Electrostatic moiré potential from twisted hexagonal boron nitride layers.

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Charge Carrier Inversion in a Doped Thin Film Organic Semiconductor Island.

Inducing an inversion layer in organic semiconductors is a highly nontrivial, but critical, achievement for producing organic field-effect transistor (OFET) devices, which rely on the generation of inversion, accumulation, and depletion regimes for successful operation. Here, we develop a pulsed bias technique to characterize the dopant type of any organic material system, without prior knowledge or characterization of the material in question. We use this technique on a pentacene/PTCDI heterostructure and thus deduce that pentacene is exhibiting n-doped like response. The source of the additional charges in the pentacene island can be identified by charging rings in the dissipation channel of the noncontact atomic force microscopy (AFM) signal, a typical signature for localized charge transfer from the AFM tip to the sample. Additionally, through tip-induced band-bending, we generate inversion, depletion, and accumulation regimes over a 20 nm radius, three monolayer thick n-doped pentacene island. Our findings demonstrate that nanometer-scale lateral extent and thickness are sufficient for an OFET device to operate in the inversion regime.

Nanoscale force sensing of an ultrafast nonlinear optical response.

The nonlinear optical response of a material is a sensitive probe of electronic and structural dynamics under strong light fields. The induced microscopic polarizations are usually detected via their far-field light emission, thus limiting spatial resolution. Several powerful near-field techniques circumvent this limitation by employing local nanoscale scatterers; however, their signal strength scales unfavorably as the probe volume decreases. Here, we demonstrate that time-resolved atomic force microscopy is capable of temporally and spatially resolving the microscopic, electrostatic forces arising from a nonlinear optical polarization in an insulating dielectric driven by femtosecond optical fields. The measured forces can be qualitatively explained by a second-order nonlinear interaction in the sample. The force resulting from this nonlinear interaction has frequency components below the mechanical resonance frequency of the cantilever and is thus detectable by regular atomic force microscopy methods. The capability to measure a nonlinear polarization through its electrostatic force is a powerful means to revisit nonlinear optical effects at the nanoscale, without the need for emitted photons or electrons from the surface.

Amplitude Dependence of Resonance Frequency and its Consequences for Scanning Probe Microscopy.

With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments using noncontact frequency modulation atomic force microscopy is based on the accurate measurement of the resonance frequency shift due to the tip-sample interaction. Here, we experimentally show that the resonance frequency of oscillating probes used for SPM experiments change systematically as a function of oscillation amplitude under typical operating conditions. This change in resonance frequency is not due to tip-sample interactions, but rather due to the cantilever strain or geometric effects and thus the resonance frequency is a function of the oscillation amplitude. Our numerical calculations demonstrate that the amplitude dependence of the resonance frequency is an additional yet overlooked systematic error source that can result in nonnegligible errors in measured interaction potentials and forces. Our experimental results and complementary numerical calculations reveal that the frequency shift due to this amplitude dependence needs to be corrected even for experiments with active oscillation amplitude control to be able to quantify the tip-sample interaction potentials and forces with milli-electron volt and pico-Newton resolutions.

Fully Quantized Electron Transfer Observed in a Single Redox Molecule at a Metal Interface.

Long-range electron transfer is a ubiquitous process that plays an important role in electrochemistry, biochemistry, organic electronics, and single molecule electronics. Fundamentally, quantum mechanical processes, at their core, manifest through both electron tunneling and the associated transition between quantized nuclear vibronic states (intramolecular vibrational relaxation) mediated by electron-nuclear coupling. Here, we report on measurements of long-range electron transfer at the interface between a single ferrocene molecule and a gold substrate separated by a hexadecanethiol quantum tunneling barrier. These redox measurements exhibit quantized nuclear transitions mediated by electron-nuclear coupling at 4.7 K in vacuum. By detecting the electric force associated with redox events by atomic force microscopy (AFM), with increasing AFM oscillation amplitude, the intensity of the observed  cantilever resonance frequency shift peak increases and then exhibits a series of discrete steps that are indicative of quantized nuclear transitions. The observed peak shapes agree well with a single-electron tunneling model with quantized nuclear state transitions associated with the conversion of the molecule between oxidized and reduced electronic states. This technique opens the door to simultaneously investigating quantized electron and nuclear dynamics in a diverse range of systems.

Review of time-resolved non-contact electrostatic force microscopy techniques with applications to ionic transport measurements.

Recently, there have been a number of variations of electrostatic force microscopy (EFM) that allow for the measurement of time-varying forces arising from phenomena such as ion transport in battery materials or charge separation in photovoltaic systems. These forces reveal information about dynamic processes happening over nanometer length scales due to the nanometer-sized probe tips used in atomic force microscopy. Here, we review in detail several time-resolved EFM techniques based on non-contact atomic force microscopy, elaborating on their specific limitations and challenges. We also introduce a new experimental technique that can resolve time-varying signals well below the oscillation period of the cantilever and compare and contrast it with those previously established.

Calibration of the oscillation amplitude of electrically excited scanning probe microscopy sensors.

Atomic force microscopy (AFM) is an analytical surface characterization tool which can reveal a sample's topography with high spatial resolution while simultaneously probing tip-sample interactions. Local measurement of chemical properties with high-resolution has gained much popularity in recent years with advances in dynamic AFM methodologies. A calibration factor is required to convert the electrical readout to a mechanical oscillation amplitude in order to extract quantitative information about the surface. We propose a new calibration technique for the oscillation amplitude of electrically driven probes using the principle of energy balance. Our technique relies on the measurement of the energy input to maintain the oscillation amplitude constant. With the measurement of the energy input to the probe, a mechanical oscillation amplitude is calculated and a calibration factor to convert the electrical readout in volts to a mechanical oscillation amplitude in Ångströms is obtained. We demonstrate the application of the new technique with a quartz tuning fork including the qPlus configuration, while the same principle can be applied to other piezoelectric resonators such as length extension resonators or piezoelectric cantilevers. The calibration factor obtained by this technique is found to be in agreement with using the thermal noise spectrum method for capsulated and decapsulated tuning forks and tuning forks in the qPlus configuration.

Relating Franck-Condon blockade to redox chemistry in the single-particle picture.

In this work, we explore Franck-Condon blockade in the "redox limit," where nuclear relaxation processes occur much faster than the rate of electron transfer. To this end, the quantized rate expressions for electron transfer are recast in terms of a quantized redox density of states (DOS) within a single phonon mode model. In the high temperature regime, this single-particle picture formulation of electron transfer is shown to agree well with the semi-classical rate and DOS expressions developed by Gerischer and Hopfield. Upon incorporation into a two electrode formulation, utilizing the master equation approach, the low temperature quantized conductance features of Franck-Condon blockade are reproduced. Moreover, at sufficiently large reorganization energies, it is argued that Franck-Condon blockade should also be observable in room temperature systems. In general, this work aims to further bridge descriptions of electron transfer and transport in the single-particle picture.

Measuring Spatially Resolved Collective Ionic Transport on Lithium Battery Cathodes Using Atomic Force Microscopy.

One of the main challenges in improving fast charging lithium-ion batteries is the development of suitable active materials for cathodes and anodes. Many materials suffer from unacceptable structural changes under high currents and/or low intrinsic conductivities. Experimental measurements are required to optimize these properties, but few techniques are able to spatially resolve ionic transport properties at small length scales. Here we demonstrate an atomic force microscope (AFM)-based technique to measure local ionic transport on LiFePO4 to correlate with the structural and compositional analysis of the same region. By comparing the measured values with density functional theory (DFT) calculations, we demonstrate that Coulomb interactions between ions give rise to a collective activation energy for ionic transport that is dominated by large phase boundary hopping barriers. We successfully measure both the collective activation energy and the smaller single-ion bulk hopping barrier and obtain excellent agreement with values obtained from our DFT calculations.

Quantum state readout of individual quantum dots by electrostatic force detection.

Electric charge detection by atomic force microscopy (AFM) with single-electron resolution (e-EFM) is a promising way to investigate the electronic level structure of individual quantum dots (QDs). The oscillating AFM tip modulates the energy of the QDs, causing single electrons to tunnel between QDs and an electrode. The resulting oscillating electrostatic force changes the resonant frequency and damping of the AFM cantilever, enabling electrometry with a single-electron sensitivity. Quantitative electronic level spectroscopy is possible by sweeping the bias voltage. Charge stability diagram can be obtained by scanning the AFM tip around the QD. e-EFM technique enables to investigate individual colloidal nanoparticles and self-assembled QDs without nanoscale electrodes. e-EFM is a quantum electromechanical system where the back-action of a tunneling electron is detected by AFM; it can also be considered as a mechanical analog of admittance spectroscopy with a radio frequency resonator, which is emerging as a promising tool for quantum state readout for quantum computing. In combination with the topography imaging capability of the AFM, e-EFM is a powerful tool for investigating new nanoscale material systems which can be used as quantum bits.

Rapid Mechanically Controlled Rewiring of Neuronal Circuits.

CNS injury may lead to permanent functional deficits because it is still not possible to regenerate axons over long distances and accurately reconnect them with an appropriate target. Using rat neurons, microtools, and nanotools, we show that new, functional neurites can be created and precisely positioned to directly (re)wire neuronal networks. We show that an adhesive contact made onto an axon or dendrite can be pulled to initiate a new neurite that can be mechanically guided to form new synapses at up to 0.8 mm distance in <1 h. Our findings challenge current understanding of the limits of neuronal growth and have direct implications for the development of new therapies and surgical techniques to achieve functional regeneration. Significance statement: Brain and spinal cord injury may lead to permanent disability and death because it is still not possible to regenerate neurons over long distances and accurately reconnect them with an appropriate target. Using microtools and nanotools we have developed a new method to rapidly initiate, elongate, and precisely connect new functional neuronal circuits over long distances. The extension rates achieved are ≥60 times faster than previously reported. Our findings have direct implications for the development of new therapies and surgical techniques to achieve functional regeneration after trauma and in neurodegenerative diseases. It also opens the door for the direct wiring of robust brain-machine interfaces as well as for investigations of fundamental aspects of neuronal signal processing and neuronal function.

Improved atomic force microscopy cantilever performance by partial reflective coating.

Optical beam deflection systems are widely used in cantilever based atomic force microscopy (AFM). Most commercial cantilevers have a reflective metal coating on the detector side to increase the reflectivity in order to achieve a high signal on the photodiode. Although the reflective coating is usually much thinner than the cantilever, it can still significantly contribute to the damping of the cantilever, leading to a lower mechanical quality factor (Q-factor). In dynamic mode operation in high vacuum, a cantilever with a high Q-factor is desired in order to achieve a lower minimal detectable force. The reflective coating can also increase the low-frequency force noise. In contact mode and force spectroscopy, a cantilever with minimal low-frequency force noise is desirable. We present a study on cantilevers with a partial reflective coating on the detector side. For this study, soft (≈0.01 N/m) and stiff (≈28 N/m) rectangular cantilevers were used with a custom partial coating at the tip end of the cantilever. The Q-factor, the detection and the force noise of fully coated, partially coated and uncoated cantilevers are compared and force distance curves are shown. Our results show an improvement in low-frequency force noise and increased Q-factor for the partially coated cantilevers compared to fully coated ones while maintaining the same reflectivity, therefore making it possible to combine the best of both worlds.

Revealing energy level structure of individual quantum dots by tunneling rate measured by single-electron sensitive electrostatic force spectroscopy.

We present theoretical and experimental studies of the effect of the density of states of a quantum dot (QD) on the rate of single-electron tunneling that can be directly measured by electrostatic force microscopy (e-EFM) experiments. In e-EFM, the motion of a biased atomic force microscope cantilever tip modulates the charge state of a QD in the Coulomb blockade regime. The charge dynamics of the dot, which is detected through its back-action on the capacitavely coupled cantilever, depends on the tunneling rate of the QD to a back-electrode. The density of states of the QD can therefore be measured through its effect on the energy dependence of tunneling rate. We present experimental data on individual 5 nm colloidal gold nanoparticles that exhibit a near continuous density of state at 77 K. In contrast, our analysis of already published data on self-assembled InAs QDs at 4 K clearly reveals discrete degenerate energy levels.

Scanning gate imaging of two coupled quantum dots in single-walled carbon nanotubes.

Two coupled single wall carbon nanotube quantum dots in a multiple quantum dot system were characterized by using a low temperature scanning gate microscopy (SGM) technique, at a temperature of 170 mK. The locations of single wall carbon nanotube quantum dots were identified by taking the conductance images of a single wall carbon nanotube contacted by two metallic electrodes. The single electron transport through single wall carbon nanotube multiple quantum dots has been observed by varying either the position or voltage bias of a conductive atomic force microscopy tip. Clear hexagonal patterns were observed in the region of the conductance images where only two sets of overlapping conductance rings are visible. The values of coupling capacitance over the total capacitance of the two dots, C(m)/C(1(2)) have been extracted to be 0.21 ∼ 0.27 and 0.23 ∼ 0.28, respectively. In addition, the interdot coupling (conductance peak splitting) has also been confirmed in both conductance image measurement and current-voltage curves. The results show that a SGM technique enables spectroscopic investigation of coupled quantum dots even in the presence of unexpected multiple quantum dots.

Transient adhesion and conductance phenomena in initial nanoscale mechanical contacts between dissimilar metals.

We report on transient adhesion and conductance phenomena associated with tip wetting in mechanical contacts produced by the indentation of a clean W(111) tip into a Au(111) surface. A combination of atomic force microscopy and scanning tunneling microscopy was used to carry out indentation and to image residual impressions in ultra-high vacuum. The ∼7 nm radii tips used in these experiments were prepared and characterized by field ion microscopy in the same instrument. The very first indentations of the tungsten tips show larger conductance and pull-off adhesive forces than subsequent indentations. After ∼30 indentations to a depth of ∼1.7 nm, the maximum conductance and adhesion forces reach steady state values approximately 12 ×  and 6 ×  smaller than their initial value. Indentation of W(111) tips into Cu(100) was also performed to investigate the universality of tip wetting phenomena with a different substrate. We propose a model from contact mechanics considerations which quantitatively reproduces the observed decay rate of the conductance and adhesion drops with a 1/e decay constant of 9-14 indentation cycles. The results show that the surface composition of an indenting tip plays an important role in defining the mechanical and electrical properties of indentation contacts.

Room-temperature single-electron charging detected by electrostatic force microscopy.

We use atomic force microscopy to measure electron addition spectra of individual Au nanoparticles that exhibit Coulomb blockade at room temperature. The cantilever tip charges individual nanoparticles supported on an ultra-thin NaCl film via single-electron tunneling from the metal back electrode. The tunneling is detected by measuring frequency shift and damping of the oscillating cantilever. Finite element electrostatic calculations indicate that the total nanoparticle capacitance is dominated by mutual capacitance to the back electrode.

Minimum threshold for incipient plasticity in the atomic-scale nanoindentation of Au(111).

The formation of the smallest permanent indentation in a Au(111) surface is studied by scanning tunneling microscopy and atomic force microscopy in ultrahigh vacuum. The 9.5 nm radius W(111) indenter was characterized in situ by field ion microscopy. Elastic and plastic indentations are identified both in the residual impression image and by features in their force-displacement curves such as the sink-in depth, pop-ins, and hysteresis energy. Plasticity is best identified quantitatively in the force-displacement curves by the sink-in depth. The minimum of plastic damage producible in the substrate is associated with an energy budget of ∼70 eV.

Layer-by-layer growth of sodium chloride overlayers on an Fe(001)-p(1 × 1)O surface.

Ultra-thin NaCl films epitaxially grown on an Fe(001)-p(1 × 1)O surface have been investigated in ultra-high vacuum by non-contact atomic force microscopy and low energy electron diffraction. It has been found that at temperatures below 145 °C NaCl initially grows as monoatomic thick islands on substrate terraces, while at temperatures above 175 °C biatomic thick islands are also formed at substrate step edges. Both types of islands have the same Fe(001)-O[100] [parallel] NaCl(001)[110] orientation, leading to a (4 × 4) superstructure, where the NaCl unit cell is oriented at 45° with respect to the substrate. Interestingly, no c(2 × 2) superstructure with the NaCl unit cell oriented at 0° has been observed. The oxygen on the iron surface promotes layer-by-layer growth, resulting in atomically flat films with 40-60 nm wide terraces at coverages ranging from 0.75 to 12 ML. Such NaCl films are of much higher quality than MgO films grown on Fe(001) and Fe(001)-p(1 × 1)O surfaces and represent a unique epitaxial system of an alkali halide on a pure metallic substrate. The reduced number of defects and the layer-by-layer mode of growth make this system very attractive for applications where an atomically defined tunnel barrier is required to control the properties of a device.

Conductivity of an atomically defined metallic interface.

A mechanically formed electrical nanocontact between gold and tungsten is a prototypical junction between metals with dissimilar electronic structure. Through atomically characterized nanoindentation experiments and first-principles quantum transport calculations, we find that the ballistic conduction across this intermetallic interface is drastically reduced because of the fundamental mismatch between s wave-like modes of electron conduction in the gold and d wave-like modes in the tungsten. The mechanical formation of the junction introduces defects and disorder, which act as an additional source of conduction losses and increase junction resistance by up to an order of magnitude. These findings apply to nanoelectronics and semiconductor device design. The technique that we use is very broadly applicable to molecular electronics, nanoscale contact mechanics, and scanning tunneling microscopy.

Stochastic noise in atomic force microscopy.

Having reached the quantum and thermodynamic limits of detection, atomic force microscopy (AFM) experiments are routinely being performed at the fundamental limit of signal to noise. A critical understanding of the statistical properties of noise leads to more accurate interpretation of data, optimization of experimental protocols, advancements in instrumentation, and new measurement techniques. Furthermore, accurate simulation of cantilever dynamics requires knowledge of stochastic behavior of the system, as stochastic noise may exceed the deterministic signals of interest, and even dominate the outcome of an experiment. In this article, the power spectral density (PSD), used to quantify stationary stochastic processes, is introduced in the context of a thorough noise analysis of the light source used to detect cantilever deflections. The statistical properties of PSDs are then outlined for various stationary, nonstationary, and deterministic noise sources in the context of AFM experiments. Following these developments, a method for integrating PSDs to provide an accurate standard deviation of linear measurements is described. Lastly, a method for simulating stochastic Gaussian noise from any arbitrary power spectral density is presented. The result demonstrates that mechanical vibrations of the AFM can cause a logarithmic velocity dependence of friction and induce multiple slip events in the atomic stick-slip process, as well as predicts an artifactual temperature dependence of friction measured by AFM.