Anisotropic effective mass approximation model to calculate multiple subband structures at wide-gap semiconductor surfaces: Application to accumulation layers of SrTiO₃ and ZnO

Abstract We propose a simplified theoretical model that well reproduces the dispersion curves of the multiple subbands in a two-dimensional electron gas in the accumulation layer at the surfaces of wide-gap semiconductors. The electronic band structures containing multiple subbands with different orbital characteristics are derived by self-consistently solving the Poisson-Schrödinger equations with anisotropic effective mass approximations. Calculations were carried out on the two-dimensional electron gas states formed at the surfaces of SrTiO₃ and ZnO for comparison. The calculated subband structures at the SrTiO₃ surface were in excellent agreement with available angle-resolved photoelectron spectroscopy data, confirming the validity of the present model. The calculations further indicate the existence of a high electron density, exceeding 2 × 10²¹ cm^-3 and a high electric field of 20 MVcm^-1 at the surface. Moreover, photoelectron-escape depths are discussed quantitatively and photoelectrons from the first subband are found to dominate the total photoelectron intensity in the spectra.