On the nature of mathematical incorrectness of the inverse problem of ellipsometry for supersthin surface films

The nature of the mathematical incorrectness of the inverse problem of ellipsometry for superthin (below 10 nm) transparent surface films on uniform substrates is studied. It is shown that the mathematical incorrectness in this case is caused not only by experimental errors in measuring polarization angles, but also by an inadequate choice of the reflecting medium model leading to inaccurate setting of substrate parameters, which are considered to be known, and by ignoring a very thin (on the order of 0.1 nm) transition layer on the film-substrate interface. These conclusions are not only qualitative, but are confirmed by real experiments and numerical simulations carried out using a special mathematical program.