Phonon-Assisted Resonant Tunneling of Electrons in Graphene-Boron Nitride Transistors

van der Waals Contact for Two-Dimensional Transition Metal Dichalcogenides

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have emerged as highly promising candidates for next-generation electronics owing to their atomically thin structures and surfaces devoid of dangling bonds. However, establishing high-quality metal contacts with TMDs presents a critical challenge, primarily attributed to their ultrathin bodies and delicate lattices. These distinctive characteristics render them susceptible to physical damage and chemical reactions when conventional metallization approaches involving "high-energy" processes are implemented. To tackle this challenge, the concept of van der Waals (vdW) contacts has recently been proposed as a "low-energy" alternative. Within the vdW geometry, metal contacts can be physically laminated or gently deposited onto the 2D channel of TMDs, ensuring the formation of atomically clean and electronically sharp contact interfaces while preserving the inherent properties of the 2D TMDs. Consequently, a considerable number of vdW contact devices have been extensively investigated, revealing unprecedented transport physics or exceptional device performance that was previously unachievable. This review presents recent advancements in vdW contacts for TMD transistors, discussing the merits, limitations, and prospects associated with each device geometry. By doing so, our purpose is to offer a comprehensive understanding of the current research landscape and provide insights into future directions within this rapidly evolving field.

Probing the Inelastic Electron Tunneling via the Photocurrent in a Vertical Graphene van der Waals Heterostructure

Inelastic electron tunneling (IET), accompanied by energy transfer between the tunneling charge carriers and other elementary excitations, is widely used to investigate the collective modes and quasiparticles in solid-state materials. In general, the inelastic contribution to the tunneling current is small compared to the elastic part and is therefore only prominent in the second derivative of the tunneling current with respect to the bias voltage. Here we demonstrate a direct observation of the IET by measuring the photoresponse in a graphene-based vertical tunnel junction device. Characteristic peaks/valleys are observed in the bias-voltage-dependent tunneling photocurrent at low temperatures, which barely shift with the gate voltage applied to graphene and diminish gradually as the temperature increases. By comparing with the second-order differential conductance spectra, we establish that these features are associated with the phonon-assisted IET. A simple model based on the photoexcited hot-carrier tunneling in graphene qualitatively explains the response. Our study points to a promising means of probing the low-energy elementary excitations utilizing the graphene-based van der Waals (vdW) heterostructures.

Exciton-assisted electron tunnelling in van der Waals heterostructures

The control of elastic and inelastic electron tunnelling relies on materials with well-defined interfaces. Two-dimensional van der Waals materials are an excellent platform for such studies. Signatures of acoustic phonons and defect states have been observed in current-to-voltage measurements. These features can be explained by direct electron-phonon or electron-defect interactions. Here we use a tunnelling process that involves excitons in transition metal dichalcogenides (TMDs). We study tunnel junctions consisting of graphene and gold electrodes separated by hexagonal boron nitride with an adjacent TMD monolayer and observe prominent resonant features in current-to-voltage measurements appearing at bias voltages that correspond to TMD exciton energies. By placing the TMD outside of the tunnelling pathway, we demonstrate that this tunnelling process does not require any charge injection into the TMD. The appearance of such optical modes in electrical transport introduces additional functionality towards van der Waals material-based optoelectronic devices.

Correlated insulator collapse due to quantum avalanche via in-gap ladder states

The significant discrepancy observed between the predicted and experimental switching fields in correlated insulators under a DC electric field far-from-equilibrium necessitates a reevaluation of current microscopic understanding. Here we show that an electron avalanche can occur in the bulk limit of such insulators at arbitrarily small electric field by introducing a generic model of electrons coupled to an inelastic medium of phonons. The quantum avalanche arises by the generation of a ladder of in-gap states, created by a multi-phonon emission process. Hot-phonons in the avalanche trigger a premature and partial collapse of the correlated gap. The phonon spectrum dictates the existence of two-stage versus single-stage switching events which we associate with charge-density-wave and Mott resistive phase transitions, respectively. The behavior of electron and phonon temperatures, as well as the temperature dependence of the threshold fields, demonstrates how a crossover between the thermal and quantum switching scenarios emerges within a unified framework of the quantum avalanche.

Graphene FETs with high and low mobilities have universal temperature-dependent properties

We use phenomenological modelling and detailed experimental studies of charge carrier transport to investigate the dependence of the electrical resistivity,ρ, on gate voltage,V_g, for a series of monolayer graphene field effect transistors with mobilities,μ, ranging between 5000 and 250 000 cm²V^-1s^-1at low-temperature. Our measurements over a wide range of temperatures from 4 to 400 K can be fitted by the universal relationμ=4/eδnmaxfor all devices, whereρmaxis the resistivity maximum at the neutrality point andδnis an 'uncertainty' in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of carrier density,n. This relation is consistent with thermal broadening of the carrier distribution and the presence of the disordered potential landscape consisting of so-called electron-hole puddles near the Dirac point. To demonstrate its utility, we combine this relation with temperature-dependent linearised Boltzmann transport calculations that include the effect of optical phonon scattering. This approach demonstrates the similarity in the temperature-dependent behaviour of carriers in different types of single layer graphene transistors with widely differing carrier mobilities. It can also account for the relative stability, over a wide temperature range, of the measured carrier mobility of each device.

Long-Range Nonequilibrium Coherent Tunneling Induced by Fractional Vibronic Resonances

We study the influence of a linear energy bias on a nonequilibrium excitation on a chain of molecules coupled to local vibrations (a tilted Holstein model) using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and homogeneous polaron dynamics. Remarkably, resonance between the phonon energy ℏω and the bias δ_ϵ occurs not only at integer but also fractional ratios δ_ϵ/(ℏω) = m/n, which effect long-range n-bond m-phonon tunneling. These observations are reproduced in a model calculation of a recently demonstrated Cy3 system, and the effect of dipole-dipole-type non-nearest-neighbor coupling and vibrationally relaxed initial states is also considered. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.

Direct probing of phonon mode specific electron-phonon scatterings in two-dimensional semiconductor transition metal dichalcogenides

Electron–phonon scatterings in solid-state systems are pivotal processes in determining many key physical quantities such as charge carrier mobilities and thermal conductivities. Here, we report direct probing of phonon mode specific electron–phonon scatterings in layered semiconducting transition metal dichalcogenides WSe₂, MoSe₂, WS₂, and MoS₂ through inelastic electron tunneling spectroscopy measurements, quantum transport simulations, and density functional calculation. We experimentally and theoretically characterize momentum-conserving single- and two-phonon electron–phonon scatterings involving up to as many as eight individual phonon modes in mono- and bilayer films, among which transverse, longitudinal acoustic and optical, and flexural optical phonons play significant roles in quantum charge flows. Moreover, the layer-number sensitive higher-order inelastic electron–phonon scatterings, which are confirmed to be generic in all four semiconducting layers, can be attributed to differing electronic structures, symmetry, and quantum interference effects during the scattering processes in the ultrathin semiconducting films.

Electron–phonon scattering events in solid-state systems determine key physical quantities. Here, the authors probe momentum-conserving single- and two-phonon electron–phonon scattering events involving up to as many as eight individual phonon modes in 2D semiconductors.

Vibrational Excitation Mechanism in Tunneling Spectroscopy beyond the Franck-Condon Model

Vibronic spectra of molecules are typically described within the Franck-Condon model. Here, we show that highly resolved vibronic spectra of large organic molecules on a single layer of MoS_{2} on Au(111) show spatial variations in their intensities, which cannot be captured within this picture. We explain that vibrationally mediated perturbations of the molecular wave functions need to be included into the Franck-Condon model. Our simple model calculations reproduce the experimental spectra at arbitrary position of the scanning tunneling microscope's tip over the molecule in great detail.

Triplet Excitation and Electroluminescence from a Supramolecular Monolayer Embedded in a Boron Nitride Tunnel Barrier

We show that ordered monolayers of organic molecules stabilized by hydrogen bonding on the surface of exfoliated few-layer hexagonal boron nitride (hBN) flakes may be incorporated into van der Waals heterostructures with integral few-layer graphene contacts forming a molecular/two-dimensional hybrid tunneling diode. Electrons can tunnel through the hBN/molecular barrier under an applied voltage V_SD, and we observe molecular electroluminescence from an excited singlet state with an emitted photon energy hν > eV_SD, indicating upconversion by energies up to ∼1 eV. We show that tunneling electrons excite embedded molecules into singlet states in a two-step process via an intermediate triplet state through inelastic scattering and also observe direct emission from the triplet state. These heterostructures provide a solid-state device in which spin-triplet states, which cannot be generated by optical transitions, can be controllably excited and provide a new route to investigate the physics, chemistry, and quantum spin-based applications of triplet generation, emission, and molecular photon upconversion.

Resonant tunnelling spectroscopy of van der Waals heterosystems

The review concerns the most interesting aspects of (mainly experimental) resonance tunnelling spectroscopy studies of a new type of heterosystems called van der Waals heterostructures. The possibility to compose such systems is a result of the recent discovery of two-dimensional crystals, a new class of materials derived from graphene. The role of the angular mismatch of the crystal lattices of conductive graphene electrodes in the tunnelling of charge carriers between them, as well as the closely related issues associated with fulfillment of the conservation laws during tunnelling transitions are considered. The experimental results on inelastic tunnelling in the graphene/h-BN/graphene heterosystems with strong angular mismatch are discussed. The experiments made it possible to determine the phonon density of states spectra of the constituent layers and to detect and describe tunnelling transitions involving localized states of structural defects in the h-BN barrier. We consider new results of studies on tunnelling and magnetotunnelling in van der Waals heterosystems that demonstrate the possibilities of practical application of resonant tunnelling effects in, e.g., microwave engineering, based on realization of electronic devices having I – V curves with negative differential conductance (NDC) regions at tunnelling through defect levels of the barrier layers in such systems. These studies revealed two new types of heterosystems characterized by the formation of NDC regions as a result of resonant tunnelling through the defect levels in the h-BN barrier and by defect-assisted generation of tunnelling current.

The bibliography includes 40 references.

Resonant Tunneling Induced Enhancement of Electron Field Emission by Ultra-Thin Coatings

The emission of electrons from the surface of a material into vacuum depends strongly on the material’s work function, temperature, and the intensity of electric field. The combined effects of these give rise to a multitude of related phenomena, including Fowler-Nordheim tunneling and Schottky emission, which, in turn, enable several families of devices, ranging from vacuum tubes, to Schottky diodes, and thermionic energy converters. More recently, nanomembrane-based detectors have found applications in high-resolution mass spectrometry measurements in proteomics. Progress in all the aforementioned applications critically depends on discovering materials with effective low surface work functions. We show that a few atomic layer deposition (ALD) cycles of zinc oxide onto suspended diamond nanomembranes, strongly reduces the threshold voltage for the onset of electron field emission which is captured by resonant tunneling from the ZnO layer. Solving the Schroedinger equation, we obtain an electrical field- and thickness-dependent population of the lowest few subbands in the thin ZnO layer, which results in a minimum in the threshold voltage at a thickness of 1.08 nm being in agreement with the experimentally determined value. We conclude that resonant tunneling enables cost-effective ALD coatings that lower the effective work function and enhance field emission from the device.

Magnetic 2D materials and heterostructures

The family of two-dimensional (2D) materials grows day by day, hugely expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals (vdW) heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member: 2D magnets. The situation has changed over the past 2 years with the introduction of a variety of atomically thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus on the case of the two most studied systems-semiconducting CrI₃ and metallic Fe₃GeTe₂-and illustrate the physical phenomena that have been observed. Special attention will be given to the range of new van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.

Planar and van der Waals heterostructures for vertical tunnelling single electron transistors

Despite a rich choice of two-dimensional materials, which exists these days, heterostructures, both vertical (van der Waals) and in-plane, offer an unprecedented control over the properties and functionalities of the resulted structures. Thus, planar heterostructures allow p-n junctions between different two-dimensional semiconductors and graphene nanoribbons with well-defined edges; and vertical heterostructures resulted in the observation of superconductivity in purely carbon-based systems and realisation of vertical tunnelling transistors. Here we demonstrate simultaneous use of in-plane and van der Waals heterostructures to build vertical single electron tunnelling transistors. We grow graphene quantum dots inside the matrix of hexagonal boron nitride, which allows a dramatic reduction of the number of localised states along the perimeter of the quantum dots. The use of hexagonal boron nitride tunnel barriers as contacts to the graphene quantum dots make our transistors reproducible and not dependent on the localised states, opening even larger flexibility when designing future devices.

Magnetoresistance in Co-hBN-NiFe Tunnel Junctions Enhanced by Resonant Tunneling through Single Defects in Ultrathin hBN Barriers

Hexagonal boron nitride (hBN) is a prototypical high-quality two-dimensional insulator and an ideal material to study tunneling phenomena, as it can be easily integrated in vertical van der Waals devices. For spintronic devices, its potential has been demonstrated both for efficient spin injection in lateral spin valves and as a barrier in magnetic tunnel junctions (MTJs). Here we reveal the effect of point defects inevitably present in mechanically exfoliated hBN on the tunnel magnetoresistance of Co-hBN-NiFe MTJs. We observe a clear enhancement of both the conductance and magnetoresistance of the junction at well-defined bias voltages, indicating resonant tunneling through magnetic (spin-polarized) defect states. The spin polarization of the defect states is attributed to exchange coupling of a paramagnetic impurity in the few-atomic-layer thick hBN to the ferromagnetic electrodes. This is confirmed by excellent agreement with theoretical modeling. Our findings should be taken into account in analyzing tunneling processes in hBN-based magnetic devices. More generally, our study shows the potential of using atomically thin hBN barriers with defects to engineer the magnetoresistance of MTJs and to achieve spin filtering, opening the door toward exploiting the spin degree of freedom in current studies of point defects as quantum emitters.

Moiré-Modulated Conductance of Hexagonal Boron Nitride Tunnel Barriers

Monolayer hexagonal boron nitride (hBN) tunnel barriers investigated using conductive atomic force microscopy reveal moiré patterns in the spatial maps of their tunnel conductance consistent with the formation of a moiré superlattice between the hBN and an underlying highly ordered pyrolytic graphite (HOPG) substrate. This variation is attributed to a periodc modulation of the local density of states and occurs for both exfoliated hBN barriers and epitaxially grown layers. The epitaxial barriers also exhibit enhanced conductance at localized subnanometer regions which are attributed to exposure of the substrate to a nitrogen plasma source during the high temperature growth process. Our results show clearly a spatial periodicity of tunnel current due to the formation of a moiré superlattice and we argue that this can provide a mechanism for elastic scattering of charge carriers for similar interfaces embedded in graphene/hBN resonant tunnel diodes.

Nanoscale momentum-resolved vibrational spectroscopy

Vibrational modes affect fundamental physical properties such as the conduction of sound and heat and can be sensitive to nano- and atomic-scale structure. Probing the momentum transfer dependence of vibrational modes provides a wealth of information about a materials system; however, experimental work has been limited to essentially bulk and averaged surface approaches or to small wave vectors. We demonstrate a combined experimental and theoretical methodology for nanoscale mapping of optical and acoustic phonons across the first Brillouin zone, in the electron microscope, probing a volume ~10¹⁰ to 10²⁰ times smaller than that of comparable bulk and surface techniques. In combination with more conventional electron microscopy techniques, the presented methodology should allow for direct correlation of nanoscale vibrational mode dispersions with atomic-scale structure and chemistry.

Magnitude of the current in 2D interlayer tunneling devices

Using the Bardeen tunneling method with first-principles wave functions, computations are made of the tunneling current in graphene/hexagonal-boron-nitride/graphene (G/h-BN/G) vertical structures. Detailed comparison with prior experimental results is made, focusing on the magnitude of the achievable tunnel current. With inclusion of the effects of translational and rotational misalignment of the graphene and the h-BN, predicted currents are found to be about 15×  larger than experimental values. A reduction in this discrepancy, to a factor of 2.5×, is achieved by utilizing a realistic size for the band gap of the h-BN, hence affecting the exponential decay constant for the tunneling.

Direct Probing of the Electronic Structures of Single-Layer and Bilayer Graphene with a Hexagonal Boron Nitride Tunneling Barrier

The chemical and mechanical stability of hexagonal boron nitride (h-BN) thin films and their compatibility with other free-standing two-dimensional (2D) crystals to form van der Waals heterostructures make the h-BN-2D tunnel junction an intriguing experimental platform not only for the engineering of specific device functionalities but also for the promotion of quantum measurement capabilities. Here, we exploit the h-BN-graphene tunnel junction to directly probe the electronic structures of single-layer and bilayer graphene in the presence and the absence of external magnetic fields with unprecedented high signal-to-noise ratios. At a zero magnetic field, we identify the tunneling spectra related to the charge neutrality point and the opening of the electric-field-induced bilayer energy gap. In the quantum Hall regime, the quantization of 2D electron gas into Landau levels (LL) is seen as early as 0.2 T, and as many as 30 well-separated LL tunneling conductance oscillations are observed for both electron- and hole-doped regions. Our device simulations successfully reproduce the experimental observations. Additionally, we extract the relative permittivity of three-to-five layer h-BN and find that the screening capability of thin h-BN films is as much as 60% weaker than bulk h-BN.

Modulation of the electronic and mechanical properties of phagraphene via hydrogenation and fluorination

Adsorption-induced semimetal–semiconductor and semimetal–insulator transitions were determined and strain-induced insulator–semiconductor transition was identified in phagraphene.

Signatures of Phonon and Defect-Assisted Tunneling in Planar Metal-Hexagonal Boron Nitride-Graphene Junctions

Electron tunneling spectroscopy measurements on van der Waals heterostructures consisting of metal and graphene (or graphite) electrodes separated by atomically thin hexagonal boron nitride tunnel barriers are reported. The tunneling conductance, dI/dV, at low voltages is relatively weak, with a strong enhancement reproducibly observed to occur at around |V| ≈ 50 mV. While the weak tunneling at low energies is attributed to the absence of substantial overlap, in momentum space, of the metal and graphene Fermi surfaces, the enhancement at higher energies signals the onset of inelastic processes in which phonons in the heterostructure provide the momentum necessary to link the Fermi surfaces. Pronounced peaks in the second derivative of the tunnel current, d²I/dV², are observed at voltages where known phonon modes in the tunnel junction have a high density of states. In addition, features in the tunneling conductance attributed to single electron charging of nanometer-scale defects in the boron nitride are also observed in these devices. The small electronic density of states of graphene allows the charging spectra of these defect states to be electrostatically tuned, leading to "Coulomb diamonds" in the tunneling conductance.

Hexagonal Boron Nitride Tunnel Barriers Grown on Graphite by High Temperature Molecular Beam Epitaxy

We demonstrate direct epitaxial growth of high-quality hexagonal boron nitride (hBN) layers on graphite using high-temperature plasma-assisted molecular beam epitaxy. Atomic force microscopy reveals mono- and few-layer island growth, while conducting atomic force microscopy shows that the grown hBN has a resistance which increases exponentially with the number of layers, and has electrical properties comparable to exfoliated hBN. X-ray photoelectron spectroscopy, Raman microscopy and spectroscopic ellipsometry measurements on hBN confirm the formation of sp²-bonded hBN and a band gap of 5.9 ± 0.1 eV with no chemical intermixing with graphite. We also observe hexagonal moiré patterns with a period of 15 nm, consistent with the alignment of the hBN lattice and the graphite substrate.

Effects of Electrode Layer Band Structure on the Performance of Multilayer Graphene-hBN-Graphene Interlayer Tunnel Field Effect Transistors

Interlayer tunnel field-effect transistors based on graphene and hexagonal boron nitride (hBN) have recently attracted much interest for their potential as beyond-CMOS devices. Using a recently developed method for fabricating rotationally aligned two-dimensional heterostructures, we show experimental results for devices with varying thicknesses and stacking order of the graphene electrode layers and also model the current-voltage behavior. We show that an increase in the graphene layer thickness results in narrower resonance. However, due to a simultaneous increase in the number of sub-bands and decrease of sub-band separation with an increase in thickness, the negative differential resistance peaks becomes less prominent and do not appear for certain conditions at room temperature. Also, we show that due to the unique band structure of odd number of layer Bernal-stacked graphene, the number of closely spaced resonance conditions increase, causing interference between neighboring resonance peaks. Although this can be avoided with even number of layer graphene, we find that in this case the bandgap opening present at high biases tend to broaden the resonance peaks.