The Theory of (y-n Junctions in Semiconductors and p-n 

 Junction Transistors 



By W. SHOCKLEY 



In a single crystal of semiconciuclor the inii>urity concentration may vary 

 from />-ty])e to «-tyi)e producing a mechanically continuous rectifying junction. 

 The theory of potential distribution and rectification ior p-n junctions isdeveloi)ed 

 with emphasis on germanium. The currents across the junction arc carried In' 

 the diffusion of holes in ;/-t\pc material and electrons in /)-type material, re- 

 sulting in an admittance for a simple case varying as (1 + uot,,Y'~ where Xp is the 

 lifetime of a hole in the //-region. Contact potentials across p-n junctions, carrj-- 

 ing no current, may develop when hole or electron injection occurs. The principles 

 and theory of a p-n-p transistor are described. 



Table of Contents 



1. Introduction 



2. Potential Distribution and Capacity of Transition Region 



2.1 Introduction and Definitions 



2.2 Potential Distribution in the Transition Region 



2.3 The Transition-Region Capacity 



2.4 The Abrupt Transition 



^. General Conclusions Concerning the Junction Characteristic 



4. Treatment of Particular Models 



4.1 Introduction and Assumptions 



4.2 Solution for Hole Flow into the H-Region 



4.3 D-C. Formulae 



4.4 Total Admittance 



4.5 Admittance Due to Hole Flow in a Retarding Field 



4.6 The Effect of a Region of High Rate of Generation 



4.7 Patch Effect in p-n Junctions 



4.8 Final Comments 



5. Internal Contact Potentials 



6. p-n-p Transistors 



Vppendix I A Theorem on Junction Resistance 



Vppendix II Admittance in a Retarding Field 



\l)pendix III Admittance for Two Layers 



\l)pendix IV Time Constant for the Capacity of the Transition Region 



Vppendix V The Effect of Surface Recombination 



\ppendix VI The Effect of Trapjiing upon the Diffusion Process 



\l)pendix VII Solutions of the Space Charge Equation 



Vppendix VIII List of Symbols 



1. Introduction 



AS TS well known, silicon and germanium may be either «-type or 

 /)-type semiconductors, depending on which of the concentrations 

 Nd of donors or A^^ of acceptors, is the larger. If, in a single samjile, there 

 is a transition from one type to the other, a rectifying photosensitive p-n 

 junction is formed.^ The theory of such junctions is in contrast to those 



' I'"or a review of work on silicon and germanium during the war see H. C. Torrey and 

 C. A. VVhitmcr, Crystal Rectifiers, McGraw-Hill Book Company, Inc., New York (1948). 

 P-n junctions were investigated before the war at Hell Telephone Laboratories by R. S. 

 Ohl. Work on p-n junctions in germanium has been published b\' the grouj) at Purdue 



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