Error propagation in fixed-point ellipsometric inversions

T Easwarakhanthan, P Pigeat
2003 Measurement science and technology  
Direct fixed-point inversions have been commonly used in ellipsometry for rapid determination of the optical constants and thickness of transparent and absorbing films formed on substrates. We formulate here the statistical covariance matrices of these optical parameters sought from a fixed-wave multiple sample, and multiple and single angle of incidence ellipsometric data using different known fixed-point inversions. Maple software used in the covariance matrix formulation offers the advantage
more » ... of avoiding the manual calculation of the number of literal derivatives involved. The error propagation inherent in the inversions can thus be readily studied as a function of optical parameters before optical characterization with regard to the uncertainty produced in these parameters and to the correlation between them. We verify quantitatively, using illustrative examples, that strong parameter correlation is synonymous with large parameter uncertainties in these fixed-point inversions and show that the multiple sample-based inversions bring out relatively small uncertainties accompanied by low parameter correlation when the film thickness ranges are chosen appropriately.
doi:10.1088/0957-0233/14/4/316 fatcat:nnmb627ggjc3vimzrsy2wshy7q