THEORY OF THE SWEPT INTRINSIC STRUCTURE 1261 



which says that the disturbance in carrier concentration varies expo- 

 nentially as .t/L, . 



Equation (4.4) can be integrated once to give 



where So is the value of s at the center of the intrinsic region where s is a 

 maximum. 



As recombination becomes unimportant, s becomes small compared 

 to unity and (4.5) approaches the form 



'dsY 1 /, So^^ 



(4.6) 



\dx/ Lj" 

 and the solution joins onto the no-recombination solution. 



Joining onto the Cubic. 



We have seen that the solution joins onto the no recombination solu- 

 tion, in the region where particle flow is by diffusion so that the no 

 recombination solution has the form s = A — (.r/2L,:) . This is readily 

 transformed to the form (4.6) with 



^ = So (l - ^) (4.7) 



Thus the one arbitrary parameter so in the recombination solution 

 determines the parameter A in the cubic that the recombination solution 

 approaches. Since the maximum value of So under reverse bias is unity, 

 the maximum value of /I is f . Negative values of A correspond to solu- 

 tions where recombination is always negligible. 



The s versus x Curve 



To find s versus x we integrate (4.5). There is one constant of integra- 

 tion, which is fixed by the choice of x = 0. We have taken a: = at the 

 point where dE/dx = ds/dx = on the cubic. To make the recombina- 

 tion solution join the cubic we choose the constant of integration so that 

 the recombination solution extrapolates to s = at {x/2Lif = A. Then 



^ = Vl-^f /„, f , , =^ (4.8) 



2Li 2 Jo v3(so — s) — (so' — s^) 



which can be expressed in terms of elliptic integrals. 



