FLOW OF. ELECTRONS AND HOLES IN GERMANIUM 



597 



in the (P, G)-plane, and/" and/+ may be obtained by solving for them in 

 equations (56). 



For the intrinsic semiconductor, this method can be appHed analytic- 

 ally, and the solution so obtained serves at the same time as an approxi- 

 mation for large relative hole concentrations in the n-type semiconductor, 

 for which the method is otherwise essentially graphical or numerical in 

 the general case. Making use of the symmetry of the solutions for the 

 intrinsic semiconductor about a source, it follows from (57) and (58) 

 that 



(b + 1)^ 



G+ = -G~ = 



(61) 



U 



t'-^l]^* 



(b + 1)^ 



2b 



whence 



(62) 



■' b + 1 2 L"^' 6 + ij C- 



/ b+1^2i^' 6 + lJc+* 



It is easily verified that this result holds approximately for large relative 

 concentrations in the n-type semiconductor. Three simple special cases 

 of (62) might be considered: The first is 



fc- = -C+ = - ic 

 (63) 



I/- =/+=/«• 



This is the rather trivial case of symmetrical flows from a source which 



supplies all currents. A second special case is that for which C~ and C"*" 



are both positive, say, and such that there is no hole flow to the left 



against the field. It is readily found that, for this case, 



(64) 



b+ 1 



/e- 



1 



r = 0; /■" = 



b+ 1. 

 2 



C+ - 



^4-^[/"n-i-J-- 



/e 



6+ 1/. + 1/(6+ 1)- 



Here, the drift from the left under the applied field of holes normally 

 present in the intrinsic semiconductor just cancels the diffusion from the 

 source to the left.^^ A third special case is that in which the total current 



^' Using the numerically obtained solutions, the validity of (64) as an approximation 

 for large concentrations in «-type germanium may be seen as follows: For /, equal to 

 unity and C( , C~ and C+ equal to 2, 1.5, and 3.5 respectively, P^ is about 0.6 and 

 the fraction of injected holes which flows against the field is nearly one-half; doubling 

 these current densities increases P" to 1.45 and decreases the fraction to about one-fourth, 

 and the fraction is less than about one-tenth if the current densities are increased so that 

 C" exceeds 15 



