DC FIELD IN A "sWEPT INTRINSIC" SEMICONDUCTOR 693 



be eliminated, but the transcendental equations to be solved for A, B, 

 C, and V would become quite formidable.) 



It should be noted that (75) permits an easy determination whether 

 the formulae for B < I or those f or B > 1 should be used in any partic- 

 ular case. Since $(1) = 7r/2, 



B^ liov A"'Le-^"-''' ^ T, (76) 



Appendix II 



CONDITIONS FOR 2ab <3C A, A~^ 



It has been stated without proof in the foregoing analysis that the 

 conditions (40) imply 2AB «: A, A~^ (and hence also AB « 1). This 

 must now be demonstrated. 



For B not » 1, (40a-40d) are sufficient, for (41) shows that A « 1. 

 However, f or 5 ;::>> 1, the product AB is not necessarily small because of 

 A <^ 1 and additional limitations are required. To establish suitable 

 additional conditions we shall consider combinations of U, L, and A 

 for which AB is very small and estimate the conditions under which 

 this smallness begins to weaken. 



By eliminating U between (41) and (43) we can write 



$(B) w \LA^'\ 

 or 



B"%{B) ^ \L{ABf'\ (77) 



Now for /c ?^ 1, 



Therefore, for B » 1 



Substitution of (78) into (77) now yields 



tnBx 2-"'UABf'\ 

 or 



B « exp [2-"'UABf'\ (79) 



