DESIGN THEORY OF JUNCTION TRANSISTORS 1303 



Use of equations (7a) and (7b) leads to: 



i^ X sinh {sx/L) ,, 



- (p.o - p„) coth («)o/L)] ^ e*"' 



(9) 



The complete solution for hole density in the base layer is: 



_ \{VcO - Pn) - {peO - Pn)e"°^n _,/^ 



L 2 sinh (?/;o/L) J 



L 2 sinh (swo/L) J 



-[ 



(10) 



2 sinh (st^o/L) J 



iiJi i„< sinh (sx/L) r, . u / /r\ 



+ L ^ sinh (.Wi^) f(^^" - ^'^^ ^^^^ (^«/^) 



— (pcO — Pn) COth {w^lVi\ 



The hole-current density in the base layer is found from equation 

 (10) by the use of the equation for diffusion current 



/.= -,Z>.| (11) 



which yields 



J ^P ( ( \ cosh (x/L) f . 



/.= -<? -^ (^(Pco - P.) -^h^^;;^ - (P- - P») • 



cosh [(a; — w^lL\ cosh {sx/L) i^t 



sinh (wo/L) ''^ sinh (swo/L) 



cosh [(sx — stt;o)/J^l t«« , w;i t«< cosh {sx/L) 

 sinh {swo/L) L sinh {swo/L) 



[{peo — Pn) csch (w;o/I/) — (pco " ^n) coth {wq/L)] 



Hole-current densities at emitter and collector may be found by 

 substitution of a: = and x = Wq respectively. The first two terms in 

 equation (12) give dc current components* which may be attributed to 



* With some labor, these terms may be converted to Shockley's equation (5.6). 



