THEORY OF THE SWEPT INTRINSIC STRUCTURE 1249 



The No-Recojnhination Solution 



Here recombination is small compared to generation, r « g. This will 

 be so in at least part of the intrinsic region for reverse biases of more 

 than a few kT/q. The E versus x curve turns out to be given by a 

 simple, cubic algebraic equation. 



The Recombination, or Charge Neutrality, Solution 



Here 7i — ja is small compared to n + p, so the particle flow is by dif- 

 fusion. We shall find that the s versus x curve is given by a third degree 

 elliptic integral. As we move away from the center of the intrinsic 

 region and toward the junctions, recombination becomes small com- 

 pared to generation and the recombination solution goes into the no- 

 recombination solution. In the region where both solutions hold, the 

 solution has the simple form s = I/aE = A — x' where A is a constant 

 that must be less than f and the unit of length is twice the diffusion 

 length. 



As the bias on an NIP structure is increased and the space charge 

 penetrates through the intrinsic region, the region where the recombina- 

 tion is important will shrink and eventually disappear. 



Fig. 1 is a schematic plot of the field distribution for the case where 

 the applied bias is large compared to the built-in potential drop but not 

 large enough to sweep all the carriers out of the intrinsic region. As the 

 voltage is increased, the drop in field in the intrinsic region will become 

 less and finally the field distribution will be almost flat from junction to 

 junction. Only half of the intrinsic region is shown in Fig. 1. For equal 

 mobilities the field distribution will be symmetrical about the center 

 Xi of the intrinsic region. 



The illustration shows the recombination solution (1), which holds 

 near the center of the intrinsic region and overlaps (2), the no-recom- 

 bination solution. The junction solution (3) joins continuously onto the 

 no-recombination solution at the point .To and rapidly breaks away and 

 approaches the zero-current solution at the junction. The figure is sche- 

 matic and has not been drawn to scale. In most cases of interest, the low 

 fields in the recombination region will be much lower and the junction 

 solution will hold over a smaller fraction of the intrinsic region. 



It is convenient to take x = not at the center .r, of the intrinsic 

 region but at the minimum on the no-recombination solution. As the 

 applied bias increases, x, approaches zero. 



Unequal Mobilities 



In the general case of unequal mobilities, it is no longer so that / is 

 pure drift except at the junctions. However we can define a linear com- 



