SHOT NOISE IN DIODES 



597 



and 



{kTY (dy^y- _ Nhni 

 (e) {dx) e 



where 





X 



— ( v 



1 - €^P{4y) + 2^^j +/3(5), (14) 



V), 



1 = 



kT' 



P{x) 



2 r^ 



Vtt Jo 



The fact that both a(d) and /3(5) 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(5) and ^{d), 

 respectively. This results in expressions for dx/d-q 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. 



kT 



X — 



Fir/) 



1 



Nhm 



Nhm 



4i--] 



I 



i' a(8)dri 

 *(77) 



(15) 



and 



fiv) 



r Nhm It ,y' 



i'^^H 



S 





(16) 



where for convenience 



FW) = 



Jo 



fiv) = r 



Jo 



dr] 



dt] 



$(,,) = Te"- 1+ e''P(V^) -2^^]''' 

 <p(7,) = h"- 1 -e^P{^y)+2^-l 



(17) 



