1206 THE BELL SYSTEM TECHi^ICAL JOURNAL, OCTOBER 1951 



The currents flowing are obtained from the current densities from the 

 relation 



/ = 12r2 II -Fi 



where 12 is the soHd angle (with respect to the origin) within which the 

 flow field lies. (If the current source is surrounded by the homogeneous 

 semiconductor, 12 = 47r; if it lies on a flat surface of a large slab, 12 = lir, 

 etc.) So we have 



I^ = l;U^^eNL(j^A - 1^ (148) 



^Q^^eNL(j^A + 1^ (149) 



1 ~r e ^ 



/ = - QeNL\ (fin + fip) ~A + {tin - lip) 



(150) 



We shall now obtain expressions for the mathematical parameters B^ A, 

 Lj and M in terms of meaningful physical quantities: Ip , In , °0oo and (P^. 

 (Subscript oo refers to values of variables as r becomes very large.) We 

 shall take our reference voltage as the voltage "at infinity" so thafUoo = 0. 

 Setting 1/r = in (141) and (142) we obtain 



e^) 



= ^A ( ^ I + M 

 and 



from which follows (for A 9^ 0) 



kT 



and 



^ = I In ^ + 1 (151) 



M = -^(Poo. (152) 



eN 

 From (148) and (149) we readily find (for I ?^ 0) 



e flpln — tlnlp 



