowed sputtering is an integral equation ∫Q2db A(b,c)X(b+c,b)=Y(c), c∈Q1 using compact supports Q1 , Q2 of dimension 2 and exploiting a function of sputtered layer Y∈L2(Q1) , a source function X∈C(Q2×Q1) and a musk function A∈L2(Q1×Q2) . 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 and Y ; – a main inverse problem of synthesis the shadowing mask parameters and a mask function A using restored X and prescribed Y . Properties of integral operator of these problems let solving in a stable manner both inverse problems. Besides the methods of their solving and their properties make it possible to approach a predicted function of a sputtered layer with any given accuracy.