CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 549 



temperatures when rii achieves a very large value it may not be possible 

 to have A~ exceed n, , and no effect due to the acceptor will be observable. 

 This is simply a mathematical reflection of the fact that the hypothetical 

 compound e'^e~ in (2.1) is highly dissociated at high temperatures so that 

 the holes contributed by the acceptor cannot cause the exhaustion of 

 electrons in the solution. 



In Reference 6 the system described in (2.1) was investigated for the 

 purpose of testing (3.4). The concentrations, Z)"*" and A~, of lithium and 

 boron respectively were determined by measuring the electrical resis- 

 tivities of the crystal specimens before and after immersion in molten 

 tin contaning lithium. Some typical results of these experiments are 

 shown in Fig. 3 which contains three Z)"*" versus A~ isotherms for the 

 temperatures 249°, 310°, and 404°C. For the case shown the tin phase 

 contained 0.18 per cent lithium by weight. 



The points in the figure represent experimental findings, while the 

 drawn curves are based on theory. The agreement between theory and 

 Ij experiment is very good, in fact the overall accuracy appears to be bet- 

 ter than 1 per cent. These isotherms are only a few of a large group ob- 

 tained at different temperatures and with differently proportioned ex- 

 ternal phases. The accuracy in all of these is of the same order. 

 I Various of the features of (3.4) listed above are apparent in the curves 

 of Fig. 3. For example at large values of ^~ the curves are straight lines, 

 thus validating (3.5). Also, the inversion of the temperature coefficient 

 of solubility with doping is apparent for the curves cross one another, 

 md whereas, at low dopings (low A~) the solubility is an increasing func- 



on of temperature, at high dopings it decreases with increasing tempera- 

 ture. Finally we note that D'^ remains more or less independent of A~ 

 until A~ exceeds n,- , confirming (3.7). Values of n,- appear in the Figure. 



The possible increases in solubility above Do^ are really quite large. 

 For example in Fig. 3 the largest increase is of the order of a factor of 

 10^ However in some experiments increases of 10 have been observed. 

 These effects truly represent profound interactions between impurities 

 which are present in highly attenuated form. Thus the number of atoms 

 per cubic centimeter in crystal silicon is of the order of 5 X 10 cm" . 

 Interactions at doping levels as low as 10^* cm~^, as appear in Fig. 3, 

 therefore take place at atom fraction levels of about 2 X 10 . 



In Fig. 4 we show a curve of lithium solubility at room temperature 

 in gallium-doped germanium. The curve is wholly experimental; no 

 attempt has been made to apply theory. The symbols D and A~ are 

 once more used for the donor and acceptor. In this case the curve again 

 exhibits some of the general features required by (3.4). The measure- 



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