34 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



1) at the same time in the cycle 



A(Fo + consta) = -0.10 



2) when 6 7l = 



A(Fo + const2) = -0.13 



3) when 8Vb = 



A(Fo + consta) = -0.12. 



All four results are consistent within the probable experimental accuracy 

 and give an average result of A(Fo + const2) = —0.12 instead of zero 

 as one might expect from the simple picture. This indicates that thfe 

 trap distributions are different on the two surfaces. The constant part 

 of Vd is proportional to — (Na — Nb) and from equation (10) one would 

 expect Fo to decrease as Na increases with respect to Nb , thus AFo 

 and A const2 should be of the same sign and additive so that A const2 

 is less than 0.12 volts; assuming that ^d/Kd is the order of 2 X 10~^ cm, 

 this indicates that A(Na — Nb) is the order of 3 X lO^Vper cm^ which is 

 small compared with the probable trap density, Na , Nd , of the order 

 of 10^* per cm^ as we shall see in the next paragraph. 



Assuming that to/Ko in equation (13a) is the order of 2 X 10~^ cm 

 one can calculate (uaoPboY obtaining 4.1 X 10^° and 5.5 X 10^^ for 

 samples A and D respectively. Using these values one can solve for St 

 in equation (37) and obtain for the case of Fo = the value 5.0 X 10"^^ 

 cm for the average capture cross section of the surface traps. The 

 values of St , riao and pbo depend on what one takes for Fo . The relations 

 are 



„ ^ 5 X 10-^^ 

 ' cosh iSFo ' 



n„o = 5 X 10'' exp [-^Vo] , 



Pw = 5 X 10'° exp [iSFo] . 



This dependence is shown in the graph in Fig. 19. As already mentioned 

 there are reasons for thinking that Vo is less than zero. If one takes 

 —0.06 volts as a reasonable value then one gets St = 10~'^ cm^ Uao 

 = 5 X 10 /cm and Pao = 5 X lOVcm^ respectively. One can push these 

 calculations still further to estimate Na , Nb , Ea and Eb . One knows 

 that Ea and -Eb must be greater than l/kT. Also Na and A^6 should be 

 less than the number of germanium atoms per cm^ of surface which is 

 1.4 X 10"/cm'. Values of Na and Nb of the order of 1 X lO'Vcm' for the 

 number of traps per cm* with energies Ea and —Eb of the order of 0.2 



