Gan Nanotubes
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Mat. Res. Soc. Proc. Vol. 537 © 1999 Materials Research Society
the initial nucleation seeds for GaN nT formation will play a crucial role for growth. We find that an intermediate phase which is composed of [4,6,10] polygons may play as a nucleation seed during the growth. THEORETICAL APPROACHES We adopt in this work self-consistent charge density-functional-based tight-binding (SCCDFITB) approach. The SCC-DFFB method uses a basis of numerically obtained s, p, and d atomic orbitals. Hamiltonian overlap matrix elements are evaluated by two-center approach. Charge transfer is taken into account through the incorporation of a self-consistency scheme for Mulliken charges based on the second-order expansion of the Kohn-Sham energy in terms of charge density fluctuations. The diagonal elements of the Hamiltonian matrix employed are then modified by the charge-dependent contributions in order to describe the change in the atomic potentials due to the charge transfer. The off-diagonal elements have additional charge-
dependent terms due to the Coulomb potential of ions. They decay as 1/r and thus account for the Madelung energy of the system. Further details of the SCC-DFTB method have been published elsewhere [15]. RESULTS AND DISCUSSION Various GaN crystal phases exist under different experimental growth conditions [12]. The Wurtzite phase is the thermodynamically stable structure at ambient conditions, whereas the zincblende (ZB) phase can be stabilized on various cubic substrates [16, 17]. We first calculate the total binding energies of ZB and graphitic phases of GaN using SCC-DFTFB method in order to study the relative stabilities. We choose a cubic supercell of 216 atoms for ZB GaN and 200 atoms for the graphitic sheet. Periodic boundary conditions are applied along the x-, y-, and zdirections. For the graphitic pha~e, a large vacuum region between graphitic sheets is included. Figure 1 shows total binding-energy curves obtained by the SCC-DFFB calculations. The binding energy of the ZB GaN is -5.91 eV/atom with the nearest neighbor distance of 1.950 A, or equivalently the cubic lattice constant of 4.503 A. The calculated bulk modulus is 195 GPa, in good agreement with the reported local-density-approximation results [18]. A considerable amount of electron charge (0.56 e) is transferred from Ga atom to N atom, resulting in an ionic bonding nature. The binding energy of the graphitic GaN is -5.55 eV/atom with the nearest neighbor distance of 1.775 A, smaller than that of the ZB GaN. This difference in the binding energy suggests the graphitic GaN to be energetically unfavorable over the ZB or the wurtzite GaN. Yet this small magnitude of the energy difference opens the possibility of forming graphitic sheets as a metastable phase. We next calculate the strain energy per atom required in order to wrap up a graphitic sheet into a tube. Periodic boundary conditions are applied with vacuum regions (10 A) between tubes. Strain energies decrease with increasing the tube diameter as expected (Fig. 2). We note that strain
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