DC FIELD IN A "sWEPT INTRINSIC" SEMICONDUCTOR 673 



or 



1 — sn 



for B > I. 



Note: 



((ii-;)'(^')^--"') 



F[k, ^] s f 

 Jo 



Vl - k^sin^d 



is the Elliptic Integral of First Kind, usually tabu- 

 lated for 



O<0<L < k <1. 

 2i 



im 



4'-i] 



is the Complete Elliptic Integral of First Kind. 



sn[/!;, F\ = sin 

 and 



cn[A;, F\ = cos 



are Jacobian Elliptic Functions associated with 



When A , B, and C are prescribed, (38b) or (39b) gives the normalized 

 potential ^^ as a function of the normalized distance y. The normalized 

 hole concentration p, electron concentration n, and field intensity E 

 are then given as functions of y by (33), (34), and (36). 



In a following section it will be shown that, subject to the reasonable 

 assumptions 



Ae-"", A-'e-"" « 1, (40a, b) 



L » A-'«, A"^ (40c, d) 



A, C, and B are given in terms of the normalized potential a,t y = 0, 

 the normalized thickness of the intrinsic region, and the parameter 

 A ^ {N/Pf^' by 



