THEORY OF THE SWEPT INTRINSIC STRUCTURE 1263 



this means that the amount of recombination in the interval from 

 X = to a; = L is just equal to the excess amount of generation in the 

 interval from the center of the intrinsic region to x = 0. 



If the applied reverse bias is less than a few kT/q then recombination is 

 important even at the junction and there is no joining onto a no-recom- 

 bination solution. In this case (4.9) says that for a given choice of cur- 

 rent (and hence of L) the boundary comes where 



Example. Fig. 6, which we discussed briefly in Section III, is a plot 

 of the field and carrier distributions for L = 2Li and So = 0.95, for which 

 A = 0.665. The hole and electron densities were found from (3.7) and 

 p -{- 71 = 2niS where s is found from Fig. 5. When s approaches So (4.8) 

 for X versus s takes the simple form 



•^ '^i So S /'lIlN 



ZLi 1 — So^ 



This will be accurate when So — s is small compared to 1/so — So . We 

 have used (4.11) to evaluate the s versus x curve beyond the range of 

 the So = 0.95 curve in Fig. 5. 



It is seen that the recombination solution in Fig. 6 joins the cubic 

 in the range where n and p are still almost equal. 



Variable Lifetime. 



Finally consider the general case where the variation in r with car- 

 rier density cannot be neglected. Then, with n = p = UiS, (2.15) be- 

 comes r = To + (tj — To)s and Li" in (4.4) is replaced by Dt[1 + (tj/tq — 

 l)s] where Tj/tq is given by (2.17). The more general form of (4.4) can 

 be solved graphically after one integration. The solution will join onto a 

 cubic if (ri/ro — l)s becomes small compared to unity before space 

 charge becomes important. This will be so if (t,/to — Vf'I/aEi is small 

 compared to unity. 



V. THE JUNCTION SOLUTION 



In this section we consider the solution near the junctions, where 

 the assumption / = usE breaks down. We shall deal with reverse biases 

 of at least a few kT/q so that recombination is negligible at the junctions. 

 The junction solution will therefore join onto the no-recombination 

 solution. We shall use the cubic solution in the no recombination region. 



Again it is convenient to use dimensionless variables with Ei as the 



