DC FIELD IN A "sWEPT INTRINSIC" SEMICONDUCTOR 687 



or 



Then substitution of (47) into (43) yields 



L « 2e"%{B) exp [l (^^)"' *(B)] . (48) 



For fixed r/, (47) and (48) are parametric equations of a function Ua(L). 

 These equations were used to compute the curves of Fig. 11 in which 

 U - /nA is plotted against L for 77 = 0.05, 0.1, 0.5, 0.9 and 0.95. This 

 figure gives a quantitative picture of the dependence of the field pene- 

 tration parameter rj on impressed voltage and intrinsic region thickness. 

 [The ordinate U — InK is 3^ the total voltage drop across the intrinsic 

 layer in (kT/q) units.]. 



The foregoing analysis clarifies the progressive elimination of the low 

 field region near the center of the intrinsic material as the applied volt- 

 age is increased for fixed L. Now the high field regions near y = and 

 y = L will be described. Making use of (41), together with 



cosh U w\eU 

 and 



2AB « A, A~^ 



implied by (40), in (36) leads to 



m)^e-"\"' (49) 



and to 



— (0) ;^ -i e-'A. (50) 



di) 



Hence a length characterizing the ''space charge layer thickness" at 

 ?/ = is 



^(0) _, o 1/2 A -1/2 



^ 2e"'K-"\ 



dy 

 Similarly, for the p-intrinsic interface at y = L, we have 



E{L) ^ e-"'K-"\ (52) 



^ (L) ^ -he-'K-\ (53) 



dy 



I 



