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Hydrogenated Diamond Surfaces.

Carbon (100) and (111) facets are commonly observed during the growth of diamond-like films via chemical vapour deposition, and have for this reason been the subject of increasing attention in recent years. For C(100), atomically smooth surfaces can be grown, and so the study of this surface is in some ways more attractive. Moreover, it is unique amongst the low-index surfaces in that it possesses two dangling bonds per surface carbon atom, leading to some particularly interesting surface chemistry. Chemical vapour deposition occurs from a hydrogen atom / hydrocarbon mixture, and hydrogenation of the carbon surface is an intrinsic part of the process. An understanding of the hydrogenated surface is therefore of particular importance.

A quantum mechanical description is deemed necessary because the extended electronic states of the carbon substrate lead to many-body forces, not easily describable by classical potentials. The advantage of a tight-binding (TB) formulation is that, in exchange for a limited amount of parameterisation, one can simulate larger samples of the chosen system than is at present possible with ab initio methods. We present results for several hydrogenated C(100) surfaces based on a new TB parameterisation.


Parameterisations.

In the simplest tight-binding formulation, the total energy of the system is written as a band energy term plus a sum over repulsive pair potentials. The band energy term equals the sum of occupied eigenvalues obtained from a minimal basis TB Hamiltonian. Harrison suggested a universal parameterisation for sp-bonded materials, with the transfer integrals t(r) of the TB Hamiltonian varying with the interatomic distance r as (r_0/r)**2, and the pair potentials phi(r) as (r_0/r)**4.

Although Harrison's parameterisation gives good results for the diamond structures of C and Si close to equilibrium, its transferability to other structures is poor. Consequently, Goodwin, Skinner and Pettifor for Si, and later Goodwin for C, proposed a modified scaling behaviour which gave improved transferability:


s(r) = s(r_0) * (r_0 / r)^n * exp [ n ( -(r / r_c)^n_c + (r_0 / r_c)^n_c ) ]

with s = t or phi. Following the Goodwin-Skinner-Pettifor approach, Wang and Mak have derived C-C and C-H parameters suitable for hydrocarbons in a wide range of bonding situations. Their parameter set is, however, relatively large. Adopting the original C-C parameters of Goodwin, we have derived new parameters for C-H and H-H interactions, such that the total parameter set is limited in size ("Model 1"). We believe that many properties of C/H systems should follow from the form of the sp-bonding, and not be dependent on extensive parameterisation.

Xu, Wang, Chan and Ho developed a similar TB model for carbon, but replaced the pairwise form for the repulsive energy by the embedded-atom-like form:


E_rep = \sum_i f (\sum_j  \phi(r_{ij}) )

where the function f is a 4th order polynomial. Davidson and Pickett have extended this parameterisation to C/H systems, and given some results for hydrogenated carbon surfaces (using 2 C atoms per layer, k-point sampling, and steepest descent minimisation). They include a term

E_U = U \sum_i (q_i - q_i0)^2

in the energy to reduce charge transfer. We give results also for this model ("Model 2").


Methods.


Results.

Tables I-VI compare the predicted geometries from CG minimisation for Models (1) and (2), with the ab intitio calculations of Furthmü ller et al, Europhys. Lett. 28, 659 (1994) and Yang et al, Phys. Rev. B 48, 5261 (1993). Representative geometries are shown in Figs. 1-6.

[ Tables I-VI ].

Problems and future direction


m.d.winn@dl.ac.uk
Last modified: Mon Jun 30 12:21:06 BST 1997