The spectroscopic ellipsometry measurement of non-polar freestanding GaN: comparison between isotropic and anisotropic models

Abstract

For anisotropic materials, the pseudo-dielectric function (DF) from isotropic model is often applied in spectroscopic ellipsometry data analysis instead of the DF from anisotropic model because of its simplicity. Whether this approximation is applicable depends on the discrepancy between the pseudo-DF and the DF, which we find to be related to the illumination configuration greatly. For the ellipsometry spectra obtained from a non-polar freestanding GaN in two configurations with the c-axis perpendicular and parallel to the incident plane respectively, both anisotropic model and isotropic model are used to compare the difference between the fitted absorption coefficient and pseudo-absorption coefficient. As a consequence, the discrepancy between the two coefficients is less than 10 even at the absorption edge when electric field is perpendicular to the c-axis, while the discrepancy exceeds 40 at the absorption edge when electric field is parallel to the c-axis. These results indicate that the approximation of using isotropic model instead of anisotropic model is reasonable in the former configuration, while it is not applicable in the latter configuration and will render an overestimation of bandgap. The above two different discrepancies could be explained by the first-order term approximation of pseudodielectric function. We further demonstrate the necessity for anisotropic model by comparing the deviations of the crystal-field splitting obtained from anisotropic and isotropic model with the theoretical value respectively.