A detailed study of the physics of off-state breakdown in state-of-the-art lattice-matched and pseudomorphic InAlAs/InGaAs MODFETs is presented. It is found that, similarly to heterojunction avalanche photodiodes, breakdown in these devices is a two-step process. First, electrons are injected from the gate into the channel through thermionic-field emission. Second, because of the large conduction-band offset and the electric field in the insulator, these electrons enter the channel hot and immediately relax their energy through impact-ionization. The findings obtained suggest that there is considerable room for breakdown voltage engineering in InAlAs/InGaAs MODFETs by the use of a higher-barrier low-InAs insulator, a thicker undoped barrier-layer, and enhancement of the channel bandgap by quantum confinement. >