THEORY OF THE SWEPT INTRINSIC STRUCTURE 1279 



In the region of low fields where E^ is comparable to or less than I, 

 (7.3) would have to be solved graphically or on a machine. At higher 

 fields the equation is easily integrated as discussed below. 



Case of Pure Drift 

 When the flow is entirely by drift, E^ » / and (7.3) becomes 



5^ = £ + " (^-^^ 



which is made integrable by the substitution E = yx. A family of solu- 

 tions for positive E throughout the v region is 



{E - a,xT{E + a.xT- = Eo"'^"' (7.5) 



where 2ai = \/4 + «' + « and 2a2 = -vZ-i -\- a- — a and Eo is the 



value of E at x = 0. For an intrinsic region N = a = and (7.5) reduces 



to E^ = Eq' + x^, which is the same as (3.9) for negative .4. Fig. 9 shows 



several curves for \'arious values of Eo . These remain above, and at 



5 large distances approach, the asymptotic solutions E = aix on the 



I right of the origin and E = —a2X on the left. These curves differ from the 



corresponding curves for an intrinsic region in that the straight line 



I asymptotes now have slopes of ai and — oo instead of ±1. Toward the P 



I side the slope is greater because the positive change qN of the excess do- 



I nors is added to the charge of holes. Toward the A^ side of the v re- 



' gion the slope is reduced because A^ compensates to some extent for the 



I electron charge. As a increases and the v region becomes more n type, 



the solution approaches that for a simple NP junction, where E = ax 



on the A^ side. 



Another set of solutions of (7.4) are given by 



(ai.r - EY^aox + E)"' = ai^'aa^V (7.6) 



Several of these are shown in Fig. 9. They remain below the linear 

 asymptotes and go through zero field at x = ±:Xc . Actually these will 

 join onto solutions of the more general equation (7.3) when E becomes 

 small and the diffusion term becomes important. 



Rccomhinaiion. When the fixed charge density is small compared to the 

 intrinsic hole and electron density the treatment of recombination in 

 Section IV remains \'alid. The recombination solution joins onto a solu- 

 tion of (7.3) at small fields. When N is comparable to ??» the recombina- 

 tion solution is difficult even with the assumption of charge neutrality. 



