40 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



Here gt is the rate of thermal generation of electrons from occupied 

 traps to the conduction band. Since, for equilibrium conditions, / = 0, 

 we have: 



gt = VnSntrisPt/nt . (A. 17) 



It may be verified easily that gt is independent of Ef and Vb . The 

 ratio, 



net = nspt/nt = Nc exp [{Et - Ec)/kT], (A.18) 



is the equilibrium concentration of electrons in the conduction band 

 when the Fermi level is at the level of the traps. The expression (A. 16) 

 is again the linear approximation. Thus 



1/Rnt = e^VnSntrisPt . (A. 19) 



Similarly, we have 



1/Rpt = e^VpSptPsUt . (A.20) 



We shall show that the ratio 



Rnt/Rpt = {vnSpt/vpSnt)(Psnt/nsPt)y (A.21) 



may be expected to be small compared with unity for a-traps and large 

 compared with unity for 6-traps. First consider a-traps. If anything, 

 'Spa < Sna , bccausc holes must give up a larger energy than conduction 

 electrons in going to a-traps. The second factor is small compared with 

 unity if 



Ps « net , (A.22) 



with net defined by (A.18). This will be the case if the a-traps are closer 

 to the conduction band than the top of the valence band at the surface 

 is to the Fermi level. According to Postulate II, this should always be 

 the case. 



Similarly, for 6-traps 



Rpt/Rnt « 1 (A.23) 



if 



n. « pw , (A.24) 



where 



Pvi = p.nt/pt = N, exp [-(Et - Ev)/kT]. (A.25) 



is the concentration of holes in the valence band when the Fermi level 

 is at the level of the traps. 



