Electron mobilities in gallium, indium, and aluminum nitrides

Abstract

Electron mobilities in GaN and InN are calculated, by variational principle, as a function of temperature for carrier concentrations of 10¹⁶, 10¹⁷, and 10¹⁸ cm⁻³ with compensation ratio as a parameter. Both GaN and InN have maximum mobilities between 100 and 200 K, depending on the electron density and compensation ratio, with lower electron density peaking at lower temperature. This is due to the interplay of piezoelectric acoustic phonon scattering at low carrier concentrations and ionized impurity scattering at higher carrier concentrations. Above 200 K, polar mode optical phonon scattering is the mobility limiting process. The 300 and 77 K electron and Hall mobilities as functions of carrier concentration in the range of 10¹⁶–10²⁰ cm⁻³ and compensation ratio are also calculated. The theoretical maximum mobilities in GaN and InN at 300 K are about 1000 and 4400 cm² V⁻¹ s⁻¹, respectively, while at 77 K the limits are beyond 6000 and 30 000 cm² V⁻¹ s⁻¹, respectively. We compare the results with experimental data and find reasonable correlation, but with evidence that structural imperfection and heavy compensation play important roles in the material presently available. Only phonon limited scattering processes are considered in the calculation of the mobility in AlN since it is an insulator of extremely low carrier concentration. We find a phonon limited electron mobility of about 300 cm² V⁻¹ s⁻¹ at 300 K.