Modelling microdefect distribution in dislocation-free Si crystals grown from the melt

Abstract

Various microdefects formed as a result of the condensation of native point defects and impurities are known to be present in dislocation-free melt-grown Si crystals. Here we report the results of computer modelling of the distribution of microdefects in the Czochralski (CZ) crystal growth of silicon. Our approach is based on the main assumptions of the Voronkov theory. We use the values of axial temperature gradient and cooling rate measured during crystal growth. The numerical calculations quantitatively reproduce experimental data such as the transition between the vacancy and interstitial microdefects when the pulling rate is changed passing through a critical value, the size and shape of the regions of interstitial (A and B) defects and vacancy-related A′ defects, the position and shape of the defect-free zone in Si crystals 8–16 cm in diameter. From fits of the calculations to the observed microdefect patterns, the activation energy for point-defect migration was estimated to be 1.3 eV (for temperatures from melting point to 1273 K). We show how to evaluate the radial distribution of axial temperature gradient near the growth interface from the actual microdefect patterns revealed in Si crystals.