FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



571 



transport velocity and loosely referred to as the transport velocity of 

 added carriers, of course differs in general from the transport velocity 

 proper, defined as the ratio of flow density to concentration; its general 

 definition, which is applicable to the steady state, has been introduced to 

 facilitate later interpretations. 



2.3 Reduction of the fundamental equations to dimensionless form 

 2.31 The general case 



In order to obtain solutions in forms which exhibit such generality as 

 they may possess, the fundamental equations are to advantage written 

 in terms of dimensionless dependent and independent variables which are 

 the original variables measured in suitable units. Through formal con- 

 sideration of the equations (1), in conjunction with (3) or with (4) and (6), 

 these units can be so chosen that the system of reduced equations will 

 exhibit independent parameters on which it may be considered to depend. 

 The best choice of suitable units is by no means unique; those choices 

 which have been made are natural ones, in that they have been found to 

 result in greater formal simplicity and ease of interpretation in the theory 

 than others which may be equally valid in principle. 



The choice for an n-type semiconductor consists in definitions of di- 

 mensionless variables and parameters as follows: 



= \P,Tt 



(8) 



kT LIT 



X = x/Lp , Y = y/Lp , Z = z/Lp ; Lp = 



U = t/T 



P = /»/(«o - pu); Pi) = po/{no - po) = goT '(«o - pa) 



N = n/(no — po); No = «o/(«8 — po) 



C ^ I 7„ = Ea/Eo = fxEa/iDp/T^; h ^ (ToEo ; £o ^ kT/eLp 



Cp = Ip/Io 



C,i = — I„//o 



F = E/Eo 



W = V/EoLp = eV/kT 



_Q ^ r/Tp . 



The rectangular cartesian space coordinates are .v, y, and z. The quantity 

 T is the mean lifetime of holes for concentrations of added holes small 

 compared with the thermal-equilibrium electron concentration, »o ; and 

 (To is the conductivity of the normal semiconductor. The hole mobility, 



