SURFACE PROPERTIES OF GERMANIUM 33 



carrier one can easily show that when 8Vl = 0, 



(Vb- Vo) = (1/2^) In 6. 



This follows from equations (15), (21), (22) and (38). The rest of the 

 results hardly need comment. 



It is interesting to compare differences in contact potential, etc., for 

 units A and D. In equation (2) the Fermi energy has been included in 

 the constant. This equation predicts that if the trap distributions on 

 both surfaces are the same, then when the contact potentials of both 

 surfaces are equal the values of Vd should also be equal and the dif- 

 ference between the Fb's should be equal and opposite to the differences 

 between the Fermi energies in electron volts. This equation can be 

 written 



c.p. = (Vb - Vo) - (Vbo - Vo) + Vd+Vo + const . (40) 



In comparing units we shall use A*s to denote differences and these 

 differences are always taken A-D. 



For the case where Ac.p. = 0, A(Vb — Vo) can be read from Fig. 18 

 and A(Vbo — Vo) from Table 11. We have then 



A(Fz> + Fo + const) = -0.05 . 



This indicates that our simple picture is not quite right. If AVd were 

 zero for this case it should follow from equation (12) that both 

 A2^ sinh ^{Vb — Vbo) and the difference in the const in this equation 

 should be zero. It turns out, however, that A2^ sinh ^(Vb — Vbo) is 

 not zero but +0.07. Equation (12) can be substituted into equation 

 (40) giving 



c.p. = {Vb - Vo) - {Vbo - Vo) + 2H sinh KVb - Vbo) 



(41) 



+ Fo + const2 . 



Where the constant now includes the constant part of Vd and is labeled 

 const2 to distinguish it from the constant in equation (40). We have 

 then for Ac.p. = 



A(Fo 4- consta) = -0.12. 



This difference A(7o + consta) can be calculated three other ways, 

 using the experiment results and theoretical values where necessary. 

 These ways are 



