28 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



However, in the transistors described here the base region produces the 

 major contribution to the observed alpha-cutoff frequency and it is more 

 appropriate to use the expression 



2irCcin + Re) 



where n = base resistance. This cutoff frequency could be raised by in- 

 creasing the collector voltage, but the allowable power dissipation in the 

 mounting determines an upper limit for this voltage. It should b noted 

 that an increase in the doping of the collector material would raise the 

 cutoff since the spreading resistance is inversely proportional to Na , 

 while the junction capacity for constant collector voltage is only pro- 

 portional to Na . 



The low-frequency alpha of the transistor ranged from 0.95 to 0.99 

 with some exceptional units as high as 0.998. The factors to be con- 

 sidered here are the emitter efficiency y and the transport factor (3. 

 The transport factor is dependent upon the lifetime in the base region, 

 the recombination velocity at the surface immediately surrounding the 

 emitter, and the geometry. The geometrical factor of the ratio of the 

 emitter dimensions to the base layer thickness is > 10, indicating that 

 solutions for a planar geometry may be assumed.^ If a lifetime in the base 

 region of 1 microsecond and a surface recombination velocity of 2,000 

 cm/sec is assumed a perturbation calculation gives 



iS = 0.995 



The high value of ^ obtained with what is estimated to be a low base 

 region lifetime and a high surface recombination velocity indicates that 

 the observed low frecjuency alpha is most probably limited by the 

 emitter injection efficiency. As for the emitter injection efficiency, within 

 the accuracy to which the impurity concentrations in the emitter re- 

 growth layer and the base region are known, together with the thick- 

 nesses of these two regions, the calculated efficiency is consistent with 

 the experimentally observed values. 



Considerations of Transit Time 



An examination of what agreement (^xists between the alpha-cutoff 

 frequency and the physical measurements of the base region involves 

 the me(;hanism of transport of minority carriers through the active 

 regions of the transistor. The "active regions" include the space charge 



