40S 



BELL SYSTEM TECHNICAL JOIRXAL 



tweeii the front and the rear of the transient disturbance; this parabola, if 

 continued, would have its vertex at the origin. After a sufficiently long time 

 a steady state will be reached in which the field for positive x has the uni- 

 form value El and the density of holes the uniform value nu • 



It is possible to measure ;/;, as a function of / for fixed x by using a closely 

 spaced pair of probes to measure the potential gradient E, and convcxting E 

 to Hh by (3); alternatively, the current to a single negatively biased probe 

 can be used as a measure of ;;/. , if calibrated by the two-probe method. The 



t 



rihi 



Fig. 3— Schematic variation of hole density «/, with time / after the start of the injected 

 current, at some given distance downstream from the injection electrode, in the approxi- 

 mation neglecting dilTusion and recombination. 



portion of this curve of ih, against / for which < ;/a < uni is given, in the 

 present approximation, by 



where 



, s x[(iie -\- fih)nh -^ Heno] e 

 t = x/V{nh) = / • I -N 



HelXhrnKja -\- Je) 



= /^[l + (1 + txi,/tie)nh/n^- 



tf = x/EoHh 



(14) 



(15) 



is the time of arrival of the front of the disturbance. This curve is a parabola, 

 as shown in Fig. 3; if continued, the parabola would have its vertex on the 

 negative Hh axis, as shown. The rear of the disturbance, at which un becomes 

 constant and equal to hhi , arrives at a time Ir given by inserting Uhi from 

 (12) into (14): 



Ih = If/[\ - (1 + tJi./fJih)jenja + je)]' 



(16) 



