CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 563 



which can be known for all temperatures when 7 and jS have been deter- 

 mined. Reiss, Fuller, and Pietruszkiewicz used two of the points near 

 Curve B in Fig. 9, above 1,000°C, to define values of No for use in (5.7). 

 Then t was computed from (5.7) at these two temperatures. From these 

 values of t, 7 and (3 were determined, and from these, in turn, w was 

 calculated for all temperatures down to 200°C. Using t, Nd was computed 

 from (5.7) over the entire experimental range of temperature. The result 

 is Curve B of Fig. 9 which fits the experimental points very well. 



Another check on the validity of the theory (which has not yet been 

 accomplished) would be the following. At high temperatures (5.7) re- 

 duces to 



^. = i^.« + |^^^^f4L+^ (5.8) 



l2 + TiN^yil + Vl + (2n,/A^z,o)2]J 



i.e., Nd is a linear function of Na with the slope (in brackets) depending 

 upon X. Measurement of this slope at one temperature would thus pro- 

 vide an independent evaluation of tt. 



A little thought concerning the scheme outlined in (5.2) leads one to 

 wonder why the introduction of boron really increases the solubility of 

 lithium because the same mechanism could be applied to the case in 

 which boron is absent, i.e., to Curve A of Fig. 9. Thus, if B~ is replaced 

 by a silicon atom in Figs. 10 and 11, the entire scheme can be adopted 

 unchanged, except that Si replaces B~. Thus 



Li (external) <=± Li"^ -{- e~ 



^ + + 



Si + e+ 



+ Ti 



D eV (5.9) 



-f 

 e 



u 



LiSi 



and one wonders why LiB~ should be more stable than Li Si. A possible 

 answer is the following: 



The tetrahedral covalent radius of boron is 0.88 A. This is to be con- 

 trasted with the tetrahedral radius of silicon which is 1.17 A. When 

 boron is substituted in the silicon lattice it therefore produces consider- 

 able local compressive strain. This strain is partially relieved when a 

 \ acancy is formed adjacent to the boron. Thus the energy required to 

 form a vacancy near a boron ion in silicon is less than is required for its 



