The Bell System Technical Journal 



Vol. XXIX October, 1950 No. 4 



Copyright, 1950, American Telephone and Telegraph Company 



Theory of Relation between Hole Concentration and 

 Characteristics of Germanium Point Contacts 



By J. BARDEEN 



(Manuscript Received Apr. 7, 1950) 



The theory of the relation between the current-voltage characteristic of a 

 metal-point contact to w-type germanium and the concentration of holes in the 

 vicinity of the contact is discussed. It is supposed that the hole concentration has 

 been changed from the value corresponding to thermal equilibrium by hole in- 

 jection from a neighboring contact (as in the transistor), by absorption of light 

 or by application of a magnetic field (Suhl effect). The method of calculation 

 is based on treating separately the characteristics of the barrier layer of the con- 

 tact and the flow of holes in the body of the germanium. A linear relation be- 

 tween the low-voltage conductance of the contact and the hole concentration is 

 derived and compared with data of Pearson and Suhl. Under conditions of no 

 current flow the contact floats at a potential which bears a simple relation, 

 previously found empirically, with the conductance. When a large reverse 

 voltage is applied the current flow is linearly related to the hole concentration, 

 as has been shown empirically by Haynes. The intrinsic current multiplication 

 factor, a, of the contact can be derived from a knowledge of this relation. 



I. Introduction 



IN DISCUSSIONS of the theory of rectification at metal-semiconductor 

 contacts, it is usually assumed that only one type of current carrier 

 is involved: conduction electrons in »-type material or holes in /J-type 

 material.^ In the case of metal-point contacts to high-purity «-type 

 germanium, such as is used in transistors and high-back-voltage varistors, 

 it is necessary to consider flow by both electrons and 'holes. A large part 

 of the current in the direction of easy flow (metal point positive) con- 

 sists of holes which flow into the w-type germanium and increase the 

 conductivity of the material in the vicinity of the contact.^-' The con- 

 ductivity is increased not only by the presence of the added holes but 

 also by^the additional conduction electrons which flow in to balance the 

 positive space charge of the holes. There is a small concentration of^holes 

 normally present in the germanium under equilibrium conditions with no 



' For a discussion of the nature of current flow in semi-conductors see the "Editorial 

 Note" in Bdl Sys. Tech. Jour. 28, 335 (1949). 



'J. Bardeen and W. H. Brattain, Bell Sys. Tech. Jour. 28, 239 (1949). 



' W. Shockley, G. L. Pearson and J. R. Haynes, Bell Sys. Tech. Jour. 28, 344 (1949). 



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