536 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



XII. Investigation of Ion Pairing by Its Effect on Carrier Mobility 601 



XIII. Relaxation Studies 607 



XIV. The Effect of Ion Pairing on Energy Levels 610 



XV. Research Possibilities 611 



Acknowledgements 613 



Appendix A — The Effect of Ion Pairing on Solubility 613 



Appendix B — Concentration Dependence of Diffusivity in the Pres- 

 ence of Ion Pairing 617 



Appendix C — Solution of Boundary Value Problem for Relaxation. . 619 



Appendix D —Minimization of the Diffusion Potential 623 



Appendix E — Calculation of Diffusivities from Conductances of 



Diffusion Layers 626 



Glossary of Symbols 630 



References 634 



I. INTRODUCTION 



The effort of Wagner' and his school to bring defects in solids into the 

 domain of chemical reactants has provided a framework within which • 

 various abstruse statistical phenomena can be viewed in terms of the 

 intuitive principle of mass action.^ Most of the work to date in this field ' 

 has been performed on oxide and sulfide semiconductors or on ionic com- '[ 

 pounds such as silver chloride. In these materials the control of defects ■ 

 (impurities are to be regarded as defects) is not all that might be desired, i 

 and so with a few exceptions, experiments have been either semiquanti- . 

 tative or even qualitative. i 



With the emergence of widespread interest in semi-conductors, cul- : 

 minating in the perfection of the transistor, quantities of extremely pure , 

 single crystal germanium and silicon have become available. In addition 

 the physical properties, and even the quantum mechanical theory of the 

 behavior of these substances have been widely investigated, so that a 

 great deal of information concerning them exists. Coupled with the fact 

 that defects in them, especially impurities, are particularly susceptible 

 to control, these circumstances render germanium and silicon ideal sub- 

 stances in which to test many of the concepts associated with defect I 

 interactions. 



This view was adopted at Bell Telephone Laboratories a few years ago 

 when experimental work was first undertaken. Not only has it been 

 possible to demonstrate quantitatively the validity of the mass action 

 principle applied to defects, but new kinds of interactions have been 

 discovered and studied. Furthermore new techniques of measurement 

 have been developed which we feel open the way for broader investiga- 

 tion of a still largely unexplored field. 



In fact solids (particularly semiconductors like germanium and silicon) 



