Molecular-dynamics calculations of energetics and geometries of steps on diamond C(001)

Abstract

The diamond C͑001͒ surface has been observed by scanning tunneling microscopy ͑STM͒ to dimerize similar to Si͑001͒. STM also observed the formation of single-and double-layer steps in this surface. Using an ab initio multicenter molecular-dynamics method, our calculations for the relaxed geometries and the corresponding energetics of these steps show that the detailed structures of these steps are intrinsically different from that of type-A and type-B steps of Si͑001͒ obtained by Chadi. These differences can be attributed to the preference of carbon atoms near the edges of the lower terrace to form dimers with strong mixed single and double bonds rather than to rebond to the edge atoms. ͓S0163-1829͑98͒05127-3͔Studies of homoexpitaxial diamond films by chemical vapor deposition have recently been made toward the growth of high-quality single-crystalline diamond films and the understanding of growth mechanism. Morphological studies using scanning tunneling microscopy ͑STM͒ and low-energy electron diffraction have found (2ϫ1) reconstruction and singlelayer steps on the homoepitaxial diamond C͑001͒ films. 1-7 Double-layer steps with step edges parallel to the dimer rows have also been observed in coexistence with single-layer steps when the diamond ͑001͒ surface was annealed in hydrogen plasma. 6-10 Following Chadi, 11 we shall denote single-layer steps S A and S B and double-layer steps D A and D B as the steps with step edges that run parallel and perpendicular to the dimer rows on the upper terraces, respectively. STM measurements found that step edges of S A were almost straight, whereas those of S B were ragged with many kinks. These observations suggested that S A steps have a formation energy lower than that of S B similar to Si͑001͒ grown by molecular beam epitaxy. The occurrence of D A steps and the absence of D B steps in STM observations suggested that the formation energy of the D A step is lower than that of the D B step in contrast to Si͑001͒, which led Kuang et al. 10 to suggest that the saturation of dangling bonds by hydrogen atoms present in the experimental environment might reverse the preference of D B .To understand these STM observations, we have carried out this study using the ab initio multicenter molecular dynamics ͑MD͒ method of Sankey and Niklewski. 12 This method is based on the norm-conserving pseudopotential method 13,14 with s, p x , p y , and p z local-orbital basis set and has been shown to work well for semiconductor systems 15-18 and diamond. 19 The theoretical lattice constant of 3.7 Å ͑about 3.7% error from the experimental value 20 of 3.567 Å͒ determined by bulk diamond calculations using a cubic unit cell and repeated five-and six-layer slab ͑or supercell͒ models are used for S A and S B steps. For D A and D B steps, only repeated six-layer-slab models are used. The need for choosing both five-and six-layer supercell models for S A and S B steps will be described later. We have chosen a (11ϫ2) unit cell for all steps. For S A and S B steps, twelve surface atoms per unit cell f...

Contribution of steps to optical properties of vicinal diamond (100):H surfaces

“…It is clear that similar conditions pertain on vicinal diamond surfaces 13,14 with the crucial difference that on hydrogen plasma-treated diamond (100) surfaces, like those studied here, STM results have revealed the presence of D A steps, and D B steps are absent. 13 The possible equilibrium geometries of diamond (100) surfaces in the presence of single and double steps have been investigated.…”

“…13 The possible equilibrium geometries of diamond (100) surfaces in the presence of single and double steps have been investigated. 14 Interestingly, the equilibrium geometries previously proposed by Chadi for Si(100) 28 may not be the most stable ones on the diamond (100) surface. The driving force for this difference is that diamond is stiffer and more likely to form double bonds than Si.…”

“…6 The realization of the potential of diamond in applications such as optoelectronics and electronic devices 7,8 is dependent not only on controlling the growth of the material but also on understanding its surface electronic structure and in particular the influence of hydrogen. 4 In order to optimize growth processes it is useful to develop techniques for the in situ monitoring of diamond growth and in particular to monitor the behavior of surface steps, [9][10][11][12][13][14] the anisotropic etching of which by atomic hydrogen is known to be important in the production of smooth diamond (100) [C(100)] surfaces. 10 Reflection anisotropy spectroscopy (RAS) 15,16 is a technique that has found application in monitoring the growth of Si, Ge, and III-V compounds [17][18][19][20][21] and the interfaces that are important in the integration of Si, Ge, and GaAs technologies.…”

“…We compare the empirical step spectral signatures with the results of theoretical calculations, within Density Functional Theory (DFT) 36 and the GW 37 method, for the flat and stepped surfaces using the models suggested by Chadi 28 and Tsai and Yeh. 14…”

The fascinating physics of carbon surfaces: first-principles study of hydrogen on C(0 0 1), C(1 1 1) and graphene

“…Just ideal (flat, no defects, no steps) geometries will be here considered. Of course, real surfaces are much more complicated, presenting domains, terraces, and many other unavoidable deviations from the perfect, ideal models we use (see for example [7,8,9,10]). Along with such C surfaces, we will look at the effect of hydrogen coverage on graphene.…”