Numerical ellipsometry: Methods for selecting measurements and techniques for advanced analysis applied to β-gallium oxide

Abstract

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 the authors (Urban and Barton) have addressed this for orthorhombic, anisotropic films on substrates. Here, the authors treat the case of reflection from a single anisotropic, monoclinic β-Ga2O3 crystal, which is nondepolarizing as determined by Mueller matrix measurements and has a smooth, flat surface. Prior work on Ga2O3 by one author (Schubert et al.) used a very large dataset requiring more than 45 days of instrument time to collect. In the previous work, the sample optical response, ɛ, was determined over a restricted wavenumber range using just over 5 days of measurements. The work here shows how more accurate results can be obtained with approximately 5% of the data or just less than seven hours of instrument time assuming scaling. The data reduction mainly affects measurement time and has little effect on compute time in these days of fast computers. The reduction in measurements has been accomplished by excluding measurements that are less useful due to large instrument-reported estimated experimental errors (σ), noise (low intensity), and mathematical insensitivity to the desired solutions. Examples using two β-Ga2O3 crystals, (010) and (−201), are presented. Solutions are found using each crystal independently. From 20 to 40 numerical solutions to the model equations are found at each wavenumber using the reduced dataset as these allow an analysis of measurement accuracy. Further data reductions are expected in future works.