CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 607 



dence in 1.83 X 10~^ than in 1.61 X 10~^ cm. More work is necessary, 

 however, before a real decision can be made. 



A feature of Table V is the fact that gallium, aluminum, and indium 

 exhibit orthodox behavior, i.e., the measured a's are in both cases slightly 

 less than those expected on the basis of the addition of radii. The in- 

 ternal consistency of the theory gains support from the fact that gal- 

 lium and aluminum behave similarly as the Pauling a's tabulated in 

 Table V predict. In fact if 1.83 X 10~ cm is taken as the more reliable 

 indium value the three cases fail to match the Pauling radii by about the 

 same amount, a result which implies that the disparity is due to the same 

 cause, i.e., failure of the dielectric continuum concept. 



Another feature of Table V is the fact that boron is out of line to the 

 extent that the measured a exceeds the Pauling a by 50 per cent. A pos- 

 sible explanation is the following. The tetrahedral radii of boron and 



o o 



germanium are poorly matched (0.88 A and 1.26 A, respectively). The 

 strain in the boron-germanium bond may appear as a distortion of the 

 germanium atom in such a way as to increase the effective size of the 

 boron ion. This strain was mentioned before in Section V where it was 

 invoked to explain the stability of LiB~ complex in silicon. 



XIII, RELAXATION STUDIES 



The relaxation time discussed in Section X has been studied experi- 

 mentally. The following procedure was used. A specimen was warmed 

 to 350°K where a considerable amount of pair dissociation occurred, and 

 then cooled quickly by plunging into liquid nitrogen. It was then rapidly 

 transferred to a constant temperature bath, held at a temperature where 

 pair formation took place at a reasonable rate, and the change in sample 

 conductivity (as pairing took place) was measured as a function of time. 



The principle upon which this measurement is based is the following. 

 At a given temperature the occurrence of pairing does not change the 

 carrier concentration, only the carrier mobility. As a result the measure- 

 ment of conductivity is effectively a measurement of relative mobility. 

 During relaxation the densities of charged impurities are changed, at the 

 most, by amounts of the order of 50 per cent. Over this range, the mobil- 

 ity may be considered a linear function of scatterer density. The depend- 

 ence of conductivity on time, as pairing takes place, must be of the form 



c ^ a„-^ e-"' (13.1) 



where cr^ is the conductivity when ^ = co , and r is the relaxation time de- 

 fined in section X while $ is some unknown constant, depending among 



