THEORY OF THE SWEPT IXTRINSIC STRUCTURE 1271 



Again there are t^^■o o\-erIapping ranges where the solution has a simple 

 form : 



Range 1. Here E' is small compared to 21 /Ea . This will be so even 

 when E becomes large compared to Eq . Setting Ci = 2Eo/I and y = 

 E — Eo in equation (5.22) and integrating gives 



X ^0 — ^ /\/ ~~r~ 



E, r^"^" dy 



I X Vci^ + If 



(5.23) 



^ ,/Eo . , -1 /E - Eo\ 



and 



V - Vo 



IT /9F (5.24) 



= ^ y Y (Vci^ + (^ - E,r- - ri) + 2Eo(x - .To) 



Range 2. Here E is large compared to Eq . It follows from Eq « I 

 that E is also large compared to Ci . Setting ci = 21 /Eq we have 



•^'- dE 



L - X = V2£ / f 

 Jr e 



E VWT~c? 



Joining (5.21) and (5.23) where they overlap we have in range (2) 



X — Xo = £ a/ ~ hi I ^3 



'Mf. 



E 



C2 



+ \/c.^ + E' 



(5.26) 



Putting X = L and /i" = Ej in (5.26) gives the length f, — .r„ in which 

 the junction solution holds. If Ej is lai'ge compared io c.> , then 



^=y/|(«i (5.27) 



where as before Zo = Eo/I^'^ and Z is given by (5.16). Fig. 7 is a plot of 

 (L — Xo)/l versus zo . The two approximations (5.15) and (5.27) for 

 Zn « 1 and Zo ^ I respectively are shown dashed. Both become inaccu- 

 rate as they are extended toward zo = I. The point at ^o = 1 was ob- 

 tained graphically. Each approximation is in error by about 28 per cent 

 here. The error will decrease as each approximation is (wtendod away 

 from 00 = 1 toward its range of validity. 

 The voltage in Range 2 is given by 



