526 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



At high frequencies, 7 is determined by the ratio of acceptor density 

 in the emitter to donor density in the base as 



1 



7hf = " 



1 4- ^ 



/I 



Obviously, since the effective donor density in the base must be large 

 to give low ohmic base resistance, the effective acceptor density in the 

 emitter must be even larger if high frequency 7 is to be close to unity. 



Base Region Design 



Base region thickness, w, and the diffusion constant. Dp , determine 

 the diffusion transit time for holes from injection by the emitter to 

 collection by the field of the depletion layer. 



For circular electrodes, which are useful, easily made, and easily ana- 

 lyzed, the ohmic base resistance for the active region of the base between 

 emitter and collector depends on base resistivity, pb, and base thickness 

 as follows : 



' = ^^ = 1 (2) 



If w is made small, n' can be reduced only by making No large. Although 

 large reductions in Vb can be made, increasing Nd is ultimately a self- 

 defeating procedure for several reasons: as No is increased both Dp 

 and the electron mobility, iin, decrease, thus increasing hole transit time 

 and also partially off-setting the reduction in ri by Nd • In addition, the 

 capacitance of the emitter depletion region varies approximately as 

 Nd''^, thus diverting more ac emitter current from hole injection. This 

 capacitance is 



where Ve is the average electrostatic potential across the emitter de- 

 pletion layer. Equations (1) to (3) show the conflicts which necessarily 

 arise in base region design for very high frequencies. The limiting design 

 combines very small w, large Nd , small emitter area A « , and relatively 



