The essential role played by the physics of Zener tunneling of electrons from the barrier to the drain in finding the solutions to the field, energy‐balance, and quantum transport equations in AlGaSb/InAs/AlGaSb double‐barrier structures is pointed out. It is shown that the self‐consistent physical consideration on these equations is crucial in obtaining interesting and realistic novel hysteresis phenomena of the trapped hole charge in an AlGaSb barrier. There exist solutions to the above equations which do not incorporate the physics of Zener tunneling, which are therefore physically untenable.