Engineering analysis of microdefect formation during silicon crystal growth

The quality of single crystalline silicon wafers used as substrates for microelectronic devices is measured in terms of the type, size and number density of microdefects formed during crystal growth and subsequent processing. Native point defects—vacancies and self-interstitials—and impurities, such as oxygen and carbon, in the silicon crystal convect, diffuse, react and aggregate, driven by species super-saturation, to form defect structures at densities that are microscopically visible. We model defect dynamics using diffusion–reaction theory in which defect types are represented as chemical species and have concentrations that are governed by conservation laws, chemical thermodynamics and kinetics, using self-consistent values of equilibrium, transport and kinetic parameters for point defects and impurities. We refer to this approach as crystal defect dynamics analysis. The purpose of this paper is to demonstrate that this approach leads to a wide range of predictions that are consistent with experiments. The results presented here focus on the two-dimensional predictions of microdefect structures under growth conditions where both voids (cluster of vacancies) and self-interstitial aggregates are seen in regions of the crystal separated by the oxidation-induced stacking fault ring (OSF-ring). The location and structure of the OSF-ring is predicted in terms of point defect dynamics near the melt/crystal interface, which results in an annular region with almost balanced point defect concentrations (centered at r≡RΔ=0), and in terms of a peak (centered at r≡RCV,max) in the residual vacancy concentration after cluster formation. This residual vacancy concentration facilitates oxide precipitation during crystal growth, which seeds stacking fault formation during subsequent oxidation. Calculations show that RCV,max⩽RΔ=0 with both values scaling with V/G(R), where V is the crystal pull rate and G(R) is the axial temperature gradient at r=R along the melt/crystal interface. An annulus just outside the OSF-ring (centered at r≡Rfree,RCV,max⩽Rfree⩽RΔ=0) is identified where almost no microdefects are present, thereby identifying the temperature field that leads to almost perfect silicon.