Simultaneous determination of bulk isotropic and surface-induced anisotropic complex dielectric functions of semiconductors from high speed Mueller matrix ellipsometry

We have measured spectra from similar to 2 to 5 eV in all 15 elements of the normalized Mueller matrix for (110) Si at an angle of incidence of theta(a)similar to70degrees, as an initial demanding performance test of a novel dual rotating-compensator multichannel ellipsometer. The Mueller matrix spectra, deduced from 36 waveform integrals collected over a single optical cycle of 0.25 s, can be analyzed to extract the bulk isotropic dielectric function epsilon(b) = epsilon(1b) - iepsilon(2b) and the surface-induced dielectric function anisotropy Deltaepsilon(s) = Deltaepsilon(1s) - iDeltaepsilon(2s) ,- Starting from the 15 Mueller matrix elements, six sample parameters are determined, namely the real and imaginary-parts of the complex amplitude reflection ratios p(pp), p(ps), and p(sp). The surface-induced anisotropic response (Deltaepsilon(s))d=[epsilon(s)(110)-epsilon(s)(001)]d is deduced from an average of four independent spectra, two in p,p and two in pp, = - to, 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 (Deltaepsilon(s))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 provide bulk isotropic and surface- or interface-induced anisotropic optical responses. (C) 2004 Elsevier B.V. All rights reserved.