We investigate AlGaN/GaN HEMTs which show a large increase in measured off-state breakdown voltage, VBR, from near-VT to deep-off state VGS conditions, accompanied by a positive shift in measured VT, when these devices are stressed electrically by alternating ID–VGS and ID–VDS measurements. We show that, if stress is assumed to cause spatially uniform changes, the above variations in VBR and VT can be explained in terms of increased ionized deep acceptor trap concentration in the GaN buffer. We also show that, the near-VT VBR is due to space-charge limited current while the deep off-state VBR is due to impact ionization. Our simulations predict that the incorporation of a field plate in the device can enhance the latter VBR significantly, but may not change the former VBR much. © Springer Nature Switzerland AG 2019.