Ultrathin GaN Nanowires: Electronic, Thermal, and Thermoelectric Properties

We present a comprehensive computational study of the electronic, thermal, and thermoelectric (TE) properties of gallium nitride nanowires (NWs) over a wide range of thicknesses (3--9 nm), doping densities ($10^{18}$--$10^{20}$ cm$^{-3}$), and temperatures (300--1000 K). We calculate the low-field electron mobility based on ensemble Monte Carlo transport simulation coupled with a self-consistent solution of the Poisson and Schr\"odinger equations. We use the relaxation-time approximation and a Poisson-Schro\"dinger solver to calculate the electron Seebeck coefficient and thermal conductivity. Lattice thermal conductivity is calculated using a phonon ensemble Monte Carlo simulation, with a real-space rough surface described by a Gaussian autocorrelation function. Throughout the temperature range, the Seebeck coefficient increases while the lattice thermal conductivity decreases with decreasing wire cross section, both boding well for TE applications of thin GaN NWs. However, at room temperature these benefits are eventually overcome by the detrimental effect of surface roughness scattering on the electron mobility in very thin NWs. The highest room-temperature $ZT$ of 0.2 is achieved for 4-nm-thick NWs, while further downscaling degrades it. In contrast, at 1000 K, the electron mobility varies weakly with the NW thickness owing to the dominance of polar optical phonon scattering and multiple subbands contributing to transport, so $ZT$ increases with increasing confinement, reaching 0.8 for optimally doped 3-nm-thick NWs. The $ZT$ of GaN NWs increases with increasing temperature beyond 1000 K, which further emphasizes their suitability for high-temperature TE applications.