Tight Binding Modeling of Properties Related to Field Emission from Nanodiamond Clusters
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Tight Binding Modeling of Properties Related to Field Emission from Nanodiamond Clusters Denis A. Areshkin1, Olga A. Shenderova1, Victor V. Zhirnov1,2, Alexander F. Pal,3 John J. Hren1, and Donald W. Brenner1 1 North Carolina State University, Raleigh, NC 2 Semiconductor Research Corporation, Research Triangle Park NC 3 Troitsk Institute for Innovation and Fusion Research, Troitsk, Russia ABSTRACT The electronic structure of nanodiamond clusters containing between 34 and 913 carbon atoms was calculated using a tight-binding Hamiltonian. All clusters had shapes represented by an octahedron with (111) facets with the top and the bottom vertices truncated to introduce (100) surfaces. The tight-binding Hamiltonian consisted of environment-dependent matrix elements, and C-H parameters fit to reproduce energy states of the cyclic C6 and methane. The calculations predict a density of states similar to bulk diamond for clusters with radii greater than ~2.5nm, and insignificant differences in the potential distribution between the clusters and bulk diamond for radii greater than ~1nm. Hydrogen passivated nanodiamond clusters are estimated to have an electron affinity of approximately -1.8 eV. INTRODUCTION Recent experimental measurements of field-emission properties of diamond nanoclusters on silicon field-emitter arrays have demonstrated desirable properties for cold-cathode applications, including low emission thresholds, high emission currents and good current stability [1]. Some of these properties, however, appear to depend on the origin and processing of the nanodiamond clusters, and hence the details of their structure, including particle size and surface conditions. To better understand the molecular origins of field emission characteristics of nanodiamond clusters, a series of tight-binding calculations on regular-shaped structures with radii up to approximately 2.5nm have been carried out. Both pure carbon clusters and clusters with hydrogen termination were studied. These calculations, which use an environmentally dependent tight binding (EDTB) model [2], suggest that the size dependence of the density of states (DOS) is insignificant for radii greater than about 2.0-2.5 nm. In contrast, the dependence of the electron potential on cluster size is largely independent of cluster size down to radii of approximately 1 nm. TIGHT BINDING PARAMETRIZATION To reproduce the bulk diamond band gap and a qualitative description of the band structure, an EDTB model for carbon was used [2]. The tight-binding (TB) scaling function developed by Xu et al. [3] and parameterized by Davidson and Pickett (DP) [4] was used for the C-H interactions. To obtain a reasonable bulk DOS, a set of values for the C-H hopping and onsite matrix elements differing from the DP model were developed. These parameters, listed as Present Work in Table I, were generated by fitting the energies of the occupied electronic states
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in ethane to their counterparts calculated from density functional theory. The latter values were calculated using comm
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