22 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



The theory is based on the following postulates: 



I. Changes in c.p. with ambient result from changes in ui and the 

 consequent changes in Vb and Vd • 



c.p. = 7^ + 7^ + const. (2) 



The charge o-/ is largely compensated by charges in the surface traps. 

 The barrier height, Vb , is determined by the requirement of electrical 

 neutrality: 



(Ti = e{na — Vb) + const. (3) 



Since Vb and Vd are of the same order, the net charge per unit area 

 in the space-charge layer will be smaller than ai in the approxim.ate 

 ratio (d/Ib and may be neglected. 



II. Traps of type a have energies above Ep and of type h below Ep 

 for all values of Vb attained in the different ambients used. More ex- 

 actly 



Ea - eVB - Ep > kT, (4) 



Ep-E,+ bVb > kT, (5) 



for all Vb . One may then use the Boltzmann approximations for Ua 

 and pb : 



_ Na 



'''^ - 1+ exp [{Ea - eVs - Ep)/kT] (6) 



- Na exp [{Ep - Ea + eVB)/kn 



__ Nb 



P* - 1-1- exp [{Er - Eb + eVB)/kT\ (7) 



-- Nb exp [{Eb - bVb - Ep)/kT]. 



It is not necessary for our arguments to assume that all traps of each 

 type have the .same energy. The only requirement is that the distributions 

 of trap energies are such that the a-traps are always above and the 6-traps 

 always below the Fermi level for any ambient. 



III. Creation of electron-hole pairs by absorption of light occurs near 

 the surface in a distance that is small compared with the diffusion 

 length. Optical constants of germanium indicate that practically all of 

 the light with energy sufficient to create electron-hole pairs is absorbed 

 within a distance of 10~^ cm of the surface. The diffusion length is of 

 the order of 0.2 cm. 



IV. In the presence of light, the concentration of electrons in a-traps 



