DESIGN THEORY OF JUNCTION TRANSISTORS 1281 



9E C9 j- 



Yr^V^ 



Ctc 



4B 

 Fig. 3 — Theoretical equivalent circuit for "one-dimensional" transistor. 



currents are used and the admittances and barrier capacitances are 

 written on a per square centimeter basis. It will be noted that transverse 

 voltage drops resulting from base spreading resistance are ignored in 

 developing the expressions of this section. 



A number of physical mechanisms are involved in the admittances 

 for minority carrier flow. The forward current across the emitter junction 

 rises as an exponential of the emitter to base region voltage. This is the 

 result of the thermal energy distribution of minority carriers and is com- 

 mon to all thermionic emission. A natural effect of this exponential de- 

 pendence is that a given change in the voltage results in a fixed per cent 

 change in the current, thus producing an ac admittance which is pro- 

 portional to the average or dc emitter current. For several reasons not 

 all of the current which flo\ys through the emitter junction is collected. 

 First, some of the emitter current consists of electrons diffusing into the 

 emitter body and of displacement current through the emitter depletion 

 layer capacitance. These effects are expressed in the emission factor or 7, 

 which is the ratio of the hole current injected into the base region to 

 the total emitter current. Further, some of the injected holes recombine 

 in the base layer. Those which are collected suffer a transit delay which 

 results in a phase difference between emitter and collector currents. These 

 two effects are summed up in the forward current transport factor or (3, 

 which is the ratio of the minority carrier current reaching the collector 

 to that injected by the emitter. Finally, the current of holes entering 

 the collector from the base gives rise to a much smaller flow of electrons 

 from the collector to the base, thus producing a collector multiplication 

 factor or a*, which is the ratio of total carrier current crossing the col- 

 lector junction to the hole current entering it from the base. 



Although the most important minority carrier flow originates at the 

 emitter, this flow is altered by changes in collector reverse voltage. As 

 the collector reverse potential is increased, the base region becomes 



