Paper EL-ThA11
Numerical Ellipsometry: Methods for Selecting Measurements and Techniques for Advanced Analysis Applied to β -Gallium Oxide

Thursday, October 24, 2019, 5:40 pm, Room A215

Ellipsometry is an optical technique through which properties of materials may be determined from measurements of light reflecting from or transmitting through a sample. Usually the measurements require data processing and a key issue is determining which measurements to make. Previously two of us (Urban and Barton)[1] have addressed this for orthorhombic, anisotropic films on substrates and here we treat the case of reflection from a single anisotropic, monoclinic β-Ga₂O₃ crystal which is non-depolarizing and has a smooth, flat surface. Prior work on Ga₂O₃ by one author (Schubert)[2] used a very large dataset containing measurements at each wavenumber for three angles of incidence and 5 azimuth angles for each of 2 crystal orientations. Step 1 in that process was to determine the best-fit permittivity tensor, ε, using Levenberg-Marquardt least squares regression. Here we present methods to determine practically the same ε using a substantially reduced subset of the same data. We exclude measurements which are less useful due to large instrument-reported estimated experimental errors (σ), noise (low intensity), and mathematical insensitivity to the desired solutions. From 10 to 30 numerical solutions to the model equations are found at each wavenumber using the reduced data set as these allow an analysis of measurement accuracy. Solutions are found using each crystal independently. The number of measurements is reduced by a factor of 25 or so depending on the options selected with further reductions expected in future works. Examples using two β-Ga₂O₃ crystals, (010) and (-201) are presented.

1. F.K. Urban III and D. Barton, Thin Solid Films, 663, pp 116-1251, (2018)

2. M. Schubert, R. Korlacki, S. Knight, T. Hofmann, S. Schöche, V. Darakchieva, E. Janzén, B. Monemar, D. Gogova, Q.-T. Thieu et al., Phys.Rev.B 93, 125209 (2016).