16 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



The base width 



W = ^ — a 



can be obtained from Figs. 9 and 10. a, 13 and iv can be converted to 

 centimeters by nuiltiplying by the appropriate value of Li . 



4.2 Emitter Efficiency 



With the hmits a and /3 determined above, the integrals h and 1 2 can 

 be calculated. Examination of the integrals shows that h is closely pro- 

 portional to ri/r2 and also to r2 . On the other hand I2 is closely propor- 

 tional to r2 and essentially independent of ri/r2 . Thus, the ratio of 

 /2//1 which determines 7 depends primarily on ri/r2 . Fig. 11 is a plot 

 of the constant /2//1 contours in the ri/T2 — X plane for lo/h ii^ the 

 range from — 1.0 to —0.01. The graph is for r2 = 10 . Since from (3.2) 



7 = 



1 



1 _ ^h 



Dnh 



(4.4) 



for an n-p-n transistor, and assuming Dp/Dn = /^ for silicon, then 



to' 



(0- 



10' 



10 



10 



20 50 



100 200 



500 1000 



Fig. 10 — (Collector junction dopth (in rodurod units) as a function of the sur- 

 face concuMit.ration (in reduced units) of llie dilfusaiit wliicli determines the con- 

 ductivity type of the l)ase layer (I'.') and liie ratio of tlie dilTusioii lengths (X) of 

 the tAvo diffusing inii)urifies. 



