THEORY OF THE SWEPT INTRINSIC STRUCTURE 



1269 



dE 



L-x=V2S^r^ 



En 



^2£ ^etnh- i - ctnh- i") (5.13) 



£"0 



En 



En 



From Eq ^ / it follows that Ranges 1 and 2 overlap. By joining the 

 two solutions in the overlap region, the solution in Range 2 can be 

 written as 



£ 



X — Xq = 



\/2Ec 



(n 



8En^ E — En 



I E -\- Eo 



(5.14) 



Putting E = Ej in (5.14) gives the distance over which the junction 

 solution holds. In general we will be interested in cases where Ej is 

 large compared to Eq so (5.14) becomes 



L — .To _ 3 (n2zQ 

 I 2 2o 



(5.15) 



where I = \^&/I^'^ and as before 2o = Eq/V^. In conventional units 



I = 2L 



L2 



(5.16) 



Fig. 7 is a plot of (L — Xd)/1 versus Zq . In germanium at room tempera- 

 ture £,Li will be around 10~ cm. Thus the junction solution will hold 

 over a region that is small compared to L if L is large compared to 

 3 X 10"^ cm. 



Again it is convenient to use the relation & = '\/2kT/q to express 

 the voltage in terms of kT/q. 



'") (3.17) 



Je \dx/ q 



Ej" — Eo 



T?2 TP 2 



By joining the two solutions in the overlap region, the voltage in Range 

 2 can be expressed as 



kT 



2Eo\ ^g> 



e;-) 



(5.18) 



Setting V = V j and E = Ej in (5.18) gives the total voltage drop in 

 the region where the junction solution holds. Let AF be the difference 

 between Fy — Fo and the built in voltage drop at the junction. Then 

 substituting (5.6) with Ec — Eq into (5.18) and subtracting the built in 

 drop we have for AF, 



AT = ^ 



9 L 



(n 



En 



Eo_ 



s 



p -i 



(5.19) 



