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

Abstract

We have measured spectra from ∼2 to 5 eV in all 15 elements of the normalized Mueller matrix for (110) Si at an angle of incidence of θa∼70°, 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 εb=ε1b−iε2b and the surface-induced dielectric function anisotropy Δεs=Δε1s−iΔε2s. Starting from the 15 Mueller matrix elements, six sample parameters are determined, namely the real and imaginary parts of the complex amplitude reflection ratios ρpp, ρps, and ρsp. The surface-induced anisotropic response (Δεs)d=[εs(11̄0)−εs(001)]d is deduced from an average of four independent spectra, two in ρsp and two in ρps=−ρsp using the first order term in d/λ from an expansion of the partial transfer matrix. Here d is the surface anisotropic layer thickness and λ is the vacuum wavelength. Because both the real and imaginary parts of (Δεs)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.