Distribution and Cross- Sections of Fast 

 States on Germanium Surfaces 



By C. G. B. GARRETT and W. IL BRATTAIN 



(Manuscript recieved May 10, 1956) 



A theoretical treatment uf the Jield effect, tiurface photo-voltage and surface 

 recombination phenomena has been carried out, starting with the Hall- 

 Shockley-Read model and generalizing to the case of a continuous trap dis- 

 tribution. The theory is applied to the experimental results given in the 

 previous paper. One concludes that the distribution of fast surface states is 

 such that the density is loivest near the centre of the gap, increasing sharply 

 as the accessible limits of surface potential are approached. From the sur- 

 face photo-voltage measurements one obtains an estimate of 150 for the ra- 

 tio (a-p/an) of the cross-sections for transitions into a state from the valence 

 and conduction bands, showing that the fast states are largely acceptor-type. 

 On the assumption that surface recombination takes place through the fast 

 states, the cross-sectioris are found to be: dp '-^6 X 10"^ cm and o-„ -^ 

 4 X 10"'' cm~. 



I. INTRODUCTION 



The existence of traps, or "fast" states, on a semiconductor surface, 

 becomes apparent from three physical experiments: measurements of 

 field effect, of surface photovoltage,' and of surface recombination ve- 

 locity s. Results of combined measurements of these three quantities on 

 etched surfaces of p- and r?-type germanium have been presented in 

 the preceding paper. ^ The present paper is concerned with the conclu- 

 sions which may be drawn from these experiments as to the distribution 

 in energy of these surface traps, and the distribution of cross-sections 

 for transitions between the traps and the conduction and valence bands. 



The statistics of trapping at a surface level has been developed by 

 Brattain and Bardeen^ and by Stevenson and Keyes,^ following the work 

 on body trapping centers of Half and of Shockley and Read. 



It is known that surface traps are numerous on a mechanically dam- 

 aged surface or on a surface that has been bombarded but not annealed; 



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