The tight-binding method

The principle of the tight-binding method is to expand the wave functions of the electrons in a basis of atomic orbitals. Indeed, the physics of silicon for example is dominated (around the band gap) by the hybridization of the 3s, 3p (and 3d) orbitals of the Si atoms (see Fig. 1). Since atomic orbitals are localized in real space, their interactions are limited to a few nearest neighbors. Computing these interactions with a self-consistent ab initio method such as density functional theory is, however, very expensive for a few thousand atoms. The interactions between atomic orbitals are, nonetheless, usually close to bulk interactions in such systems. In the semi-empirical tight-binding framework, they are therefore adjusted to reproduce the bulk band structures, then transferred to the nanostructures. This approach is very efficient and accurate enough when the bonding does not differ too much from the bulk reference.

Fig. 1: (top) From silicon atoms to bulk silicon: links between then atomic orbitals and the bulk band structure. (bottom) The s, p, and d orbitals.

Since the interactions between atomic orbitals are limited to first, second or third nearest neighbors, the tight-binding hamiltonian is "sparse" (most matrix elements are zero): This makes the tight-binding method very appropriate for the design of "order N" methods whose computational cost scales linearly with the number N of atoms. For example, the cost of a matrix/vector product scales as N for a sparse tight-binding hamiltonian instead of N² for a dense matrix. The optical properties of a million atom system can therefore be computed within a few hours on a desktop computer.

Fig. 2: Multiscale modelling - Ab initio calculations on few atom systems are used to provide inputs to semi-empirical atomistic methods such as tight-binding, then to large-scale calculations based, e.g., on finite-element modelling. These methods can also be coupled together to describe different parts of the system with very different length or time scales.

As an atomistic approach, the tight-binding method is well suited to the description of atomic-scale features such as impurities, defects, electron-phonon coupling, etc... It can be used in a multi-scale modelling strategy as a transition from ab initio to large-scale finite element modelling (see Fig. 2).

The TB_Sim code

Fig. 3: The capabilities of TB_Sim.

The capabilities of TB_Sim are summarized on Fig. 3. In particular, TB_Sim features:

• Valence force field models for structural relaxation and phonons.
• Tight-binding and multi-bands k.p models for the electronic structure.
• Efficient Jacobi-Davidson algorithms for the calculation of one-particle states (diagonalization of large and sparse hamiltonian matrices).
• Self-energy and excitonic corrections (optical properties).
• Transport with the classical and quantum Kubo-Greenwood methods, and with Non-Equilibrium Green Functions.
• ...

The code is parallelized for OpenMP and MPI architectures. It can also make use of graphics cards (GPU) accelerators. TB_Sim has received in 2012 the third prize in the Bull-Fourier contest (high performance computing) for its parallel performances.

Contacts:

Coordinator and contact person:

• Yann-Michel Niquet (CEA/INAC/SP2M/L_Sim), coordinator.
  
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Developers:

• François Triozon (CEA/LETI/MINATEC).
• Christophe Delerue (CNRS/IEMN, Lille, France).
• Aurélien Lherbier (UCL, Louvain-La-Neuve, Belgium).
• Manuel Cobian (CEA/INAC).
• Viet-Hung Nguyen (CEA/INAC).
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Other contributors:

• Stephan Roche (ICN, Barcelona, Spain).
• Sylvain Latil (CEA/IRAMIS).
• Martin Persson (Former postdoc @ CEA/INAC/SP2M/L_Sim).
• Dulce Camacho (Former PhD student @ CEA/INAC/SP2M/L_Sim).
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A few illustrations using TB_Sim:

Fig. 4: (left) The electron (a) and hole (b) energy levels in InAs/InP nanowire heterostructures with radius R=10 nm as a function of the thickness tInAs of the InAs layer. (right) The corresponding conduction band wave functions for tInAs=4 nm and tInAs=16 nm. From Y. M. Niquet and D. Camacho Mojica, "Quantum dots and tunnel barriers in InAs/InP nanowire heterostructures: Electronic and optical properties", Phys. Rev. B 77, 115316 (2008).

Fig. 5: (top) (a) Density of states of an ideal (dashed line) and boron-doped graphene sheets for several boron concentrations Cd. (b, c) Local density of states on a boron and nitrogen impurity. (bottom) (a) Semiclassical conductivity at room temperature as a function of the carrier energy and Cd. Dotted lines correspond to the zero temperature limit. (b) Semiclassical conductivities for electrons and holes as a function of the carrier density and for Cd=0.5%. From A. Lherbier, X. Blase, Y. M. Niquet, F. Triozon and S. Roche, "Charge transport in chemically doped 2D graphene", Phys. Rev. Lett. 101, 036808 (2008).

Publications using TB_Sim:

1. Electronic structure and transport properties of Si nanotubes.
   J. Li, T. Gu, C. Delerue and Y. M. Niquet,
   Journal of Applied Physics 114, 053706 (2013).

2. Residual strain and piezoelectric effects in passivated GaAs/AlGaAs core-shell nanowires.
   M. Hocevar, L. T. T. Giang, R. Songmuang, M. den Hertog, L. Besombes, J. Bleuse, Y. M. Niquet and N. T. Pelekanos,
   Applied Physics Letters 102, 191103 (2013).

3. Highly defective graphene: A key prototype of two-dimensional Anderson insulators.
   A. Lherbier, S. Roche, O. A. Restrepo, Y. M. Niquet, A. Delcorte and J. C. Charlier,
   Nano Research 6, 326 (2013).

4. Performances of strained nanowire devices: Ballistic versus scattering-limited currents.
   V. H. Nguyen, F. Triozon, F. D. R. Bonnet and Y. M. Niquet,
   IEEE Transactions on Electron Devices 60, 1506 (2013).

5. Size dependence of the exciton transitions in colloidal CdTe quantum dots.
   E. Groeneveld, C. Delerue, G. Allan, Y. M. Niquet and C. de Mello Donega,
   Journal of Physical Chemistry C 116, 23160 (2012).

6. Carrier mobility in strained Ge nanowires.
   Y. M. Niquet and C. Delerue,
   J. Appl. Phys. 112, 084301 (2012).

7. Effects of strains on the mobility in silicon nanowires.
   Y. M. Niquet, C. Delerue and C. Krzeminski,
   Nano Letters 12, 3545 (2012).

8. Strain state of GaN nanodisks in AlN nanowires studied by medium energy ion spectroscopy.
   D. Jalabert, Y. Curé, K. Hestroffer, Y. M. Niquet and B. Daudin,
   Nanotechnology 23, 425703 (2012).

9. Atomistic Boron-doped graphene field-effect transistors: A route toward unipolar characteristics.
   P. Marconcini, A. Cresti, F. Triozon, G. Fiori, B. Biel, Y. M. Niquet, M. Macucci and S. Roche,
   ACS Nano 6, 7942 (2012).

10. Gate-controllable negative differential conductance in graphene tunneling transistors.
    V. H. Nguyen, Y. M. Niquet and P. Dollfus,
    Semicond. Sci. Technol. 27, 105018 (2012).

11. Transport properties of graphene containing structural defects.
    A. Lherbier, S. M. M. Dubois, X. Declerck, Y. M. Niquet, S. Roche and J. C. Charlier,
    Physical Review B 86, 075402 (2012).

12. Detection of a large valley-orbit splitting in silicon with two-donor spectroscopy.
    B. Roche, E. Dupont-Ferrier, B. Voisin, M. Cobian, X. Jehl, R. Wacquez, M. Vinet, Y. M. Niquet and M. Sanquer,
    Physical Review Letters 108, 206812 (2012).

13. Impurity-limited mobility and variability in gate-all-around silicon nanowires.
    Y. M. Niquet, H. Mera and C. Delerue,
    Applied Physics Letters 100, 153119 (2012).

14. Fully atomistic simulations of phonon-limited mobility of electrons and holes in <001>, <110> and <111>-oriented Si nanowires.
    Y. M. Niquet, C. Delerue, D. Rideau and B. Videau,
    IEEE Transactions on Electron Devices 59, 1480 (2012).

15. Band offsets, wells, and barriers at nanoscale semiconductor heterojunctions.
    Y. M. Niquet and C. Delerue,
    Physical Review B 84, 075478 (2011).

16. Two-dimensional graphene with structural defects: Elastic mean free path, minimum conductivity, and Anderson transition.
    A. Lherbier, S. M. M. Dubois, X. Declerck, S. Roche, Y. M. Niquet and J. C. Charlier,
    Physical Review Letters 106, 046803 (2011).

17. Atomistic modeling of electron-phonon coupling and transport properties in n-type [110] silicon nanowires.
    W. Zhang, C. Delerue, Y. M. Niquet, G. Allan and E. Wang,
    Physical Review B 82, 115319 (2010).

18. Charged impurity scattering and mobility in gated silicon nanowires.
    M. P. Persson, H. Mera, Y. M. Niquet, C. Delerue and M. Diarra,
    Physical Review B 82, 115318 (2010).

19. The structural properties of GaN/AlN core-shell nanocolumn heterostructures.
    K. Hestroffer, R. Mata, D. Camacho, C. Lecrere, G. Tourbot, Y. M. Niquet, A. Cros, C. Bougerol, H. Renevier and B. Daudin,
    Nanotechnology 21, 415702 (2010).

20. Accumulation capacitance of narrow band gap metal-oxide-semiconductor capacitors.
    E. Lind, Y. M. Niquet, H. Mera and L. E. Wernersson,
    Applied Physics Letters 96, 233507 (2010).

21. Stark effect in GaN/AlN nanowire heterostructures: Influence of strain relaxation and surface states.
    D. Camacho and Y. M. Niquet,
    Physical Review B 81, 195313 (2010).

22. Quantum transport in graphene nanoribbons: effects of edge reconstruction and chemical reactivity.
    S. Dubois, A. Lopez-Bezanilla, A. Cresti, F. Triozon, B. Biel, J.-C. Charlier and S. Roche,
    ACS Nano 4, 1971 (2010).

23. Elastic strain relaxation in GaN/AlN nanowire superlattice.
    O. Landré, D. Camacho, C. Bougerol, Y. M. Niquet, V. Favre-Nicolin, G. Renaud, H. Renevier and B. Daudin,
    Physical Review B 81, 153306 (2010).

24. Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging.
    V. Favre-Nicolin, F. Mastropietro, J. Eymery, D. Camacho, Y. M. Niquet, B. M. Borg, M. E. Messing, L. E. Wernersson, R. E. Algra, E. P. A. M. Bakkers, T. H. Metzger, R. Harder and I. K. Robinson,
    New Journal of Physics 12, 035013 (2010).

25. Simulation, modeling and characterization of quasi-ballistic transport in nanometer sized field effect transistors: from TCAD to atomistic simulation.
    S. Roche, T. Poiroux, G. Lecarval, S. Barraud, F. Triozon, M. Persson and Y. M. Niquet,
    International Journal of Nanotechnology 7, 348 (2010).

26. Application of Keating's valence force field model to non-ideal wurtzite materials.
    D. Camacho and Y. M. Niquet,
    Physica E 42, 1361 (2010).

27. The structural properties of GaN insertions in GaN/AlN nanocolumn heterostructures.
    C. Bougerol, R. Songmuang, D. Camacho, Y. M. Niquet, R. Mata, A. Cros and B. Daudin,
    Nanotechnology 20, 295706 (2009).

28. Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances.
    B. Biel, F. Triozon, X. Blase and S. Roche,
    Nano Letters 9, 2725 (2009).

29. Chemical functionalization effects on armchair graphene nanoribbon transport.
    A. Lopez-Bezanilla, F. Triozon and S. Roche,
    Nano Letters 9, 2537 (2009).

30. Carbon nanotube chemistry and assembly for electronic devices.
    V.Derycke, S.Auvray, J.Borghetti, C.-L.Chung, R.Lefèvre, A.Lopez-Bezanilla, K.Nguyen, G.Robert, G.Schmidt, C.Anghel, N.Chimot, S.Lyonnais, S.Streiff, S.Campidelli, P.Chenevier, A.Filoramo, M. F.Goffman, L.Goux-Capes, S.Latil, X.Blase, F.Triozon, S.Roche and J.-P.Bourgoin,
    Comptes-Rendus Physique 10, 330 (2009).

31. Multiscale simulation of carbon nanotube devices.
    C. Adessi, R.Avriller, X.Blase, A.Bournel, H.Cazin d?Honincthun, P.Dollfus, S.Frégonèse, S.Galdin-Retailleau, A.López-Bezanilla, C.Maneux, H.Nha Nguyen, D.Querlioz, S.Roche, F.Triozon and T.Zimmer,
    Comptes-Rendus Physique 10, 305 (2009).

32. Anomalous doping effects on charge transport in graphene nanoribbons.
    B. Biel, X. Blase, F. Triozon and S. Roche,
    Physical Review Letters 102, 096803 (2009).

33. Effect of the chemical functionalization on charge transport in carbon nanotubes at the mesoscopic scale.
    A. Lopez-Bezanilla, F. Triozon, S. Latil, X. Blase and S. Roche,
    Nano Letters 9, 940 (2009).

34. Band structure effects on the scaling properties of [111] InAs nanowire MOSFETs.
    E. Lind, M. Persson, Y. M. Niquet and L. E. Wernersson,
    IEEE Transactions on Electron Devices 56, 201 (2009).

35. Orientational dependence of charge transport in disordered silicon nanowires.
    M. P. Persson, A. Lherbier, Y. M. Niquet, F. Triozon and S. Roche,
    Nano Letters 8, 4146 (2008).

36. Charge transport in chemically doped 2D graphene.
    A. Lherbier, X. Blase, Y. M. Niquet, F. Triozon and S. Roche,
    Physical Review Letters 101, 036808 (2008).

37. Scanning tunnelling spectroscopy of cleaved InAs/GaAs quantum dots at low temperatures.
    A. Urbieta, B. Grandidier, J. P. Nys, D. Deresmes, D. Stiévenard, A. Lemaître, G. Patriarche and Y. M. Niquet,
    Physical Review B. 77, 155313 (2008).

38. Screening and polaronic effects induced by a metallic gate and a surrounding oxide on donor and acceptor impurities in silicon nanowires.
    M. Diarra, C. Delerue, Y. M. Niquet and G. Allan,
    Journal of Applied Physics 103, 073703 (2008).

39. Quantum dots and tunnel barriers in InAs/InP nanowire heterostructures:Electronic and optical properties.
    Y. M. Niquet and D. Camacho Mojica,
    Physical Review B 77, 115316 (2008).

40. Quantum transport length scales in silicon-based semiconducting nanowires:Surface roughness effects.
    A. Lherbier, M. P. Persson, Y. M. Niquet, F. Triozon and S. Roche,
    Physical Review B. 77, 085301 (2008).

41. Transport length scales in disordered graphene-based materials:Strong localization regimes and dimensionality effects.
    A. Lherbier, B. Biel, Y. M. Niquet and S. Roche,
    Physical Review Letters 100, 036803 (2008).

42. Strain and shape of epitaxial InAs/InP nanowires measured by grazing incidence X-ray techniques.
    J. Eymery, F. Rieutord, V. Favre-Nicolin, O. Robach, Y. M. Niquet, L. Fröberg, T. Mårtensson and L. Samuelson,
    Nano Letters 7, 2596 (2007).

43. Effects of a shell on the electronic properties of nanowire superlattices.
    Y. M. Niquet,
    Nano Letters 7, 1105 (2007).

44. Quantum communication with quantum dots spins.
    C. Simon, Y. M. Niquet, X. Caillet, J. Eymery, J. P. Poizat and J. M. Gérard,
    Physical Review B 75, 081302(R) (2007).

45. Ionization energy of donor and acceptor impurities in semiconductor nanowires:Importance of dielectric confinement.
    M. Diarra, Y. M. Niquet, C. Delerue and G. Allan,
    Physical Review B 75, 045301 (2007).

46. Electronic and optical properties of InAs/GaAs nanowire superlattices.
    Y. M. Niquet,
    Physical Review B 74, 155304 (2006).

47. Electronic structure of semiconductor nanowires.
    Y. M. Niquet, A. Lherbier, N. H. Quang, M. V. Fernandez-Serra, X. Blase and C. Delerue,
    Physical Review B 73, 165319 (2006).

More publications and links to journal sites can be found here.

Last update: October 22, 2013.