title: Theory of mid-gap quantum transport through single molecule
title: new approach to transport modeling of nanoelectronic devices
titleType: Subtitle
Creators: name: Sangtarash, Sara
Publisher: name: Lancaster University
Year: 2017

description: Molecules due to their very small sizes, possess discrete energy levels
      and electrons can transmit from one side of the molecule to the other with
      high probability if their energy coincides with molecular energy levels.
      In the weak coupling limit such on-resonance electron transport is
      described by the simple Lorentzian-shaped Breit-Wigner formula. On the
      other hand, electrons with energy different than the molecular energy
      levels have to tunnel through the energy gap between two molecular energy
      levels (off resonance transmission). Consequently the electron
      transmission probability is much smaller than on resonance regime.
      Interesting phenomena including quantum interference could be observed in
      this regime at room temperature. In this thesis, I discuss both regimes
      though, my main aim is to introduce a new theory called ”mid- gap theory”
      to predict the conductance ratio between different connectivities driven
      by quantum interference (QI) in the tunneling regime. 
      
      Both theory and experiment have focused primarily on elucidating the
      conditions for the appearance of constructive or destructive interference.
      In the simplest case, where electrons are injected at the Fermi energy EF
      of the electrodes, constructive QI arises when EF coincides with a
      delocalized energy level En of the molecule. Similarly a simple form of
      destructive QI occurs when EF coincides with the energy Eb of a bound
      state located on a pendant moiety. Unless energy levels are tuned by
      electrostatic, electrochemical or mechanical gating, molecules located
      within a junction rarely exhibit these types of QI, because EF is usually
      located in the HOMO-LUMO (H-L) gap. Furthermore few analytic formulas are
      available, which means that pre-screening of molecules often requires
      expensive numerical simulations. For this reason, discussions have often
      focused on conditions for destructive or constructive QI when EF is
      located at the centre of the H-L gap. In this thesis, based on a simple
      description of connectivity, I demonstrate that the conductance ratio
      between two different connectivities of a core molecule could be predicted
      simply by using the ratio between two magic numbers of the core molecule.
      This will be discussed in the chapters 4-6. This simple theory not only
      predicts conductance ratios, but it could be used also to propose new
      strategies for molecular electronic design and applications such as single
      molecule switches and thermoelectricity. 
      
      In this thesis after an introduction to nano and molecular electronics, I
      discuss general ideas about nanoscale transport and the methods which
      could be applied to model nano and molecular scale devices. In chapter 3,
      on resonance transport is discussed. For a wide variety of molecules, the
      conductance G decays with length L as Aexp(−βL) and it is widely accepted
      that the attenuation coefficient β is determined by position of the Fermi
      energy of the electrodes relative to the energy gap of the molecular
      bridge, whereas the terminal anchor groups which bind the molecule to the
      electrodes contribute to A. In contrast with this expectation, in chapter
      3, I demonstrate that gateway orbitals located on the anchor groups can
      significantly decrease the value of β, thereby creating a new design
      strategy for realizing low-conductance molecular wires. In chapters 4-6, I
      introduce mid-gap theory and drive a mid-gap ratio rule (MRR) which is an
      exact formula for conductance ratios of tight-binding representations of
      molecules in the weak coupling limit, when the Fermi energy is located at
      the centre of the HOMO-LUMO (H-L) gap. It does not depend on the size of
      the H-L gap and is independent of asymmetries in the contacts. I also show
      how conductance ratios change, when one of the carbon atoms within the
      parent polycyclic aromatic hydrocarbons (PAH) core is replaced by a
      heteroatom to yield a daughter molecule. I show that this heteroatom
      substitution could be used to enhance the conductance in a PAH molecule by
      several orders of magnitude. A good agreement between this new simple
      theory and experiment shows that, the MRR provides a useful tool to
      predict the conductances of PAH molecules prior to synthesis. Therefore it
      could be used to design molecules with desirable properties or to propose
      new molecular devices.