A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 29 



region of the collector junction. The transit time through this region 

 is no longer a negligible factor. A short calculation will show that with 

 — 10 volts on the collector junction, the space charger layer is about 

 4 X 10"^ cm thick and that the frequency cutoff associated with trans- 

 port through this region is approximately 3,000 mc/sec. 



The remaining problem is the transport of minority carriers through 

 the base region. Depending upon the boundary conditions existing at the 

 surface of the germanium during the diffusion process, considerable 

 gradients of the impurity density in the surface layer are possible. How- 

 ever, the problem of what boundary conditions existed during the diffu- 

 sion process employed in the fabrication of these transistors w^ill not be 

 discussed here because of the many uncertainties involved. Some quali- 

 tative idea is necessary though of how electric fields arising from impurity 

 gradients may affect the frequency behavior of a transistor in the limit 

 of low injection. 



If one assumes a constant electric field as would result from an ex- 

 ponential impurity gradient in the base region of a transistor, then the 

 continuity eciuation may be solved for the distribution of minority 

 carriers.* From the hole distribution one can obtain an expression for 

 the transport factor j3 and it has the form 



/3 = e" 



r? sinh Z -{- Z cosh Z 



where 



1, Ne IqE 

 ^"2^^iV; = 2^^' 



z ^ [i^ + ,r' 



IV' 



Ne = donor density in base region at emitter junction 

 Nc = donor density in base region at collector junction 



E = electric field strength 

 Dp = diffusion constant for holes 



w = width of the base layer 



