KXCKS.S SKMICONDl'CTOK llO/J: rKA.XSI'ORT M)'> 



Xole that the velocity of advance of the rear of the disturbance is less than 

 that with which the holes drift in the steady-state field £i . In other words, 

 wave velocity and i)arlicle \-elocity must be distinguished in phenomena of 

 this sort, although they happen to coincide at the front of the disturbance. 



The discussion just given has been based on the assumption that /'„ and 

 /, are independent of time, and that they both flow from left to right in Kig. 1. 

 Time changes in the currents are easily taken into account in the n,, con- 

 struction of iMg. 2: according to (4), it is merely necessary to move the 

 various points of the curve of iii,. against x to the right with the variable 

 velocity V{iih , l) instead of the constant velocity V{nk); in addition, ni,i 

 will in general not be a constant, so that the part of the curve for small x 

 will no longer be a horizontal line. As for the restriction that the currents 

 all flow from left to right, only a change of notation is needed to make all 

 formulas apply to the case where all currents flow from right to left; and 

 the case where part oije flows to the right and part to the left can, obviously, 

 occur only under conditions where the assumptions of this section are not 

 fultilled, i.e., can occur only if electrons are removed at .v = or if both 

 diffusion and recombination are important. For, if diffusion is negligible, 

 the existence of a potential maximum at .v = implies a convergence of 

 electrons from both sides onto the plane x = 0, and recombination alone 

 cannot annihilate electrons at a finite rate in an infinitesimal volume. 



Mention has already been made of the fact that equations such as (12) 

 and (13) give an infinite density of holes when je/ja = Mft/Me , and are non- 

 sensical for larger values of je/ja ■ It is easy to see why any theory which 

 neglects diffusion must break down for values of je/ja of this size and larger 

 if no electrons are removed by the injection electrode. If je/ja is too large, 

 any positive field just to the right of the injection plane .v = will cause 

 more electrons to flow in the negative .v-direction than can be carried off 

 by the current ja which flows in the region of negative x. This difficulty 

 cannot be eliminated by making the field smaller in the region of small 

 l)ositive .V, since making the field smaller requires a higher density of holes 

 to carry the hole current /, ; and this in turn requires a higher density of 

 electrons to preserve electrical neutrality. Thus, though it may be possible 

 to realize experimental conditions under which the approximations of this 

 section are valid for moderate values oi jjja , increase of >//« above the 

 critical value will always result in the building up of an enormously high 

 density of holes and electrons near .v = 0, and one must then consider 

 diffusive transport and possibly other phenomena such as breakdown ot the 

 assumption that no electrons are removed by the injection electrode. 



It will be shown below that the effect of recombination on the curves of 

 ;//, against x at various times / can be taken into account by using a geometri- 

 cal construction similar to that of Fig. 2 except that, instead of moving the 



