Interactions between Solute Atoms and Defects in Silicon and Germanium

Abstract

<p> A thermodynamic investigation of interactions between solute atoms and defects (other solute atoms, electrons, phonons, and grain boundaries) has been conducted by solubility measurements of copper and gold in silicon and germanium. The major objective of the investigation was to gain a further understanding of the physical state of solute atoms and their interactions with defects in homopolar crystals. An attempt was also made to extend the theory and experimental results of equilibrium studies to kinetic phenomena associated with device manufacture. An experimental study of the kinetics of solute precipitation at dislocations was also carried out by electrical conductivity measurements. </p> <p> Original contributions which have been obtained from the results of this program are listed below. </p> <p> (1) The relative partial molar enthalpies and entropies of solution for the various systems are </p> <p> ∆Ħ_Cu (in Si)=37.3±0.5 Kcal./mole, ∆S⁻ᵉˣ_Cu(in Si)=7.1±0.4 cal./mole-ºK, </p> </p> ∆Ħ_Cu (in Ge)=41.3±0.7 Kcal./mole, ∆S⁻ᵉˣ_Cu(in Ge)=10.3±0.6 cal./mole-ºK, </p> <p> ∆Ħ_Au (in Si)=43.8±1.4 Kcal./mole, ∆S⁻ᵉˣ_Au(in Si)=6.8±1.0 cal./mole-ºK, </p> <p> ∆Ħ_Au (in Ge) ≳ 45 Kcal./mole, and ∆S⁻_Au(in Ge) ≳ 15 cal./mole-ºK. </p> <p> The partial molar enthalpy and entropy of copper in silicon with respect to Cu₃Si are 40.2±0.5 Kcal./mole and 9.7±0.5 cal./mole-°K, respectively. </p> <p> (2) Solubility measurements, metallography, and X-ray studies yielded evidence for delayed nucleation of intermediate compounds in copper-silicon diffusion couples. </p> <p> (3) The solubility of copper in vapor grown polycrystalline silicon is much greater than that in single crystal material below 800°C. The ratio of the grain boundary solubility to the single crystal solubility was estimated to be of the order of 5 x 10⁵. The high interaction energy between copper and grain boundaries in silicon (approximately 1.5 eV) was ascribed to chemical bonding. </p> <p> (4) Arsenic doping of germanium (such that the semiconductor remains intrinsic) enhances the solubility of copper in this material. This effect was quantitatively described by a theory of complex formation. </p> <p> (5) A study of the solubility of copper in p-type silicon indicated that copper is incompletely ionized in intrinsic silicon at elevated temperatures (≃1000°C). </p> <p> (6) The solubility of gold in silicon is decreased by boron doping, and this was explained on the basis of a low (less than unity) donor/acceptor ratio of substitutional gold. </p> <p> (7) The rate equation describing the precipitation of copper in silicon has a time exponent of 0.687±0.043. </p> <p> (8) Generalized phenomenological equations for ternary diffusion in covalent semiconductors were developed and it was demonstrated that information about diffusion phenomena may often be obtained from equilibrium measurements. </p> <p> (9) A quasi-steady state experiment was designed whereby copper segregated to regions of high boron concentration (in silicon) during a heat treatment operation, in qualitative agreement with theory. </p>