EXCESS SEMICONDUCTOR HOU TRANSPORT 



411 



which can be substituted into (17) to give a differential equation for nu alone: 



> r (jihUh 1 _ ^ ^ ("A 



dill, 



dJ 



.1^ 



e d: 



(«o + 2nh) ~ 

 ox 



, kT d 



(22) 



The first term on the right represents drift, the second recombination, and 

 the third diffusion. This holds whether j is constant in time or not. How- 

 ever, as the remainder of this memorandum will be devoted to the case 

 where the currents involved are held constant after their initiation, it will 

 be convenient to simplify the notation by introducing a current-dependent 

 scale for x and writing the equation in terms of the dimensionless variables 



V = nu/uo , s = t/r, ^ = x/EqUht 

 In terms of these (22) becomes simply 



XeHoile/jilh-i 



ds 



[r 



+ (1 -f fXh/iJ.e)v . 



- R{v) 



+ 



(D'l 



(1 + 2v) 



^ 

 d^ 



Ll + (1 +M;yiu>J 



(23) 



(24) 



where R{v) = j^(l + v) for pure volume recombination, ox = v for a surface 

 recombination uninfluenced by the electron density, and where 



/ = {kTe (J-ello/nhT) 

 \\I2 



(25) 

 (TQ{kT/e HhrY 



Numerically the characteristic field is, at 300°K, with fih = 1700 cm-/v sec, 



{kT/eiiHTf = 3.90 (T/lfjLs)~"^ volts/cm (26) 



Note that the importance of the diffusion term in (24) goes down in- 

 versely as the square of the current density used and inversely as the square 

 of the recombination time; this is because an increase in the distance the 

 holes travel decreases the distance they diffuse by decreasing the concen- 

 tration gradient, and also makes a given diffusion distance less serious by 

 comparison with the total distance traveled. Note also that, if /Xe = Ma , 



the last term of (24) reduces simply to ( - I — ^ , but that, if ^u,. ^ m, , the 



diffusion term is not a simple second derivative. 



' G. L. Pearson, paper Q9 presented at the Washington Meeting of the American 

 Physical Society, April 29, 1949. 



