EXc/'iss sK.\ti(0.\nrcr()M ik >/./■: TK.wsroRT 4>.> 



ot" Sfi tioii 5 shows llial tin- theory nl Set tioii 1, with its iic^lot I (tf ditfusifjii, 

 will givr ;i useful a|)|)r()\iniatir)n to the truth whciK'xcr the ticid in which 

 the holes migrate is suniciently strong ^e.g., strong enough to make the 

 current (lensit\- / >, 100 ./, where J is given by (25) and (26). The obtaining 

 of "sufficiently strong" I'lelds without excessive heating or other undesirable 

 effects is facilitated by the use of specimens with as long a recombination 

 time r as possible, and by the use of specimens of low conductivity. How- 

 ever, it is hard to sa_\- how low the conductivity can be made without danger 

 that the "no trapping" assumption will break down, since for this assumption 

 to be valid the density of hole traps must be « the density of donors. 



The numerical predictions of the theory depend u{)on the way in which 

 the rate of recombination is assumed to depend upon the concentrations of 

 electrons and holes, i.e., upon the form of the function R(p) introduced in 

 (17) and (18). The full curves of Figs. 5 and 6 give the steady-state depend- 

 ence of Hh on .V for two simple assumptions regarding R(v), the dependence 

 corresponding to an}' given boundary value iihi at .v = being simply ob- 

 tained by a suitable horizontal shift of the curve plotted. When the currents 

 are held constant after their initiation, the auxiliary time scale in these 

 figures can be used to construct the transient disturbance at any time, by 

 the methods described in connection with the examples of Figs. 7 and 8. 



These results should hold for a plane-parallel arrangement of electrodes or, 

 to a good approximation, for electrodes placed along the length of a narrow- 

 filament, provided the hh appearing in the equations is interpreted as a cross- 

 sectional average of the hole density and provided the other assumptions 

 given in Section 1 are fulfilled. It is easy to see, however, that practically 

 the same equations apply to cases of cylindrical or spherical geometry, in 

 the approximation where diffusion is neglected. For, in these cases, the 



d \ d 



original equations (17) and (18) merely have Z^,(' ' ') replaced by ~ 7~ (r • • • ) 



1 a . . , 



or ~ — (r- • • •); if the diffusion terms are neglected the solution is the same 

 r^ or 



as before with .v replaced by r-/2 (cylindrical case) or r^/i (spherical case) 

 and with j replaced by I lird (cylindrical case, d = thickness of sample, 

 / = total current) or by / Aw (spherical case). However, it may be difficult 

 to realize experimentally conditions approximating cylindrical or spherical 

 geometry which satisfy the requirement that diffusion effects be small. 



.\nother generalization which is easily made is the removal of the assump- 

 tion that no electrons are withdrawn by the electrode at .v = 0. As far as 

 conditions to the right of .v = are concerned (Fig. 1), the only change 

 required in the diffusionless theory is to interpret y^ as the current density 

 leaving the emitter electrode in the form of holes, rather than as the total 

 current from the emitter electrode, and to interpret ja as the sum of the 



