and 



FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1211 



In accordance with the results of Section M, we choose for (P the most 

 general harmonic function with spherical symmetry: 



(P = A--}- B {A,B: arbitrary constants). (175) 



From (119) then, for A 7^ 



V = H \n(A--i- b\ + G (176) 



and from (175), (176), (143), and (144) 



/, = ifiMp.i(5+^) (177) 



/n = ^UnneA(S-^\ (178) 



I = ^QeA ^{^JLn + ^ip)H - inn - Mp) y] • 

 From (177) and (178) we obtain 



(179) 



A = '^ ^" (180) 



QfJLptlnkT 



fj = ^^ ^i-nlp + l^pln (181) 



e Unlp — y^pln 

 and from (175) and (176) for \)« = 0: 



B = (9^ (182) 



and 



G= -HlnB = -^^i4^±^ln(P«. (183) 



e fJin^p — ^p^n 



The condition (Poo > UV | = introduces the restriction (for A 9^ 0): 



Evidently this implies no real restriction for ju„/p — txjjn < (i.e., ^ < 0), 

 but introduces a minimum radius — of the same kind we have already dis- 

 cussed—when nJp — f^pln > (i.e., A > 0). 



