Influence of excitons and electric fields on the dielectric function of GaN: Theory and experiment

Abstract

The shape of the complex dielectric function (DF) of nitride semiconductors in the vicinity of the band gap is strongly influenced by the electron-hole interaction (excitonic effects). Here, the influence of electric fields on the optical response is theoretically studied and compared to experimental data. An exact and numerically fast method is presented allowing the calculation of the imaginary part of the DF in the whole range of reasonable field strengths $F$. The real part of the DF is calculated via the Kramers-Kronig transformation. We discuss how the field influences position, magnitude, and broadening of the ground-state excitonic resonance as well as the absorption far below the band gap. In contrast to the one-electron picture, a linear increase of the energy position of the ground-state resonance is obtained for large $F$ values. Electroreflectance (ER) spectroscopy carried out on an $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterojunction at low temperature demonstrates the sensitivity of the optical response to field changes. Using the calculated field-dependent values of the DF, the ER spectra of both the GaN channel layer and the AlGaN barrier layer are fully reproduced despite the inhomogeneous field distribution. The excellent agreement emphasizes the theoretical approach.