PRISX'IPLKS OF TRAXSISTOR ACTfOX 265 



(4) One of the authors^' has observed a change in contact potential with 

 Hght similar to that expected for a barrier layer at the free surface. 



Prior to Benzer's experiments, Meyerhof^ had shown that the contact 

 l^otential difference measured between different metals and silicon showed 

 little correlation with rectification, and that the contact potential differ- 

 ence between n- and p-type silicon surfaces was small. There is thus 

 evidence that the barrier layers in both germanium and silicon are internal 

 and occur at the free surface". 



In the development of the mathematical theory of the space-charge layer 

 at a rectifier contact, Schottky and Spenke'^ point out the possibility of a 

 change in conductivity type between the surface and the interior if the 

 potential rise is sutlficiently large. The conductivity is p-type if the Fermi 

 level is closest to the tilled band, n-type if it is closest to the conduction 

 band. In the illustration (Fig. 15), the potential rise is so large that the 

 tilled band is raised up to a position close to the Fermi level at the surface. 

 This situation is believed to apply to germanium. There is then a thin 

 layer near the surface whose conductivity is p-type, superimposed on the 

 n-type conductivity in the interior. Schottky and Spenke call the layer of 

 opposite conductivity type an inversion region. 



Referring to Eqs. (3.5a and 3.5b) for the concentrations, it can be seen 

 that since Ce and Ci, are of the same order of magnitude, the conductivity 

 type depends on whether if,- is larger or smaller than ipi,. The conductivity 

 is n-t}q3e when 



iPe < 1/2 Ea, ipk > 1/2 Eo, (4.1) 



and is p-t>'pe when the reverse situation applies. The maximum resistiv- 

 ity occurs at the position where the conductivity type changes and 



^e ~ <j5A ~ 1/2 Eg. (4.2) 



The change from n- to p-type will occur if 



<p.. > 1/2 Ea, (4.3) 



or if the overall potential rise, ^pt,, is greater than 



1/2 Ea - <p.o, (4.4) 



where </),o is the value of (^,. in the interior. Since for high-back-voltage 

 germanium. Eg ~ 0.75 e.v. and <p,o -^ 0.25 e.v., a rise of more than 0.12 

 e.v. is sufficient for a change of conductivity type to occur. A rise of 0.50 

 e.v. will bring the filled band close to the Fermi level at the surface. 



Schottky" relates the thickness of the space charge layer with a potential 

 rise as follows. Let p be the average change density, assumed constant for 

 simplicity, in the space charge layer. In the interior p is compensated by 



