The charge-control relations are rigorously derived from thecarrier transport and continuity equations for a bipolar transistorwith an arbitrary three-dimensional geometry, arbitrary base impuritydistribution, arbitrary recombination mechanisms (including spatialnonuniformity), and for both low and high injection levels. A one-to-onecorrespondence is maintained between internal processes and thecharge-control parameters, so that conceptual understanding of, andinsight into, device operation is enhanced. In the absence of recombination,the average carrier velocity is used to obtain the averagecarrier transit time across the base region. The current is then obtainedas the ratio of injected base charge to the average transittime. In the presence of recombination, the injected carriers aredivided into two groups according to whether they recombine or arecollected. The collected current is then obtained as the ratio of thecollected charge to the average transit time of the collected carriers.The Beaufoy-Sparkes "collector time constant" is related to the carriertransit time and is given a conceptual interpretation as a collectionlifetime in analogy with the recombination lifetime. A recombinationtransit time is introduced in analogy with the collection transit time.
The theory, which is generally valid up to frequencies of theorder of the reciprocal transit time, is extended to include high injectionlevels and some second-order phenomena, such as the Early effectand nonideal base contacts. It is pointed out that the integration ofthe basic equations over the base region may lead to a loss of detailedinformation, so that the charge-control theory may accurately describeonly the average behavior of the device; a solution of this difficultyis suggested. The Ebers-Moll circuit relations are derived from charge-controlprinciples so that a charge-control interpretation of the Ebers-Mollparameters and an electrical interpretation of the charge-controlparameters is obtained. This leads to the conclusion that the short-circuitsaturation currents are of more fundamental significance thanare the open-circuit saturation currents.
Finally, the separation of injected carriers into recombiningand nonrecombining components is used to obtain a conceptually clearderivation of the principle of reciprocity for a transistor.
