Modeling and characterization of a cantilever-based near-field scanning microwave impedance microscope

Johnson-noise-limited cancellation-free microwave impedance microscopy with monolithic silicon cantilever probes

Microwave impedance microscopy (MIM) is an emerging scanning probe technique for nanoscale complex permittivity mapping and has made significant impacts in diverse fields. To date, the most significant hurdles that limit its widespread use are the requirements of specialized microwave probes and high-precision cancellation circuits. Here, we show that forgoing both elements not only is feasible but also enhances performance. Using monolithic silicon cantilever probes and a cancellation-free architecture, we demonstrate Johnson-noise-limited, drift-free MIM operation with 15 nm spatial resolution, minimal topography crosstalk, and an unprecedented sensitivity of 0.26 zF/√Hz. We accomplish this by taking advantage of the high mechanical resonant frequency and spatial resolution of silicon probes, the inherent common-mode phase noise rejection of self-referenced homodyne detection, and the exceptional stability of the streamlined architecture. Our approach makes MIM drastically more accessible and paves the way for advanced operation modes as well as integration with complementary techniques.

Visualization of Mesoscopic Conductivity Fluctuations in Amorphous Semiconductor Thin-Film Transistors

Charge transport in amorphous semiconductors is considerably more complicated than the process in crystalline materials due to abundant localized states. In addition to device-scale characterization, spatially resolved measurements are important to unveiling electronic properties. Here, we report gigahertz conductivity mapping in amorphous indium gallium zinc oxide (a-IGZO) thin-film transistors by microwave impedance microscopy (MIM), which probes conductivity without Schottky barrier's influence. The difference between the dc and microwave conductivities reflects the efficacy of the injection barrier in an accumulation-mode transistor. The conductivity exhibits significant nanoscale inhomogeneity in the subthreshold regime, presumably due to trapping and release from localized states. The characteristic length scale of local fluctuations, as determined by the autocorrelation analysis, is about 200 nm. Using a random-barrier model, we can simulate the spatial variation of the potential landscape, which underlies the mesoscopic conductivity distribution. Our work provides an intuitive way to understand the charge transport mechanism in amorphous semiconductors at the microscopic level.

Mechanically Gated Transistor

Silicon-based field effect transistors have underpinned the information revolution in the last 60 years, and there is a strong desire for new materials, devices, and architectures that can help sustain the computing power in the age of big data and artificial intelligence. Inspired by the Piezo channels, a mechanically gated transistor abandoning electric gating altogether, achieving an ON/OFF ratio over three orders of magnitude under a mechanical force of hundreds of nN is developed. The two-terminal device utilizes flexoelectric polarization induced by strain gradient, which modulates the carrier concentration in a Van der Waals structure significantly, and it mimics Piezo channels for artificial tactile perception. This simple device concept can be easily adapted to a wide range of semiconducting materials, helping promote the fusion between mechanics and electronics in a similar way as mechanobiology.

MilliKelvin microwave impedance microscopy in a dry dilution refrigerator

Microwave impedance microscopy (MIM) is a near-field imaging technique that has been used to visualize the local conductivity of materials with nanoscale resolution across the GHz regime. In recent years, MIM has shown great promise for the investigation of topological states of matter, correlated electronic states, and emergent phenomena in quantum materials. To explore these low-energy phenomena, many of which are only detectable in the milliKelvin regime, we have developed a novel low-temperature MIM incorporated into a dilution refrigerator. This setup, which consists of a tuning-fork-based atomic force microscope with microwave reflectometry capabilities, is capable of reaching temperatures down to 70 mK during imaging and magnetic fields up to 9 T. To test the performance of this microscope, we demonstrate microwave imaging of the conductivity contrast between graphite and silicon dioxide at cryogenic temperatures and discuss the resolution and noise observed in these results. We extend this methodology to visualize edge conduction in Dirac semi-metal cadmium arsenide in the quantum Hall regime.

Non-volatile electric-field control of inversion symmetry

Competition between ground states at phase boundaries can lead to significant changes in properties under stimuli, particularly when these ground states have different crystal symmetries. A key challenge is to stabilize and control the coexistence of symmetry-distinct phases. Using BiFeO₃ layers confined between layers of dielectric TbScO₃ as a model system, we stabilize the mixed-phase coexistence of centrosymmetric and non-centrosymmetric BiFeO₃ phases at room temperature with antipolar, insulating and polar semiconducting behaviour, respectively. Application of orthogonal in-plane electric (polar) fields results in reversible non-volatile interconversion between the two phases, hence removing and introducing centrosymmetry. Counterintuitively, we find that an electric field 'erases' polarization, resulting from the anisotropy in octahedral tilts introduced by the interweaving TbScO₃ layers. Consequently, this interconversion between centrosymmetric and non-centrosymmetric phases generates changes in the non-linear optical response of over three orders of magnitude, resistivity of over five orders of magnitude and control of microscopic polar order. Our work establishes a platform for cross-functional devices that take advantage of changes in optical, electrical and ferroic responses, and demonstrates octahedral tilts as an important order parameter in materials interface design.

Developments of Interfacial Measurement Using Cavity Scanning Microwave Microscopy

In the field of materials research, scanning microwave microscopy imaging has already become a vital research tool due to its high sensitivity and nondestructive testing of samples. In this article, we review the main theoretical and fundamental components of microwave imaging, in addition to the wide range of applications of microwave imaging. Rather than the indirect determination of material properties by measuring dielectric constants and conductivity, microwave microscopy now permits the direct investigation of semiconductor devices, electromagnetic fields, and ferroelectric domains. This paper reviews recent advances in scanning microwave microscopy in the areas of resolution and operating frequency and presents a discussion of possible future industrial and academic applications.

Superior photo-carrier diffusion dynamics in organic-inorganic hybrid perovskites revealed by spatiotemporal conductivity imaging

The outstanding performance of organic-inorganic metal trihalide solar cells benefits from the exceptional photo-physical properties of both electrons and holes in the material. Here, we directly probe the free-carrier dynamics in Cs-doped FAPbI₃ thin films by spatiotemporal photoconductivity imaging. Using charge transport layers to selectively quench one type of carriers, we show that the two relaxation times on the order of 1 μs and 10 μs correspond to the lifetimes of electrons and holes in FACsPbI₃, respectively. Strikingly, the diffusion mapping indicates that the difference in electron/hole lifetimes is largely compensated by their disparate mobility. Consequently, the long diffusion lengths (3~5 μm) of both carriers are comparable to each other, a feature closely related to the unique charge trapping and de-trapping processes in hybrid trihalide perovskites. Our results unveil the origin of superior diffusion dynamics in this material, crucially important for solar-cell applications.

Electrostatic tip effects in scanning probe microscopy of nanostructures

Electrical scanning probe microscopies (SPM) use ultrasharp metallic tips to obtain nanometer spatial resolution and are a key tool for characterizing nanoscale semiconducting materials and systems. However, these tips are not passive probes; their high work functions can induce local band bending whose effects depend sensitively on the local geometry and material properties and thus are inherently difficult to quantify. We use sequential finite element simulations to first explore the magnitude and spatial distribution of charge reorganization due to tip-induced band bending (TIBB) for planar and nanostructured geometries. We demonstrate that tip-induced depletion and accumulation of carriers can be significantly modified in confined geometries such as nanowires compared to a bulk planar response. This charge reorganization is due to finite size effects that arise as the nanostructure size approaches the Debye length, with significant implications for a range of SPM techniques. We then use the reorganized charge distribution from our model to describe experimentally measured quantities, using in operando scanning microwave impedance microscopy measurements on axial p-i-n silicon nanowire devices as a specific example. By incorporating TIBB, we reveal that our experimentally observed enhancement (absence) of contrast at the p-i (i-n) junction is explained by the tip-induced accumulation (depletion) of carriers at the interface. Our results demonstrate that the inclusion of TIBB is critical for an accurate interpretation of electrical SPM measurements, and is especially important for weakly screening or low-doped materials, as well as the complex doping patterns and confined geometries commonly encountered in nanoscale systems.

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi₄Br₄ is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

Inorganic Low k Cage-molecular Crystals

For the interlayer dielectric in microelectronics, light element compounds are preferably accepted due to less electronic polarization. Here, the nontrivial dielectric nature of the Sb₄O₆ cage-molecular crystal, known as α-antimony trioxide (α-Sb₂O₃), is reported. The gas-phase synthesized α-Sb₂O₃ nanoflakes are of high crystal quality, from which the abnormal local admittance responses were revealed by scanning microwave impedance microscopy (sMIM). The remarkably low dielectric constant (k), 2.0∼2.5, is corroborated by the analysis of the thickness-dependent sMIM-capacitance signal. In light of the theoretical calculations, the ultralow molecular density and the significantly suppressed ionic polarization are both crucial to the highly reduced k. Combining with the excellent optical band gap, thermal stability, and breakdown strength, α-Sb₂O₃ is a promising low k dielectric.

Advanced Modelling Techniques for Resonator Based Dielectric and Semiconductor Materials Characterization

This article reports recent developments in modelling based on Finite Difference Time Domain (FDTD) and Finite Element Method (FEM) for dielectric resonator material measurement setups. In contrast to the methods of the dielectric resonator design, where analytical expansion into Bessel functions is used to solve the Maxwell equations, here the analytical information is used only to ensure the fixed angular variation of the fields, while in the longitudinal and radial direction space discretization is applied, that reduced the problem to 2D. Moreover, when the discretization is performed in time domain, full-wave electromagnetic solvers can be directly coupled to semiconductor drift-diffusion solvers to better understand and predict the behavior of the resonator with semiconductor-based samples. Herein, FDTD and frequency domain FEM approaches are applied to the modelling of dielectric samples and validated against the measurements within the 0.3% margin dictated by the IEC norm. Then a coupled in-house developed multiphysics time-domain FEM solver is employed in order to take the local conductivity changes under electromagnetic illumination into account. New methodologies are thereby demonstrated that open the way to new applications of the dielectric resonator measurements.

Mapping of integrated PIN diodes with a 3D architecture by scanning microwave impedance microscopy and dynamic spectroscopy

This work addresses the need for a comprehensive methodology for nanoscale electrical testing dedicated to the analysis of both "front end of line" (FEOL) (doped semiconducting layers) and "back end of line" (BEOL) layers (metallization, trench dielectric, and isolation) of highly integrated microelectronic devices. Based on atomic force microscopy, an electromagnetically shielded and electrically conductive tip is used in scanning microwave impedance microscopy (sMIM). sMIM allows for the characterization of the local electrical properties through the analysis of the microwave impedance of the metal-insulator-semiconductor nanocapacitor (nano-MIS capacitor) that is formed by tip and sample. A highly integrated monolithic silicon PIN diode with a 3D architecture is analysed. sMIM measurements of the different layers of the PIN diode are presented and discussed in terms of detection mechanism, sensitivity, and precision. In the second part, supported by analytic calculations of the equivalent nano-MIS capacitor, a new multidimensional approach, including a complete parametric investigation, is performed with a dynamic spectroscopy method. The results emphasize the strong impact, in terms of distinction and location, of the applied bias on the local sMIM measurements for both FEOL and BEOL layers.

Nanoscale Conductivity Imaging of Correlated Electronic States in WSe_{2}/WS_{2} Moiré Superlattices

We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe_{2}/WS_{2} heterostructures using microwave impedance microscopy. The noncontact microwave probe allows us to observe the Mott insulating state with one hole per moiré unit cell that persists for temperatures up to 150 K, consistent with other characterization techniques. In addition, we identify for the first time a Mott insulating state at one electron per moiré unit cell. Appreciable inhomogeneity of the correlated states is directly visualized in the heterobilayer region, indicative of local disorders in the moiré superlattice potential or electrostatic doping. Our work provides important insights on 2D moiré systems down to the microscopic level.

Unveiling defect-mediated carrier dynamics in monolayer semiconductors by spatiotemporal microwave imaging

The optoelectronic properties of atomically thin transition-metal dichalcogenides are strongly correlated with the presence of defects in the materials, which are not necessarily detrimental for certain applications. For instance, defects can lead to an enhanced photoconduction, a complicated process involving charge generation and recombination in the time domain and carrier transport in the spatial domain. Here, we report the simultaneous spatial and temporal photoconductivity imaging in two types of WS2 monolayers by laser-illuminated microwave impedance microscopy. The diffusion length and carrier lifetime were directly extracted from the spatial profile and temporal relaxation of microwave signals, respectively. Time-resolved experiments indicate that the critical process for photoexcited carriers is the escape of holes from trap states, which prolongs the apparent lifetime of mobile electrons in the conduction band. As a result, counterintuitively, the long-lived photoconductivity signal is higher in chemical-vapor deposited (CVD) samples than exfoliated monolayers due to the presence of traps that inhibits recombination. Our work reveals the intrinsic time and length scales of electrical response to photoexcitation in van der Waals materials, which is essential for their applications in optoelectronic devices.

Unexpected Giant Microwave Conductivity in a Nominally Silent BiFeO3 Domain Wall

Nanoelectronic devices based on ferroelectric domain walls (DWs), such as memories, transistors, and rectifiers, have been demonstrated in recent years. Practical high-speed electronics, on the other hand, usually demand operation frequencies in the gigahertz (GHz) regime, where the effect of dipolar oscillation is important. Herein, an unexpected giant GHz conductivity on the order of 10³ S m^-1 is observed in certain BiFeO₃ DWs, which is about 100 000 times greater than the carrier-induced direct current (dc) conductivity of the same walls. Surprisingly, the nominal configuration of the DWs precludes the alternating current (ac) conduction under an excitation electric field perpendicular to the surface. Theoretical analysis shows that the inclined DWs are stressed asymmetrically near the film surface, whereas the vertical walls in a control sample are not. The resultant imbalanced polarization profile can then couple to the out-of-plane microwave fields and induce power dissipation, which is confirmed by the phase-field modeling. Since the contributions from mobile-carrier conduction and bound-charge oscillation to the ac conductivity are equivalent in a microwave circuit, the research on local structural dynamics may open a new avenue to implement DW nano-devices for radio-frequency applications.

Modern Scattering-Type Scanning Near-Field Optical Microscopy for Advanced Material Research

Infrared and optical spectroscopy represents one of the most informative methods in advanced materials research. As an important branch of modern optical techniques that has blossomed in the past decade, scattering-type scanning near-field optical microscopy (s-SNOM) promises deterministic characterization of optical properties over a broad spectral range at the nanoscale. It allows ultrabroadband optical (0.5-3000 µm) nanoimaging, and nanospectroscopy with fine spatial (<10 nm), spectral (<1 cm^-1 ), and temporal (<10 fs) resolution. The history of s-SNOM is briefly introduced and recent advances which broaden the horizons of this technique in novel material research are summarized. In particular, this includes the pioneering efforts to study the nanoscale electrodynamic properties of plasmonic metamaterials, strongly correlated quantum materials, and polaritonic systems at room or cryogenic temperatures. Technical details, theoretical modeling, and new experimental methods are also discussed extensively, aiming to identify clear technology trends and unsolved challenges in this exciting field of research.

Visualization of Local Conductance in MoS2/WSe2 Heterostructure Transistors

The vertical stacking of van der Waals (vdW) materials introduces a new degree of freedom to the research of two-dimensional (2D) systems. The interlayer coupling strongly influences the band structure of the heterostructures, resulting in novel properties that can be utilized for electronic and optoelectronic applications. Based on microwave microscopy studies, we report quantitative electrical imaging on gated molybdenum disulfide (MoS₂)/tungsten diselenide (WSe₂) heterostructure devices, which exhibit an intriguing antiambipolar effect in their transfer characteristics. Interestingly, in the region with significant source-drain current, electrons in the n-type MoS₂ and holes in the p-type WSe₂ segments are nearly balanced, whereas the heterostructure area is depleted of mobile charges. The spatial evolution of local conductance can be ascribed to the lateral band bending and formation of depletion regions along the line of MoS₂-heterostructure-WSe₂. Our work vividly demonstrates the microscopic origin of novel transport behaviors, which is important for the vibrant field of vdW heterojunction research.

Energy-Resolved Photoconductivity Mapping in a Monolayer-Bilayer WSe2 Lateral Heterostructure

Vertical and lateral heterostructures of van der Waals materials provide tremendous flexibility for band-structure engineering. Because electronic bands are sensitively affected by defects, strain, and interlayer coupling, the edge and heterojunction of these two-dimensional (2D) systems may exhibit novel physical properties, which can be fully revealed only by spatially resolved probes. Here, we report the spatial mapping of photoconductivity in a monolayer-bilayer WSe₂ lateral heterostructure under multiple excitation lasers. As the photon energy increases, the light-induced conductivity detected by microwave impedance microscopy first appears along the heterointerface and bilayer edge, then along the monolayer edge, inside the bilayer area, and finally in the interior of the monolayer region. The sequential emergence of mobile carriers in different sections of the sample is consistent with the theoretical calculation of local energy gaps. Quantitative analysis of the microscopy and transport data also reveals the linear dependence of photoconductivity on the laser intensity and the influence of interlayer coupling on carrier recombination. Combining theoretical modeling, atomic-scale imaging, mesoscale impedance microscopy, and device-level characterization, our work suggests an exciting perspective for controlling the intrinsic band gap variation in 2D heterostructures down to a regime of a few nanometers.

Functional Scanning Force Microscopy for Energy Nanodevices

Energy nanodevices, including energy conversion and energy storage devices, have become a major cross-disciplinary field in recent years. These devices feature long-range electron and ion transport coupled with chemical transformation, which call for novel characterization tools to understand device operation mechanisms. In this context, recent developments in functional scanning force microscopy techniques and their application in thin-film photovoltaic devices and lithium batteries are reviewed. The advantages of scanning force microscopy, such as high spatial resolution, multimodal imaging, and the possibility of in situ and in operando imaging, are emphasized. The survey indicates that functional scanning force microscopy is making significant contributions in understanding materials and interfaces in energy nanodevices.

Interferometric imaging of nonlocal electromechanical power transduction in ferroelectric domains

The electrical generation and detection of elastic waves are the foundation for acoustoelectronic and acoustooptic systems. For surface acoustic wave devices, microelectromechanical/nanoelectromechanical systems, and phononic crystals, tailoring the spatial variation of material properties such as piezoelectric and elastic tensors may bring significant improvements to the system performance. Due to the much slower speed of sound than speed of light in solids, it is desirable to study various electroacoustic behaviors at the mesoscopic length scale. In this work, we demonstrate the interferometric imaging of electromechanical power transduction in ferroelectric lithium niobate domain structures by microwave impedance microscopy. In sharp contrast to the traditional standing-wave patterns caused by the superposition of counterpropagating waves, the constructive and destructive fringes in microwave dissipation images exhibit an intriguing one-wavelength periodicity. We show that such unusual interference patterns, which are fundamentally different from the acoustic displacement fields, stem from the nonlocal interaction between electric fields and elastic waves. The results are corroborated by numerical simulations taking into account the sign reversal of piezoelectric tensor in oppositely polarized domains. Our work paves ways to probe nanoscale electroacoustic phenomena in complex structures by near-field electromagnetic imaging.

Nanoscale linear permittivity imaging based on scanning nonlinear dielectric microscopy

A nanoscale linear permittivity imaging method based on scanning nonlinear dielectric microscopy (SNDM) was developed. The ∂C/∂z-mode SNDM (∂C/∂z-SNDM) technique described herein employs probe-height modulation to suppress disturbances originating from stray capacitance and to improve measurement stability. This method allows local permittivity distributions to be examined with extremely low noise levels (approximately 0.01 aF) by virtue of the highly sensitive probe. A cross-section of a multilayer oxide film was visualized using ∂C/∂z-SNDM as a demonstration, and numerical simulations of the response signals were conducted to gain additional insights. The experimental signal intensities were found to be in a good agreement with the theoretical values, with the exception of the background components, demonstrating that absolute sample permittivity values could be determined. The signal profiles near the boundaries between different dielectrics were calculated using various vibration amplitudes and the boundary transition widths were obtained. The beneficial aspects of higher-harmonic response imaging are discussed herein, taking into account assessments of spatial resolution and quantitation.

Quantitative measurements of nanoscale permittivity and conductivity using tuning-fork-based microwave impedance microscopy

We report quantitative measurements of nanoscale permittivity and conductivity using tuning-fork (TF) based microwave impedance microscopy (MIM). The system is operated under the driving amplitude modulation mode, which ensures satisfactory feedback stability on samples with rough surfaces. The demodulated MIM signals on a series of bulk dielectrics are in good agreement with results simulated by finite-element analysis. Using the TF-MIM, we have visualized the evolution of nanoscale conductance on back-gated MoS₂ field effect transistors, and the results are consistent with the transport data. Our work suggests that quantitative analysis of mesoscopic electrical properties can be achieved by near-field microwave imaging with small distance modulation.

Optically coupled methods for microwave impedance microscopy

Scanning Microwave Impedance Microscopy (MIM) measurement of photoconductivity with 50 nm resolution is demonstrated using a modulated optical source. The use of a modulated source allows for the measurement of photoconductivity in a single scan without a reference region on the sample, as well as removing most topographical artifacts and enhancing signal to noise as compared with unmodulated measurement. A broadband light source with a tunable monochrometer is then used to measure energy resolved photoconductivity with the same methodology. Finally, a pulsed optical source is used to measure local photo-carrier lifetimes via MIM, using the same 50 nm resolution tip.

In situ analytical techniques for battery interface analysis

Interface is a key to high performance and safe lithium-ion batteries or lithium batteries.

Impact of grain boundaries on efficiency and stability of organic-inorganic trihalide perovskites

Organic–inorganic perovskite solar cells have attracted tremendous attention because of their remarkably high power conversion efficiencies. To further improve device performance, it is imperative to obtain fundamental understandings on the photo-response and long-term stability down to the microscopic level. Here, we report the quantitative nanoscale photoconductivity imaging on two methylammonium lead triiodide thin films with different efficiencies by light-stimulated microwave impedance microscopy. The microwave signals are largely uniform across grains and grain boundaries, suggesting that microstructures do not lead to strong spatial variations of the intrinsic photo-response. In contrast, the measured photoconductivity and lifetime are strongly affected by bulk properties such as the sample crystallinity. As visualized by the spatial evolution of local photoconductivity, the degradation process begins with the disintegration of grains rather than nucleation and propagation from visible boundaries between grains. Our findings provide insights to improve the electro-optical properties of perovskite thin films towards large-scale commercialization.

Probing the nanoscale photoconductivity of methylammonium lead triiodide is important for understanding the microstructures of the solar cell devices, but scanning probe methods suffer from sample degradation. Here Chu et al. solve the problem with noncontact microwave impedance microscopy.

Full-wave modeling of broadband near field scanning microwave microscopy

A three-dimensional finite element numerical modeling for the scanning microwave microscopy (SMM) setup is applied to study the full-wave quantification of the local material properties of samples. The modeling takes into account the radiation and scattering losses of the nano-sized probe neglected in previous models based on low-frequency assumptions. The scanning techniques of approach curves and constant height are implemented. In addition, we conclude that the SMM has the potential for use as a broadband dielectric spectroscopy operating at higher frequencies up to THz. The results demonstrate the accuracy of previous models. We draw conclusions in light of the experimental results.

Tailoring Semiconductor Lateral Multijunctions for Giant Photoconductivity Enhancement

Semiconductor heterostructures have played a critical role as the enabler for new science and technology. The emergence of transition-metal dichalcogenides (TMDs) as atomically thin semiconductors has opened new frontiers in semiconductor heterostructures either by stacking different TMDs to form vertical heterojunctions or by stitching them laterally to form lateral heterojunctions via direct growth. In conventional semiconductor heterostructures, the design of multijunctions is critical to achieve carrier confinement. Analogously, successful synthesis of a monolayer WS₂ /WS_2(1-x) Se_2x /WS₂ multijunction lateral heterostructure via direct growth by chemical vapor deposition is reported. The grown structures are characterized by Raman, photoluminescence, and annular dark-field scanning transmission electron microscopy to determine their lateral compositional profile. More importantly, using microwave impedance microscopy, it is demonstrated that the local photoconductivity in the alloy region can be tailored and enhanced by two orders of magnitude over pure WS₂ . Finite element analysis confirms that this effect is due to the carrier diffusion and confinement into the alloy region. This work exemplifies the technological potential of atomically thin lateral heterostructures in optoelectronic applications.

Nondestructive imaging of atomically thin nanostructures buried in silicon

It is now possible to create atomically thin regions of dopant atoms in silicon patterned with lateral dimensions ranging from the atomic scale (angstroms) to micrometers. These structures are building blocks of quantum devices for physics research and they are likely also to serve as key components of devices for next-generation classical and quantum information processing. Until now, the characteristics of buried dopant nanostructures could only be inferred from destructive techniques and/or the performance of the final electronic device; this severely limits engineering and manufacture of real-world devices based on atomic-scale lithography. Here, we use scanning microwave microscopy (SMM) to image and electronically characterize three-dimensional phosphorus nanostructures fabricated via scanning tunneling microscope-based lithography. The SMM measurements, which are completely nondestructive and sensitive to as few as 1900 to 4200 densely packed P atoms 4 to 15 nm below a silicon surface, yield electrical and geometric properties in agreement with those obtained from electrical transport and secondary ion mass spectroscopy for unpatterned phosphorus δ layers containing ~10¹³ P atoms. The imaging resolution was 37 ± 1 nm in lateral and 4 ± 1 nm in vertical directions, both values depending on SMM tip size and depth of dopant layers. In addition, finite element modeling indicates that resolution can be substantially improved using further optimized tips and microwave gradient detection. Our results on three-dimensional dopant structures reveal reduced carrier mobility for shallow dopant layers and suggest that SMM could aid the development of fabrication processes for surface code quantum computers.

Low-energy structural dynamics of ferroelectric domain walls in hexagonal rare-earth manganites

Domain walls (DWs) in ferroic materials, across which the order parameter abruptly changes its orientation, can host emergent properties that are absent in the bulk domains. Using a broadband (10⁶ to 10¹⁰ Hz) scanning impedance microscope, we show that the electrical response of the interlocked antiphase boundaries and ferroelectric DWs in hexagonal rare-earth manganites (h-RMnO₃) is dominated by the bound-charge oscillation rather than free-carrier conduction at the DWs. As a measure of the rate of energy dissipation, the effective conductivity of DWs on the (001) surfaces of h-RMnO₃ at gigahertz frequencies is drastically higher than that at dc, whereas the effect is absent on surfaces with in-plane polarized domains. First-principles and model calculations indicate that the frequency range and selection rules are consistent with the periodic sliding of the DW around its equilibrium position. This acoustic wave-like mode, which is associated with the synchronized oscillation of local polarization and apical oxygen atoms, is localized perpendicular to the DW but free to propagate along the DW plane. Our results break the ground to understand structural DW dynamics and exploit new interfacial phenomena for novel devices.

Quantitative analysis of effective height of probes in microwave impedance microscopy

A quantitative approach is used to determine an effective height of probe beyond which the capacitance contribution is not significant in microwave impedance microscopy (MIM). We compare the effective height for three different modes of measurement, i.e., capacitance C(l) (l is the tip-sample distance), derivative of capacitance (C'(l)), and second derivative of capacitance (C″(l)). We discuss the effects of tip geometry and sample properties such as relative permittivity and sample height on the effective height with examples and analyze the implication on the spatial resolution of MIM. Finally, our results are verified by microwave impedance microscopy (MIM) measurement.

Picosecond Electric-Field-Induced Threshold Switching in Phase-Change Materials

Many chalcogenide glasses undergo a breakdown in electronic resistance above a critical field strength. Known as threshold switching, this mechanism enables field-induced crystallization in emerging phase-change memory. Purely electronic as well as crystal nucleation assisted models have been employed to explain the electronic breakdown. Here, picosecond electric pulses are used to excite amorphous Ag_{4}In_{3}Sb_{67}Te_{26}. Field-dependent reversible changes in conductivity and pulse-driven crystallization are observed. The present results show that threshold switching can take place within the electric pulse on subpicosecond time scales-faster than crystals can nucleate. This supports purely electronic models of threshold switching and reveals potential applications as an ultrafast electronic switch.

Uncovering edge states and electrical inhomogeneity in MoS2 field-effect transistors

The understanding of various types of disorders in atomically thin transition metal dichalcogenides (TMDs), including dangling bonds at the edges, chalcogen deficiencies in the bulk, and charges in the substrate, is of fundamental importance for TMD applications in electronics and photonics. Because of the imperfections, electrons moving on these 2D crystals experience a spatially nonuniform Coulomb environment, whose effect on the charge transport has not been microscopically studied. Here, we report the mesoscopic conductance mapping in monolayer and few-layer MoS2 field-effect transistors by microwave impedance microscopy (MIM). The spatial evolution of the insulator-to-metal transition is clearly resolved. Interestingly, as the transistors are gradually turned on, electrical conduction emerges initially at the edges before appearing in the bulk of MoS2 flakes, which can be explained by our first-principles calculations. The results unambiguously confirm that the contribution of edge states to the channel conductance is significant under the threshold voltage but negligible once the bulk of the TMD device becomes conductive. Strong conductance inhomogeneity, which is associated with the fluctuations of disorder potential in the 2D sheets, is also observed in the MIM images, providing a guideline for future improvement of the device performance.

Scanning Probe Microwave Reflectivity of Aligned Single-Walled Carbon Nanotubes: Imaging of Electronic Structure and Quantum Behavior at the Nanoscale

Single-walled carbon nanotubes (SWNTs) are 1-dimensional nanomaterials with unique electronic properties that make them excellent candidates for next-generation device technologies. While nanotube growth and processing methods have progressed steadily, significant opportunities remain in advanced methods for their characterization, inspection, and metrology. Microwave near-field imaging offers an extremely versatile "nondestructive" tool for nanomaterials characterization. Herein, we report the application of nanoscale microwave reflectivity to study SWNT electronic properties. Using microwave impedance microscopy (MIM) combined with microwave impedance modulation microscopy (MIM(2)), we imaged horizontal SWNT arrays, showing the microwave reflectivity from individual nanotubes is extremely sensitive to their electronic properties and dependent on the nanotube quantum capacitance under proper experimental conditions. It is shown experimentally that MIM can be a direct probe of the nanotube-free carrier density and the details of their electronic band structure. We demonstrate spatial mapping of local SWNT impedance (MIM), the density of states (MIM(2)), and the nanotube structural morphology (AFM) simultaneously and with lateral resolution down to <50 nm. Nanoscale microwave reflectivity could have tremendous impact, enabling optimization of enriched growth processes and postgrowth purification of SWNT arrays while aiding in the analysis of the quantum physics of these important 1D materials.

Direct Imaging of Dynamic Glassy Behavior in a Strained Manganite Film

Complex many-body interaction in perovskite manganites gives rise to a strong competition between ferromagnetic metallic and charge-ordered phases with nanoscale electronic inhomogeneity and glassy behaviors. Investigating this glassy state requires high-resolution imaging techniques with sufficient sensitivity and stability. Here, we present the results of a near-field microwave microscope imaging on the strain-driven glassy state in a manganite film. The high contrast between the two electrically distinct phases allows direct visualization of the phase separation. The low-temperature microscopic configurations differ upon cooling with different thermal histories. At sufficiently high temperatures, we observe switching between the two phases in either direction. The dynamic switching, however, stops below the glass transition temperature. Compared with the magnetization data, the phase separation was microscopically frozen, while spin relaxation was found in a short period of time.

Thickness-Dependent Dielectric Constant of Few-Layer In₂Se₃ Nanoflakes

The dielectric constant or relative permittivity (ε(r)) of a dielectric material, which describes how the net electric field in the medium is reduced with respect to the external field, is a parameter of critical importance for charging and screening in electronic devices. Such a fundamental material property is intimately related to not only the polarizability of individual atoms but also the specific atomic arrangement in the crystal lattice. In this Letter, we present both experimental and theoretical investigations on the dielectric constant of few-layer In2Se3 nanoflakes grown on mica substrates by van der Waals epitaxy. A nondestructive microwave impedance microscope is employed to simultaneously quantify the number of layers and local electrical properties. The measured ε(r) increases monotonically as a function of the thickness and saturates to the bulk value at around 6-8 quintuple layers. The same trend of layer-dependent dielectric constant is also revealed by first-principles calculations. Our results of the dielectric response, being ubiquitously applicable to layered 2D semiconductors, are expected to be significant for this vibrant research field.

Thermal Oxidation of WSe2 Nanosheets Adhered on SiO2/Si Substrates

Because of the drastically different intralayer versus interlayer bonding strengths, the mechanical, thermal, and electrical properties of two-dimensional (2D) materials are highly anisotropic between the in-plane and out-of-plane directions. The structural anisotropy may also play a role in chemical reactions, such as oxidation, reduction, and etching. Here, the composition, structure, and electrical properties of mechanically exfoliated WSe2 nanosheets on SiO2/Si substrates were studied as a function of the extent of thermal oxidation. A major component of the oxidation, as indicated from optical and Raman data, starts from the nanosheet edges and propagates laterally toward the center. Partial oxidation also occurs in certain areas at the surface of the flakes, which are shown to be highly conductive by microwave impedance microscopy. Using secondary ion mass spectroscopy, we also observed extensive oxidation at the WSe2-SiO2 interface. The combination of multiple microcopy methods can thus provide vital information on the spatial evolution of chemical reactions on 2D materials and the nanoscale electrical properties of the reaction products.

Direct Imaging of Nanoscale Conductance Evolution in Ion-Gel-Gated Oxide Transistors

Electrostatic modification of functional materials by electrolytic gating has demonstrated a remarkably wide range of density modulation, a condition crucial for developing novel electronic phases in systems ranging from complex oxides to layered chalcogenides. Yet little is known microscopically when carriers are modulated in electrolyte-gated electric double-layer transistors (EDLTs) due to the technical challenge of imaging the buried electrolyte-semiconductor interface. Here, we demonstrate the real-space mapping of the channel conductance in ZnO EDLTs using a cryogenic microwave impedance microscope. A spin-coated ionic gel layer with typical thicknesses below 50 nm allows us to perform high resolution (on the order of 100 nm) subsurface imaging, while maintaining the capability of inducing the metal-insulator transition under a gate bias. The microwave images vividly show the spatial evolution of channel conductance and its local fluctuations through the transition as well as the uneven conductance distribution established by a large source-drain bias. The unique combination of ultrathin ion-gel gating and microwave imaging offers a new opportunity to study the local transport and mesoscopic electronic properties in EDLTs.

Quantitative sub-surface and non-contact imaging using scanning microwave microscopy

The capability of scanning microwave microscopy for calibrated sub-surface and non-contact capacitance imaging of silicon (Si) samples is quantitatively studied at broadband frequencies ranging from 1 to 20 GHz. Calibrated capacitance images of flat Si test samples with varying dopant density (10(15)-10(19) atoms cm(-3)) and covered with dielectric thin films of SiO2 (100-400 nm thickness) are measured to demonstrate the sensitivity of scanning microwave microscopy (SMM) for sub-surface imaging. Using standard SMM imaging conditions the dopant areas could still be sensed under a 400 nm thick oxide layer. Non-contact SMM imaging in lift-mode and constant height mode is quantitatively demonstrated on a 50 nm thick SiO2 test pad. The differences between non-contact and contact mode capacitances are studied with respect to the main parameters influencing the imaging contrast, namely the probe tip diameter and the tip-sample distance. Finite element modelling was used to further analyse the influence of the tip radius and the tip-sample distance on the SMM sensitivity. The understanding of how the two key parameters determine the SMM sensitivity and quantitative capacitances represents an important step towards its routine application for non-contact and sub-surface imaging.

Toward air-stable multilayer phosphorene thin-films and transistors

Few-layer black phosphorus (BP), also known as phosphorene, is poised to be the most attractive graphene analogue owing to its high mobility approaching that of graphene, and its thickness-tunable band gap that can be as large as that of molybdenum disulfide. In essence, phosphorene represents the much sought after high-mobility, large direct band gap two-dimensional layered crystal that is ideal for optoelectronics and flexible devices. However, its instability in air is of paramount concern for practical applications. Here, we demonstrate air-stable BP devices with dielectric and hydrophobic encapsulation. Microscopy, spectroscopy, and transport techniques were employed to elucidate the aging mechanism, which can initiate from the BP surface for bare samples, or edges for samples with thin dielectric coating, highlighting the ineffectiveness of conventional scaled dielectrics. Our months-long studies indicate that a double layer capping of Al2O3 and hydrophobic fluoropolymer affords BP devices and transistors with indefinite air-stability for the first time, overcoming a critical material challenge for applied research and development.

Quantitative impedance characterization of sub-10 nm scale capacitors and tunnel junctions with an interferometric scanning microwave microscope

We present a method to characterize sub-10 nm capacitors and tunnel junctions by interferometric scanning microwave microscopy (iSMM) at 7.8 GHz. At such device scaling, the small water meniscus surrounding the iSMM tip should be reduced by proper tip tuning. Quantitative impedance characterization of attofarad range capacitors is achieved using an 'on-chip' calibration kit facing thousands of nanodevices. Nanoscale capacitors and tunnel barriers were detected through variations in the amplitude and phase of the reflected microwave signal, respectively. This study promises quantitative impedance characterization of a wide range of emerging functional nanoscale devices.

Mesoscale imperfections in MoS2 atomic layers grown by a vapor transport technique

The success of isolating small flakes of atomically thin layers through mechanical exfoliation has triggered enormous research interest in graphene and other two-dimensional materials. For device applications, however, controlled large-area synthesis of highly crystalline monolayers with a low density of electronically active defects is imperative. Here, we demonstrate the electrical imaging of dendritic ad-layers and grain boundaries in monolayer molybdenum disulfide (MoS2) grown by a vapor transport technique using microwave impedance microscopy. The micrometer-sized precipitates in our films, which appear as a second layer of MoS2 in conventional height and optical measurements, show ∼ 2 orders of magnitude higher conductivity than that of the single layer. The zigzag grain boundaries, on the other hand, are shown to be more resistive than the crystalline grains, consistent with previous studies. Our ability to map the local electrical properties in a rapid and nondestructive manner is highly desirable for optimizing the growth process of large-scale MoS2 atomic layers.

Near-field microwave scanning probe imaging of conductivity inhomogeneities in CVD graphene

We have performed near-field scanning microwave microscopy (SMM) of graphene grown by chemical vapor deposition. Due to the use of probe-sample capacitive coupling and a relatively high ac frequency of a few GHz, this scanning probe method allows mapping of local conductivity without a dedicated counter electrode, with a spatial resolution of about 50 nm. Here, the coupling was enabled by atomic layer deposition of alumina on top of graphene, which in turn enabled imaging both large-area films, as well as micron-sized islands, with a dynamic range covering a low sheet resistance of a metal film and a high resistance of highly disordered graphene. The structures of graphene grown on Ni films and Cu foils are explored, and the effects of growth conditions are elucidated. We present a simple general scheme for interpretation of the contrast in the SMM images of our graphene samples and other two-dimensional conductors, which is supported by extensive numerical finite-element modeling. We further demonstrate that combination of the SMM and numerical modeling allows quantitative information about the sheet resistance of graphene to be obtained, paving the pathway for characterization of graphene conductivity with a sub-100 nm special resolution.

Cryogenic microwave imaging of metal-insulator transition in doped silicon

We report the instrumentation and experimental results of a cryogenic scanning microwave impedance microscope. The microwave probe and the scanning stage are located inside the variable temperature insert of a helium cryostat. Microwave signals in the distance modulation mode are used for monitoring the tip-sample distance and adjusting the phase of the two output channels. The ability to spatially resolve the metal-insulator transition in a doped silicon sample is demonstrated. The data agree with a semiquantitative finite element simulation. Effects of the thermal energy and electric fields on local charge carriers can be seen in the images taken at different temperatures and dc biases.

Calibrated nanoscale capacitance measurements using a scanning microwave microscope

A scanning microwave microscope (SMM) for spatially resolved capacitance measurements in the attofarad-to-femtofarad regime is presented. The system is based on the combination of an atomic force microscope (AFM) and a performance network analyzer (PNA). For the determination of absolute capacitance values from PNA reflection amplitudes, a calibration sample of conductive gold pads of various sizes on a SiO(2) staircase structure was used. The thickness of the dielectric SiO(2) staircase ranged from 10 to 200 nm. The quantitative capacitance values determined from the PNA reflection amplitude were compared to control measurements using an external capacitance bridge. Depending on the area of the gold top electrode and the SiO(2) step height, the corresponding capacitance values, as measured with the SMM, ranged from 0.1 to 22 fF at a noise level of ~2 aF and a relative accuracy of 20%. The sample capacitance could be modeled to a good degree as idealized parallel plates with the SiO(2) dielectric sandwiched in between. The cantilever/sample stray capacitance was measured by lifting the tip away from the surface. By bringing the AFM tip into direct contact with the SiO(2) staircase structure, the electrical footprint of the tip was determined, resulting in an effective tip radius of ~60 nm and a tip-sample capacitance of ~20 aF at the smallest dielectric thickness.

Ultrathin topological insulator Bi2Se3 nanoribbons exfoliated by atomic force microscopy

Ultrathin topological insulator nanostructures, in which coupling between top and bottom surface states takes place, are of great intellectual and practical importance. Due to the weak van der Waals interaction between adjacent quintuple layers (QLs), the layered bismuth selenide (Bi(2)Se(3)), a single Dirac-cone topological insulator with a large bulk gap, can be exfoliated down to a few QLs. In this paper, we report the first controlled mechanical exfoliation of Bi(2)Se(3) nanoribbons (>50 QLs) by an atomic force microscope (AFM) tip down to a single QL. Microwave impedance microscopy is employed to map out the local conductivity of such ultrathin nanoribbons, showing drastic difference in sheet resistance between 1-2 QLs and 4-5 QLs. Transport measurement carried out on an exfoliated (<or=5 QLs) Bi(2)Se(3) device shows nonmetallic temperature dependence of resistance, in sharp contrast to the metallic behavior seen in thick (>50 QLs) ribbons. These AFM-exfoliated thin nanoribbons afford interesting candidates for studying the transition from quantum spin Hall surface to edge states.

Mesoscopic percolating resistance network in a strained manganite thin film

Many unusual behaviors in complex oxides are deeply associated with the spontaneous emergence of microscopic phase separation. Depending on the underlying mechanism, the competing phases can form ordered or random patterns at vastly different length scales. By using a microwave impedance microscope, we observed an orientation-ordered percolating network in strained Nd(1/2)Sr(1/2)MnO3 thin films with a large period of 100 nanometers. The filamentary metallic domains align preferentially along certain crystal axes of the substrate, suggesting the anisotropic elastic strain as the key interaction in this system. The local impedance maps provide microscopic electrical information of the hysteretic behavior in strained thin film manganites, suggesting close connection between the glassy order and the colossal magnetoresistance effects at low temperatures.

Hierarchy of electronic properties of chemically derived and pristine graphene probed by microwave imaging

Local electrical imaging using microwave impedance microscope is performed on graphene in different modalities, yielding a rich hierarchy of the local conductivity. The low-conductivity graphite oxide and its derivatives show significant electronic inhomogeneity. For the conductive chemical graphene, the residual defects lead to a systematic reduction of the microwave signals. In contrast, the signals on pristine graphene agree well with a lumped-element circuit model. The local impedance information can also be used to verify the electrical contact between overlapped graphene pieces.

Tapping mode microwave impedance microscopy

We report tapping mode microwave impedance imaging based on atomic force microscope platforms. The shielded cantilever probe is critical to localize the tip-sample interaction near the tip apex. The modulated tip-sample impedance can be accurately simulated by the finite-element analysis and the result agrees quantitatively to the experimental data on a series of thin-film dielectric samples. The tapping mode microwave imaging is also superior to the contact mode in that the thermal drift in a long time scale is totally eliminated and an absolute measurement on the dielectric properties is possible. We demonstrated tapping images on working nanodevices, and the data are consistent with the transport results.