Electrostatic screening effects on a model system for molecular electronics

Molecular electronics is a promising replacement for the conventional silicon-based semiconductors by reducing the device dimensions down to the sub-nanometer level, potentially extending Moore's law for the era of quantum computing. In a typical molecular electronics, two contact electrodes are bridged by a single organic molecule, whose energy levels for its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) can be modulated by an external electric field. In the absence of electrical resistivity, the conductivity of a quantum transport device such as molecular electronics is primarily determined by the energy level matching between the molecule's frontier orbitals and the electrodes' Fermi surface. Therefore, it is critical for us to understand the shifts of molecular orbitals upon the application of a given biased potential across the metal electrodes, which polarizations can effectively reduce the voltage through the central molecule.Recently, we implemented a hybrid DFT/FEM (density functional theory/finite element method) approach that can automatically account for the electrostatic screening effect for a closed quantum system embedded in an open region of good conductor. Specifically, the electron density profile of a quantum system is first determined by DFT. Then, the obtained electrostatic potential on its boundary surface servers as the Dirchlet boundary condition for a Laplace equation solver to evaluate the position-dependent Hartree potential that will be added to the Hamiltonian of the quantum system in the subsequent evaluation cycle until the convergence of its electronic structure is achieved. Using the MUMPS software as our multifrontal massively parallel sparse direct solver, our DFT package of CP2K enables the hundred-core simulations of a sulfur-anchored Ag20-Pyridine-Ag20 molecular junction (Fig. 1) under a wide biased potential range on the Sun Constellation Cluster at Texas Advanced Computing Center. It is found that the memory usage per core can be substantially reduced by up to 80% through the activation of MUMPS's out-of-core facility, while the overall computation performance is nearly unaffected by storing the matrix of factors on disk as temporary files. For example, one of our model systems with a size of 6A X 6A X 6A and a DFT grid resolution of 0.2A only requests a working space of 2.6 Gigabytes per process under the out-of-core mode, compared to 13.8 Gigabytes per process when the whole factorized matrix is stored in memory. Very encouragingly, the initialization times spent on the analysis and factorization of a sparse matrix are almost same under the two matrix-storage modes, even when its size is over 1 million.As shown in Fig. 2, the applied biased potential, Vbias, has substantial influence on the relative bias voltage across the central pyridine molecule, which is defined as the ratio between the external voltage, Vext, and |Vbias|. When |Vbias| = 1 eV, the induced polarization of the Ag electrodes screens out approximately 60% of the applied biased potential, resulting in an effective biased voltage of ± 0.4eV across the pyridine molecule. When |Vbias| increases to 10 eV, the electrode polarization is fully saturated and becomes the dominant contributor to the bias voltage for the pyridine molecule as manifested by the negligible Vext. The saturation of the electrode polarization is further justified by increasing |Vbias| to 100 eV, where Vext is nearly invariant. Our hybrid DFT/FEM simulation results, taken together, suggest that the electronic polarization of the metal electrodes play an important role in governing the effective bias voltage across the central organic molecule in a molecular junction.