Real time Mueller matrix ellipsometry and its applications

In this thesis research, a multichannel spectroscopic Mueller matrix ellipsometer has been developed in the optical configuration denoted PC 1r(o1)SC2r(o2)A. In this notation, P, S, and A represent the polarizer, sample, and analyzer, and C 1r(o1) and C2r(o2) represent two MgF2 biplate compensators that rotate at frequencies of o 1/2pi = 10 Hz and o2/2pi = 6 Hz, synchronized for a ratio o1:o2 of 5:3. The primary focus of this research involves extension of the ellipsometer to real-time Mueller matrix spectroscopy of surface modification and thin-film growth utilizing high-speed multichannel detection with a wide spectral range.; In this thesis, instrumentation calibration procedures are demonstrated including alignment of the two MgF2 zero-order biplate compensators, determination of the retardance and phase spectra for the compensators, determination of the offset angles for the optical elements, and characterization of the spectral response function of the ellipsometer. The latter calibration allows the (1,1) element of the Mueller matrix to be determined, thus yielding the unnormalized Mueller matrix. The relationship that describes the real (1,1)-normalized Mueller matrix in terms of the complex (2,2)-normalized Jones matrix is inverted, and consistent results are obtained for the complex amplitude transmission and reflection ratios from multiple independent expressions. Thus six real sample parameters, namely the real and imaginary parts of the complex amplitude reflection ratios r&d5;pp, r&d5;ps and r&d5;sp are determined from the 15 real Mueller matrix elements, some by multiple methods. The spectra in the complex amplitude reflection ratios can be analyzed to extract the bulk isotropic dielectric function 3b=31b-i3 2b and the surface-induced dielectric function anisotropy D3&d5;s=D 31s-iD3 2s for cubic single crystals. The surface-induced anisotropic response, defined by D3&d5; d=&sqbl0;3s1 1&d1;0-3 s001&sqbr0;d for the (110) surface, for example, is deduced from an average of four independent spectra, two in r&d5;sp and two in r&d5;sp= -r&d5; ps {09}using the first order term in d/lambda from an expansion of the partial transfer matrix. Here d is the surface anisotropic layer thickness and lambda is the vacuum wavelength. Because both the real and imaginary parts of &parl0;D3&d5;&parr0; d are now accessible, the results can be fit using a Kramers-Kronig (K-K) consistent oscillator model. The key advantage of the newly-developed instrument is the ability to perform spectroscopic measurements in real time that simultaneously provides bulk isotropic and surface- or interface-induced anisotropic optical responses of cubic crystals. (Abstract shortened by UMI.)...