Early growth of silicon on sapphire. II. Models

Abstract

We analyze data obtained on the morphology of (100) silicon on (011̄2) sapphire at early stages of growth. For the sake of simplicity and concreteness, we assume, perhaps incorrectly, that isolated growth islands are hemispherical. In order to account for the observation that the rate of increase of deposited silicon has achieved the bulk value at surface coverages of 50% or less, we postulate a ’’collection zone’’ around each growing island. Material falling in this zone is assumed to all diffuse to the growing island. For our experiments, the width of this zone is some tens of angstroms. We show that the growth rate of {110} islands is not significantly different than that of (100) islands. The eventual disappearance of {110} Si for full growths can be ascribed to the tendency to reduce the high-energy contact area between (100) and {110} Si. The logarithm of (100) island density appears to be proportional to (growth time)1/2. A simple model of island coalescence yields such a dependence, the proportionality constant being essentially equal to the (initial nucleation site density)1/4 multiplied by the (growth rate)1/2. The model for individual island growth in conjunction with the coalescence model yields a satisfactory explanation of the observed time dependence of island density, of surface coverage, and of total deposited volume. We suggest that, under the high effective supersaturations used in the growth of silicon on sapphire, island growth and coalescence are not dominated by surface energies. We speculate that nucleation of silicon on sapphire occurs by a type of homogeneous surface mechanism, rather than being due to either ’’dirt’’ on the substrate or crystallographic defects in the sapphire substrate.