In April 2006 Prof. Thomas Frauenheim was appointed to a professorship at the University of Bremen. With his move from Paderborn to Bremen the foundation of the BCCMS as a central research establishment began.
The BCCMS group is involved in projects in three important fields of Physics:
1- Biophysics
2- Solid State and Semiconductors
3- Surfaces and Interfaces
Beyond this the BCCMS is the driving force behind the development of a Density Functional Theory based Tight Binding method called DFTB, both with respect to extending the method itself as well as with respect to embedding the DFTB within QMM-schemes.
BCCMS (Bremen Center for Computational Materials Science), Universität Bremen, 3. Stock des TAB Gebäudes, Am Fallturm 1, 28359 Bremen
The task to describe quantum transport is challenging. Despite thirty years have passed since the first suggestion of single molecule as electronic functional unit, many problems and issues are still open to debate and require a large effort from the fields of quantum chemistry and theoretical physics. Due to the quantum nature of the problem, the transport properties of the entire system of electrodes and molecule(s) are not just the sum of its parts but have to be considered simultaneously on equal footing. At the same time, the molecule itself constitutes a strongly inhomogeneous system with many correlated quantum particles, while the part of the electrodes, except for the region of the junctions, can be described straightforwardly using conventional theory and formalism from solid state physics.
A theoretical description of such a molecular subsystem is already a substantial problem of many-body physics. The presence of leads that connect the system to the outside, macroscopic world makes this task not simpler. In contrast, the fact that the necessary contacts have to be treated as macroscopic systems, i.e. infinitely many degrees of freedom, causes a complexity that must be addressed with new ideas and approaches. Finally, the “environmental” embedding present in experiments (and in real life) can substantially influence the transport through the molecule, and therefore should be properly addressed as well.
The group of the University of``Tor Vergata´´, Rome, in collaboration with the group of Prof. Thomas Frauenheim, has developed a quantum transport code (gDFTB) which is a Non Equilibrium Green Function (NEGF) implementation for transport over the DFTB method.
The code DFTB is based on an approximate Density Functional Theory (DFT) formulation of a tight-binding-like (DFTB)-Hamiltonian with an expansion in minimal basis sets [Elstner98, Frauenheim00,Frauenheim02], allowing to treat a large number of atoms. The code allows calculations of large systems of O(1000) atoms on single processors and O(10000) atoms on parallel architectures or in so called Order-N realizations.
The NEGF formalism provides a consistent mathematical framework for the inclusion of many-body physics, relevant at the nanoscale. In particular it allows for the inclusion of several effects of great importance in simulations and description of molecular devices:
Considering all the needs of molecular electronics, the gDFTB code has passed a series of subsequent steps in its development in order to achieve the final target of including all the necessary ingredients in a consistent, coherent and computationally affordable scheme. The first version of the code was developed in the Equilibrium Green’s Function (EGF) scheme to describe completely coherent and ballistic transport across molecules, including the effect of the open boundary conditions due to the presence of the leads but neglecting consistency with the applied bias. Successful applications of this code have been applied to study transport across various molecular systems including alkanethiols [Pecchia04c] and dithiophenelyne [Pecchia03], the effect of adsorbtion of benzyne on carbon nanotubes [Pecchia02], studies of STM of PTCDA on Si [Szuc03] and the determination of the Shottky barrier PTCDA/Ag,Al surfaces [Picozzi03].
The following step (2002-2003) has been the inclusion of the voltage within a self-consistent solution of the quantum problems within NEGF [DiCarlo02]. Charge reorganization in the molecule and in the junctions can be obtained by solving the Poisson equation inside the device region with the appropriate boundary conditions. Such code has been primarily applied to study transport in Carbon Nanotubes (CNT) as coaxially gated FETs [Latessa05]. In the picture it is shown the charge distribution in a single wall CNT coaxially gated. The red region is charged by electrons.
The third step (2003-2004) consisted in the inclusion of the inelastic transport due to electron-phonon interactions. The gDFTB code has been extended to account for scattering by molecular vibrations within the NEGF formalism in the Born approximation (BA) and self-consistent BA (SCBA). This allows calculation of the electron-phonon scattering strength and power emission in molecules [Pecchia04b, Pecchia05].
Moreover the electron-phonon interaction can be used to simulate Inelastic Electron Tunneling Spectroscopy (IETS) measurements. This technique has provided to be a powerful tool to investigate the geometry and the conducivity property of molecular devices using the inelastic scattering of electrons due to molecular vibrations. The second derivative of the current respect to the bias applied shows a collection of peaks induced by this electron-phonon interaction. In our simulations we have tested an octane-di-thiol molecule between gold electrodes and show the different IET spectra when the bonding site of the molecule is changed.
A well known deficiency of density-functional theory in the LDA/GGA approximation is a significant underestimation of the band-gap of molecules and semiconductors as the method generally lacks the correct inclusion of electronic exchange and correlation. Since a key aspect of the project is to compute transport properties across molecules and molecules on semiconducting substrates, a proper description of bandgaps is crucial. A well established approach to overcome these deficiencies is the calculation of the quasiparticle self-energy within the GW approximation [Hedin].
The Frauenheim group recently implemented the GW approximation [Niehaus05] to the self energy in the calculation of quasi-particle energies within DFTB. Up to now, this approach was realized in the framework of numerically demanding first-principles methods, see e.g. [Aryaset98] and references therein, as well as empirical tight-binding schemes [e.g. Delerue00]. In the latter case there is a very unfortunate need to reparameterize if new systems are going to be studied. The GW approach using the typical DFTB kind of approximations has the advantage that no empirical parameters enter the scheme. In this way heteronuclear systems like those appearing in molecular conduction settings can be studied. In addition, the numerical efficiency of the approximations allows simulations of hundreds of atoms to be performed. This is a prerequisite for transport calculations were usually some fraction of the leads must be included in the calculations.
At present the GW code has been successfully tested for a series of organic molecules [Niehaus05]. It was found that molecular levels close to the Fermi energy are described in very good agreement with first principles methods, while the accuracy for orbitals higher and lower in energy is less convincing. Since only the frontier orbitals play an active role in the conduction, the utilization of the DFTB-GW method in transport calculations seems to be promising. In fact it has already been applied to coherent transport within the EGF formalism with model (jellium) leads [Pecchia05], where the effect of the gap opening was demonstrated.
[Aryasetiawan] F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 61 (1998) 237 and references therein.
[Delerue00] C. Delerue, M. Lannoo, G. Allan. Phys. Rev. Lett. 84 (2000) 2457.
[DiCarlo02] A. Di Carlo, M. Gheorghe, A. Bolognesi, P. Lugli, M. Sternberg, G. Seifert, and Th. Frauenheim, Journal of Computational Electronics 1 (2002) 109; A. Di Carlo, M. Gheorghe, P. Lugli, M. Sternberg, G. Seifert, and Th. Frauenheim, Physica B 314 (2002) 86.
[Elstner98] M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, Th. Frauenheim, S. Suhai, and G. Seifert, Phys. Rev. B 58 (1998) 7260.
[Frauenheim00] Th. Frauenheim, G. Seifert, M. Elstner, Z. Hajnal, G. Jungnickel, D. Porezag, S. Suhai, and R. Scholz, A self-consistent charge density-functional based tight-binding method for predictive materials simulations in physics, chemistry and biology, pss (b), 217/1 (2000) 41.
[Frauenheim02] Th. Frauenheim, G. Seifert, M. Elstner, T. Niehaus, C. Köhler, M. Amkreutz, M. Sternberg, Z. Hajnal, A. Di Carlo, and S. Suhai, Atomistic simulations of complex materials: ground-state and excited-state properties, J. Phys. -Cond. Matter 14, (2002) 3015.
[Hedin] L. Hedin. Phys. Rev., 139 (1965) A796, L. Hedin and S. Lundqvist. Solid State Physics, Advances in Research and Aplication. Academic Press, New York, (1996).
[Latessa05] L. Latessa, A. Pecchia, A. Di Carlo, and P. Lugli, Phys. Rev. B 72 (2005) 035455.
[Niehaus05] T. A. Niehaus, M. Rohlfing, F. Della Sala, A. Di Carlo, and Th. Frauenheim, Quasiparticle energies for large molecules, Phys. Rev. A 71, 022508 (2005)
[Pecchia02] A. Pecchia, M. Gheorghe, A. Di Carlo, P. Lugli, Synt. Met. 138, 89 (2002)
[Pecchia03] A. Pecchia, M. Gheorghe, A. Di Carlo, P. Lugli, T. A. Niehaus, Th. Frauenheim, R. Sholz, Role of thermal vibrations in molecular wire conduction, Physical Review B 68, (2003) 235321
[Pecchia04a] A. Pecchia and A. Di Carlo, Atomistic theory of transport in organic and inorganic nanostructures, Rep. Prog. Phys 67 (2004) 1497.
[Pecchia04b] A. Pecchia, A. Di Carlo, A. Gagliardi, S. Sanna, Th. Frauenheim, R. Gutierrez., Incoherent Electron-Phonon Scattering in Octanethiols, Nano Lett. 4 (2004) 2109.
[Pecchia04c] A. Pecchia, M. Gheorghe, L. Latessa, A. Di Carlo, P. Lugli, IEEE- Trans. On Nanotech. 3, 353 (2004)
[Pecchia05] A. Pecchia, A. Di Carlo, A. Gagliardi, T.A. Niehaus, Th. Frauenheim, Atomistic simulation of the electronic transport in organic nanostructures: electron-phonon and electron-electron interactions, to appear in: J. Comp. Elect. 4 (2005) 79.
[Picozzi03] S. Picozzi, A. Pecchia, M. Gheorghe, A. Di Carlo, P. Lugli, B. Delley, M. Elstner, Physical Review B 68, (2003), 195309.
[Szuc03] B. Szucs, Z. Hajnal, Th. Frauenheim, C. Gonzales, J. Ortega, and F. Flores, Appl. Surf. Sci. 212 (2003) 861.