Reaction dynamics of H₂ and D₂ on Si(100) and Si(111)

Experimental and theoretical results on the dynamics of dissociative adsorption and recombinative desorption of hydrogen molecules on silicon are reviewed.

The temperature dependence of the desorption rates for H₂ and D₂ on Si(100) and Si(111) corresponds to a desorption barrier of 2.3-2.4 eV. Adsorption is phonon assisted: the sticking coefficient increases strongly with surface temperature, corresponding to an activation energy of 0.65 eV at a gas temperature of 300 K (with little isotope effect). It also increases with incident gas energy. The adsorption barrier is strongly reduced by the presence of defects and steps on the surface and by preadsorbed H atoms at inter-dimer positions. The barrier at steps, for instance, is only of the order of 0.1 eV. The state-resolved energetics of the desorbing particles shows an excess energy (including translational energy) above thermal which is small compared to the activation barrier to adsorption. The angular dependence of sticking and desorption is strongly forward peaked (∝(cos θ)^10 to 11 or ∝(cos θ)^3 to 4 depending on azimuth).

Molecular vibrations show vibrational heating in desorption (with a strong isotope effect) and vibrationally assisted sticking at higher temperatures. On the other hand, molecular rotations show cooling in desorption.

Ab initio generalized gradient approximation slab calculations for the H₂ interaction with the dimers of Si(100)2×1 and with the Si `adatoms' on Si(111)7×7 all indicate the existence of strong lattice relaxations near the adsorption sites and the transition state geometries in qualitative agreement with the observed phonon-assisted sticking. The energetically lowest transition state on Si(100) is the inter-dimer state which also has the highest elastic relaxation energy (about 0.33 eV). The barrier of the asymmetric intra-dimer state is slightly higher but the relaxation energy is only half as big. There is also a symmetric intra-dimer transition state with an even higher barrier. It may, nevertheless, contribute to sticking and desorption due to a large phase space.

The slab calculations yield good values for the desorption barrier heights of 2.3 to 2.5 eV. They also lead to a good semiquantitative understanding of the existence of highly reactive sites near steps and preadsorbed H atoms at inter-dimer states. The absolute values of adsorption barriers, however, come out consistently too low by about 0.2 to 0.4 eV. Since in our review we are not so much interested in pursuing the consequences of ab initio calculations in detail but more in a model describing the experimental data quantitatively, we allow ourselves to readjust the ab initio results slightly to obtain good fits to the data. Because of the uncertainties of the ab initio results, the relation of model parameters to the various transition states is uncertain as well.

The strong phonon assistance of sticking can be modelled fairly well by taking only a single lattice displacement coordinate at the adsorption site into account. Together with the six degrees of freedom of the molecule, one obviously needs a model with at least seven degrees of freedom. We will present a seven-dimensional Hamiltonian which we treat in a seven-dimensional time-independent coupled-channel calculation. The results of this calculation agree well with experimental data. Most of the results are more or less independent of the particular transition state mediating the reaction. An exception, perhaps, is the angular dependence of sticking coefficients and desorption fluxes. We discuss several alternatives for explaining the observed angular distributions in terms of possible transition states.