Equalibrium Thermochemistry of Solid and Liquid Alloys of Germanium and of Silicon. II. The Retrograde Solid Solubilities of Sb in Ge, Cu in Ge and Cu in Si

Abstract

The solubilities of antimony in solid germanium and copper in solid silicon were found to increase with temperature as had been observed previously for copper in germanium, i.e., these binary alloys possess retrograde solidus curves. It is shown theoretically that this phenomenon can occur in solutions with simple properties, for example, in an ideal liquid solution in equilibrium with a dilute solid solution for which the differential heat of solution of the solute is independent of composition and temperature and the differential entropy of solution is ideal. The logarithms of the distribution coefficients of antimony and copper in germanium, and copper in silicon are linear functions of the reciprocal of the absolute temperature. Extrapolation to the melting point of germanium gives the distribution coefficients of antimony and copper at this temperature. A similar extrapolation to the melting point of silicon is made for copper in silicon. Measurements of the distribution coefficients near the melting points were made during the growth of single crystals and found to be in agreement with the extrapolated distribution coefficients. The complete solidus curves between the melting points of germanium or silicon and the respective eutectic tempertures have been constructed for antimony and copper in germanium and for copper in silicon.

Ga segregation in Czochralski-Si crystal growth with B codoping

“…Thurmond and Struthers [8], established a general equation for the partitioning of an impurity in a dilute solution to Si crystal based on thermodynamical considerations, as follows:…”

“…Based on the theory of Thurmond and Struthers [8], Weiser [9] evaluated DH S I for several dopants, which is the dominant factor in the estimation of segregation coefficient of impurities. Hence, the analytical calculation of the equilibrium segregation coefficient mainly depends on DH S I , described by the following equation for impurity doping in a Si crystal [9]:…”

“…Thurmond and Struthers [8] established a theory for the partitioning of impurities in a dilute solution to crystal based on thermodynamics. By following the theory of Thurmond and Struthers, Weiser [9] calculated the segregation coefficients of Group III-V impurities in Si and Ge crystals.…”

“…The segregation phenomenon of codoped Ga and B in CZ-Si crystal growth has been investigated by comparison with simply Ga-doped and simply B-doped Si crystal growth. The segregation behavior of Ga and B was analyzed based on the work of Thurmond and Struthers [8] and Weiser [9].…”

Ga segregation during Czochralski-Si crystal growth with Ge codoping

“…Thurmond and Struthers [9] established a general thermodynamic equation for the partitioning of an impurity in a dilute solution to a Si crystal,…”