Abstrucf-InAIAs/n+-InCaAs HFET's on InP have demonstrated a high breakdown voltage in spite of the narrow bandgap of the InGaAs channel. In order to understand this unique feature, we have carried out a systematic temperature-dependent study of off-state breakdown. We find that off-state breakdown at room-temperature is drain-gate limited and that the breakdown voltage shows a negative temperature coefficient. Based on these and other findings, we propose that off-state breakdown is a two-step process. First, electrons are injected by thermionicfield emission from the gate to the insulator. Second, electrons enter into the high-field drain-gate region of the channel hot, and relax their energy through impact-ionization. This combined mechanism explains our experimental observations that off-state breakdown in InAIAs/n+-InCaAs HFET's depends both on channel and insulator design. Our findings are relevant to other InAIAs/InGaAs HFET's, such as the MODFET, as well as HFET's based on other narrow-bandgap materials.