1300 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



the barrier layers* by drift. Base-layer thickness w depends on collector 

 potential Ve through variation of the collector barrier thickness Xm . 

 Variations of emitter barrier thickness are unimportant. The junctions 

 are parallel. 



Currents and Potentials 



The currents and potentials studied are those at the collector and 

 emitter barriers. Unless otherwise specified, "potential" implies dif- 

 ference in majority carrier Fermi levels, i.e., externally applied potential, 

 rather than difference in electrostatic potential. The collector reverse 

 potential is assumed to be many multiples of kT/q(e.g. > 0.5 volts), 

 so that the classical p-n diode reverse conductance may be neglected. 

 At 0.5 volt, this is of the order of 10~^^ mhos. It decreases in magnitude 

 one decade per sixty millivolts of bias potential. 



Base Resistance 



Majority carrier resistance in the base layer is not considered here. 



Other Assumptions 



Surface effects are excluded . from consideration. In addition, several 

 mathematical approximations of little physical consequence appear in 

 the text as needed. 



1.2 METHOD 



The procedure employed is substantially that used by Shockley with 

 some additions. First, minority carrier concentrations on both sides of 

 each barrier are related to the barrier potentials. 



The dc minority carrier distribution in each of the three transistor 

 regions is then computed from these boundary conditions with the aid 

 of the continuity equation. 



Next, small-signal ac perturbations of the barrier potentials and of 

 the minority carrier densities at the barriers are used in the same way 

 to find ac distributions of the minority carriers. The effects of voltage 

 dependence of base-layer thickness are found by means of a small- 

 signal ac perturbation of the position of the collector side of the base 

 layer. The resulting ac distribution of minority carriers is computed as 

 before. 



Finally, dc and ac currents at emitter and collector barriers are com- 



* I.e., charge depletion layers. 



