Anisotropic dielectric functions of (0001) sapphire from spectroscopic ellipsometry and first-principles study

Abstract

This work aims at understanding and predicting the high-temperature anisotropic dielectric functions of (0001) sapphire over the entire infrared-visible-ultraviolet spectrum via the state-of-the-art infrared variable angle spectroscopic ellipsometry (IR-VASE) and first-principles method without empirical parameters. Upon measuring the high-symmetry orientation of c-plane surface, the IR-VASE determines the anisotropic infrared dielectric functions of (0001) sapphire for wavelengths ranging from 10 to 25μm and temperatures from 300 to 573K. As ellipsometry experiments indicate, the maxima of ordinary infrared dielectric functions consistently decrease and shift to longer wavelength as temperature increases. By fitting ellipsometry data with the Lorentz oscillator model, the Lorentz parameters, e.g., oscillator strength, resonance frequency and broadening parameter, for infrared-active phonon modes are obtained to interpret the temperature effect. Moreover, the calculated vibration frequencies at varying temperatures by the first-principles method coincide with the positions of infrared absorption peaks, indicating that infrared optical absorption mainly arises from the coupling of incident photon with lattice vibration. In the visible–ultraviolet spectral range, the first-principles and lattice dynamics methods are combined to understand the temperature effect on dielectric functions of (0001) sapphire. This method reproduces the essential feature of previous room-temperature reflectivity experiments and detects the slight change of dielectric functions as temperature increases. The convincing results enable us to predict the high-temperature visible–ultraviolet dielectric functions of (0001) sapphire by the first-principles method.