THEORY OF THE SWEPT INTRINSIC STRUCTURE 1259 



tually get to the point where a longer intrinsic region is required. Finally 

 for a given current we reach a minimum voltage which corresponds to an 

 infinite length of intrinsic region. Another way of saying this is that, 

 when recombination becomes important, the length L defined in terms of 

 the current by / = qg2L = qrii/rL is no longer the half length of the 

 intrinsic region. 



Equivalent Generation Length 



We shall continue to define L by / = qnilrh. Thus L is an equivalent, 

 or effective, half length of current generation and not the half length of 

 the intrinsic region. By definition L is the length such that the amount 

 of generation alone in the length L is equal to the net amount of genera- 

 tion (generation minus recombination) in the total half length of the 

 intrinsic region. Hence 



gL = [ \g - r)dx (4.1) 



where Xi is at the center of the intrinsic region and Xp at the IP junction. 

 We shall for the most part deal with reverse biases of at least a few kT/g, 

 in which case recombination is negligible at the junctions. Then the exact 

 solution becomes the no- recombination solution before reaching the junc- 

 tions. We shall continue to take x = at the point dE/dx = ds/dx = 

 on the no-recombination solution which the exact solution approaches 

 as recombination becomes negligible. 



Simplifying Assumptions 



The general differential equation with recombination will be the 

 same as for no-recombination except that g — r replaces g. From (3.1) 

 and (3.2) 



From (2.12) and (2.13) and Poisson's equation 



r = !^ = A^ + p Y _ (^ - P)^ = s' - 9 (— —\ a '\) 

 g n? V 2n, / (2n,) ^ \E, dx ) "-^"^^ 



The following analysis will be based on the assumption of charge neu- 

 trality. That is we neglect terms m p — n in comparison with those in 

 p -\- n.\n particular this means: 



(1) The charge flows by drift so / = asE. This is the same assumption 



