DESIGN THEORY OF JUNCTION TRANSISTORS 1307 



where 



'■--K"-5l.)VLK"-£l)M 



. It may be shown that the boundary conditions on f{y) are : 

 at?/ = 0, / = 0; at?/ = 00, / = 0. 

 Application of these values to equation (23) results in 



in which r2 is obtained using the negative square root. 

 The electron density in the collector is now given by 



^coiKZo 

 The electron current is given by 



In = n,qDn l-m^e"^'' + e'''' ^-^-' (m^ - m,e''' - r.ene'^A . (26) 



At the collector junction, the ac component reduces to 



npqDnfJinm2r2Ei 



Now, since Ei = ppjpcj , the collector multiplication factor 



{I pel ~\~ Inclj/Ipcl 



is 



a* = l + '-^^^ (28b) 



(Tpc tcoMo 



The effect of collector multiplication as given in equations (28a) and 

 (28b) is included in the general admittance expressions given later. 



Finally, no mention has been made of the admittances associated 

 with barrier capacitances. Since the currents which charge these are 

 majority carrier currents, there are no input-output interactions except 

 those associated with majority carrier resistance of the base layer [an 

 effect not analyzed in this study]. These capacitances add directly to 

 input and output admittances. Shockley* gives methods for calculating 

 these capacitances. 



* Loc. cit,, vol. 28, page 435. 



