446 BELL SYSTEM TECHNICAL JOURNAL 



current required to change the potential distribution in the transition region 

 is related to other hole currents is discussed in Section 4.1. 



Under our assumptions, after the voltage V is applied, a steady state is 

 reached involving no current hence Vipj, = V<pn = 0. Consequently, both 

 ^pp and ipn are constant and 



iPp — ^n = ^s? (2.25) 



since the holes are being suj)plied from a source at a potential d^p higher than 

 for the electrons. 

 We shall then have 



p = me'^^""^^"^ = iHe'^"'-'^^"'' (2.26) 



n = me"^*-'''^"'' = me'^'^-"'^"^ (2.27) 



where 



'Pi = (fp + ^n)/2, (pp = (pi -\- 8ip/2, ipn = ipi — V/2 (2.28) 

 and 



n, = me"''"'^. (2.29) 



Thus the effect of applying the potential dip in the pseudo-equilibrium case 

 is equivalent to changing nt to wi just as if the energy gap had been reduced 

 by qdip. 



In the ^-region, )i « p and so that p = —ax is a good approximation. 

 Similarly, in the ;i-region, we set h = ax. Hence we have in the /^-region 



;/, = ^1 + (5^/2) - (kT/q) In (-ax/m) (2.30) 



and in the ^-region 



^Jy ^ ^,- (5^/2) + (kT/q) In {ax/ Hi). (2.31) 



Hence the effect of dip is to shift \{/ in the /^-region upwards by dip compared 

 to \{/ in the «-region. This is an example of the general result that \p — ipp 

 tends to remain constant at a given point in the />-region no matter what dis- 

 turbances occur and \}/ — ip,, tends to remain constant in the //-region. 



The Capacity for Ihc Xeiilnil Case K « / 



For the neutral case, we calculate the total number of holes, P, between 

 Xc and .V6 as a function of 8ip. The charge of these holes is qP and the effective 

 capacity is q dP d dip. As explained above, we are really interested in the 

 change in number of holes in the transition region. However, the value of P 

 is relatively insensitive to the location of the limits .Xa and .Vb so long as they 

 lie in regions where the conductivity approaches the maximum values in the 



