438 BKLL SYSTEM TECHNICAL JOURNAL 



cases are advantageous as emitters in transistor applications using «-type 

 material for the base. 



Where the hole current flows in relatively low resistance n-type material, 

 it is governed by the diffusion equation and the concentration falls off as 

 exp(— x/Lp) where Lp is the diffusion length: 



L = VD^>. 



Here D is the diffusion constant for holes and r^ their mean lifetime. The 

 lifetime may be controlled either by surface recombination or volume re- 

 combination. Surface recombination is important if the specimen has a 

 narrow cross-section. 



Under a-c. conditions, the diffusion current acquires a reactive component 

 corresponding to a capacity. In addition, a capacitative current is required 

 to produce the changing potential distribution in the transition region 

 itself. 



In the following sections we shall consider the behavior of the junction 

 analytically, treating first the potential distribution in the transition region 

 and the charges required change the voltage across it in a pseudo-equilibrium 

 case. We shall then consider d-c. rectification and a-c. admittance. 



2. Potential Distribution and Capacity or Transition Region 



2.1 Introduction and Definitions 



We shall suppose in this treatment that all donors and acceptors are 

 ionized (a good apj^roximation for Ge at room temperature) so that w-e have 

 to deal with four densities as follows: 



n = density of electrons in conduction band 



p = density of holes in valence-bond band 



Nd = density of donors 



Xa = density of accej^tors 



The total charge density is 



p= q(p- n + Nd - No), (2.1) 



where q is the electronic charge. We shall measure electrostatic potential 

 \p in the crystal, as shown in Fig. 2, from such a point, approximately mid- 

 way in the energy gap, that if the Fermi level tp is equal to i/', the concentra- 

 tions of holes and electrons are equal to the concentration »,• = pi char- 



2 H. Suhl and W. Shocklcy Pliys. Rev. 75 1617 (1949). 



^ A difference in effective masses for holes and electrons will cause a shift of \p from the 

 midiKiint between the l)ands. 



