CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 539 



gram of silicon, exhibited in Fig. 1. The conduction band, the valence 

 band, and the forbidden gap are shown. Lithium and boron both intro- 

 duce localized energy states in the range of forbidden energies. The state 

 for lithium lies just below the bottom of the conduction band while that 

 for boron lies just over the top of the valence band. The separations in 

 energy between most donors or acceptors and their nearest bands are of 

 the order of hundredths of an electron volt while the breadths of the for- 

 bidden gaps in germanium or silicon are of the order of one electron volt. 



Process 1 in Fig. 1 involving a transition between the donor level and 

 conduction band corresponds to the ionization of lithium in (2.1). Proc- 

 ess 2 is the ionization of boron while process 3 represents hole-electron 

 recombination and generation. The various energies of transition are the 

 heats of reaction of the chemical-like changes in (2.1). 



Proceeding in the chemists fashion one might argue as follows concern- 

 ing (2.1). If e'^e' is a stable compound, as it is at fairly low temperatures, 

 then its formation should exliaust the solution of electrons, forcing the 

 set of lithium equilibria to the right. In this way the presence of boron, 

 supplying holes toward the formation of e'^e", increases the solubility of 

 lithium. In fact if e"*" is regarded as the solid state analogue of the hydro- 

 gen ion in aqueous solution, and e~ as the counterpart of the hydroxyl 

 ion, then the donor, lithium, may be considered a base while boron, may 

 be considered an acid. Furthermore e'*"e~ must correspond to water. 

 Thus the scheme in (2.1) is analogous to a neutralization reaction in 

 which the weakly ionized substance is e'*"e~. 



If the immobile boron atoms were replaced by immobile donors, e.g., 

 I phosphorus atoms, a reduction, rather than an increase, in the solubility 



IT 



BORON LEVELS (ACCEPTORS) 



x : ;w>/.-v v.^;i::-.:-:VX;^;;;v valence band v. 



DISTANCE 



Fig. 1 — Energy band diagram showing the chemical equilibria of (2.1). 



