FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1181 



It will be observed that (23) is equivalent to the condition 



div 11 = (24) 



established as Theorem 9. 

 (In terms of (P, (10) becomes 



,°, ^ _ eU- M.) [fa ^ ^ \ _^ ,^ _ kT 



Lvi ^ + ^) Srad "^ - Y ^""^"^ ^)1 • 



(25) 



In most of the following sections we shall find it expedient to consider 

 separately the cases N 9^ and N = (associated respectively with semi- 

 conductors of the extrinsic and intrinsic conductivity types). For the case 

 y ^ 0, use will be made frequently of new dependent variables ^ and 3C 

 defined by: 



■a^^(P (26) 



kT 

 3Q, = V- — iS> = V-'\l, (27) 



That is, 



(P-gnt (28) 



t) = ni + 3C (29) 



will be substituted into relations involving (P and V to obtain the corre- 

 sponding relations in terms of "U and 3C. Incidentally, it will be noted that 

 11 and 3C have the dimensions of voltage. 



In terms of *U and JC the basic equations (21)-(23) can be written: 



divgrad.= -^[cH + |^,^] (30) 



div[^grad(at+ac)]=f:[cR + g;^^] (31) 



div [grad 3C + ^ ai grad (U + JC) J = (32) 



wherein (R will be considered as (R(^). 



It will be observed that, in the absence of recombination and time varia- 

 tion, (30)-(32) reduce to 



div grad OC = (33) 



and [A^ ^ 0] 



div [ai grad (ni -h OC)] = (34) 



