SUKFAGE PROPERTIES OF GERMANIUM 37 



number, type and distribution in energy of the surface traps. One has 

 therefore a tentative model of the Ge surface that should be very useful 

 in any further investigation of its properties. 



ACKNOWLEDGMENTS 



We wish to acknowledge the help and assistance of all our colleagues 

 who have contributed in many ways to make this investigation a 

 success. We wish to mention in particular E. G. Dreher and R. E. Enz 

 who took most of the experimental data, H. R. Moore who designed 

 and made the electronic equipment used in making the measurements, 

 and Conyers Herring for suggestions regarding the theory of large 

 amplitude signals. 



Appendix 



We have assumed (Postulate IV) that traps of type a are in equi- 

 librium with electrons in the conduction band and that traps of type h 

 are in equilibrium with holes in the valence band. We wish to show that 

 this is not really a separate assumption but follows as a consequence of 

 Postulate II if the density of traps is not too high. For simplicity, we 

 shall restrict the discussion in the appendix to the limiting case of small 

 departures from equilibrium so that the equations are linear. The 

 problem may then be discussed most conveniently by means of quasi- 

 Fermi levels* or imrefs, <f>n and <f>p , for the conduction electrons and 

 holes, respectively. 



Departures 50n and 8<f)p , of the imrefs from the Fermi level are a 

 measure of the departures of the concentrations, dn and 8p , from their 

 equilibrium values : 



rii = n -i- dn = n exp (— /350n), (A.l) 



pi = p -}- 8p = pexp (iS5</)p). (A.2) 



The imrefs in the interior are then 



a.. = iln(l + |). (A.4) 



Correspondingly, the imrefs at the surface are defined by: 



Usi = ns + 8ns = n exp W(Vb + 8Vb - 8<f>ns)l (A.5) 



Pel = Ps + 8ps = p exp [-KVb + 8Vb - 8<f>ps)]. (A.6) 



* Reference 2, pages 302-308. 



