HOLE CONCENTRATION AND POINT CONTACTS 49S 



lions are not linear. Accordingly, to a close approximation, we may take 

 for the added hole current: 



lirTh 



" 26 (^g - pa) _ b{b - 1) bXf + (^> + D^ gl .^ . 



. b+\ {b + \y-''^bNf+{b+ \)p„y ^ 



which is the generalization of Eq. (34) of the text. 



The value of pba and thus of I pa may then be found by equating this 

 expression with that of Eq. (3) for I pa. This procedure yields the trans- 

 cendental equation: 



Pba = 



2b{pba - p a) _ bib - \)Nf bXf + (6 + Dpba 



. b+ \ (6+1)2 ''^bNf+ {b+ 1)^J' 



(8B) 



where a is again defined by Eq. (6) of the text. This equation must be 

 solved in general by numerical methods for a particular case. The equa- 

 tion simplifies for pa either large or small compared with Nj . The latter 

 case is treated in the text. The opposite limiting case of large hole con- 

 centrations is treated below. 



For pa large compared with X j , the logarithm may be neglected, so 

 that 



p,a = -2ab{p,a - pa)/{b + 1). (9B) 



If, as in the text, it is assumed that a is small in comparison with unity, 

 there results: 



Pba = 2abpa/{b + 1), (lOB) 



and, using (3): 



I pa = -[2b/ {b -f \)]pakTiXpA/H . (IIB) 



This differs from (7) by a factor 2b/ {b -\- 1). The equation corresponding to 

 (8) will have this additional factor, and also the expression for the con- 

 ductance, G, which, for large hole concentrations is: 



G = Go + \2b/{b + \)\{ai5<j,A/bn){pa/no), (12B) 



in place of (38) of the text. Equation (16) which relates floating potential 

 and conductance is general, and applies for arbitrary hole concentration. 



