A Charge Control Relation for Bipolar Transistors

Abstract

We give a relation which links emitter and collector junction voltages, V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eb</inf> and V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eb</inf> , collector current I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , and the total charge Q <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> of carriers that enter through the base terminal (electrons in a pnp transistor): <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$I_{c} = const{e^(aV_{eb / kT}) - e^(aV_{eb / kT})\over Q_{b}}.$</tex> This relation is valid for high injection conditions, subject only to minor restrictions. The significance for device modeling is discussed.