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SPECIAL SECTION ON NANOMATERIALS AND NANOMECHANICS

# Interactions of Carbon Atoms and Dimer Vacancies on the Si(001) Surface

[+] Author and Article Information
Cristian V. Ciobanu

Division of Engineering,  Colorado School of Mines, Golden, CO 80401cciobanu@mines.edu

Department of Computer Science,  University of California, Los Angeles CA 90095

Ryan M. Briggs

Division of Engineering,  Colorado School of Mines, Golden, CO 80401

J. Eng. Mater. Technol 127(4), 462-467 (May 08, 2005) (6 pages) doi:10.1115/1.2019898 History: Received February 07, 2005; Revised May 08, 2005

## Abstract

We investigate the interactions between substitutional carbon atoms on the defect free, $(2×1)$ reconstructed Si(001) surface, and bring evidence that the interaction energy differs significantly from the inverse-cube distance dependence that is predicted by the theory of force dipoles on an elastic half-space. Based on Tersoff potentials, we also calculate the interactions between carbon atoms and dimer vacancies. The calculations indicate that dimer vacancies (DVs) are strongly stabilized by fourth-layer C atoms placed directly underneath them. By use of simple model Monte Carlo simulations, we show that the computed interactions between carbon atoms and DVs lead to self-assembled vacancy lines, in qualitative agreement with recent experimental results.

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## Figures

Figure 5

Surface energy of the (2×N) reconstruction on C∕Si(001) as a function of N, plotted for different values of the chemical potential μC. The solid dots show the locations N* of the surface energy minima, which move towards smaller values with increasing μC.

Figure 6

Optimal value N* as a function of the chemical potential μC. The chemical potential range that corresponds to experimentally relevant carbon coverages is −7.63eV<μC<−7.19eV.

Figure 4

Heat capacity of a model system with 32 carbon atoms, calculated during a slow cooling from T=0.95eV∕kB down to T=0.05eV∕kB. The initial and final configurations (A and B, respectively) show that the carbon atoms (solid circles) form complexes with the DVs (empty squares), which assemble into long linear structures during annealing.

Figure 3

Interaction energies w (in electron-volts) between (a) two DVs, (b) two C atoms, (c) one C atom and one DV, and (d) two CDV complexes plotted as functions of their separation d measured along the dimer row direction. The interactions are sizeable only when the two entities lie in the same dimer row (solid circles) or in adjacent dimer rows (open circles). The substitutional carbon atoms considered here belong to the α sites in the fourth layer. The distance d (horizontal axis) is expressed as integer multiples of the dimer spacing a=3.84Å.

Figure 2

Contour plots of the magnitudes (in angstroms) of atomic displacements caused by a substitutional carbon atom in the first layer (a), and in a fourth layer α-site (b). The displacements are computed with respect to the defect-free Si(001) surface. The locations of the surface atoms are shown by the small dots, to help visualize the (2×1) reconstruction. A quarter of the slab has been blanked in order to show the displacement contours in different planes.

Figure 1

Atomic structure of a CDV complex on Si(001), with the carbon atom shown in gray

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