12G2 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



1.0 



0.9 



0.8 



0.7 



0.6 



0.5 



0.4 



0.3 



0.2 



0.1 



-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 



X/2Ll 



Fig. 5 — Variation of s = -plni = n/n; in the range where recombination is 

 important. 



Deep in an infinitely long intrinsic region the carrier densities ap- 

 proach their normal values n = 7? = n, , or s = 1. Putting So = 1 in 

 (4.8), we find that as s approaches So = \-,x becomes infinite. This will 

 be the solution for a simple intrinsic-extrinsic junction. Fig. 5 is a plot 

 of s versus x for various values of So . The dashed curves represent the 

 corresponding no-recombination solution s = ^ — {x/2LiY. 





The IP Junction 



It remains to find the position of the IP boundary. We now show that 

 if recombination is unimportant at the junction, so that the solution 

 joins onto a no-recombination solution, then the position of the junction 

 is at a; = L where L is the effective length of current generation and 

 a* = is the point where dE/dx = ds/dx = on the no-recombination 

 solution (which of course will not be valid at x = 0). The proof is as 

 follows: From the definition (4.1) of L and (4.2) 



L = /;"(l-./,)rfx = 2L/£'|,(g-.)*- 



= 2Lv 



_dx \E{' 



(4.9) 



If the boundary comes where recombination is negligible so that 

 {E/Eif - s = (a-/2L,)' - A, then (4.9) gives Xj, = L. Physically 



