Calculation of Hole Concentrations in Zn Doped GaAs Nanowires

We have previously demonstrated that we can grow p-type GaAs nanowires using Zn doping during gold catalyzed growth with aerotaxy. In this investigation, we show how to calculate the hole concentrations in such nanowires. We base the calculations on the Zhang-Northrup defect formation energy. Using density functional theory, we calculate the energy of the defect, a Zn atom on a Ga site, using a supercell approach. The chemical potentials of Zn and Ga in the liquid catalyst particle are calculated from a thermodynamically assessed database including Au, Zn, Ga, and As. These quantities together with the chemical potential of the carriers enable us to calculate the hole concentration in the nanowires self-consistently. We validate our theoretical results against aerotaxy grown GaAs nanowires where we have varied the hole concentration by varying the Zn/Ga ratio in the aerotaxy growth.