470 



HELL SYSTEM TECHNICAL JOURNAL 



The function p{x) which satisfies these boundary conditions and the equation 



= (5.4) 





is 



^(^) =P-+ ^o"^w n^^ ^«^^ (^/^-) + , \ f ^K , sinh (x/L,) 

 2 cosh (w/Lp) 2 sinh {w/Lp) 



(5.5) 



^EMITTER, e 



COLLECTOR, C 



5° = ^f + Vtj 



i" 5 -J A 



V3 = V3 +.93 



(b) 



-w vv 



DISTANCE THROUGH SAMPLE X- 



^b 



Fig. 10 — Model used for calculation of internal contact potential and to illustrate p-n-p 



transistor. 



(a) Semiconductor with two p-n junctions and ohmic metal contacts. 



(b) Quasi Fermi levels showing internal contact potential between h and c. 



which gives rise to a hole current across Ji into Pi of amount 

 dp I 



Ip = -qD 



doc x="ij 



2Z-, 



(11/ I ID IS) I 



= 2X ^^' ~ ^^^ ^°^^ -J- ^ {2pn - pi - po) tanh — 

 [(/>! - Pn) (coth ~ - tanh 1^^ 



^p)J 



- (A' - A,.) { coth ~ + tanh ~ 



)] 





OSP /kT 



- 1] 



Lsinh {2w/Lp) tanh {2w/L 

 = csch (2w/Ap)/po(v?J - coth (2wLp)Ipo((Pc) > 



(5.6) 



