Criteria for the choice of the optimal point in the solution of the incorrect inverse ellipsometric problem for ultrathin surface films

The present work is devoted to the analysis of the ill-posed inverse ellipsometric problem. Manifestations of the incorrectness of the problem are described for the case of ultrathin films. Special attention is given to the criteria for the choice of the optimal point. It is shown that an obvious and frequently used criterion expressed as a condition on the difference functional S0 ≤ δ2, where δ is an average error in the measurement of polarization angles, is practically useless in our case in the region of strong incorrectness. New criteria for the choice of the optimal point are therefore suggested. As a result, a stable solution of the inverse ellipsometric problem is obtained, which permits one to study successfully the surface films in the thickness range of 2 to 10 nm.