POLYNOMIAL SOLUTION FOR 2 THICKNESSES OF A MULTILAYER SYSTEM FROM A SINGLE ELLIPSOMETRIC MEASUREMENT

It is shown that the unknown thicknesses of any two transparent layers in an arbitrary multilayer system from a single ellipsometric measure ment can be found by the solution of an eighth-degree real polynomial. The method gives directly all the possible physical solutions, which are computed from the real roots of the polynomial. The coefficients o f the polynomial are determined by the angle of incidence, the refract ive indices of all the phases, and the thicknesses of the other layers . The method is used on a simulated system of air/silicon nitride/sili con oldde/silicon. (C) 1996 Optical Society of America