Intrinsic limits on electron mobility in dilute nitride semiconductors

A fundamental connection is established between the composition-dependence of the conduction band edge energy and the $n$-type carrier scattering cross section in the ultradilute limit for semiconductor alloys, imposing general limits on the carrier mobility in such alloys. From the measured nitrogen composition dependence of the bandgap in $GaAs1−xNx,$ the carrier scattering cross section of substitutional nitrogen defects in GaAs is estimated to be 0.3 $nm2.$ Within an independent scattering approximation, the carrier mobility is then estimated to be $∼1000 cm2/V s$ for a nitrogen atomic concentration of 1%, comparable to the highest measured mobility in high-quality GaInNAs samples at these N concentrations, but substantially higher than that found in many samples. This gives an intrinsic upper bound on the carrier mobility in these materials.