SURFACE PROPERTIES OF GERMANIUM 23 



is in equilibrium with the concentration of electrons in the conduction 

 band and holes in 6-traps are in equilibrium with holes in the valence 

 band. The barrier height is adjusted so that the total charge in both 

 types of traps is unchanged by illumination. We shall show in the ap- 

 pendix that the resistance to flow of electrons from the conduction band 

 across the space-charge layer and into a-traps is small compared with 

 the resistance to flow of electrons from the valence band to the traps. 

 Similar considerations apply to flow of holes to 6-traps from the valence 

 band as compared with flow from the conduction band. 



V. Recombination is limited by holes going into traps of type a 

 and electrons going into traps of type h. The two types of traps act 

 in parallel for recombination. The contributions to the surface re- 

 combination velocity are proportional to psUa and UsPb , respectively. 

 These products are independent of Vb and thus of ambient if postulates 

 II and IV are satisfied. If other types of traps were important in re- 

 combination, one would expect Vs to depend on ambient, contrary to 

 what is observed. 



Postulates I and II are used to relate Vb and c.p. with changes in 

 ambient. Postulates III, IV, and V are used to relate (Ac.p.)l with 

 Vb and the trap densities, and also to obtain an expression for the 

 surface recombination velocity. 



As Vb is made more positive, corresponding to a decrease in barrier 

 height for electrons, na increases and pb decreases. It will be convenient 

 for the theoretical discussion to introduce the particular barrier po- 

 tential Vbo , for which Ua = Pb . With use of the Boltzmann approxi- 

 mations in Equations (6) and (7), this gives 



exp 12^Vbo\ = (Nb/Na) exp [{Ea + ^6 - 2E,)/kT)] 

 = {Pbo/nao){p/n), 



where /3 = e/kT. The last form follows from the definitions of pbo and 

 Uao and by noting that exp [2(Ei - Ef)/^!] = p/n. We then have 



Ua/Pb = exp [2/3(7b - Vbo)1 (9) 



As so defined, Vbo depends on the Fermi level and thus on the con- 

 ductivity of the specimen. We shall let Fo be the value of Vbo for an 

 intrinsic specimen. From (8) 



Uao/Pbo = exp [-2/3Fo]. (10) 



If riao = Pbo , then Vo will be zero. Postulate II sets limits on Vo , but Vo 

 is otherwise undetermined in our experiments. 



