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BELL SYSTEM TECHNICAL JOURNAL 



The equations (29) and (30) of course apply only to the portion of the 

 curve of v against ^ which is derived from starting points vo on the v axis 

 which are less than the maximum value vi corresponding to the value m.i 

 given by (12): The points for pq < vi are merely initiated at time 5 = and 

 propagated by the differential equation from then on; the point v ^ vi , 

 ^ = 0, on the other hand, remains a source at all times from the initiation 

 of the injection onward. Thus the complete curve of v against ^ for any 

 positive 5 follows the dotted construction of Fig. 4 from the ^ axis up to 

 where it intersects the full curve corresponding to j/q = n , after which it 



4ccx 



Fig. 4 — Schematic illustration of the method of constructing the curve of hole density 

 fih against distance x from the injection electrode at some given time, taking account of 

 recombination but neglecting diffusion. 



follows the latter curve, as indicated by the crosses m the figure. The steady- 

 state distribution is thus simply the full curve for vo = fi • 



For explicit calculation for the case of pure volume recombination one 

 must insert <I> = 1/[1 + (1 + Hh/t^e)v\\ R = v{\ ^ v) into (29) and (30). 

 The integrations are easily carried out and give 



1 + (4 + Hh/(J'e)vo 



^ = 



+ In 



1 + (1 + yih/iJ-^n 



+ ^, In 

 [same with v instead of I'ol 



1 + (1 + Hh/lJ-e)V0 



1 + J^o 



= In 



1 +V0 



- In 



1 +P 



(31a) 

 (32a) 



