TB_Sim is a tight-binding code developed at CEA Grenoble. It is able to compute the structural, electronic, optical and transport properties of various kinds of nanostructures such as semiconductor nanocrystals and nanowires or carbon nanotubes.

  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 to 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 modeling - 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 modeling. These methods can also be used 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 modeling strategy as a transition from ab initio to large-scale finite element modeling.

  The TB_Sim code

Fig. 3: 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.
• 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 Kubo-Greenwood and Non-Equilibrium Green Functions formalism.
• ...

  Contacts:

Coordinator and contact person:

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

Developers:

• François Triozon (CEA/LETI/MINATEC).
• Aurélien Lherbier (PhD student, CNRS/LTM and CEA/INAC/SP2M/L_Sim).
• Martin Persson (CEA/INAC/SP2M/L_Sim).
• Dulce Camacho (PhD student, CEA/INAC/SP2M/L_Sim).

Other contributors:

• Stephan Roche (CEA/INAC/SPSMS/GT).
• Sylvain Latil (CEA/IRAMIS).

  A few illustrations using TB_Sim:

(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. Taken 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).

(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%. Taken 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).

  A few publications using TB_Sim:

1. Band structure effects on the scaling properties of [111] InAs nanowire MOSFETs,
   E. Lind, M. Persson, Y. M. Niquet and L. E. Wernersson,
   IEEE Trans. Electron Devices 56, 201 (2009).
2. 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).
3. Charge transport in chemically doped 2D graphene,
   A. Lherbier, X. Blase, Y. M. Niquet, F. Triozon and S. Roche,
   Phys. Rev. Lett. 101, 036808 (2008).
4. 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,
   Phys. Rev. B. 77, 155313 (2008).
5. 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,
   J. Appl. Phys. 103, 073703 (2008).
6. Quantum dots and tunnel barriers in InAs/InP nanowire heterostructures: Electronic and optical properties,
   Y. M. Niquet and D. Camacho Mojica,
   Phys. Rev. B 77, 115316 (2008).
7. 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,
   Phys. Rev. B. 77, 085301 (2008).
8. Transport length scales in disordered graphene-based materials: Strong localization regimes and dimensionality effects,
   A. Lherbier, B. Biel, Y. M. Niquet and S. Roche,
   Phys. Rev. Lett. 100, 036803 (2008).
9. 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).
10. Effects of a shell on the electronic properties of nanowire superlattices,
    Y. M. Niquet,
    Nano Letters 7, 1105 (2007).
11. Quantum communication with quantum dots spins,
    C. Simon, Y. M. Niquet, X. Caillet, J. Eymery, J. P. Poizat and J. M. Gérard,
    Phys. Rev. B 75, 081302(R) (2007).
12. Ionization energy of donor and acceptor impurities in semiconductor nanowires: Importance of dielectric confinement,
    M. Diarra, Y. M. Niquet, C. Delerue and G. Allan,
    Phys. Rev. B 75, 045301 (2007).
13. Electronic and optical properties of InAs/GaAs nanowire superlattices,
    Y. M. Niquet,
    Phys. Rev. B 74, 155304 (2006).
14. Electronic structure of semiconductor nanowires,
    Y. M. Niquet, A. Lherbier, N. H. Quang, M. V. Fernandez-Serra, X. Blase and C. Delerue,
    Phys. Rev. B 73, 165319 (2006).

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