I.
The onset of the Kirk effect in bipolar junction transistors (BJTs) [1] and the field collapse effect in double heterojunction bipolar transistors [2] takes place when the electric field at some point in the collector vanishes. Conventionally, one defines the onset of the Kirk effect in BJTs as the current density at which the electric field vanishes at the base collector metallurgical junction. However, when the doping is nonuniform the electric field may vanish at some point inside the depletion region before it vanishes at the junction. As the current density increases beyond threshold the direction of the electric field is reversed at that point, electrons are reflected, and consequently accumulate next to the junction. The onset of base push-out is therefore defined in this case by the vanishing electric field inside the depletion region rather than at the junction itself. In this letter, we describe how the onset of the Kirk field collapse effects varies with the dopant atom profile in the collector. We show that a dopant profile weighted toward the base can enhance the onset by more than 50% compared to the uniform dopant concentration case, if the electron velocity in the collector is constant. For brevity, we refer throughout this letter to the field collapse effect also as the Kirk effect.