962 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



Three cases will be treated. In all of these it will be supposed that the 

 width of the filament parallel to the magnetic field is relatively large, 

 so that effects from the edges can be neglected. Also, we are concerned 

 only with average effects over the long dimension of the filament. This 

 permits us to deal with a one-dimensional problem. We shall consider 

 first the case in which holes are supposed to be injected from the sur- 

 faces, and the two surfaces have equal and rather large recombina- 

 tion rates. In Fig. 9, part (a) shows how holes injected from each 

 surface are distributed across the thickness in the absence of a mag- 

 netic field, and part (b) shows the distribution with a moderate field. 

 The form of these distributions may be determined from the following 

 arguments. 



H=0 



H>0 



THICKNESS ' 



THICKNESS' 



(a) (b) 



Fig. 9 — Excess hole density across the thickness dimension, (a) with no magnetic 

 field, (b) with moderate magnetic field. 



If we suppose a steady hole current Jo emitted from the left-hand 

 surface of the filament, then a relatively high concentration pi of holes 

 will appear directly in front of the surface. Some of these holes will re- 

 combine upon the surface, the rate Ji being given by 



Ji = PiSq 



where S is the recombination constant for the surface. The balance of 

 the holes will diffuse through the filament to recombine upon the right 

 surface at a rate 



J2 = p^Sq 



and we note that Ji -\- J2 = J. Because of the high recombination rate, 

 P2 w'ill be very small; hence, J2 will be much smaller than Ji . In the ab- 

 sence of a magnetic field the gradient is uniform, and the concentrations 

 will be linear, as shown in part (a) of the figure. An identical argument 



