In strained high-electron-mobility transistors (HEMTs) with In As as the channel, excess electrons and holes are generated in the drain region by impact ionization. In the source region, electrons are injected to recombine with accumulated holes by the Auger process. This causes the shift of the gate potential, VGS,shift, for HEMTs. For a system where electrons and holes coexist, we established a theory taking into account the non parabolicity of the conduction band in the InAs channel. This theory enables us to rigorously determine not only the energy states and the concentration profiles for both carriers but also the VGS,shift due to an accumulation of holes. We have derived the Auger recombination theory which takes into account the Fermi-Dirac statistics and is applicable to an arbitrary shape of potential energy. The Auger recombination lifetime τA for InAs-PHEMTs was estimated as a function of the sheet hole concentration, ρs, and τA was on the order of psec for ρs exceeding 1012cm-2.