THEORY OF THE SWEPT INTRINSIC STRUCTURE 



1245 



region. Particle flow is away from the center of the intrinsic region. 

 Carriers are generated in the intrinsic region and flow out at the two ends, 

 the electrons going out on the N side and holes on the F side. Thus J is 

 positive near the IP junction and negative near the NI junction. 

 From the definitions of / and J and equations (2.2) 



- = nE{p -\- n) - D -J- {-p - 11) 

 q ax 



J = m£'(p - n) - D^(p-\-n) 



(2.3) 



It is convenient to express the equations in terms of E and a dimen- 

 sionless variable 



s = 



n + p 

 2ni 



(2.4) 



I which measures how "swept" the region is. In normal intrinsic material 

 s = 1. In a completely swept region s = 0; at the junctions with highly 



'' extrinsic material s ^ I. Using Poisson's equation to express p — n in 

 terms of E, equations (2.3) become 



r J, qD ctE 



1 = asE - ■ — -— 

 a ax- 



J = 



d_ 

 dx 



2a 



- 27uDs 



(2.5) 



where a = 2 /x n,g is the conductivity of intrinsic material. The particle 

 flow J is thus seen to be the gradient of a flow potential that depends 

 only on E and s. 



Equations (2.5) can be written in the form 



[ 



a\ sE - £■ 



drE 



dx^ 





(2.6) 



(2.7) 



where £ — \/kT/2aniq is the Debye length in intrinsic material and 



V2kT 





q& 



(2.8) 



is a field characteristic of the material and temperature. Specifically Ex 

 is \/2 times the field required to give a voltage drop kT/q in a Debye 



