SHOT NOISE IN DIODES 



597 



and 



{kTY {drjffY- ^ Nhm 

 {e) {dx) € 



\ a 



X 



e" - 1 - e'-PCVr?) + 2 



+ /3(5), (14) 



where 



.=^(F'-F), 





2 /"^ 



■rfx. 



The fact that both a{b) and ^{b) are very small greatly simplifies 

 the solution for the distance coordinate x in (13) and (14). The 

 process is to invert the two equations, respectively, extract the square 

 root, and then expand the right-hand side in powers of a(6) and /3(5), 

 respectively. This results in expressions for dx/dr] which can be 

 integrated term by term. However, the small values of a(8) and /3(5) 

 allow powers higher than the first to be disregarded, and hence. 



F(v') 



1 



kT' 



and 



«^ r Nhm 



f(v) 



3/2 



I 



"i' a(8)dr] 



(15) 



L 



^-'Y 



1. f 



r Nhm lir , 1 





(16) 



where for convenience 



r — 



Jo r el - 1 



C?T7 



/(>?) 



Jo 



[ 



+ e^P(Vr,)-2^^j^'"' 



Te"- 1 -6''P(V^) + 2^^r' 



<V) = 



,v - 1 -e''P(Vt7) + 2,P^ 



(17) 



