We investigate AlGaN/GaN high electron mobility transistors with 0.7 \mu \text{m} gate length whose measured off-state breakdown voltage, {V}_{BR} , increased from 28 V at gate-source bias, V_{GS} = - 4.1 V (near threshold, {V}_{T} ) to 87-138 V at \text{V}_{GS} = - 9.5 V (deep off-state); this {V}_{BR} rise was accompanied by a positive {V}_{T} shift of 0.17-0.5 V; devices with larger {V}_{T} shift showed larger {V}_{BR} rise. Our prior work showed that the near-threshold {V}_{BR} is due to space-charge limited current, which is a signature of buffer traps. Our analysis of the above observations of the present work shows the following: The deep off-state {V}_{BR} is due to impact ionization induced avalanche. The correlation between {V}_{T} shift and {V}_{BR} rise implies that barrier and/or buffer traps play a role in governing {V}_{BR}. Although different models involving surface, barrier and buffer traps can simulate the combination of positive {V}_{T} shift and large {V}_{BR} rise, DC electric stress most likely affects the surface and barrier traps but not buffer traps. © 2001-2011 IEEE.