358 BELL SYSTEM rECHNICAL JOURNAL 



insufficient energy to carry away the "excilon energy" oi a hole-electron 

 pair and, therefore, the release of energy will require the cooperation of 

 several phonons with a correspondingly small transition probability. 



When a square pulse of holes is injected in an experiment like that of 

 Fig. 1, the leading and trailing edges of the current at the collector point 

 are deformed for several reasons. Due to the high local fields at the emitter 

 point, some of the holes actually start their paths in the wrong direction — i.e. 

 away from the collector; these lines of flow later bend forward so that those 

 holes also pass by the collector point but with a longer transit time than 

 holes which initially started towards the collector. A spread in transit times 

 of this sort is probably largely responsible for the loss of gain at high fre- 

 quencies in transistors. For the experiments described below, however, 

 this effect is negligible compared to two others which we shall now describe; 



On top of the systematic drift of holes in the electric field, there is super- 

 imposed a random spreading as a result of their thermal motion. This would 

 cause a sharp pulse of holes to become spread so that after drifting for a 

 time td the hole concentration would extend over a distance proportional 

 to -y/Dtd where D, the diffusion constant for holes, = kTup/q = 45 cm-/sec. 

 As a result of this effect, the leading and trailing edges of the square wave 

 of emission current become spread out w'hen they arrive at the collector. 

 This is shown in Fig. 8, curve A for the leading edge and B for the trailing 

 edge. The points are 10 microsecond marker intervals traced from an oscillo- 

 scope, the time being measured from the instant at which the emitter 

 current starts. For A and B the emitter current was so small compared to 

 the current /& that the holes produced a negligible modulation of conductiv- 

 ity and each hole moved in essentially the same electric field. It is to be 

 observed that the wave shapes are nearly symmetrical in time about the 

 half rise point and that the .1 and B waves are identical except for sign. 

 This is just the result to be expected from diffusion. Furthermore, analysis 

 shows that the spread in arrival time is in good quantitative agreement with 

 the theoretical wave shape using the diffusion constant appropriate for holes. 

 For this case the mid-point of the rise, corresponding to the crossing point 

 of the curves, gives the average arrival time and has been used to obtain an 

 accurate measure of the mobility. 



Curves C and D correspond to conditions in which the emitter current 

 was relatively large — two thirds of the base current. High imjiedance sources 

 are used so that h is constant and h is a good flat topped wave. For the 

 currents used in this experiment, the conductivity is appreciably modulated 

 by the presence of holes. This accounts for the shape of curve C, correspond- 

 ing to the arrival of holes at the collector. It is seen that this curve is not 

 symmetrical but is much more gradual towards later times. The reason for 



