FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1205 



R. Sample Application of the Results of Section L: Sphekicai. 

 Symmetry, N 9^ 



As an example of the solutions included in the results of Section L we 

 consider the case of a spherically symmetric field about a point (or spherical) 

 source of current. 



We take, as the most general harmonic function having spherical 

 symmetry, 



3C = Zi+ if (140) 



r 



(I, M: arbitrary constants). 



For the time being we shall assume Z 5^ and M ^ 0. Then from (10(J) 

 and (28) and (29) we have 



L 



and 



•0 = Ia( ^-^-^/- )+M+^ (141) 



<P^glA( ^-^.-^A ). (142) 

 In terms of V and (P, (3) and (4) can be written 



l^j^ = Z^ [{(? - N) grad "U + y grad (p\ (143) 



and 



— fin e 

 2 



\((P + N) grad -U - — grad (P (144) 



which yield upon substitution of (141) and (142): 



i='-^^NL(^^A-l)lr. (145) 



and 



i = \^.eNL(^A + iy-,U (146) 



where Ti is the unit radial vector. The total current density is obtained by 

 adding (151) and (152): 



= 1 eNL K/Xn + Alp) j^ ^ + (Mn - Mp) j y, Ti- 



(147) 



