Control of Intrinsic Point Defects in Single-Crystal Si and Ge Growth from a Melt

Abstract

The so called Voronkov criterion defines a critical value Γcrit of the ratio \(\varGamma = v/G\) of the pulling rate v over the thermal gradient G at the crystal-melt/interface of a growing crystal. For Γ > Γcrit, the crystal is vacancy-rich and can contain large vacancy clusters that are detrimental for gate oxide performance and for thin film epitaxial growth. For Γ < Γcrit, the crystal is self-interstitial-rich and in the worst case will contain dislocation clusters. For Γ ≈ Γcrit, the crystal is free of grown-in intrinsic point defect clusters and optimal for device processing. Analytical expressions have been derived describing Γcrit as function of intrinsic point defect parameters. The impact of thermal stress \(\sigma _{th}\) at the crystal-melt interface and of crystal doping on Γcrit will be clarified. As \(\sigma _{th}\) increases with increasing crystal diameter, controlling G and v will become a real challenge for the development of future 450 mm diameter, defect free Si crystals. The possible application of the Voronkov criterion for Ge single-crystal growth from a melt will also briefly be discussed. Besides the impact of stress on intrinsic point defect formation energies and diffusivities, DFT calculations also suggest that near the crystal-melt interface, assumed to be stress free, the formation energy of the intrinsic point defects is lower than in the bulk of the crystal. This leads to thermal equilibrium concentrations of intrinsic point defects at the crystal-melt interface that are considerably different from those in the bulk which should be taken into account when applying the Voronkov criterion and also for intrinsic defect engineering in general. The Voronkov criterion was established for a flat interface. During crystal growth the crystal-melt interface is however curved which will have a significant impact on the diffusion of the intrinsic point defects. The impact of this curvature is discussed in detail both theoretically and experimentally.