HOLE CONCENTRATION AND POINT CONTACTS 473 



entering the barrier region per second is given by the following expres- 

 sion from kinetic theory: 



pbVaA/A, (2) 



where Va is the average thermal velocity, 2(2kT/Trmy''^, of a hole and A 

 is the contact area. This expression gives the average number of particles 

 which cross an area A from one side per second in a gas with concentra- 

 tion pb. It follows that the current due to the added holes is: 



I pa = -ePbaVaA/4. (3) 



Since, by convention, a current flowing into the semiconductor ispositive, 

 a current of holes flowing from the interior to the contact is negative. 



The diffusion current resulting from the added holes depends on the 

 difference between pba and pa- We shall show in Section III that when pa 

 is small compared with the normal electron concentration, 



Ipa = 2irrbkTlXp{pba — pa), (4) 



where tb is the radial distance to the outer boundary of the barrier layer 

 and jXp is the hole mobility. The value of pba is found by equating (4) 

 and (3), i.e., the added current flowing from the interior to the barrier 

 layer and the current flowing across the barrier layer. This gives 



where a, defined by 



pba/ pa - a/(l + a), (5) 



a = 4(kT/erb)tJip/va, (6) 



is the ratio of the velocity acquired by a hole in a field 4kT/erb to thermal 

 velocity. This ratio is generally a small number so that the a in the de- 

 nominator of (5) can be neglected in comparison with unity. Equation 

 (3) then becomes: 



Ipa = —eapaVaA/4: = — p akTiXpA / Yb- (7) 



If pa is not assumed small, a similar procedure may be used but the 

 expressions for Ipa in terms of pa are more complicated than (4) and (7) 



It is possible that the added hole current, Ipa, will affect the contact in 

 such a way as to change the normal current flowing. If there is such a 

 change, one might expect it to be proportional to Ipa as long as Ipa is 

 sufficiently small. The total current flow may then be expressed in terms 

 of an "intrinsic a" for the contact as follows: 



/ = h{Vc) - a Ipaipa). (8) 



