Thermoelectric Limitations of Graphene Nanodevices at Ultrahigh Current Densities.

Graphene is atomically thin, possesses excellent thermal conductivity, and is able to withstand high current densities, making it attractive for many nanoscale applications such as field-effect transistors, interconnects, and thermal management layers. Enabling integration of graphene into such devices requires nanostructuring, which can have a drastic impact on the self-heating properties, in particular at high current densities. Here, we use a combination of scanning thermal microscopy, finite element thermal analysis, and operando scanning transmission electron microscopy techniques to observe prototype graphene devices in operation and gain a deeper understanding of the role of geometry and interfaces during high current density operation. We find that Peltier effects significantly influence the operational limit due to local electrical and thermal interfacial effects, causing asymmetric temperature distribution in the device. Thus, our results indicate that a proper understanding and design of graphene devices must include consideration of the surrounding materials, interfaces, and geometry. Leveraging these aspects provides opportunities for engineered extreme operation devices.

Quantum interference enhances the performance of single-molecule transistors.

Quantum effects in nanoscale electronic devices promise to lead to new types of functionality not achievable using classical electronic components. However, quantum behaviour also presents an unresolved challenge facing electronics at the few-nanometre scale: resistive channels start leaking owing to quantum tunnelling. This affects the performance of nanoscale transistors, with direct source-drain tunnelling degrading switching ratios and subthreshold swings, and ultimately limiting operating frequency due to increased static power dissipation. The usual strategy to mitigate quantum effects has been to increase device complexity, but theory shows that if quantum effects can be exploited in molecular-scale electronics, this could provide a route to lower energy consumption and boost device performance. Here we demonstrate these effects experimentally, showing how the performance of molecular transistors is improved when the resistive channel contains two destructively interfering waves. We use a zinc-porphyrin coupled to graphene electrodes in a three-terminal transistor to demonstrate a >104 conductance-switching ratio, a subthreshold swing at the thermionic limit, a >7 kHz operating frequency and stability over >105 cycles. We fully map the anti-resonance interference features in conductance, reproduce the behaviour by density functional theory calculations and trace back the high performance to the coupling between molecular orbitals and graphene edge states. These results demonstrate how the quantum nature of electron transmission at the nanoscale can enhance, rather than degrade, device performance, and highlight directions for future development of miniaturized electronics.

Connections to the Electrodes Control the Transport Mechanism in Single-Molecule Transistors.

When designing a molecular electronic device for a specific function, it is necessary to control whether the charge-transport mechanism is phase-coherent transmission or particle-like hopping. Here we report a systematic study of charge transport through single zinc-porphyrin molecules embedded in graphene nanogaps to form transistors, and show that the transport mechanism depends on the chemistry of the molecule-electrode interfaces. We show that van der Waals interactions between molecular anchoring groups and graphene yield transport characteristic of Coulomb blockade with incoherent sequential hopping, whereas covalent molecule-electrode amide bonds give intermediately or strongly coupled single-molecule devices that display coherent transmission. These findings demonstrate the importance of interfacial engineering in molecular electronic circuits.

Phase-Coherent Charge Transport through a Porphyrin Nanoribbon.

Since the early days of quantum mechanics, it has been known that electrons behave simultaneously as particles and waves, and now quantum electronic devices can harness this duality. When devices are shrunk to the molecular scale, it is unclear under what conditions does electron transmission remain phase-coherent, as molecules are usually treated as either scattering or redox centers, without considering the wave-particle duality of the charge carrier. Here, we demonstrate that electron transmission remains phase-coherent in molecular porphyrin nanoribbons connected to graphene electrodes. The devices act as graphene Fabry-Pérot interferometers and allow for direct probing of the transport mechanisms throughout several regimes. Through electrostatic gating, we observe electronic interference fringes in transmission that are strongly correlated to molecular conductance across multiple oxidation states. These results demonstrate a platform for the use of interferometric effects in single-molecule junctions, opening up new avenues for studying quantum coherence in molecular electronic and spintronic devices.

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction.

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8 ns, a value dependent on the molecular charge state.

Statistical signature of electrobreakdown in graphene nanojunctions.

Controlled electrobreakdown of graphene is important for the fabrication of stable nanometer-size tunnel gaps, large-scale graphene quantum dots, and nanoscale resistive switches, etc. However, owing to the complex thermal, electronic, and electrochemical processes at the nanoscale that dictate the rupture of graphene, it is difficult to generate conclusions from individual devices. We describe here a way to explore the statistical signature of the graphene electrobreakdown process. Such analysis tells us that feedback-controlled electrobreakdown of graphene in the air first shows signs of joule heating-induced cleaning followed by rupturing of the graphene lattice that is manifested by the lowering of its conductance. We show that when the conductance of the graphene becomes smaller than around 0.1 G0, the effective graphene notch width starts to decrease exponentially slower with time. Further, we show how this signature gets modified as we change the environment and or the substrate. Using statistical analysis, we show that the electrobreakdown under a high vacuum could lead to substrate modification and resistive-switching behavior, without the application of any electroforming voltage. This is attributed to the formation of a semiconducting filament that makes a Schottky barrier with the graphene. We also provide here the statistically extracted Schottky barrier threshold voltages for various substrate studies. Such analysis not only gives a better understanding of the electrobreakdown of graphene but also can serve as a tool in the future for single-molecule diagnostics.

Implementation of Quantum Level Addressability and Geometric Phase Manipulation in Aligned Endohedral Fullerene Qudits.

Endohedral nitrogen fullerenes have been proposed as building blocks for quantum information processing due to their long spin coherence time. However, addressability of the individual electron spin levels in such a multiplet system of 4 S3/2 has never been achieved because of the molecular isotropy and transition degeneracy among the Zeeman levels. Herein, by molecular engineering, we lifted the degeneracy by zero-field splitting effects and made the multiple transitions addressable by a liquid-crystal-assisted method. The endohedral nitrogen fullerene derivatives with rigid addends of spiro structure and large aspect ratios of regioselective bis-addition improve the ordering of the spin ensemble. These samples empower endohedral-fullerene-based qudits, in which the transitions between the 4 electron spin levels were respectively addressed and coherently manipulated. The quantum geometric phase manipulation, which has long been proposed for the advantages in error tolerance and gating speed, was implemented in a pure electron spin system using molecules for the first time.

Charge transport through extended molecular wires with strongly correlated electrons.

Electron-electron interactions are at the heart of chemistry and understanding how to control them is crucial for the development of molecular-scale electronic devices. Here, we investigate single-electron tunneling through a redox-active edge-fused porphyrin trimer and demonstrate that its transport behavior is well described by the Hubbard dimer model, providing insights into the role of electron-electron interactions in charge transport. In particular, we empirically determine the molecule's on-site and inter-site electron-electron repulsion energies, which are in good agreement with density functional calculations, and establish the molecular electronic structure within various oxidation states. The gate-dependent rectification behavior confirms the selection rules and state degeneracies deduced from the Hubbard model. We demonstrate that current flow through the molecule is governed by a non-trivial set of vibrationally coupled electronic transitions between various many-body ground and excited states, and experimentally confirm the importance of electron-electron interactions in single-molecule devices.

Large amplitude charge noise and random telegraph fluctuations in room-temperature graphene single-electron transistors.

We analyze the noise in liquid-gated, room temperature, graphene quantum dots. These devices display extremely large noise amplitudes. The observed noise is explained in terms of a charge noise model by considering fluctuations in the applied source-drain and gate potentials. We show that the liquid environment and substrate have little effect on the observed noise and as such attribute the noise to charge trapping/detrapping at the disordered graphene edges. The trapping/detrapping of individual charges can be tuned by gating the device, which can result in stable two-level fluctuations in the measured current. These results have important implications for the use of electronic graphene nanodevices in single-molecule biosensing.

Understanding resonant charge transport through weakly coupled single-molecule junctions.

Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of non-interacting Landauer theory as well as the conventional single-mode Franck-Condon model. Instead, we model overall charge transport as a sequence of non-adiabatic electron transfers, with rates depending on both outer and inner-sphere vibrational interactions. We show that the transport properties of our molecular junctions are determined by a combination of electron-electron and electron-vibrational coupling, and are sensitive to interactions with the wider local environment. Furthermore, we assess the importance of nuclear tunnelling and examine the suitability of semi-classical Marcus theory as a description of charge transport in molecular devices.

Charge-state assignment of nanoscale single-electron transistors from their current-voltage characteristics.

The electronic and magnetic properties of single-molecule transistors depend critically on the molecular charge state. Charge transport in single-molecule transistors is characterized by Coulomb-blocked regions in which the charge state of the molecule is fixed and current is suppressed, separated by high-conductance, sequential-tunneling regions. It is often difficult to assign the charge state of the molecular species in each Coulomb-blocked region due to variability in the work-function of the electrodes. In this work, we provide a simple and fast method to assign the charge state of the molecular species in the Coulomb-blocked regions based on signatures of electron-phonon coupling together with the Pauli-exclusion principle, simply by observing the asymmetry in the current in high-conductance regions of the stability diagram. We demonstrate that charge-state assignments determined in this way are consistent with those obtained from measurements of Zeeman splittings. Our method is applicable at 77 K, in contrast to magnetic-field-dependent measurements, which generally require low temperatures (below 4 K). Due to the ubiquity of electron-phonon coupling in molecular junctions, we expect this method to be widely applicable to single-electron transistors based on single molecules and graphene quantum dots. The correct assignment of charge states allows researchers to better understand the fundamental charge-transport properties of single-molecule transistors.

Metal Atom Markers for Imaging Epitaxial Molecular Self-Assembly on Graphene by Scanning Transmission Electron Microscopy.

Direct imaging of single molecules has to date been primarily achieved using scanning probe microscopy, with limited success using transmission electron microscopy due to electron beam damage and low contrast from the light elements that make up the majority of molecules. Here, we show single complex molecule interactions can be imaged using annular dark field scanning TEM (ADF-STEM) by inserting heavy metal markers of Pt atoms and detecting their positions. Using the high angle ADF-STEM Z1.7 contrast, combined with graphene as an electron transparent support, we track the 2D monolayer self-assembly of solution-deposited individual linear porphyrin hexamer (Pt-L6) molecules and reveal preferential alignment along the graphene zigzag direction. The epitaxial interactions between graphene and Pt-L6 drive a reduction in the interporphyrin distance to allow perfect commensuration with the graphene. These results demonstrate how single metal atom markers in complex molecules can be used to study large scale packing and chain bending at the single molecule level.

Atomic Scale Imaging of Reversible Ring Cyclization in Graphene Nanoconstrictions.

We present an atomic level study of reversible cyclization processes in suspended nanoconstricted regions of graphene that form linear carbon chains (LCCs). Before the nanoconstricted region reaches a single linear carbon chain (SLCC), we observe that a double linear carbon chain (DLCC) structure often reverts back to a ribbon of sp2 hybridized oligoacene rings, in a process akin to the Bergman rearrangement. When the length of the DLCC system only consists of ∼5 atoms in each LCC, full recyclization occurs for all atoms present, but for longer DLCCs we find that only single sections of the chain are modified in their bonding hybridization and no full ring closure occurs along the entire DLCCs. This process is observed in real time using aberration-corrected transmission electron microscopy and simulated using density functional theory and tight binding molecular dynamics calculations. These results show that DLCCs are highly sensitive to the adsorption of local gas molecules or surface diffusion impurities and undergo structural modifications.

Geometrically Enhanced Thermoelectric Effects in Graphene Nanoconstrictions.

The influence of nanostructuring and quantum confinement on the thermoelectric properties of materials has been extensively studied. While this has made possible multiple breakthroughs in the achievable figure of merit, classical confinement, and its effect on the local Seebeck coefficient has mostly been neglected, as has the Peltier effect in general due to the complexity of measuring small temperature gradients locally. Here we report that reducing the width of a graphene channel to 100 nm changes the Seebeck coefficient by orders of magnitude. Using a scanning thermal microscope allows us to probe the local temperature of electrically contacted graphene two-terminal devices or to locally heat the sample. We show that constrictions in mono- and bilayer graphene facilitate a spatially correlated gradient in the Seebeck and Peltier coefficient, as evidenced by the pronounced thermovoltage Vth and heating/cooling response Δ TPeltier, respectively. This geometry dependent effect, which has not been reported previously in 2D materials, has important implications for measurements of patterned nanostructures in graphene and points to novel solutions for effective thermal management in electronic graphene devices or concepts for single material thermocouples.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions: A unified framework.

Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory (MT), respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled with a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression and present a series of approximations of this result valid at higher temperatures. We find that MT is often insufficient in describing the molecular charge transport characteristics and gives rise to a number of artefacts, especially at lower temperatures. Alternative expressions, retaining its mathematical simplicity, but rectifying those shortcomings, are suggested. In particular, we show how lifetime broadening can be consistently incorporated into MT, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. Our results are applied to examples building on phenomenological as well as microscopically motivated electron-vibrational coupling. We expect them to be particularly useful in experimental studies of charge transport through single-molecule junctions as well as self-assembled monolayers.

Low-Frequency Noise in Graphene Tunnel Junctions.

Graphene tunnel junctions are a promising experimental platform for single molecule electronics and biosensing. Ultimately their noise properties will play a critical role in developing these applications. Here we report a study of electrical noise in graphene tunnel junctions fabricated through feedback-controlled electroburning. We observe random telegraph signals characterized by a Lorentzian noise spectrum at cryogenic temperatures (77 K) and a 1/ f noise spectrum at room temperature. To gain insight into the origin of these noise features, we introduce a theoretical model that couples a quantum mechanical tunnel barrier to one or more classical fluctuators. The fluctuators are identified as charge traps in the underlying dielectric, which through random fluctuations in their occupation introduce time-dependent modulations in the electrostatic environment that shift the potential barrier of the junction. Analysis of the experimental results and the tight-binding model indicate that the random trap occupation is governed by Poisson statistics. In the 35 devices measured at room temperature, we observe a 20-60% time-dependent variance of the current, which can be attributed to a relative potential barrier shift of between 6% and 10%. In 10 devices measured at 77 K, we observe a 10% time-dependent variance of the current, which can be attributed to a relative potential barrier shift of between 3% and 4%. Our measurements reveal a high sensitivity of the graphene tunnel junctions to their local electrostatic environment, with observable features of intertrap Coulomb interactions in the distribution of current switching amplitudes.

Distance Measurement of a Noncovalently Bound Y@C82 Pair with Double Electron Electron Resonance Spectroscopy.

Paramagnetic endohedral fullerenes with long spin coherence times, such as N@C60 and Y@C82, are being explored as potential spin quantum bits (qubits). Their use for quantum information processing requires a way to hold them in fixed spatial arrangements. Here we report the synthesis of a porphyrin-based two-site receptor 1, offering a rigid structure that binds spin-active fullerenes (Y@C82) at a center-to-center distance of 5.0 nm, predicted from molecular simulations. The spin-spin dipolar coupling was measured with the pulsed EPR spectroscopy technique of double electron electron resonance and analyzed to give a distance of 4.87 nm with a small distribution of distances.

Spiro-Conjugated Molecular Junctions: Between Jahn-Teller Distortion and Destructive Quantum Interference.

The quest for molecular structures exhibiting strong quantum interference effects in the transport setting has long been on the forefront of chemical research. We establish theoretically that the unusual geometry of spiro-conjugated systems gives rise to complete destructive interference in the resonant-transport regime. This results in a current blockade of the type not present in meta-connected benzene or similar molecular structures. We further show that these systems can undergo a transport-driven Jahn-Teller distortion, which can lift the aforementioned destructive-interference effects. The overall transport characteristics are determined by the interplay between the two phenomena. Spiro-conjugated systems may therefore serve as a novel platform for investigations of quantum interference and vibronic effects in the charge-transport setting. The potential to control quantum interference in these systems can also turn them into attractive components in designing functional molecular circuits.

CF2 -Bridged C60 Fullerene Dimers and their Optical Transitions.

Fullerene dyads bridged with perfluorinated linking groups have been synthesized through a modified arc-discharge procedure. The addition of Teflon inside an arc-discharge reactor leads to the formation of dyads, consisting of two C60 fullerenes bridged by CF2 groups. The incorporation of bridging groups containing electronegative atoms lead to different energy levels and to new features in the photoluminescence spectrum. A suppression of the singlet oxygen photosensitization indicated that the radiative decay from singlet-to-singlet state is favoured against the intersystem crossing singlet-to-triplet transition.