576 BELL SYSTEM TECHNICAL JOURNAL 



unity, or since electrons are more mobile than holes. If b were equal to 

 unity, the field would be independent of the concentration gradient. The 

 second term thus represents a departure from Ohm's law which is due to 

 diflfusion and which is associated with the presence of current carriers of 

 differing mobiUties. It gives a non-vanishing electrostatic field for the 

 case of zero total current. The two terms in the expression for Cp are 

 likewise ohmic and diffusion terms, but here the diffusion term would be 

 present even if the hole and electron mobilities were equal. 



Boundary-condition relationships might be illustrated by some ex- 

 amples for this one-dimensional case. If it be specified that for f ' > a 

 fraction / of the total current to the right of a source at the A'-origin, 

 say, be carried by holes, then, from (18), 



(,^. dP ,, b + {b+ \) P 



f- 



c, 



b + ib + 1)P_ 



X = +0, U > 0. 



The solution in an A'-region to the right of the origin may be determined 

 by this condition and an additional one. The simplest is that for the flow 

 in the semi-infinite region, namely P — Po for A' = x>. This relationship 

 holds for some finite X for an idealized non-rectifying electrode there. 

 For the region between the source and a surface at X = Xa on which 

 there is recombination characterized by a hole transport velocity s, 

 which is also the differential transport velocity for ^ constant, it is clear 

 that C = 0, so that, for A" = Xa , 



(20) C = _J_ _a±_2^ dP ^ J_^ 



^^^^ ^' Mob+ (b+l)P dX bMo ' 



S ^ s/[Dp/t]\ s = Jp/p. 



Consistently with these examples, boundary conditions may in general be 



dP 



expressed as relationships between P, —- , and the parameter C, for given 



oX 



values of A'. 



A simple transformation of dimensionless c^uantities serves to extend all 

 of the analytical results wliich have been given for the ;/-type semi- 

 conductor to the p-iype semiconductor: Consider the substitutional 

 transformation which consists in replacing the original dimensional quan- 

 tities for holes by the corresponding ones for electrons, and vice versa, 

 and in replacing the electrostatic field by its negative. The original set of 

 fundamental equations (1) is invariant under this substitution, which 

 defines an equivalent transformation from the dimensionless quantities of 



