HOLE CONCENTRATION AND POINT CONTACTS 



471 



The problem may be divided into two parts, which can be treated 

 separately: 



(a) The first deals with the current-voltage characteristics of the space 

 charge region of the rectifying contact. The current flowing across the 

 contact is expressed as the sum of the current which would flow if the 

 hole concentration in the interior were normal and the current which 

 results from the added hole concentration. 



(b) The second is concerned with the current flow in the semiconductor 

 outside the space charge region. In general, both diffusion and conduction 



y//////////////////////////////////, 



AT OUTER BOUNDARY 

 OF SPACE -CHARGE LAYER:- 

 P=PbO' n = nbo = Nf+Pbo 

 V=V; 



|l=Io(Vc) 



'S^//////y////////////////////Ay///// 

 r 



DEEP IN INTERIOR: 



p=Po, n = no=Nf+po 



V = 



(a) EQUILIBRIUM CONCENTRATION OF HOLES IN INTERIOR 



Jl = Io(Vc)-ePbaVaA/4 



4 "//y///////////////////////////////y 



'//////////////////////////////A 



AT OUTER BOUNDARY 

 OF SPACE -CHARGE LAYER".' 



P=Pbo + Pba' n = nbo + Pba 



"^"^i- DEEP IN interior: 



p = Po + Pa, n = no + Pa 

 V=o 



(b) ADDED CONCENTRATION OF HOLES IN INTERIOR 



Fig. 1. — Model and notation used for calculation of current flow in low-voltage case. 



are important in determining the flow of carriers, although, depending on 

 conditions, one may be much more important than the other. In case the 

 applied voltage and current flow are small, holes in an »-type semi- 

 conductor move mainly by diffusion. This situation applies to the prob- 

 lems discussed in the first part of the memorandum. In Section IV we 

 discuss the opposite limiting case of large voltages in which the electron 

 current flowing is so large that the hole current is determined by the 

 electric field and diflfusion is unimportant. 



The model which is used to investigate the low-voltage case is illus- 

 trated in Fig. 1. For purposes of mathematical convenience, the contact 

 is represented as a hemisphere extending into the germanium. Recom- 

 bination, both at the surface of the semiconductor and in the interior, is 



