SURFACE PROPERTIES OF GERMANIUM 25 



The value of 8Vb , the change in potential across the space-charge 

 layer due to light, is determined by the requirement that there be no 

 net change in charge in the surface traps, or that 



5na = dpb . (16) 



The changes 8na and 8pb come both from changes in 8p and 8n and from 

 8Vb . According to postulate IV, riai = ^a + 8na is in equilibrium with 

 the conduction band and pti = Pb -\- 8pb with the valence band. 

 We have then 



riai/ria = Usi/ris = (ni/n) exp [138V b], (17) 



Pbi/Pb = Psi/ps = (pi/p) exp [-I38Vb]. (18) 



from which it follows that 



dna/ria = (ni/n) exp [^8Vb] - 1, (19) 



WPb = ipi/p) exp [-^8Vb] - 1, (20) 



^ = exp [2/3(7. - Vbo)] = y^\^"P ^-;ff^ -/ . (21) 

 Pb (ni/n) exp [138V b] — 1 



Equation (21) is a quadratic equation in exp [(38V b] which may be solved 

 to give an explicit expression for 8Vb • The role of electrons and holes 

 may be interchanged by changing the sign of 8Vb and of Vb — Vbo . 

 This accounts for the difference in behavior of n- and p-type samples. 

 The total change with light is the sum of 8Vi and 8Vb : 



(Ac.p.)^ = 8Vl = 8Vb + 8Vi . (22) 



In the analysis of the data, 8Vi is calculated theoretically from (15) 

 with 8p = 8n determined from (1) and 8Vb is obtained from the ob- 

 served (Ac.p.)l and 8Vi using (22). Equation (21) is then used to find 

 Vb — Vbo - A plot of c.p. — {Vb — Vbo) versus sinh ^{Vb — Vbo) should 

 be a straight line with slope 2H. An analysis of the observed data in 

 this manner is given in the following section. 



We turn finally to a discussion of the surface recombination velocity, 

 Vs . According to postulate V, recombination is limited by flow of holes 

 to a-traps and of conduction electrons to 6-traps. The flow of holes 

 from the valence band to a-traps (really electrons from a-traps drop 

 into the vacant levels in the valence band corresponding to the holes) 

 is proportional to the product of the hole concentration at the surface 

 Psi , and the concentration of electrons in a-traps, Uai . The reverse 

 flow is that of thermal generation of holes: electrons from the valence 



