Theory of Transient Phenomena in the Transport of Holes 

 in an Excess Semiconductor 



By CONYERS HERRING 



An analysis is given of ihe transienl behavior of ihc density of holes Hh in an 

 excess semiconductor as a function of time / and of position .v with respect to the 

 electrode from which they arc being injected. When the geometry is one-dimen- 

 sional, an exact solution for the function >th(x, I) can be constructed, provided 

 certain simplifying assumptions are fulfilled, of which the most important are that 

 there be no appreciable traijjjing of holes or electrons and that diffusion be negligi- 

 ble. An attemi)t is made to estimate the range of conditions over which the 

 neglect of ditYusion will be justified. A few applications of the theory to possible 

 experiments are discussed. 



A variety of experiments have been performed, and others are planned, 

 whicli involve measurement of transient or steady-state phenomena due to 

 the drift of positive holes along a specimen of «-type semiconductor after 

 I hey have been introduced at an injection electrode or emitter} These phe- 

 nomena are presumably a result of the interplay of drift, space-charge, re- 

 combination, and diffusion effects. This paper seeks to relate these effects to 

 the phenomena, and its principal contribution is an explicit calculation of the 

 transient phenomena outside the range of small-signal theory, for cases 

 where the geometry is one-dimensional and where certain simplifying as- 

 sumptions, notably the neglect of diffusion, are justified. Removal of some 

 of these simplifying assumptions and a more careful development of the 

 theory will be necessary in certain applications. 



Section 1 discusses the physical assumptions and boundary conditions 

 involved in setting the problem up. Section 2 contains calculations of the 

 (Hstribution of holes along the length of the semiconductor at various times, 

 for the mathematically simplest case where recombination and diffusion are 

 ignored and all currents are held constant after the start of the injection. 

 This simple case illustrates the method of attack to be used in the more 

 general calculations of Section 4, and it is hoped that this sketching of basic 

 ideas will enable the hasty reader to pass on to Section 6 without going 



' llxpL-riments of this sort have been undertaken with the objective of testing and 

 extending the theoretical interpretation of transistor action proposed by J. Bardeen and 

 W. H. Brallain, Phys. Rev., 75, 1208 (1949), especially as regards the role of volume 

 transport of holes, a role first suggested by J. N. Shive, Pliys. Rev., 75, 689 (1949). Ex- 

 ami)les of the tvpe of experiment discussed in the present paper have been described by: 

 |. R. Havnes arid W. Shocklev, Plivs. Rev., 75, 691 (1949) (transient effects); W. Shockley, 

 (;. !.. Pearson, .M. Sparks and W. H. Brattain, in a paper presented at the Cambridge 

 Meeting of the American I'h\sical Society, June 16-18, 1949 (steady-state transport); 

 \V. Shockley, (). L. Pearson, and J, R. Hayncs, Bel! .Sys. Tech. Jour., this issue (steady- 

 state and transient effects). 



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