Trajectory study of Si4 formation and decay and of exchange and abstraction reactions in Si+Si3 collisions

Abstract

The formation and subsequent decay of Si4 complexes as well as the direct exchange and abstraction processes in Si+Si3 collisions have been studied using quasiclassical trajectories on a new global Si4 potential energy surface fitted to available experimental and ab initio data, and on Bolding and Andersen’s (BA) recently formulated silicon potential for arbitrary cluster sizes. Cross sections for Si4 formation, σf(Et), were computed as a function of initial relative translational energy Et over the range 0.01 to 4.0 eV, with the Si3 internal energy described by the Boltzmann distribution at 800 K. The cross section was found to peak sharply near Et=0, as expected, and to fall off linearly at high energy. An analytical expression for kf(T), the thermal rate constant for Si4 formation, was found by averaging σf(Et) over the Maxwell–Boltzmann distribution for Et. The analytical values of kf(T) lie between 6×1014 and 8×1014 cm3/mol s for the range 800–1500 K, and are in excellent accord with trajectory calculations of kf at 800 and 1200 K. Unimolecular dissociation rate constants for Si4, kd, were calculated as a function of Et over the 0.4 to 4.0 eV. The values of kd are well described by the RRK expression, with a value of 4.67 for the effective number of vibrational modes. Averaging the dissociation rate constant over the Maxwell–Boltzmann distribution yields an average Si4 lifetime of 413 ps at 800 K, which is not long enough for a stabilizing collision to occur at pressures characteristic of low-pressure CVD experiments. The direct exchange reaction is found to be unimportant for Et less than 1 eV, since for lower relative energies essentially all reactions proceed indirectly via Si4 complex formation. Direct atomic abstraction is energetically forbidden, on average, for Et less than 0.9 eV, and is unlikely for Et less than 2 eV. At higher energies, the end-atom exchange and abstraction channels, which are statistically favored over the apex-atom channels, are dynamically favored as well. When exchange or abstraction proceeds indirectly via an Si4 intermediate, the distinction between apex-atom, end-atom, and no-reaction channels is lost. Both the direct and indirect pathways leave a large fraction of the energy and angular momentum in the reaction products. Cross sections for Si4 formation on the BA surface are smaller than those on the global Si4 surface due to the cutoff function in the BA two-body potential terms; Si4 dissociation rates for total energies between 1.3 and 2 eV above threshold agree to within a factor of 2.3 or better with corresponding values for the Si4 surface.