THEORY OF THE SWEPT INTRINSIC STRUCTURE 1267 



Reverse Bias 



Now in the intrinsic region, E^ — s = x"^ — A. Let Ec be the value 

 of E at the junction as given by the cubic, and let Sc = I/Ec be the 

 corresponding value of s. Then at the junction x^ — A = E^ — Sc . In 

 the P material equation (5.5) will still be a good approximation near 

 the junction, where the additional terms arising from the flow will be 

 negligible. Joining the solutions for the / and P regions and neglecting 

 Sc in comparison with Sp gives 



^- = 1 + ^ 



fC i Sp 



Again using sy = Sp exp [— {jqV j/kT)] we have 



Ef = E; + Sp exp [- (1 + E^/sp)] (5.6) 



■In most practical cases Ec will be small compared to Sp = P/2ni so 

 Ej will be the same as for zero bias. 



Junction Solution 



We now consider an approximate solution that joins smoothly onto 

 the cubic and has the required behavior at the junction. Let x = Xo 

 be the point where this solution is to join the cubic. Then in (5.1) x^ 

 must lie between .To and L . We can obtain two limiting forms of the 

 solution by giving x the two constant values, Xo and L respectively. 

 It will be best to take x = Xo since in practical cases the x~ term is not 

 important except near the point where the junction solution joins the 

 cubic. In all cases the uncertainty due to taking x^ = constant can be 

 estimated by comparing the solutions for x = Xo and x = L. 



With X constant, (5.1) can easily be integrated. The two boundary 

 conditions are (a) E = Ej at x = L, where Ej is given by (5.6), and (b) 

 to insure a smooth joining, the slope at x = Xo must be the same as that 

 of the cubic, namely 



2a;o 



\dx /o 2Eo + I/Eo' 

 The first integration of (5.1) with x = .To gives 



(5.7) 



'dEY ^ (cIEY 2^ 

 ,rf.T / \dx A £- 



^ - ^ (Eo' - I/Eo) - IE 

 4 Z 



(5.8) 

 where (dE/dx) is given by (5.7) and Ed^ — I/Eo = Xo — A. The E versus 



