Following a course of analysis similar to that employed by Callen in his treatment of electric breakdown in ionic crystals, we develop a simple, one-dimensional, analytical model, which describes electron transport in III–V semiconductors with a non-degenerate conduction band minimum. We focus on the polar optical phonon scattering mechanism, as this is the dominant energy loss mechanism in these materials. Equating the power gained from the field with that lost through polar optical phonon scattering, we demonstrate that beyond a certain critical electric field, dependent on the material and on the temperature, that the power gained from the field exceeds that lost due to scattering. The instability which results leads to a dramatic increase in the electron energy and is responsible for the onset of intervalley transitions. Applying this model to the specific cases of gallium arsenide and wurtzite gallium nitride, we find that the 300 K critical fields in these materials are 2.42 and 114 kV/cm, respectively. The predictions of our analytical model are compared with those of Monte Carlo simulation and are found to be in satisfactory agreement.