MA BELL SYSTEM TECJLMCAL JOLKXAL 



where 



^ ^ 1 - oxpl-uor. -(r^A^ _ (6.4) 



liOTt + {Tl/Tp) 



ti represents the effect of recoml)inati()ii and transit anj^le, w-/ , in reducing 

 the gain. 



We shall consider two limiting cases of this expression. First if cor^ is very 

 small, the new factor becomes 



= (r, tM\ - €-''''")■ (6.5) 



If Tt is much larger than t,, , so that the holes recombine before traversing 

 the filament, then the exponential is negligible and (3 becomes simply Tp ti . 

 This means that the effectiveness of the holes is reduced by the ratio of their 

 effective distance of travel to the entire length of the filament, i.e., TpTt is 

 the ratio of distance travelled in one lifetime to the entire length of the fila- 

 ment. Essentially the holes modulate only the fraction of the filament which 

 they penetrate. The transit time depends on the field in the filament which 

 is I Fr — Vj \/Lc, the absolute value being used since Vc is negative. The 

 transit time is thus 



Tt = Lr [np I 1'^ — Vj I Lj = Lc/fJ-p I Vc — Vj\. (6.6) 



For very small emitter currents Vc — Vj = RcVr/{R, + Rb) so that 



Tt = lI(R.-+ Rh) ^JipRr\V,\ (6.7) 



and Tt is inversely proportional to ]',: . For large values of I',. , Tt approaches 

 zero and approaches unity. The dependence of li upon Vc has been investi- 

 gated by measuring a and plotting it as a function of |l "'Vc\ as shown in 

 Fig. 10. The value of 



a = -(df,. dJ,)vc (6.8) 



is readily found from the ecjuivalenl circuit, using equation (5.11), lo l)e 



' Rb UeRc , , 



For the particular structure investigated, the values of Ri, and R, , obtained 

 at /< = 0, were in the ratio 1:4. The value of a obtained by extrapolating 

 the data to 1 F, I = ^c is 2.2; the value given by the formula for this case 

 with /3 = 1 , is 



a = n.2 + 0.8 X 2.5 X 7, (6.10) 



from which we lind 7 = 1.0, in agreement with the result of I-'ig. 4 that 



