FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1213 



kT 



dZ\ = V - ^ = V - 4-^(9 (N 9^ 0). 

 o el\ 



II : total current density vector. 



o 



||»: electron current density vector. 



o 



||p: hole current density vector. 



subscript "0": designates thermal equilibrium values. 



subscript "oo": designates values ''at infinity". 



Physical Constants: 



T: absolute temperature. 



e : magnitude of electronic charge. 



k : Boltzmann's constant. 



ju„: electron mobility constant. 



Hpi hole mobility constant. 



a : = 1/fip + 1/fjin . 



^ : = l//xp - 1/Mn . (Assumed p^ 0) 



y : = - — 

 ae 



N: = no — po. 

 Other Constants and Functions: 



A,B, • • • , Z ((except /, N, and T)), 



A,B,",Z, 



A, B, • • • , Z: arbitrary constants 



a,b, ■" ,z ((except e, h, k, n, p, r, t, x, y, z)), 



d,h, • • • , z: arbitrary functions of variables designated (e.g., j(t)). 



h, hi , h2 : harmonic functions of variables designated at place of usage. 



A: A{x) is defined by the relation A(:r) + In | A(x) — 1 \ = x. 



(See Figs. 1 and 2.) 

 S: S(ni) is defined by S[(R(ni)] = U 



Acknowledgment 



The author is indebted to J. Bardeen and W. van Roosbroeck for a critical 

 reading of the manuscript and a number of valuable comments. 



References 



1. W. van Roosbroeck, "Theory of the Flow of Electrons and Holes in Germanium and 



Other Semiconductors," Bell System Technical Journal, 29, 4, 560-607 (October 

 1950). 



2. J. Bardeen, "Theory of Relation Between Hole Concentration and Characteristics 



of Germanium Point Contacts," Bell System Technical Journal, 29, 4, 469-495 

 (October 1950). 



3. VV. Shockley, Electrons and Holes in Semiconductors, New York, 1950. 



