576 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



this application later in connection with the strain in the neighborhood 

 of a substitutional boron in germanium. 



Aside from its bearing on the minimum distance a, the existence of the 

 lattice will be ignored in the following considerations. 



The values of a, typical of semiconductors, are generally of the order 

 of 2 Angstroms as against 6 to 8 Angstroms for ions in liquids. This re- 

 sults from the fact that liquid ions are generally solvated. The conse- 

 quence to be expected, and indeed found, is that ion pairing will be far 

 more pronounced in semiconductors than in liquids of comparable di- 

 electric constant. 



The fact that ions have limited mobilities in semiconductors can be 

 turned to advantage by choosing a system such as lithium and boron in 

 silicon in which only one species of ion, in the case mentioned, lithium, is 

 mobile. Under these conditions it is possible to obviate the clustering 

 phenomenon, mentioned previously, which appears in liquids at high ion 

 concentrations. Clustering is prevented because the immobile ions are 

 uniformly distributed in a random manner, having been grown into the 

 crystals at high temperature where pairing and related processes are un- 

 important. The obvious complications attending cluster formation can 

 therefore be avoided. 



Of course, mobility, being limited to a single species of ion is also an 

 advantage in the theory of the transport phenomena, in such systems. 



It is convenient to list some of the effects due to pairing Avhich are to 

 be expected in semiconductors. We do so in the following compilation. 



{A) Equilihrium Phase Relations 



From (6.2) it is apparent that the pairing equilibrium should affect 

 the solubility of lithium in silicon. The same must be true for germanium 

 doped with an acceptor. Although such effects probably occur, they are 

 accompanied by influences arising from the other possible equilibria. As 

 a result the situation is somewhat complex and it is not easy (see Ap- 

 pendix A) to produce experimental conditions under which pairing will 

 be evident. For this reason quantitative investigations along these lines 

 have not yet been attempted. 



(B) Variation of Energy Levels 



When an ion pair is formed of a donor and acceptor, both the donor 

 and acceptor levels are altered. Thus the proximity of the negative ac- 

 ceptor ion increases the difficulty of return to the donor state for an 

 electron, (i.e. the donor level is raised). Likewise the acceptor level is 



