540 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



of lithium might be expected on the basis of an oversupply of electrons 

 (i.e., by the common ion effect^"). In that case we would have a base 

 displacing another base from solution. 



The intimate comparison between this kind of solution and an aqueous 

 solution is worth emphasizing not so much for what it adds to one's 

 understanding of the situation but rather for the further effects it sug- 

 gests along the lines of analogy. These additional phenomena have been 

 looked for and found, and Mill be discussed later in this article. 



The scheme shown in (2.1) should be applicable, in principle, to other 

 donors and acceptors and to germanium and other semiconductors as 

 well as silicon. Furthermore the external phase may be any one of a suit- 

 al)le variety, and need not even be liquid. Other systems, however, are 

 not as convenient, especially in regard to the ease of equilibration of an 

 impurity over the parts of an heterogeneous system. The lengths to which 

 one can go in comparing electrolytes and semiconductors are discussed 

 in a recent paper." 



In order to quantify the scheme of (2.1) it seems natural to invoke the 

 law of mass action. Treatments in which holes and electrons are in- 

 volved in mass action expressions are not new, although systems forming 

 such perfect analogies to aqueous solutions do not seem to have been 

 discussed in the past. For example, in connection with the oxidation of 

 copper Wagner " writes 



4Cu -f O2 ^ 2CU2O -f 40" + 4e+ (2.2) 



in which D ~ is a negatively charged cation vacancy in the CU2O lattice, 

 and e"^ is a hole. Wagner proceeds to invoke the law of mass action in 

 order to compute the oxygen pressure dependence in this system. 



In another example Baumbach and Wagner^^ and others have investi- 

 gated oxygen pressure over non-stoichiometric zinc oxide. They consider 

 the possible reactions 



2ZnO ;=± 2Zn + O2 t\ 



u 



2Z?i+ i^ 2Zn++ -f 2e" (2.3) 



+ 



2e- 



and apply the law of mass action. In (2.3) the various states of Zii are 

 presumably interstitial. 



Kroger and Vink have recently considered the problem in oxides and 

 sulfides in a rathcM- general way. However in none of the oxide-sulfidc 

 systems has it been possible to achieve really quantitative results. In 



