1182 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



The elegant form of this set of equations furnished the original motivation 

 for the introduction of the variables 11 and JC. The comparable equations 

 for iV = Oare 



div grad (P = (35) 



[N = 0] 



div [(? grad V] = 0. (36) 



D. The Recombination Rate Function (R 



In order to avoid undue confusion in the sequel we shall at this point 

 make some clarifying remarks concerning the function (R. As was stated in 

 the Introduction, we basically regard (R as a function oi p — po and n — no , 

 However, because of (5), any expression in p — po and n — no can be re- 

 placed by one in which (say) p is the only field variable quantity. It is then 

 convenient to regard 61 as a function of p and write it 6{(p). When dealing 

 with expressions in terms of (P and of *U, it is convenient to regard (R as a 

 function of one of these variables and to indicate this fact by writing (R((P) 

 or (R(aL). When we do this we do not mean that (R((P) (say) is the same 

 algebraic function of (P as (R{p) is of p, but rather that (R{p) is the function 

 of p obtained when one substitutes (P = N -{- 2p into (R((P). 



For example, for constant mean lifetime recombination 



(Si{p) =i{p - p^) (37a) 



To 



(R((P) = ri- ((P - (Po) (37b) 



(RCa) - ^ (ai - <u.) (37c) 



with To constant; 



and for mass-action recombination 



(5i{p) = — [p{p + N) - pouo] (38a) 



Moro 



e^N^ 

 '«('^) " 2*Vr. ((Po + N) e^' - '^°>- ^'""^ 



