274 BELL SYSTEM TECHNICAL JOURNAL 



We do no more than estimate orders of magnitude. An exact calculation, 

 taking into account the change of conductivity introduced by the emitter 

 current, loss of holes by recombination, and effect of .surface conductivity, 

 is difficult and is not attempted. 



To estimate the field produced by the collector, we assume that the col- 

 lector current is composed mainly of conduction electrons, and that the 

 electrons flow radially away from the collector. This assumption should 

 be most nearly valid when the collector current is large compared with the 

 emitter current. The field at a distance r from the collector is, 



F = pIc/2Trr^ (5.1) 



For example, if, p = 10 ohm cm, Ic = .001 amps, and r = .005 cm, F is 

 about 100 volts/cm. 

 The drift velocity of a hole in the field F is UhF. The transit time is 



J UhF yihpJ-c Jo 



where s is the separation between the emitter and collector. Integration 

 gives, 



T= ^ (5.3) 



For s = .005 cm, ixh = 1000 cmVvolt sec, p = 10 ohm cm, and Ic = .001 

 amps, T is about 0.25 X 10~^ sec. This is of the order of magnitude of the 

 transit times estimated from the phase shift in a or Z21. 



The hole current. In, is attenuated by recombination in going from the 

 emitter to the collector. If r is the average life time of a hole, Ih will be 

 decreased by a factor, e~^/''. In Section II it was found that the geometri- 

 cal factor, g, which gives the influence of separation on the interaction be- 

 tween emitter and collector, depends on the variable s/I/'^. This suggests 

 that the transit time is the most important factor in determining g. An 

 estimate'*'' of r, obtained from the data of Fig. 10, is 2 X 10~^ sec. 



Because of the effect of holes m increasing the conductivity of the ger- 

 manium in the vicinity of the emitter and collector, it can be expected that 

 the field, the life time, and the geometrical factor will depend on the emitter 

 current. The effective value of p to be used in Eqs. (5.1) and (5.2) will 

 decrease with increase in emitter current. This effect is apparently not 

 serious with the surface used in obtaining the data for Figs. 8 to 10. 



Next to be considered is the effect of the space charge of the holes on the 

 barrier layer of the collector. An estimate of the hole concentration can 

 be obtained as follows: The field in the barrier layer is of the order of 10* 



