1306 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



being negative and many times kT/q. The distribution of electrons in 

 the collector is governed by conditions (16a) and (16b) and the modified 

 continuity equation* developed by W. van Roosbroeck. 



(17) 



in which Ea is the electric field which would be associated with the total 

 current iin^np. Mo = (pp + hno)/(pp + rip) and Do = (Pp + np)/ 

 (Pp/Dn + np/Dp). 



If n is assumed to be given by n{t,x) = no{y) -\- n^ {y)e"'* and E is 

 assimied to be 



Ea{t,x) = Eo -\- Eie'"'* = pJco + Ppclpcie"^* 



in which Ico is average collector current and Ipd is the ac hole current of 

 the collector, equation (17) may be reduced to two equations 



= J^!±^) + ^p + ^p^ (18a) 



V Dot I DoMo dy dy^ 



MoDo dy Dor "^^ "^ DoMo dy '^ dy^ ^ ^ 



The solution of equation (18a) under condtiions (16a) and (16b) is 



no = Upil - e^^n (19) 



I 



where 



W2 = 



< 



^0 y V2i>oMo; "^ Dor I 



2Z)oikf, 

 Inspection of equation (19) shows that 



^" = -m2npe'^'' (20) 



It is then apparent that ni must be of the form 



ni = npe'^^'fiy) (21) 



Substitution of equation (2) and equation (21) into (18b) leads to ^ 



^^ M (^ -L '^"^O \ ^/ '^^ f ripm2ilne2 (^r,\ 



A general solution of equation (22) is 



f{y) = HzH]^ + Be'" + C/^" (23) 



* W. van Roosbroeck; private communication. 



