CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 603 



enables us to determine at what temperature, at given values of Na 

 and Nd , P/Nd is exactly 0.5. Thus consider the fact that, all other things 

 being equal, the control bridge and the one containing added lithium 

 will exhibit equal Hall mobilities at a given temperature when the con- 

 centrations of charged impurities are identical in both of them. Now the 

 concentration of such impurities in the control is simply Na • The con- 

 centration in the bridge containing lithium is 



Na + No- 2P (12.1) 



The quantity 2P is removed from Na + Nd , because each time a pair 

 forms two charged scatterers are eliminated. The condition that the 

 ; .scattering densities in both bridges be equal is then simply 



I Na = NA-\-Nn-2P 



or 



■^ = 0.5 (12.2) 



N D 



i Therefore if plots of Hall mobilities versus temperature such as those 

 I appearing in Figure 25 are continued until they cross, the temperature 

 I of crossing marks the point at which P/Nd is 0.5. 



In Fig. 26 typical crossings of this kind are shown. They are for two 



I ••17 



! different gallium doped germanium crystals, one containing 3 X 10 

 cm~^ gallium and the other 9 X 10^^ cm~^. The curves for the controls 

 and lithium saturated samples in each case are shown as plots of the 

 logarithm of Hall mobility against logarithm of absolute temperature. 



: The lines plotted in this manner are straight. The lithium content of 

 1he bridge containing 9 X 10^^ cm~^ gallium was 6.1 X 10 cm~ while 

 that in the bridge with 3 X 10^^ cm"^ gallium was 2.8 X 10^^ cm~l All 



, of these concentrations were obtained from Hall coefficient measurements 



< m the controls and the lithium doped specimens. 



As the temperature is increased the mobilities of the samples with 

 lithium are reduced and approach the mobilities of the controls. This 

 happens because pairs dissociate and more charged impurities appear. 

 1 inally when P/Nd is exactly 0.5 the curves cross. In Fig. 27 we notice 

 that mobility measurements were not performed right up to the cross 

 point, but that the straight lines have been extrapolated. This procedure 

 was adopted of necessity, because of the high diffusivity of lithium. Thus, 

 Inference to Fig. 5 shows that the solubility in doped germanium de- 



i (leases to a minimum as the temperature is raised from room tempera- 

 t ure, and there is danger of precipitation. For this reason the measure- 



