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A 10-a editie a Seminarului National de nanostiinta si nanotehnologie 18 mai 2011 Biblioteca Academiei Romane Tight-binding (TB) methods: Empirical Tight-binding.

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Presentation on theme: "A 10-a editie a Seminarului National de nanostiinta si nanotehnologie 18 mai 2011 Biblioteca Academiei Romane Tight-binding (TB) methods: Empirical Tight-binding."— Presentation transcript:

1 A 10-a editie a Seminarului National de nanostiinta si nanotehnologie 18 mai 2011 Biblioteca Academiei Romane Tight-binding (TB) methods: Empirical Tight-binding (ETB) Ab-initio Tight-Binding Capability to render the atomistic nature of phenomena. ETB - describes the electronic structure of complex systems like interfaces, defects in crystals, amorphous materials, nano-clusters, and quantum dots (3 orders of magnitude faster than ab-initio DFT][C. Delerue et al., phys.stat.sol. (b) 227, 115 (2001)]. The parameter-free DFT-TB-LMTO (tight-binding-linear muffin-tin orbitals) method has become more widely used not only for crystals, but also for low-dimensional systems like layered structures [I. Turek et al., Electronic Structure of Disordered Alloy, Surfaces, and Interfaces, Kluwer Academic Publishers 1997]. ETB assumes:(1) an orthogonal basis of states localized around atomic sites; (2) diagonal coordinate operator in this basis (gauge-invariance). Overlap and optical matrix elements : Phys. Rev. B.72, (2005) 2D Graphene The tight-binding description of highly mismatched semiconductor alloys The developments[i] in the growth of Si lattice-matched BeSe0.41Te0.59 a new class of Si based devices.[i] The gap in size and orbital energies between Se/ Te and large lattice mismatch between BeTe/ BeSe makes the virtual-crystal approximation inappropriate. The band anti-crossing (BAC) model has been introduced in order to explain the electronic structure of highly mismatched alloys like ZnSexTe1-x.[ii] [i] Clark, K. et al., J. Appl. Phys. 88, 7201 (2000); Kirk, W. P. et al., Supperlatt. Microstruct. 28, 377 (2000).[ii] [i] [ii][ii] Walukiewicz, W. et al., Phys. Rev. Lett. 85, 1552 (2000); Wu, J. et al., Phys. Rev. B 68, (2003). Application to sp3s* TB Hamiltonian PRB, , Perturbed GF due to impurity by averaging over impurity configurations. The model is directly applied to sp 3 s* Hamiltonian[+] with spin-orbit interaction.[++][+][++] The TB Hamiltonian is written in the sp 3 hybrid basis and the basis is rotated in such a way that a unit cell is formed by the anion hybrid orbitals and the cation hybrid orbitals pointed toward the anion site. The s* orbitals remain unchanged. [+] Vogl, P. Hjalmarson, H. P. and Dow,J. D. J. Phys. Chem. Solids 44, 365 (1983). [+] [++][++] Chadi, D. J. Phys. Rev. B 16, 790 (1977). Real-Space LMTO Method for Large Systems DFT, ground state theory (LDA, etc); HFA not that good for solids. Exchange-correlation potentials and quasiparticle energies in the GWA or Screened Exchange: 1-particle GF and screened Coulomb interaction in predicting bandgaps (PRL ). Too demanding! Approximate methods in order to consider correlations- good for large systems (**Solid State Communications 150, 888; 2010). TB-LMTO-ASA PRB 34, 5253, 1986 FAST CALCULATION of the Hamiltonian and GF permits the evaluation of the dielectric permittivity and the use of a dielectric scaling method to estimate the bandgap**. The bangap is improved with respect to DFT. Potential use for large systems! Spin polarization by spin dependent tunneling through an indirect barrier Phys. Rev. B. 73, , 2006: TB PMC-Physics B, 1, 13, 2008: ab-initio Windows of large spin polarization due to Fane resonances in tunneling though an indirect barrier. Atomistic Description of Nanostructures Titus Sandu National Institute for R&D in Microtechnologies, Bucharest


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