Modelling point defect dynamics in the crystal growth of silicon

Abstract

The quality of silicon single crystals grown by the Czochralski (CZ) and floating zone (FZ) methods depends on the distribution of microdefects formed by silicon vacancies and interstitials and by impurities, such as oxygen and carbon. This paper describes the first steps of an attempt to model the formation of these defects by combining atomistic-level simulation of the equilibrium, transport, and kinetics of point defects and impurities in silicon, with continuum modelling of defect transport and reaction. The continuum models are written in terms of classical equilibrium, transport and kinetic coefficients, which are estimated using atomistic simulations based on the Stillinger-Weber interatomic potential for describing the interactions of silicon atoms. Atomistic simulations are reported for the equilibrium and transport properties of interstitials and vacancies in pure silicon. Calculations predict that interstitials prefer to form 〈110〉 dumbbells in the diamond lattice and that these point defects become delocalized at elevated temperatures. A model is proposed for the recombination of vacancies and interstitials that leads to a high entropic energy barrier at high temperatures due to this delocalization. Calculations of continuum point defect distributions for a prototype, steady-state crystal growth system predict the transition between vacancy (D-defects) and interstitial (A-defects) dominated precipitation of microdefects as a function of temperature gradient, crystal pull rate and crystal radius. These predictions arein qualitative agreement with experiments for FZ-grown crystals.