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Derivation and Interpretation of a Generalized Charge-Control Theory and Reciprocity for a Bipolar Transistor


Grinthal, Edward Ted (1969) Derivation and Interpretation of a Generalized Charge-Control Theory and Reciprocity for a Bipolar Transistor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PFHF-HV33.


The charge-control relations are rigorously derived from the carrier transport and continuity equations for a bipolar transistor with an arbitrary three-dimensional geometry, arbitrary base impurity distribution, arbitrary recombination mechanisms (including spatial nonuniformity), and for both low and high injection levels. A one-to-one correspondence is maintained between internal processes and the charge-control parameters, so that conceptual understanding of, and insight into, device operation is enhanced. In the absence of recombination, the average carrier velocity is used to obtain the average carrier transit time across the base region. The current is then obtained as the ratio of injected base charge to the average transit time. In the presence of recombination, the injected carriers are divided into two groups according to whether they recombine or are collected. The collected current is then obtained as the ratio of the collected charge to the average transit time of the collected carriers. The Beaufoy-Sparkes "collector time constant" is related to the carrier transit time and is given a conceptual interpretation as a collection lifetime in analogy with the recombination lifetime. A recombination transit time is introduced in analogy with the collection transit time.

The theory, which is generally valid up to frequencies of the order of the reciprocal transit time, is extended to include high injection levels and some second-order phenomena, such as the Early effect and nonideal base contacts. It is pointed out that the integration of the basic equations over the base region may lead to a loss of detailed information, so that the charge-control theory may accurately describe only the average behavior of the device; a solution of this difficulty is suggested. The Ebers-Moll circuit relations are derived from charge-control principles so that a charge-control interpretation of the Ebers-Moll parameters and an electrical interpretation of the charge-control parameters is obtained. This leads to the conclusion that the short-circuit saturation currents are of more fundamental significance than are the open-circuit saturation currents.

Finally, the separation of injected carriers into recombining and nonrecombining components is used to obtain a conceptually clear derivation of the principle of reciprocity for a transistor.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Philosophy)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Philosophy
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Middlebrook, Robert David
Thesis Committee:
  • Unknown, Unknown
Defense Date:22 April 1969
Funding AgencyGrant Number
U. S. NavyN60530-68-C-0530
Radio Corporation of AmericaUNSPECIFIED
Record Number:CaltechTHESIS:03282017-092448714
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10110
Deposited By: Benjamin Perez
Deposited On:28 Mar 2017 19:17
Last Modified:29 Apr 2024 21:17

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