Impact of band-bending on the k-resolved electronic structure of Si-doped GaN

Band bending at semiconductor surfaces and interfaces is the key to applications ranging from classical transistors to topological quantum computing. A semiconductor particularly important for optical as well as microwave devices is GaN. What makes the material useful is not only its large bandgap but also that it can be heavily doped to become metallic. Here, we apply soft-x-ray angle-resolved photoelectron spectroscopy (ARPES) to metallic Si-doped GaN to explore the electron density and momentum-resolved band dispersions of the valence and conduction electrons varying through the surface band-bending region. We find an upward band bending, where the measured band occupation reduces toward the surface, as probed with low photon energies 1.4 keV, where the photoelectron mean free path exceeds the spatial extent of the band-bending region. Our quantitative analysis of the experimental data describes the potential variation in the band-bending region via self-consistent Poisson-Schrodinger equations. We put forward an insightful model to simulate the ARPES spectra from this region through summing up the contribution from all atomic layers, weighted by the photoelectron mean free path, under in-phase conditions achieved at particular values of the photoelectron out-of-plane momentum. The model adequately describes the peculiarities of the ARPES spectra caused by the surface band bending, including the photon-energy dependence of the apparent band occupation and Fermi-surface area, and allows accurate determination of the band-bending profile and values of the photoelectron mean free path. Finally, comparison of our data with supercell density functional theory calculations reveals the preferential location of Si atoms as substitutional for Ga, with the doped electrons entering the GaN conduction bands without formation of separate impurity states as would occur for Si interstitials. Our theoretical and experimental results resolve fundamental questions underpinning device performance of the GaN-based and other semiconductor materials in general and demonstrate a general methodology for quantitative studies of electron states in the band-bending region.