and ηι(λο) can be determined from (^,Δ) measurements at λο, and then Μι(λι) and ki(\{) can be deduced by inversion from (^,Δ) at Χ%, using the known value of d\. Clearly, the ability to vary the wavelength of the mono chromatic source is a benefit for data analysis in null ellipsometry. Spectroscopic measurements. With the near-continuous spectroscop ic capability of the automatic instru ments, the power of ellipsometry blos somed. Very effective strategies for solving three- and four-medium prob lems with absorbing films have been developed. Typically, the three-medi um techniques involve estimating the film thickness and inverting {^(λ),Α(λ)} to obtain |rai,estM,fti,est(X)|. If the guess is wrong, spurious spectroscopic arti facts will appear in the derived thinfilm optical spectra. These arise from features in the substrate spectra or from interference oscillations and are coupled into the solution only when the guess is incorrect. The correct thick ness is that which eliminates the arti facts, and the inverted (ni,est(A), ^i,est(^)| then equal the correct (ηι(λ),&ι(λ)) (13). An example of this method is given later. Another powerful analysis method was first developed for semiconductor applications but is now being applied more widely. If the sample under study is a complex η-medium structure in which each of the layers has known op tical properties, or at least is a micro scopic composite of materials of known optical properties, then all unknowns in the problem are wavelength inde pendent. Thus, linear regression can be applied to (ψ(λ),Δ(λ)}, and this pro vides the unknowns, which are the thicknesses of all layers and the volume fractions for the composite layers (14). This technique requires a library of \n(\),k(\)} data for the bulk materials, and for common semiconductors such data are available (15). Although the linear regression tech nique is important for microstructural characterization, the impact of spec troscopic ellipsometry is greatest for the characterization of electronic structure and chemical bonding ob tained through interpretation of the optical properties of surface layers. The limitation of all such measure ments is the inability to deduce infor mation on dynamic surfaces because it normally requires at least a minute, and usually much longer, to scan the monochromator over the required spectral range. Real-time measurements. The power of the automatic ellipsometer has also been demonstrated through its second mode of operation: real-time
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 17, SEPTEMBER 1, 1990 · 895 A
