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.

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.

Contrast Mechanisms in Secondary Electron e-Beam-Induced Current (SEEBIC) Imaging.

Over the last few years, a new mode for imaging in the scanning transmission electron microscope (STEM) has gained attention as it permits the direct visualization of sample conductivity and electrical connectivity. When the electron beam (e-beam) is focused on the sample in the STEM, secondary electrons (SEs) are generated. If the sample is conductive and electrically connected to an amplifier, the SE current can be measured as a function of the e-beam position. This scenario is similar to the better-known scanning electron microscopy-based technique, electron beam-induced current imaging, except that the signal in the STEM is generated by the emission of SEs, hence the name secondary electron e-beam-induced current (SEEBIC), and in this case, the current flows in the opposite direction. Here, we provide a brief review of recent work in this area, examine the various contrast generation mechanisms associated with SEEBIC, and illustrate its use for the characterization of graphene nanoribbon devices.

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.

Field-Effect Control of Graphene-Fullerene Thermoelectric Nanodevices.

Although it was demonstrated that discrete molecular levels determine the sign and magnitude of the thermoelectric effect in single-molecule junctions, full electrostatic control of these levels has not been achieved to date. Here, we show that graphene nanogaps combined with gold microheaters serve as a testbed for studying single-molecule thermoelectricity. Reduced screening of the gate electric field compared to conventional metal electrodes allows control of the position of the dominant transport orbital by hundreds of meV. We find that the power factor of graphene-fullerene junctions can be tuned over several orders of magnitude to a value close to the theoretical limit of an isolated Breit-Wigner resonance. Furthermore, our data suggest that the power factor of an isolated level is only given by the tunnel coupling to the leads and temperature. These results open up new avenues for exploring thermoelectricity and charge transport in individual molecules and highlight the importance of level alignment and coupling to the electrodes for optimum energy conversion in organic thermoelectric materials.

Molecular design and control of fullerene-based bi-thermoelectric materials.

Molecular junctions are a versatile test bed for investigating nanoscale thermoelectricity and contribute to the design of new cost-effective environmentally friendly organic thermoelectric materials. It was suggested that transport resonances associated with discrete molecular levels could play a key role in thermoelectric performance, but no direct experimental evidence has been reported. Here we study single-molecule junctions of the endohedral fullerene Sc3N@C80 connected to gold electrodes using a scanning tunnelling microscope. We find that the magnitude and sign of the thermopower depend strongly on the orientation of the molecule and on applied pressure. Our calculations show that Sc3N inside the fullerene cage creates a sharp resonance near the Fermi level, whose energetic location, and hence the thermopower, can be tuned by applying pressure. These results reveal that Sc3N@C80 is a bi-thermoelectric material, exhibiting both positive and negative thermopower, and provide an unambiguous demonstration of the importance of transport resonances in molecular junctions.

Thermopower measurements in molecular junctions.

The measurement of thermopower in molecular junctions offers complementary information to conductance measurements and is becoming essential for the understanding of transport processes at the nanoscale. In this review, we discuss the recent advances in the study of the thermoelectric properties of molecular junctions. After presenting the theoretical background for thermoelectricity at the nanoscale, we review the experimental techniques for measuring the thermopower in these systems and discuss the main results. Finally, we consider the challenges in the application of molecular junctions in viable thermoelectric devices.

Quantum thermopower of metallic atomic-size contacts at room temperature.

We report conductance and thermopower measurements of metallic atomic-size contacts, namely gold and platinum, using a scanning tunneling microscope (STM) at room temperature. We find that few-atom gold contacts have an average negative thermopower, whereas platinum contacts present a positive thermopower, showing that for both metals, the sign of the thermopower in the nanoscale differs from that of bulk wires. We also find that the magnitude of the thermopower exhibits minima at the maxima of the conductance histogram in the case of gold nanocontacts while for platinum it presents large fluctuations. Tight-binding calculations and Green's function techniques, together with molecular dynamics simulations, show that these observations can be understood in the context of the Landauer-Büttiker picture of coherent transport in atomic-scale wires. In particular, we show that the differences in the thermopower between these two metals are due to the fact that the elastic transport is dominated by the 6s orbitals in the case of gold and by the 5d orbitals in the case of platinum.

Does a cyclopropane ring enhance the electronic communication in dumbbell-type C60 dimers?

Two C60 dumbbell molecules have been synthesized containing either cyclopropane or pyrrolidine rings connecting two fullerenes to a central fluorene core. A combination of spectroscopic techniques reveals that the cyclopropane dumbbell possesses better electronic communication between the fullerenes and the fluorene. This observation is underpinned by DFT transport calculations, which show that the cyclopropane dumbbell gives a higher calculated single-molecule conductance, a result of an energetically lower-lying LUMO level that extends deeper into the backbone. This strengthens the idea that cyclopropane behaves as a quasi-double bond.

Engineering the thermopower of C60 molecular junctions.

We report the measurement of conductance and thermopower of C60 molecular junctions using a scanning tunneling microscope (STM). In contrast to previous measurements, we use the imaging capability of the STM to determine precisely the number of molecules in the junction and measure thermopower and conductance continuously and simultaneously during formation and breaking of the molecular junction, achieving a complete characterization at the single-molecule level. We find that the thermopower of C60 dimers formed by trapping a C60 on the tip and contacting an isolated C60 almost doubles with respect to that of a single C60 and is among the highest values measured to date for organic materials. Density functional theory calculations show that the thermopower and the figure of merit continue increasing with the number of C60 molecules, demonstrating the enhancement of thermoelectric preformance by manipulation of intermolecular interactions.

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.

A detailed experimental and theoretical study into the properties of C60 dumbbell junctions.

A combined experimental and theoretical investigation is carried out into the electrical transport across a fullerene dumbbell one-molecule junction. The newly designed molecule comprises two C60 s connected to a fluorene backbone via cyclopropyl groups. It is wired between gold electrodes under ambient conditions by pressing the tip of a scanning tunnelling microscope (STM) onto one of the C60 groups. The STM allows us to identify a single molecule before the junction is formed through imaging, which means unambiguously that only one molecule is wired. Once lifted, the same molecule could be wired many times as it was strongly fixed to the tip, and a high conductance state close to 10(-2) G0 is found. The results also suggest that the relative conductance fluctuations are low as a result of the low mobility of the molecule. Theoretical analysis indicates that the molecule is connected directly to one electrode through the central fluorene, and that to bind it to the gold fully it has to be pushed through a layer of adsorbates naturally present in the experiment.

Mapping Conductance and Switching Behavior of Graphene Devices In Situ.

Graphene is proposed for use in various nanodevice designs, many of which harness emergent quantum properties for device functionality. However, visualization, measurement, and manipulation become nontrivial at nanometer and atomic scales, representing a significant challenge for device fabrication, characterization, and optimization at length scales where quantum effects emerge. Here, proof of principle results at the crossroads between 2D nanoelectronic devices, e-beam-induced modulation, and imaging with secondary electron e-beam induced currents (SEEBIC) is presented. A device platform compatible with scanning transmission electron microscopy investigations is introduced. Then how the SEEBIC imaging technique can be used to visualize conductance and connectivity in single layer graphene nanodevices, even while supported on a thicker substrate (conditions under which conventional imaging fails) is shown. Finally, it is shown that the SEEBIC imaging technique can detect subtle differences in charge transport through time in nonohmic graphene nanoconstrictions indicating the potential to reveal dynamic electronic processes.

Low thermal conductivity in franckeite heterostructures.

Layered crystals are known to be good candidates for bulk thermoelectric applications as they open new ways to realise highly efficient devices. Two dimensional materials, isolated from layered materials, and their stacking into heterostructures have attracted intense research attention for nanoscale applications due to their high Seebeck coefficient and possibilities to engineer their thermoelectric properties. However, integration to thermoelectric devices is problematic due to their usually high thermal conductivities. Reporting on thermal transport studies between 150 and 300 K, we show that franckeite, a naturally occurring 2D heterostructure, exhibits a very low thermal conductivity which combined with its previously reported high Seebeck coefficient and electrical conductance make it a promising candidate for low dimensional thermoelectric applications. We find cross- and in-plane thermal conductivity values at room temperature of 0.70 and 0.88 W m-1 K-1, respectively, which is one of the lowest values reported today for 2D-materials. Interestingly, a 1.77 nm thick layer of franckeite shows very low thermal conductivity similar to one of the most widely used thermoelectric material Bi2Te3 with the thickness of 10-20 nm. We show that this is due to the low Debye frequency of franckeite and scattering of phonon transport through van der Waals interface between different layers. This observation open new routes for high efficient ultra-thin thermoelectric applications.

Exploring seebeck-coefficient fluctuations in endohedral-fullerene, single-molecule junctions.

For the purpose of creating single-molecule junctions, which can convert a temperature difference ΔT into a voltage ΔV via the Seebeck effect, it is of interest to screen molecules for their potential to deliver high values of the Seebeck coefficient S = -ΔV/ΔT. Here we demonstrate that insight into molecular-scale thermoelectricity can be obtained by examining the widths and extreme values of Seebeck histograms. Using a combination of experimental scanning-tunnelling-microscopy-based transport measurements and density-functional-theory-based transport calculations, we study the electrical conductance and Seebeck coefficient of three endohedral metallofullerenes (EMFs) Sc3N@C80, Sc3C2@C80, and Er3N@C80, which based on their structures, are selected to exhibit different degrees of charge inhomogeneity and geometrical disorder within a junction. We demonstrate that standard deviations in the Seebeck coefficient σS of EMF-based junctions are correlated with the geometric standard deviation σ and the charge inhomogeneity σq. We benchmark these molecules against C60 and demonstrate that both σq, σS are the largest for Sc3C2@C80, both are the smallest for C60 and for the other EMFs, they follow the order Sc3C2@C80 > Sc3N@C80 > Er3N@C80 > C60. A large value of σS is a sign that a molecule can exhibit a wide range of Seebeck coefficients, which means that if orientations corresponding to high values can be selected and controlled, then the molecule has the potential to exhibit high-performance thermoelectricity. For the EMFs studied here, large values of σS are associated with distributions of Seebeck coefficients containing both positive and negative signs, which reveals that all these EMFs are bi-thermoelectric materials.

Exploiting rotational asymmetry for sub-50 nm mechanical nanocalligraphy.

Nanofabrication has experienced extraordinary progress in the area of lithography-led processes over the last decades, although versatile and adaptable techniques addressing a wide spectrum of materials are still nascent. Scanning probe lithography (SPL) offers the capability to readily pattern sub-100 nm structures on many surfaces; however, the technique does not scale to dense and multi-lengthscale structures. Here, we demonstrate a technique, which we term nanocalligraphy scanning probe lithography (nc-SPL), that overcomes these limitations. Nc-SPL employs an asymmetric tip and exploits its rotational asymmetry to generate structures spanning the micron to nanometer lengthscales through real-time linewidth tuning. Using specialized tip geometries and by precisely controlling the patterning direction, we demonstrate sub-50 nm patterns while simultaneously improving on throughput, tip longevity, and reliability compared to conventional SPL. We further show that nc-SPL can be employed in both positive and negative tone patterning modes, in contrast to conventional SPL. This underlines the potential of this technique for processing sensitive surfaces such as 2D materials, which are prone to tip-induced shear or beam-induced damage.

Quantifying thermal transport in buried semiconductor nanostructures via cross-sectional scanning thermal microscopy.

Managing thermal transport in nanostructures became a major challenge in the development of active microelectronic, optoelectronic and thermoelectric devices, stalling the famous Moore's law of clock speed increase of microprocessors for more than a decade. To find the solution to this and linked problems, one needs to quantify the ability of these nanostructures to conduct heat with adequate precision, nanoscale resolution, and, essentially, for the internal layers buried in the 3D structure of modern semiconductor devices. Existing thermoreflectance measurements and "hot wire" 3ω methods cannot be effectively used at lateral dimensions of a layer below a micrometre; moreover, they are sensitive mainly to the surface layers of a relatively high thickness of above 100 nm. Scanning thermal microscopy (SThM), while providing the required lateral resolution, provides mainly qualitative data of the layer conductance due to undefined tip-surface and interlayer contact resistances. In this study, we used cross-sectional SThM (xSThM), a new method combining scanning probe microscopy compatible Ar-ion beam exit nano-cross-sectioning (BEXP) and SThM, to quantify thermal conductance in complex multilayer nanostructures and to measure local thermal conductivity of oxide and semiconductor materials, such as SiO2, SiGex and GeSny. By using the new method that provides 10 nm thickness and few tens of nm lateral resolution, we pinpoint crystalline defects in SiGe/GeSn optoelectronic materials by measuring nanoscale thermal transport and quantifying thermal conductivity and interfacial thermal resistance in thin spin-on materials used in extreme ultraviolet lithography (eUV) fabrication processing. The new capability of xSThM demonstrated here for the first time is poised to provide vital insights into thermal transport in advanced nanoscale materials and devices.

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.

Franckeite as a naturally occurring van der Waals heterostructure.

The fabrication of van der Waals heterostructures, artificial materials assembled by individual stacking of 2D layers, is among the most promising directions in 2D materials research. Until now, the most widespread approach to stack 2D layers relies on deterministic placement methods, which are cumbersome and tend to suffer from poor control over the lattice orientations and the presence of unwanted interlayer adsorbates. Here, we present a different approach to fabricate ultrathin heterostructures by exfoliation of bulk franckeite which is a naturally occurring and air stable van der Waals heterostructure (composed of alternating SnS2-like and PbS-like layers stacked on top of each other). Presenting both an attractive narrow bandgap (<0.7 eV) and p-type doping, we find that the material can be exfoliated both mechanically and chemically down to few-layer thicknesses. We present extensive theoretical and experimental characterizations of the material's electronic properties and crystal structure, and explore applications for near-infrared photodetectors.