EXCESS SEMICONDUCTOR HOLE TKANSFORT 



W7 



and (12) and (13) would make iihi infinite and £i zero when je/ja = Mft/Me . 

 This merely means that the assumptions made in this section, in particular 

 the neglect of diffusion and recombination or the assumption that.no elec- 

 trons are taken out by the injection electrode, must fail to be valid before 

 jc gets as large as tihjjiic ■ It will, in fact, be shown in Section 5 how the 

 presence of enormous concentration gradients makes it essential to consider 

 the effects of diffusion near x = whenje becomes large. 

 Putting the boundary conditions (8), (9), (10), and (11) into the wave- 



t 



n 

 C 



"hi 



uo' 



t>0 



Fig. 2 — Schematic variation of hole density nh and electric field E with distance x from 

 injection electrode and time / after the start of the injected current, in the approximation 

 neglecting diffusion and recombination. 



propagation construction described above gives the solution shown schemati- 

 cally in Fig. 2. An infinitesimal instant after / = 0, Uh is zero everywhere 

 except in an infinitesimal interval at x = 0, where it rises to a maximum 

 value Hhx given by (12). This is shown schematically in the upper left dia- 

 gram of Fig. 2. The corresponding plot of £, shown in the upper right, dips 

 down to El , which is less than either £„ or Eo , in this infinitesimal interval. 

 After a finite time has elapsed, the curves of iiu and E against .v are simply 

 those obtained by moving each point of the right-hand portions of these 

 / = 0+ curv'es a distance Vl horizontally to the right, as shown in the bottom 

 two sketches. Here V depends on the ordinate in each diagram, taking on 

 its maximum value Fquu when ii,a = or E = Eo . Since T' is proportional 

 to E^, the curve in the lower right diagram is a parabola in the range be- 



