ALBERT

Notes: An efficient implementation of microcanonical, classical variational transition-state theory based on the use of the efficient microcanonical sampling (EMS) procedure is applied to simple bond fissions in SiH2 and Si2H6 using recently constructed global potential-energy surfaces. Comparison is made with results of trajectory calculations performed on the same potential-energy surfaces. The predictions of the statistical theory agree well with and provide an upper bound to the trajectory derived rate constants for SiH2→SiH+H. In the case of Si2H6, agreement between the statistical theory and trajectory results for Si–Si and Si–H bond fission is poor with differences as large as a factor of 72. Moreover, at the lower energies studied, the statistical calculations predict considerably slower rates of bond fission than those calculated from trajectories. These results indicate that the statistical assumptions inherent in the transition-state theory method are not valid for disilane in spite of the fact that many of the mode-to-mode rate constants for intramolecular energy transfer in this molecule are large relative to the Si–Si and Si–H bond fission rates. There are indications that such behavior may be widespread among large, polyatomic molecules.

Notes: The dynamics of chemisorption and decomposition of SiH2 on Si(111)–(1×1) and recontructed Si(111)–(7×7) surfaces have been investigated using classical trajectories on a previously described [Surf. Sci. 195, 283 (1988)] potential-energy surface modified to yield the experimental bending frequencies for chemisorbed hydrogen atoms and to incorporate the results of ab initio calculations of the repulsive interaction between SiH2 and closed-shell lattice atoms. The Binnig et al. model is employed for the (7×7) reconstruction. Sticking probabilities are found to be unity on the (1×1) surface and near unity on Si(111)–(7×7). The major mode of surface decomposition on the (7×7) surface is by direct molecular elimination of H2 into the gas phase. Hydrogen atom dissociation to adjacent lattice sites is a much slower process and the chemisorbed hydrogen atoms thus formed exhibit very short lifetimes on the order of (1.13–10.6)×10−13 s. The calculated rate coefficients for these two decomposition modes are 3.4×1010 and 0.79×1010 s−1 , respectively. The rate coefficients for the corresponding reactions on the (1×1) surface are 6.6×1010 and 5.3×1010 s−1 , respectively. The rates on the (1×1) surface are faster due to the increased exothermicity released by the formation of two tetrahedral Si–Si bonds upon chemisorption compared to a single Si–Si bond on the (7×7) surface. Molecular beam deposition/decomposition experiments of SiH4 on Si(111)– (7×7) surfaces reported by Farnaam and Olander [Surf. Sci. 145, 390 (1984)] indicate that chemisorbed hydrogen atoms are not formed in the SiH4 decomposition process whereas the present calculations suggest that such a reaction, although slow, does occur subsequent to SiH2 chemisorption. It is suggested that energetic differences between SiH4 and SiH2 chemisorption are responsible for these differences.

Notes: A general method for analyzing the results of classical trajectory calculations to obtain the details of intramolecular energy transfer is described. The method is based on the determination of the time dependence of the normal mode velocities by projection of the instantaneous Cartesian velocities onto the normal mode vectors. It is shown that the method obviates the need to arbitrarily define a "bond'' or "mode'' energy as a means of following the energy flow. Average mode energies are computed using the virial theorem. For a given potential surface, the results are exact within the framework of the classical approximation. The method is applied to a study of intramolecular energy transfer in 1,2-difluoroethane. Decay rates and pathways of energy flow for initial excitation of each of the 18 vibrational modes are reported. The results obtained from the time variation of the normal mode velocities are used to extract a first-order, mode-to-mode energy transfer rate coefficient matrix. The mode-to-mode coefficients are shown to provide an excellent means of collating the energy transfer information. Their values yield a quantitative description of the energy transfer rates and a clear picture of the relative importance of the available pathways for energy flow in the system.

Notes: The unimolecular decomposition reactions of 1,2-difluoroethane upon mode-specific excitation to a total internal energy of 7.5 eV are investigated using classical trajectory methods and a previously formulated empirical potential-energy surface. The decomposition channels for 1,2-difluoroethane are, in order of importance, four-center HF elimination, C–C bond rupture, and hydrogen–atom dissociation. This order is found to be independent of the particular vibrational mode excited. Neither fluorine–atom nor F2 elimination reactions are ever observed even though these dissociation channels are energetically open. For four-center HF elimination, the average fraction of the total energy partitioned into internal HF motion varies between 0.115–0.181 depending upon the particular vibrational mode initially excited. The internal energy of the fluoroethylene product lies in the range 0.716–0.776. Comparison of the present results with those previously obtained for a random distribution of the initial 1,2-difluoroethane internal energy [J. Phys. Chem. 92, 5111 (1988)], shows that numerous mode-specific effects are present in these reactions in spite of the fact that intramolecular energy transfer rates for this system are 5.88–25.5 times faster than any of the unimolecular reaction rates. Mode-specific excitation always leads to a total decomposition rate significantly larger than that obtained for a random distribution of the internal energy. Excitation of different 1,2-difluoroethane vibrational modes is found to produce as much as a 51% change in the total decomposition rate. Mode-specific effects are also seen in the product energy partitioning. The rate coefficients for decomposition into the various channels are very sensitive to the particular mode excited. A comparison of the calculated mode-specific effects with the previously determined mode-to-mode energy transfer rate coefficients [J. Chem. Phys. 89, 5680 (1988)] shows that, to some extent, the presence of mode-specific chemistry is correlated with the magnitude of the energy transfer rate. However, the particular pathways for energy flow seem to be more important than the magnitude of the rate coefficients. It is suggested that the propensity for the energy to remainisolated in small subset of modes, such as the CH2F deformation modes or the rocking modes, is primarily responsible for the observation of mode-specific chemistry. The results clearly demonstrate that an intramolecular energy transfer rate that is fast relative to the unimolecular reaction rate is not a sufficient condition to ensure the absence of mode-specific chemicaleffects.

Notes: The unimolecular decomposition dynamics of Si2H4 have been investigated using classical trajectory methods on a global potential-energy surface fitted to the results of ab initio calculations and the available experimental data. The required phase-space averages are computed using Metropolis sampling techniques. It is found that unless the parameters of the Markov walk are adjusted for each different type of atom present, extremely long Markov walks are required to adequately cover the phase space of the system. Microcanonical rate coefficients for the decomposition of Si2H4 into all open channels are reported at energies in the range 5.0〈E〈9.0 eV. The most important dissociation channel over this energy range is three-center elimination of molecular hydrogen leading to H2 Si=Si. At energies below 7.0 eV, the other channels are, in order of importance, Si–Si bond rupture, four-center H2 elimination, and simple Si–H bond rupture. At or above 8.0 eV, four-center H2 elimination replaces Si–Si bond rupture as the second most important decomposition channel. The energy dependence of the rate coefficients is well described by an RRK expression. Three-center H2 elimination involves a simultaneous rupture of both Si–H bonds whereas the four-center elimination is found to proceed by a hydrogen atom transfer process followed by H2 elimination. Except for a small propensity to form H2 with excess rotational energy, the energy partitioning among the products is nearly statistical. A comparison study of the decomposition of Si2H4 complexes formed by the recombination of two SiH2 molecules shows that the rates for both three- and four-center H2 elimination are in agreement with those computed using a statistical distribution of the same internal energy. The rate for Si–Si bond rupture, however, is significantly larger for Si2H4 complexes formed by SiH2 recombination than for Si2H4 molecules with the same internal energy randomly distributed. The decomposition dynamics of SiH2 on the global surface are also reported.

Notes: A perturbation–trajectory method for determining the dynamics of gas–surface collision processes is described. The method is based upon the assumption that the motions of Q-zone atoms are unaffected by the collision process at the lattice surface. This assumption leads to a P-zone Hamiltonian that incorporates the effects of Q-zone motion in terms of time-varying P-zone–Q-zone interactions. The collision dynamics of the P zone are determined from an ensemble of stoichastic trajectories using this coupled Hamiltonian. The method is applied to three systems: (1) collinear inelastic atomic collisions with a ten-atom chain, (2) the inelastic scattering and absorption of NO on a Ag(111) surface, and (3) the collision and subsequent surface reactions of SiH2 on a Si(111) surface. Comparison of the perturbation results with those obtained using the full system Hamiltonian shows that under certain conditions the perturbation procedure yields very accurate results with a significant reduction in computational requirements. In general, the accuracy of the perturbation calculations increases as the incident-to-lattice-atom mass ratio decreases. A decrease in the strength of the interaction between the incident molecule and the Q zone, the incident translational energy, or the lattice temperature also improves the accuracy of the perturbation treatment. The method is therefore best suited to the study of inelastic, light-molecule collisions with heavy-atom surfaces at low temperature. Comparisons with previously reported gas–surface studies that employ a Langevin approximation are also given.

Notes: A previously formulated semiclassical wave packet method is used to investigate the importance of different surface phonon modes and the Debye surface temperature upon inelasticity in atomic gas–surface collisions. Desorption rates are calculated as a function of potential-well depth and the rate law for the process is examined. The incident beam is represented by a quantum mechanical wave packet whose momentum distribution is nearly square. This wave packet is coupled to a three-dimensional model lattice through a time-varying potential field obtained by solution of the classical motion equations for the lattice. Calculated final-state momentum and energy distributions are found to be strongly dependent upon the particular surface phonon mode into which the initial lattice energy is partitioned. In general, energy transfer occurs predominantly to and from those modes for which the lattice atom in the impact region have motion in the direction of the momentum vector of the incoming wave packet. The inelasticity of the collision is found to increase as the lattice force constants and the surface Debye temperature decrease. The peak spacings in the final-state momentum and energy distributions are found to correlate well with the surface phonon frequencies. Desorption is found to be well described by a first-order rate law for small potential-well depths. For larger well depths, the first-order decay plots begin to show an increasing amount of curvature. Desorption rate coefficients obtained from the slopes of the decay plots show an approximate exponential dependence upon the potential-well depth.

Notes: The diffusion of hydrogen atoms on a partially hydrogen-covered Si(111) surface has been studied by using Monte Carlo techniques with a potential-energy surface based on the available ab initio results and experimental data. The potential describes two kinds of binding sites, a covalent Si–H bond (top site) and an interstitial threefold bonding site (open site). Classical jump frequencies between the top and open sites were calculated using Monte Carlo variation phase-space theory with importance sampling at 300, 600, 900, and 1200 K. A new approach for treating tunneling through two-dimensional diffusional barriers is presented and used to calculate the phonon-assisted tunneling rates. This method assumes continuum-to-continuum WKB tunneling with classical Monte Carlo phase space averaging. Thermal diffusion coefficients are calculated using the jump frequencies. The diffusional barriers between the two binding sites on the equilibrium surface are 2.79 and 0.65 eV for top-to-open site and open-to-top site jumps, respectively. The calculated classical jump frequencies give Arrhenius parameters of A=1.3×1014 and 9.9×1013 s−1 Ea=2.72 and 0.59 eV for top-to-open and open-to-top site jumps, respectively. Monte Carlo techniques were used to compute the minimum energy path; the dynamical barrier is 2.64 eV for top-to-open site jumps. Tunneling rates were calculated at 300 K and estimated at higher temperatures. Due, in part, to the small width of the barrier, the tunneling rate at 300 K is 257 times larger than the classical value. Tunneling is important at room temperature, but its importance relative to the classical rate decreases with increasing temperature. The results indicate that surface phonons significantly enhance the tunneling rate.

Notes: 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.