CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 565 



ten-fold greater than in germanium may be due to the smaller width of 

 the forbidden gap in the latter. This makes for greater values of n,- and 

 according to (3.3) smaller values of Do^. 



VI. ION PAIRING 



The preceding text drew an analogy between semiconductors and 

 aqueous solutions — phenomena such as neutralization, common ion ef- 

 fects, and complex formation have been discussed. Another feature of 

 "wet" chemistry which has appealed to chemists concerns the influence 

 of coulomb forces among ions on the properties of solutions. This subject 

 is of peculiar interest because such forces are well understood, and con- 

 siderable progress can be made in the quantitative prediction of their 

 effects. 



The first really successful theoretical treatment of coulomb forces in 

 solution is the Debye-Hiickel theory.^'' This treatment recognizes the 

 long range character of coulomb forces, and endeavors to account for 

 their effects in terms of a communal interaction involving all of the ions 

 in solution. The theory has now been shown to include certain statistical 

 inconsistencies^^ which, however, are of small consequence in dilute solu- 

 tions where theory and experiment are in excellent agreement. 



The central feature of the Debye-Hiickel theory is the concept of the 

 ionic atmosphere, i.e., the time average excess concentration of ions of 

 opposite sign which accumulates in the neighborhood of a particular ion. 

 The radius of this atmosphere is measured (order of magnitude-wise) by 

 the now famous Debye length. 



" ys7q 



87rgW 



(6.1) 



ill which K is the dielectric constant of the medium, q is the charge on an 

 ion, and N is the (in this case identical) concentration of both positive 

 and negative ions. As k decreases or N increases, L becomes smaller so 

 that the atmosphere is more tightly gathered in. As this process continues 

 a stage is reached in which the atmospheres of some of the ions may 

 be best thought of as being fully constituted by a single ion of opposite 

 sign, i.e., an ion pair forms. This pair-wise interaction is so intense rela- 

 tive to the communal interaction mentioned above, that insofar as the 

 paired ions are concerned it may be regarded as the only interaction in- 

 fluencing the distribution of the pairs themselves. Unpaired ions may still 

 be treated by the communal Debye-Hiickel theory but their concentra- 

 tion must be considered as the true concentration of ions reduced by the 



