Theory of mid-gap quantum transport through single molecule : new approach to transport modeling of nanoelectronic devices

• Main Author: Sangtarash, Sara
• Other Authors: Lambert, Colin
• Published: Lancaster University 2017
• Subjects: 621.381
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.721770

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.