FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1185 



(For definition of function A see Equation (87) and Figs. 1 and 2 ) 



[K, M. -U = 1)((P), .V = 0) 



'V = A\n h(x, y,z) -\- B 

 _(P = h(x, y, z) 

 [N, O. gradCP-grad'U = 0] 



'V = h{x, y, z) 

 (P = h{x, y, z) 

 provided 

 _grad hi{x, y, s)-grad h{x, y^ z) = ^ 

 [N. grad 01 • grad 5C = 0, N 9^ 0] 



'"U = \/h^{x, y, z) H- A^(:c, y, z) 

 Ne , — 



^ = Yr ^^'^""^ ^» ^^ 



provided 

 _grad hi{x, y, s) -grad hi{.x, 3;, s) = 

 [P. grad (P- grad ^ = OJ 



"t) = li + h{x, y, z) 

 (P = ^ 



provided 

 grad (P-grad h{x^ y, z) = 0. 



G. Solutions with V = Vit) 



Our point of view in general is that (P and V (or *U and 3C) are functions 

 of three space coordinates and time, so that V = V(l) implies for example 



that — = — = — =0. That is to say, we now seek solutions for which 

 dx dy dz 



everywhere 



grad •U = 0. (39) 



From (21) and (22) this condition gives us the following restrictions on 



