CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 605 



During the course of our experiments it was discovered that precipitates 

 have a profound effect on carrier mobility, reducing it so severely, that 

 the mobility of the lithium doped bridge may never even rise above that 

 of the control. Great care must be exercised in the preparation of suitable 

 bridges to avoid the presence of precipitated lithium. Thus it may be 

 necessary to saturate the bridge at a very low temperature (see Section 

 IV, Figure 5) so that it is somewhat undersaturated at room tempera- 

 ture. This means that diffusion periods of weeks may be involved. 



In Fig. 26 the sample with Na = 9 X lO'' cm~^ and No = 6.1 X lO'* 

 cm~^ has P/Nd = 0.5 at 348°K, while the sample with AT^ = 3 x lO" 

 cm"* and No = 2.8 X 10^^ cm~* is half-paired at 440°K. This is to be 

 expected, the more heavily doped specimen remaining paired up to 

 higher temperatures. Using (9.6) and (9.3) it is possible to calculate a, 

 the distance of closest approach of a gallium and lithium ion, from each 

 of the measured cross points. 



Thus in (9.6) we set 6 = 0.5, and Na , No and T to correspond to each 

 of the cases described. Having logio Q((x), a can be determined by in- 

 terpolation in Table III and a then determined from (9.3). Of course k 

 is taken to be 16. Carrying through this procedure in connection with 

 Fig. 26 leads to the satisfying result that a = 1.71 X 10~^ cm for the 

 heavily doped sample and 1.73 X 10"* cm for the lightly doped one. 

 The values of Q, appearing in Table IV based on a = 1.7 X 10" cm there- 

 fore correspond to gallium. 



Not only is this result satisfying because the two a's agree so well 

 even though the samples involved were so different in constitution, but 

 also because it is expected on the basis of the addition of known particle 

 radii. Thus according to Pauling^^ the tetrahedral covalent radius of 

 gallium is 1.26 X 10~* cm while the ionic radius of lithium is 0.6 X 10" 

 cm. Since gallium is presumably substitutional in a tetrahedral lattice 

 we use its tetrahedral covalent radius, and since lithium is probably in- 

 terstitial we use the ionic radius. The sum of the two is 1.86 X 10 cm 

 which compares very favorably with the values of a quoted above. 



This result constitutes good evidence that lithium is interstitial, for if 

 it were somehow substitutional we might expect a to be something like 

 a germanium-germanium bond length which is 2.46 X 10" cm. Such a 

 value of a would lead to profoundly different crossing temperatures (of 

 the order of 100° lower) so that it is not very likely. 



One further point needs mention. This is the fact that as the two ions 

 approach very closely, the concept of the uniform macroscopic dielectric 

 constant, k, loses its meaning. In fact, the binding energy should be in- 

 creased (as though K were reduced). Crude estimates of the magnitude 



