On the kinetics of thermal donor formation in silicon

Abstract

A model for the kinetic growth of oxygen-related thermal donors in Czochralski silicon at about 450°C is presented. The model, which is based on the work of Suezawa and Sumino, derives forward reaction rates for the electrically active species by comparing analytic expressions for the early-time annealing kinetics with the infrared electronic absorption data. The analytic expressions, which are independent of the chemical structure of each species, result from three assumptions: (1) the donor defects beyond the first donor species (TD-1) are chemically stable at the donor formation temperature, (2) the reactions for the TD-1 and those electrically inactive clusters smaller than TD-1 are in equilibrium, and (3) the oxygen interstitial concentration remains constant for short annealing times. The parametrized values of the rate constants indicate that the forward rates of reaction vary widely between species, with a sharp peak at the reaction which takes the first electrically active species to the second. If the rate constants are taken to be of the form K = 4πRD, where R is the capture radius for the given forward reaction and D represents the effective diffusion coefficient, then the variation between reaction constants may be associated with differences in capture radii between species, with the diffusion coefficient assumed to be the value determined by Stavola et al. [Appl. Phys. Lett. 42, 73 (1983)] for “as-provided” material, which has an activation energy of 1.95 eV. The model is successfully applied to the two available sets of infrared absorption data (the Oeder-Wagner and Suezawa-Sumino data) when differences in the annealing temperatures and initial oxygen concentrations are taken into account. The best-fit parameters found by fitting the analytic expressions are then applied to a set of chemical reaction equations which characterize the formation rates of specific oxygen aggregates. The use of such a set of coupled, nonlinear differential equations, which must be solved numerically, introduces free parameters for the oxygen clusters smaller than the first thermal donor. It is shown that the assignments of a thermal donor core containing two, three, four, or five oxygen atoms are all capable of fitting the experimental data. This result indicates that a best fit to the kinetic data cannot be used to argue for a specific thermal donor core. Finally, the authors discuss possible mechanisms for the enhanced values of the capture radii.