FLOW OF ELECTRONS AND HOLES TN GERMANIUM 561 



ductor over the concentrations which obtain at thermal equilibrium is 

 fundamental to a number of related phenomena, of which transistor ac- 

 tion is a famihar instance. In an «-type semiconductor, for example, in 

 which the carriers are predominantly electrons, the carrier concentrations 

 are increased by the introduction of holes which, through a process of 

 space-charge neutralization, produce additional electrons in the same 

 numbers and concentrations. The bulk conductivity of the semiconductor 

 is thereby so increased that power gain is obtainable.^ Holes can be 

 introduced by the local application of heat, or by irradiation with light, 

 X-rays, or high-velocity electrons — in fact, by any agency which trans- 

 fers electrons from the highest filled band to the conduction band. They 

 can be introduced also through an emitter, which may be a positively 

 biased point contact or a positively biased p — n junction^, as exemplified 

 in the transistor. In this case the emitter introduces holes, which flow 

 into the volume of the semiconductor^, by the removal of electrons from 

 the filled band.-' ^ Entirely analogous considerations apply to the intro- 

 duction of electrons into a ^-type semiconductor.^ 



In their flow in a semiconductor, added electrons and holes are subject 

 to drift under electrostatic fields and to diffusion in the presence of con- 

 centration gradients as a consequence of their random thermal motions. 

 They are subject also to recombination, which results in concentration 

 gradients in source-free regions even for the steady state in one dimen- 

 sion, or which augments those which may otherwise be associated with 

 the time-dependence of the flow, or with its geometry in the steady state. 

 From fundamental equations which take into account these phenomena of 

 drift, diffusion, and recombination, for the existence of each of which 

 there is experii ental evidence^, general differential equations and 

 boundary-conditiuj i.'^lationships in suitable reduced or dimensionless 

 variables and parameters may be derived, and solutions which give the 

 concentrations and flow densities of added carriers obtained for various 

 cases of physical interest. 



This paper presents results of a theoretical analysis, along these lines, 

 of the flow of electrons and holes in semi-conductors. The treatment is 

 intended particularly for application to germanium. An initial formulation, 



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