Abstract
Charge transport through junctions consisting of insulating molecular units is a quantum phenomenon that cannot be described adequately by classical circuit laws. This paper explores tunneling current densities in self-assembled monolayer (SAM)-based junctions with the structure Ag(TS)/O2C-R1-R2-H//Ga2O3/EGaIn, where Ag(TS) is template-stripped silver and EGaIn is the eutectic alloy of gallium and indium; R1 and R2 refer to two classes of insulating molecular units-(CH2)n and (C6H4)m-that are connected in series and have different tunneling decay constants in the Simmons equation. These junctions can be analyzed as a form of series-tunneling junctions based on the observation that permuting the order of R1 and R2 in the junction does not alter the overall rate of charge transport. By using the Ag/O2C interface, this system decouples the highest occupied molecular orbital (HOMO, which is localized on the carboxylate group) from strong interactions with the R1 and R2 units. The differences in rates of tunneling are thus determined by the electronic structure of the groups R1 and R2; these differences are not influenced by the order of R1 and R2 in the SAM. In an electrical potential model that rationalizes this observation, R1 and R2 contribute independently to the height of the barrier. This model explicitly assumes that contributions to rates of tunneling from the Ag(TS)/O2C and H//Ga2O3 interfaces are constant across the series examined. The current density of these series-tunneling junctions can be described by J(V) = J0(V) exp(-β1d1 - β2d2), where J(V) is the current density (A/cm(2)) at applied voltage V and βi and di are the parameters describing the attenuation of the tunneling current through a rectangular tunneling barrier, with width d and a height related to the attenuation factor β.
Highlights
Charge transport by tunneling through metal‒molecule‒metal (MMM) junctions―junctions whose electronic features are modeled by a potential barrier1-9 and by molecular orbitals10-19― cannot be described adequately by classical diffusion, or by drift transport of charge.20-23 The classical circuit law states that the total resistance of two or more Ohmic resistors connected in series is the sum of the resistance of each resistor; that is, the sequence in which these resistors are assembled does not influence the overall current across the circuit
This paper explores tunneling current densities in self-assembled monolayer (SAM)-based junctions with the structure AgTS/O2C‒R1‒R2‒H//Ga2O3/EGaIn, where AgTS is template-stripped silver, and EGaIn is the eutectic alloy of gallium and indium; R1 and R2 refer to two classes of insulating molecular units―(CH2)n and (C6H4)m―that are connected in series and have different tunneling decay constants in the Simmons equation
To understand the condition required for eq.2 to approximate the rate of charge transport across junctions of the structure AgTS/O2C‒R1‒R2‒H//Ga2O3/EGaIn, we modeled the experimental system using two theoretical approaches in the framework of Landauer theory: (i) a multi-barrier model, using a wavefunction method; (ii) a tight-binding model, using a Green’s function method. (The Supporting Information details the mathematical derivations of eq 2 and the corresponding assumptions.) Landauer theory has been used to describe tunneling at the single-molecule level;57 here we use this theory to approximate the current density, J, across a SAM
Summary
Charge transport by tunneling through metal‒molecule‒metal (MMM) junctions―junctions whose electronic features are modeled by a potential barrier and by molecular orbitals10-19― cannot be described adequately by classical diffusion, or by drift transport of charge. The classical circuit law states that the total resistance of two or more Ohmic resistors connected in series is the sum of the resistance of each resistor; that is, the sequence in which these resistors are assembled does not influence the overall current across the circuit. (That is, using the carboxylate group to anchor the SAM to the bottom electrode, rather than a thiol, decouples the electrode and the interior of the SAM, so that the HOMO does not delocalize onto aromatic groups immediately proximate to the interface.) The contributions to rates of charge transport from the AgTS/O2C interface are constant across the series of molecules examined in this study―including both O2C−(aryl R) and O2C−(alkyl R) SAMs. When the groups (R1 and R2) at the SAM–metal interfaces interact differently with the metal electrode (as with Au/S–(aryl R) and Au/S–(alkyl R)), the independence of the tunneling current to the order of the aliphatic and aromatic groups in the interior of the SAMs that we establish for the system described here do not (and are not expected to) hold
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