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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



Integrating this from the region where E is zero gives 



KdE(x, t) = / dp{x, t) dx. 

 Jo 



(4.11) 



Equation (4.11) states that the dielectric displacement at x is equal to 

 the excess charge between the potential maximum and x. Evidently 

 during the transient following Fig. 4.2(a), the rate of change of this 

 extra charge is —8J(x, t) since the dc current is flowing in at the left 

 and an excess current 5 J flows out at the right. Hence we have 



KdhE/dt - -bJ, 



= —{bpu + pbn). 

 For the change in drift velocity we may write 

 hu = {du/dE) 8E = iM*dE. 



(4.12) 



(4.13) 



For high electric fields u increases less rapidly than linearly with E and 

 /x* is less than the low- field mobility. For very high fields fx* is nearly 

 zero and there are theoretical reasons for thinking that there may be a 

 range in which fi* is negative. We shall return to this point in the next 

 section. 



In Fig. 4.3 we show a diagrammatic representation of the transient so- 



Fig. 4.3 — Graphical representation of the dependence of SE upon time. 



