Analytical model of surface depletion in GaAs nanowires
Poisson's equation is solved to provide a comprehensive model of nanowire (NW) surface depletion as a function of interface state density, NW radius, and doping density. This model improves upon established theory by giving distinct solutions to the cases of full and partial NW depletion while implementing the charge neutrality level and accurate Fermi-Dirac statistics. To explain the underlying physics, key parameters were plotted as a function of both interface state density and NW radius, showing interesting features such as the lowering of the Fermi level in fully depleted NWs and marked increase in surface depletion width and built-in surface potential (relative to a planar film equivalent) in partially depleted NWs. Finally, examination of NW conductivity found that for NWs of radius acrit, the minimum NW radius before which the entire NW is depleted, conductivity can be reduced by up to 95% relative to bulk. Additionally, majority carrier inversion is predicted to occur in thin NWs.