814 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



ill MKS units. The initial value v{0) is then simply 8Ei times the total 

 width of the structure. 



The first effect, which takes place in a neghgible time in respect to 

 the frequencies involved, is the dielectric relaxation of the field in Pi 

 and P2 . The added current due to dEi leads to an exponential decay of 

 dE in these regions with a transfer of 8Qi and —8Qi to the two boundaries 

 of N. If Pi and P2 are thin compared to N, the resulting drop in v(t) is 

 small. In any event it can be shown by the reasoning at the end of Sec- 

 tion 2 that this contribution to D{t) adds simply the series resistance of 

 Pi and P2 to the impedance. 



The next effect is the transport of 8Qi on left side into N by hole flow 

 over the potential maximum. It will be easier, however, to discuss this 

 process after the treatment of the transient effects that occur in A'^ 

 itself. Consequently, we shall at this point assume that after a time, 

 short compared with the important relaxation time in the structure, the 

 disturbance of hole density is as shown in Fig. 4.2(a). 



Fig. 4.2(a) shows added charges -{-8Qi and —8Qi produced by a 

 disturbance denoted as 679 in the hole density. The charge —8Qi on the 

 right side is produced by an increased penetration of the space charge 

 into P2 ; it is similar to that produced by increasing reverse bias on a p-n 

 junction. 



Fig. 4.2(b) shoAvs the corresponding disturbance in electric field. This 

 disturbance is denoted by 8E which is a function of x and t. Evidently 



vit) 



f 



Jo 



8E{x, t) dx. 



(4.4) 



and this is the area under the 8E curve. 



The other parts of the figure indicate qualitatively a subsequent stage 

 in the motion and decay of 8p and 8E. Our problem is to formulate mathe- 

 matically this decay process. We shall treat the decay process in terms 



tfp 



+ 6Q, 



(a) 



-dQi 



(0 



^^=^ 



dE 



(b) 



cfE 



H 



(d) 



Fig. 4.2 — The initial stage and a subsequent stage of the transient. 



