Theoretical study on Frenkel pair formation and recombination in single crystal silicon

Abstract

Frenkel pair (FP) formation and recombination are very important mechanisms through which the concentration of intrinsic point defects (vacancy V and self-interstitial I) changes in single crystal silicon (Si). FP recombination is suggested to occur at temperatures above 1350 °C during the growth of Si crystal. Experiments using rapid thermal annealing suggest that FPs form in Si wafers. In this study, we explain the procedure for deriving an expression valid for the change in V and I concentrations (CV and CI) due to FP formation and recombination by taking into consideration that FPs can form at all lattice sites while recombination occurs at the same time when I and V encounter each other. The derived equations that are functions of the capture radius ac and recombination barrier ΔEIV can be applied to the case of CVCI < CVeqCIeq (FP formation is dominant) and that of CVCI > CVeqCIeq (FP recombination is dominant). Here, CVeq and CIeq are the thermal equilibrium concentrations of V and I, respectively. The other purpose of this study is to analyze the formation and recombination of FPs in Si crystals by applying density functional theory (DFT). The formation energy of a FP and diffusion barrier of I near V were obtained and used to evaluate the capture radius ac and energy barrier ΔEIV for FP recombination. The evaluated capture radius was ac ≃ 5 Å and the energy barrier was ΔEIV ≃ 0.05 eV. The most energetically appropriate path along which I can form from V was also suggested. DFT molecular dynamics calculations show that V and I in the capture radius recombine in 0.5 to 2.5 ps at 1350 °C.