Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Anisotropic mechanical properties of α-MoO3 nanosheets

The mechanical behaviors of 2D materials are fundamentally important for their potential applications in various fields. α-Molybdenum trioxide (α-MoO3) crystals with unique electronic, optical, and electrochemical properties, have attracted extensive attention for their use in optoelectronic and energy conversion devices. From a mechanical viewpoint, however, there is limited information available on the mechanical properties of α-MoO3. Here, we developed a capillary force-assisted peeling method to directly transfer α-MoO3 nanosheets onto arbitrary substrates. Comparatively, we could effectively avoid surface contamination arising from the polymer-assisted transfer method. Furthermore, with the help of an in situ push-to-pull (PTP) device during SEM, we systematically investigated the tensile properties of α-MoO3. The measured Young's modulus and fracture strengths along the c-axis (91.7 ± 13.7 GPa and 2.1 ± 0.9 GPa, respectively) are much higher than those along the a-axis (55.9 ± 8.6 GPa and 0.8 ± 0.3 GPa, respectively). The in-plane mechanical anisotropy ratio can reach ∼1.64. Both Young's modulus and the fracture strength of MoO3 show apparent size dependence. Additionally, the multilayer α-MoO3 nanosheets exhibited brittle fracture with interplanar sliding due to poor van der Waals interaction. Our study provides some key points regarding the mechanical properties and fracture behavior of layered α-MoO3 nanosheets.

Extra-High Mechanical and Phononic Anisotropy in Black Phosphorus Blisters

Strain is an effective strategy to modulate the electrical, optical, and optoelectronic properties of 2D materials. Conventional circular blisters could generate a biaxial stretching of 2D membranes with notable strain gradients along the hoop direction. However, such a deformation mode cannot be utilized to investigate mechanical responses of in-plane anisotropic 2D materials, for example, black phosphorus (BP), due to its crystallographic orientation dependence. Here, a novel rectangular-shaped bulge device is developed to uniaxially stretch the membrane, and further provide a promising platform to detect orientation-dependent mechanical and optical properties of anisotropic 2D materials. Impressively, the derived anisotropic ratio of Young's modulus of BP flakes is much higher than the values obtained via the nanoindentation method. The extra-high strain-dependent phononic anisotropy in Raman modes along different crystalline orientations is also observed. The designed rectangular budge device expands the uniaxial deformation methods available, allowing to explore the mechanical, and strain-dependent physical properties of other anisotropic 2D materials more broadly.

Near-Isotropic Local Attosecond Charge Transfer within the Anisotropic Puckered Layers of Black Phosphorus

Black phosphorus possesses useful two-dimensional (2D) characteristics of van der Waals coupled materials but additionally features an in-plane anisotropic puckered layer structure that deviates from common 2D materials. Three distinct directions exist within the lattice of black phosphorus: the in-plane armchair and zigzag directions and the out-of-plane direction, with each distinct phosphorus 3p partial density of states. This structural anisotropy is imprinted onto various collective long-range properties, while the extent to which local electronic processes are governed by this directionality is unclear. At the P L1 edge, the directional selectivity of the core-hole clock method was used to probe the local charge transfer dynamics of electrons excited into the 3p-derived conduction band on an attosecond time scale. Here we show that the surprisingly small anisotropy of 3p electron transfer times reflects the similarly small differences in the 3p-derived unoccupied density of states caused by the underlying phosphorus bonding angles within the puckered layers.

Identifying, Resolving, and Quantifying Anisotropy in ReS2 Nanomechanical Resonators

As an emerging two-dimensional semiconductor, rhenium disulfide (ReS₂ ) is renowned for its strong in-plane anisotropy in electrical, optical, and thermal properties. In contrast to the electrical, optical, optoelectrical, and thermal anisotropies that are extensively studied in ReS₂ , experimental characterization of mechanical properties has largely remained elusive. Here, it is demonstrated that the dynamic response in ReS₂ nanomechanical resonators can be leveraged to unambiguously resolve such disputes. Using anisotropic modal analysis, the parameter space for ReS₂ resonators in which mechanical anisotropy is best manifested in resonant responses is determined. By measuring their dynamic response in both spectral and spatial domains using resonant nanomechanical spectromicroscopy, it is clearly shown that ReS₂ crystal is mechanically anisotropic. Through fitting numerical models to experimental results, it is quantitatively determined that the in-plane Young's moduli are 127 and 201 GPa along the two orthogonal mechanical axes. In combination with polarized reflectance measurements, it is shown that the mechanical soft axis aligns with the Re-Re chain in the ReS₂ crystal. These results demonstrate that dynamic responses in nanomechanical devices can offer important insights into intrinsic properties in 2D crystals and provide design guidelines for future nanodevices with anisotropic resonant responses.

Pull-to-Peel of Two-Dimensional Materials for the Simultaneous Determination of Elasticity and Adhesion

The flexible and clinging nature of ultrathin films requires an understanding of their elastic and adhesive properties in a wide range of circumstances from fabrications to applications. Simultaneously measuring both properties, however, is extremely difficult as the film thickness diminishes to the nanoscale. Here we address such difficulties through peeling by pulling thin films off from the substrates (we thus refer to it as "pull-to-peel"). Particularly, we perform in situ pull-to-peel of graphene and MoS₂ films in a scanning electron microscope and achieve simultaneous determination of their Young's moduli and adhesions to gold substrates. This is in striking contrast to other conceptually similar tests available in the literature, including indentation tests (only measuring elasticity) and spontaneous blisters (only measuring adhesion). Furthermore, we show a weakly nonlinear Hooke's relation for the pull-to-peel response of two-dimensional materials, which may be harnessed for the design of nanoscale force sensors or exploited in other thin-film systems.

Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS2 Nanomechanical Resonators

We report on experimental measurements and quantitative analyses of nonlinear dynamic characteristics in ultimately thin nanomechanical resonators built upon single-layer, bilayer, and trilayer (1L, 2L, and 3L) molybdenum disulfide (MoS₂) vibrating drumhead membranes. This synergistic study with calibrated measurements and analytical modeling on observed nonlinear responses has led to the determination of nonlinear damping and stiffness coefficients at cubic and quintic orders for these two-dimensional (2D) resonators operating in the very high frequency (VHF) band (up to ∼90 MHz). We find that the quintic force can be ∼20% of the Duffing force at larger amplitudes, and thus, it generally cannot be ignored in a nonlinear dynamics analysis. This study provides the first quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators and elucidates their origins and dependency on engineerable parameters, setting a foundation for future exploration and utilization of the rich nonlinear dynamics in 2D nanomechanical systems.

Electrically Tunable MXene Nanomechanical Resonators Vibrating at Very High Frequencies

As an emerging class of two-dimensional (2D) layered nanomaterial, MXene exhibits a number of intriguing properties, such as good electrical conductivity and high elastic modulus, and has witnessed continued growth in related device research. However, nanoscale MXene devices which leverage both the intrinsic electrical and mechanical properties of these 2D crystals have not been experimentally studied. Here we demonstrate nanoelectromechanical resonators based on 2D MXene crystals, where Ti₃C₂T_x drumheads with a wide range of thickness, from more than 50 layers all the way down to a monolayer, exhibit robust nanomechanical vibrations with fundamental-mode frequency f₀ up to >70 MHz in the very high frequency (VHF) band, a displacement noise density down to 52 fm/Hz^1/2, and a fundamental-mode frequency-quality factor product up to f₀ × Q ≈ 6.85 × 10⁹ Hz. By combining experimental results with theoretical calculations, we independently derive the Young's modulus of 2D Ti₃C₂T_x crystals to be 270-360 GPa, in excellent agreement with nanoindentation measurements, based on which we elucidate frequency scaling pathways toward microwave frequencies. We further demonstrate electrical tuning of resonance frequency in MXene resonators and frequency-shift-based MXene vacuum gauges with responsivity of 736%/Torr and detection range down to 10^-4 Torr. Our study can lead to the design and creation of nanoscale vibratory devices that exploit the intrinsic electrical and mechanical properties in 2D MXene crystals.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Effect of stacking order on the vibration properties of bilayer black phosphorus

The effect of the stacking order of bilayer black phosphorus (BLBP) on the vibration properties is investigated by using molecular dynamics (MD) simulation and continuum modelling. The results show that the interlayer shear effect plays a very important role in the vibration behaviours of BLBPs. In MD simulation, a negative shear modulus is found in BLBP nanoresonators with stacking orders AA and AA′, which can decrease the natural frequency of the nanoresonators. The prediction of the natural frequency of the BLBP from the orthotropic sandwich plate model (OSPM) agrees with the MD simulation results very well. Moreover, for the vibration of the high-order mode, the interlayer shear modulus of the OSPM along one direction can mainly influence the natural frequency of the vibration mode, with the antinodes strictly aligning the direction for the BLBP. The results are thus important for understanding the dynamic behaviour of multilayer orthotropic nanostructures and designing multilayer orthotropic nanostructure resonators.

Utilising buckling modes for the determination of the anisotropic mechanical properties of As2S3 nanosheets

The mechanical properties and interfacial behaviour of two-dimensional (2D) materials are crucial for their use in a number of technological applications. In this paper, two buckling modes, wrinkling and buckling delamination, were used to characterize the mechanics of As₂S₃ nanosheets. The plane-strain moduli of As₂S₃ nanosheets along the armchair (AC) and zigzag (ZZ) directions were determined via periodic wrinkles to be 16.7 ± 0.5 GPa and 51.5 ± 1.9 GPa, respectively. This is one of the largest reported anisotropies of in-plane mechanical properties among 2D materials. Using the delaminated buckles, the adhesion energy of few-layer As₂S₃ nanosheets on silicon and polymer (polymethyl methacrylate and polydimethylsiloxane) substrates was determined to be 0.110 ± 0.006 and 0.022 ± 0.002 J m^-2, respectively. A buckling mode map for As₂S₃ nanosheets on different substrates is presented.

Analyzing Anisotropy in 2D Rhenium Disulfide Using Dichromatic Polarized Reflectance

In-plane anisotropy in 2D rhenium disulfide (ReS₂ ) offers intriguing opportunities for designing future electronic and optical devices, and toward such applications, it is crucial to identify the crystal orientation in such 2D anisotropic materials. Existing spectroscopy or electron microscopy methods for determining the crystalline orientation often require complicated sample preparing procedures and specialized equipment, which could sometimes limit their application. In this work, a dichromatic polarized reflectance method is demonstrated, which can quickly and accurately resolve the crystal orientation (Re-Re chain) in 2D ReS₂ crystals with different thicknesses. Furthermore, it can be readily extended to multi-chromatic schemes to achieve greater measurement capability and can be easily tailored to work for different 2D materials. The method offers a simple and effective approach for studying anisotropy in 2D materials.

Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators

Two-dimensional (2D) structures from layered materials have enabled a number of novel devices including resonant nanoelectromechanical systems (NEMS). 2D NEMS resonators are highly responsive to strain, allowing their resonance frequencies to be efficiently tuned over broad ranges, which is a feature difficult to attain in conventional micromachined resonators. In electrically configured and tuned devices, high external voltages are typically required to set and maintain different frequencies, limiting their applications. Here we experimentally demonstrate molybdenum disulfide (MoS₂) nanomechanical resonators that can be reconfigured between different frequency bands with zero maintaining voltage in a non-volatile fashion. By leveraging the thermal hysteresis in these 2D resonators, we use heating and cooling pulses to reconfigure the device frequency, with no external voltage required to maintain each frequency. We further show that the frequency spacing between the bands can be tuned by the thermal pulse strength, offering full control over the programmable operation. Such reconfigurable MoS₂ resonators may provide an alternative pathway toward small-form-factor and low-power tunable devices in future reconfigurable radio-frequency circuits with multi-band capability.

A Novel High-Speed and High-Accuracy Mathematical Modeling Method of Complex MEMS Resonator Structures Based on the Multilayer Perceptron Neural Network

MEMS resonators have become core devices in a large number of fields; however, due to their complex structures, the finite element analysis (FEA) method is still the main method for their theoretical analysis. The traditional finite element analysis method faces the disadvantages of large calculation amount and long simulation time, which limits the development of high-performance MEMS resonators. This paper demonstrates a high-speed and high-accuracy simulation tool based on the artificial neural network, where a multilayer perceptron (MLP) neural network model is constructed. The typical structural parameters of MEMS resonator are used as the input layer, and its performance indicators produced by the finite element analysis method are the output layer. After iteratively trained with 4000 samples, the cumulative error of the neural network decreases to 0.0017 and a prediction network model is obtained. Compared with the finite element analysis results, the structural accuracy error predicted by the neural network model can be controlled within 6%, but its runtime is shortened by 15,000 times. This high-speed and high-accuracy mathematical modeling method can effectively improve the analyzing efficiency and provide a promising tool for the design and optimization of different complex MEMS resonators, which exhibit remarkable accuracy and speed.

Aqueous Affinity and Interfacial Dynamics of Anisotropic Buckled Black Phosphorous

The structure of black phosphorous (BP) is similar to the honeycomb arrangement of graphene, but the layered BP is found to be buckled and highly anisotropic. The buckled surface structure affects interfacial molecule mobility and plays a vital role in various nanomaterial applications. The BP is also known for wettability, droplet formation, stability, and hydrophobicity in the aqueous environment. However, there is a gap concerning the structural and dynamical behavior of water molecules, which is available in abundance for other monoatomic and polyatomic two-dimensional (2D) materials. Motivated by the technological importance, we try to bridge the gap by explaining the surface anisotropy-facilitated behavior of water molecules on bilayer BP using classical and first principles molecular dynamics (MD) simulations. From our classical MD study, we find three distinct layers of water molecules. The water layer closest to the interface is L1, followed by L2 and L3/bulk perpendicular to the BP surface. Water molecules in the L1 layer experience some structural disintegration in hydrogen bond (HB) phenomena compared to the bulk. There is a loss of HB donor-acceptor count per water molecule. The average HB count decreases because of an elevated rate of HB formation and deformation; this would affect the dynamic properties in terms of HB lifetime. Therefore, we observe the reduced lifetime of HB in the layer in close contact with BP, which again complements our finding on the diffusion coefficient of water molecules in distinct layers. Water diffuses relatively faster with diffusion coefficient 3.25 × 10^-9 m² s^-1 in L1, followed by L2 and L3. The BP layer shows moderate hydrophobic nature. Our results also indicate the anisotropic behavior as the diffusion along the x-direction is faster than that along the y-direction. The gap in the slope of the x and y components of mean-squared displacement (MSD) complements the pinning effect in an aqueous environment. We observe blue-shifted and red-shifted libration and O-H stretching modes from the calculated power spectra for the L1 water molecules compared to the L2 and L3 molecules from first principles MD simulations. Our analysis may help understand the physical phenomena that occur during the surface wetting of the predroplet formation process observed experimentally.

Integrated Resonant Micro/Nano Gravimetric Sensors for Bio/Chemical Detection in Air and Liquid

Resonant micro/nanoelectromechanical systems (MEMS/NEMS) with on-chip integrated excitation and readout components, exhibit exquisite gravimetric sensitivities which have greatly advanced the bio/chemical sensor technologies in the past two decades. This paper reviews the development of integrated MEMS/NEMS resonators for bio/chemical sensing applications mainly in air and liquid. Different vibrational modes (bending, torsional, in-plane, and extensional modes) have been exploited to enhance the quality (Q) factors and mass sensing performance in viscous media. Such resonant mass sensors have shown great potential in detecting many kinds of trace analytes in gas and liquid phases, such as chemical vapors, volatile organic compounds, pollutant gases, bacteria, biomarkers, and DNA. The integrated MEMS/NEMS mass sensors will continuously push the detection limit of trace bio/chemical molecules and bring a better understanding of gas/nanomaterial interaction and molecular binding mechanisms.

Mechanics of free-standing inorganic and molecular 2D materials

The discovery of graphene has triggered a great interest in inorganic as well as molecular two-dimensional (2D) materials. In this review, we summarize recent progress in the mechanical characterization of free-standing 2D materials, such as graphene, hexagonal boron nitride (hBN), transition metal-dichalcogenides, MXenes, black phosphor, carbon nanomembranes (CNMs), 2D polymers, 2D metal organic frameworks (MOFs) and covalent organic frameworks (COFs). Elastic, fracture, bending and interfacial properties of these materials have been determined using a variety of experimental techniques including atomic force microscopy based nanoindentation, in situ tensile/fracture testing, bulge testing, Raman spectroscopy, Brillouin light scattering and buckling-based metrology. Additionally, we address recent advances of 2D materials in a variety of mechanical applications, including resonators, microphones and nanoelectromechanical sensors. With the emphasis on progress and challenges in the mechanical characterization of inorganic and molecular 2D materials, we expect a continuous growth of interest and more systematic experimental work on the mechanics of such ultrathin nanomaterials.

Light-Induced Anisotropic Morphological Dynamics of Black Phosphorus Membranes Visualized by Dark-Field Ultrafast Electron Microscopy

Black phosphorus (BP) is an elemental layered material with a strong in-plane anisotropic structure. This structure is accompanied by anisotropic optical, electrical, thermal, and mechanical properties. Despite interest in BP from both fundamental and technical aspects, investigation into the structural dynamics of BP caused by strain fields, which are prevalent for two-dimensional (2D) materials and tune the material physical properties, has been overlooked. Here, we report the morphological dynamics of photoexcited BP membranes observed using time-resolved diffractograms and dark-field images obtained via ultrafast electron microscopy. Aided by 4D reconstruction, we visualize the nonequilibrium bulging of thin BP membranes and reveal that the buckling transition is driven by impulsive thermal stress upon photoexcitation in real time. The bulging, buckling, and flattening (on strain release) showed anisotropic spatiotemporal behavior. Our observations offer insights into the fleeting morphology of anisotropic 2D matter and provide a glimpse into the mapping of transient, modulated physical properties upon impulsive excitation, as well as strain engineering at the nanoscale.

Strain-Engineered Anisotropic Optical and Electrical Properties in 2D Chiral-Chain Tellurium

Atomically thin materials, leveraging their low-dimensional geometries and superior mechanical properties, are amenable to exquisite strain manipulation with a broad tunability inaccessible to bulk or thin-film materials. Such capability offers unexplored possibilities for probing intriguing physics and materials science in the 2D limit as well as enabling unprecedented device applications. Here, the strain-engineered anisotropic optical and electrical properties in solution-grown, sub-millimeter-size 2D Te are systematically investigated through designing and introducing a controlled buckled geometry in its intriguing chiral-chain lattice. The observed Raman spectra reveal anisotropic lattice vibrations under the corresponding straining conditions. The feasibility of using buckled 2D Te for ultrastretchable strain sensors with a high gauge factor (≈380) is further explored. 2D Te is an emerging material boasting attractive characteristics for electronics, sensors, quantum devices, and optoelectronics. The results suggest the potential of 2D Te as a promising candidate for designing and implementing flexible and stretchable devices with strain-engineered functionalities.

Liquefaction of water on the surface of anisotropic two-dimensional atomic layered black phosphorus

The growth and wetting of water on two-dimensional(2D) materials are important to understand the development of 2D material based electronic, optoelectronic, and nanomechanical devices. Here, we visualize the liquefaction processes of water on the surface of graphene, MoS2 and black phosphorus (BP) via optical microscopy. We show that the shape of the water droplets forming on the surface of BP, which is anisotropic, is elliptical. In contrast, droplets are rounded when they form on the surface of graphene or MoS2, which do not possess orthometric anisotropy. Molecular simulations show that the anisotropic liquefaction process of water on the surface of BP is attributed to the different binding energies of H2O molecules on BP along the armchair and zigzag directions. The results not only reveal the anisotropic nature of water liquefaction on the BP surface but also provide a way for fast and nondestructive determination of the crystalline orientation of BP.

Recent progress in black phosphorus and black-phosphorus-analogue materials: properties, synthesis and applications

Black phosphorus (BP), a novel two-dimensional (2D) layered semiconductor material, has attracted tremendous attention since 2014 due to its prominent carrier mobility, thickness-dependent direct bandgap and in-plane anisotropic physical properties. BP has been considered as a promising material for many applications, such as in transistors, photonics, optoelectronics, sensors, batteries and catalysis. However, the development of BP was hampered by its instability under ambient conditions, as well as by the lack of methods to synthesize large-area and high quality 2D nanofilms. Recently, some BP-analogue materials such as binary phosphides (MPx), transition metal phosphorus trichalcogenides (MPX3), and 2D group V (pnictogens) and 2D group VI materials have attracted increasing interest for their unique and stable structures, and excellent physical and chemical properties. This article, which focuses on BP and BP-analogue materials, will present their crystal structure, properties, synthesis methods and applications. Also the similarity and difference between BP and BP-analogue materials will be discussed, and the presentation of the future opportunities and challenges of the materials are included at the end.

Anisotropic buckling of few-layer black phosphorus

When a two-dimensional material, adhered onto a compliant substrate, is subjected to compression it can undergo a buckling instability yielding to a periodic rippling. Interestingly, when black phosphorus (bP) flakes are compressed along the zig-zag crystal direction, the flake buckles forming ripples with a 40% longer period than that obtained when the compression is applied along the armchair direction. This anisotropic buckling stems from the puckered honeycomb crystal structure of bP and a quantitative analysis of the ripple period allows the determination of the Youngs's modulus of few-layer bP along the armchair direction (E_{bP_AC} = 35.1 ± 6.3 GPa) and the zig-zag direction (E_{bP_ZZ} = 93.3 ± 21.8 GPa).

The effect of strain on effective Duffing nonlinearity in the CVD-MoS2 resonator

We demonstrate all electrical measurements on NEMS devices fabricated using CVD grown monolayer MoS2. The as-grown monolayer film of MoS2 on top of the SiO2/Si wafer is processed to fabricate arrays and individual NEMS devices without the complex pick and transfer techniques associated with graphene. The electromechanical properties of the devices are on par with those fabricated using the exfoliation method. The frequency response of these devices is then used as a probe to estimate the linear thermal expansion coefficient of the material and evaluate the effect of strain on the effective Duffing nonlinearity in the devices.

The Opposite Anisotropic Piezoresistive Effect of ReS2

Mechanical strain induced changes in the electronic properties of two-dimensional (2D) materials is of great interest for both fundamental studies and practical applications. The anisotropic 2D materials may further exhibit different electronic changes when the strain is applied along different crystalline axes. The resulting anisotropic piezoresistive phenomenon not only reveals distinct lattice-electron interaction along different principle axes in low-dimensional materials but also can accurately sense/recognize multidimensional strain signals for the development of strain sensors, electronic skin, human-machine interfaces, etc. In this work, we systematically studied the piezoresistive effect of an anisotropic 2D material of rhenium disulfide (ReS₂), which has large anisotropic ratio. The measurement of ReS₂ piezoresistance was experimentally performed on the devices fabricated on a flexible substrate with electrical channels made along the two principle axes, which were identified noninvasively by the reflectance difference microscopy developed in our lab. The result indicated that ReS₂ had completely opposite (positive and negative) piezoresistance along two principle axes, which differed from any previously reported anisotropic piezoresistive effect in other 2D materials. We attributed the opposite anisotropic piezoresistive effect of ReS₂ to the strain-induced broadening and narrowing of the bandgap along two principle axes, respectively, which was demonstrated by both reflectance difference spectroscopy and theoretical calculations.

Anisotropic Thermal Conductivity of Suspended Black Phosphorus Probed by Opto-Thermomechanical Resonance Spectromicroscopy

Atomic layer semiconducting black phosphorus (P) exfoliated from its bulk crystals offers excellent properties and promises for emerging two-dimensional (2D) electronics, photonics, and transducers. It also possesses unique strong in-plane anisotropy among many 2D semiconductors, stemming from its corrugated crystal structure. As an important thermophysical aspect, probing the anisotropic thermal conductivity of black P is essential for device engineering, especially for energy dissipation and thermal management. Here, we report on measurement and analysis of anisotropic in-plane thermal conductivity of black P crystal, in a mechanically suspended device platform, by exploiting a novel opto-thermomechanical resonance spectromicroscopy (OTMRS) technique. With spatially resolved heating effects and thermomechanical resonance motions of suspended structures, anisotropic in-plane thermal conductivity (κ_AC and κ_ZZ) is determined for black P crystals of 10-100 nm thick. This study validates a new noninvasive approach to determining anisotropic thermal conductivity without any requirement of preknowledge of crystal orientation or specific configurations of structure and electrodes according to the anisotropy.

Probing the Physical Origin of Anisotropic Thermal Transport in Black Phosphorus Nanoribbons

Black phosphorus (BP) has emerged as a promising candidate for next-generation electronics and optoelectronics among the 2D family materials due to its extraordinary electrical/optical/optoelectronic properties. Interestingly, BP shows strong anisotropic transport behavior because of its puckered honeycomb structure. Previous studies have demonstrated the thermal transport anisotropy of BP and theoretically attribute this to the anisotropy in both the phonon dispersion relation and the phonon relaxation time. However, the exact origin of such strong anisotropy lacks clarity and has yet to be proven experimentally. Here, the thermal transport anisotropy of BP nanoribbons is probed by an electron beam technique. Direct evidence is provided that the origin of this anisotropy is dominated by the anisotropic phonon group velocity, verified by Young's modulus measurements along different directions. It turns out that the ratio of the thermal conductivity between zigzag (ZZ) and armchair (AC) ribbons is almost same as that of the corresponding Young modulus values. The results from first-principles calculation are consistent with this experimental observation, where the anisotropic phonon group velocity between ZZ and AC is shown. These results provide fundamental insight into the anisotropic thermal transport in low-symmetry crystals.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 μm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS₂), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Piezoelectric effects on the resonance frequencies of boron nitride nanosheets

By using molecular dynamics (MD) simulations, we find in this work that due to the piezoelectric characteristic of boron nitride (BN) nanosheets their resonance frequencies can be efficiently tuned by applying an external electric field. This finding suggests that BN nanosheet can be treated as a good building block for designing novel piezoelectrically tunable two-dimensional nanoresonators. As BN nanosheets possess an inversely stacked structure, the applied electric field has different effects on the resonance frequency of BN nanosheets with odd and even layers. The influence of piezoelectric effect on the vibration behaviours observed in MD simulations is found to significantly deviate from the prediction of the conventional Euler-Bernoulli beam model (EBM), since the EBM cannot account for the weak van der Waals interaction between neighbouring layers in BN nanosheets. To take into account the interlayer interaction in the mathematical modelling of the piezoelectric effect on the vibration of BN nanosheets, we propose here a novel multiple beam model (MBM), which can account for both interlayer stretching and shearing deformations. The MBM result is found to be in a good agreement with the MD result without any additional parameters fitting, which indicates that the present MBM can be treated as a more precise theoretical model in the future study of the vibration properties of BN nanosheets.

Electric Field Stiffening Effect in c-Oriented Aluminum Nitride Piezoelectric Thin Films

Aluminum nitride offers unique material advantages for the realization of ultrahigh-frequency acoustic devices attributed to its high ratio of stiffness to density, compatibility with harsh environments, and superior thermal properties. Although, to date, aluminum nitride thin films have been widely investigated regarding their electrical and mechanical characteristics under alternating small signal excitation, their ultrathin nature under large bias may also provide novel and useful properties. Here, we present a comprehensive investigation of electric field stiffening effect in c-oriented aluminum nitride piezoelectric thin films. By analyzing resonance characteristics in a 2.5 GHz aluminum nitride-based film bulk acoustic resonator, we demonstrate an up to 10% linear variation in the equivalent stiffness of aluminum nitride piezoelectric thin films when an electric field was applied from -150 to 150 MV/m along the c-axis. Moreover, for the first time, an atomic interaction mechanism is proposed to reveal the nature of electric field stiffening effect, suggesting that the nonlinear variation of the interatomic force induced by electric field modulation is the intrinsic reason for this phenomenon in aluminum nitride piezoelectric thin films. Our work provides vital experimental data and effective theoretical foundation for electric field stiffening effect in aluminum nitride piezoelectric thin films, indicating the huge potential in tunable ultrahigh-frequency microwave devices.

Strain-Modulated Bandgap and Piezo-Resistive Effect in Black Phosphorus Field-Effect Transistors

Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for optoelectronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-modulated bandgap significantly alters the density of thermally activated carriers; we for the first time observe a large piezo-resistive effect in black phosphorus field-effect transistors (FETs) at room temperature. The effect opens up opportunities for future development of electromechanical transducers based on black phosphorus, and we demonstrate an ultrasensitive strain gauge constructed from black phosphorus thin crystals.

Hexagonal boron nitride nanomechanical resonators with spatially visualized motion

Atomic layers of hexagonal boron nitride (h-BN) crystal are excellent candidates for structural materials as enabling ultrathin, two-dimensional (2D) nanoelectromechanical systems (NEMS) due to the outstanding mechanical properties and very wide bandgap (5.9 eV) of h-BN. In this work, we report the experimental demonstration of h-BN 2D nanomechanical resonators vibrating at high and very high frequencies (from ~5 to ~70 MHz), and investigations of the elastic properties of h-BN by measuring the multimode resonant behavior of these devices. First, we demonstrate a dry-transferred doubly clamped h-BN membrane with ~6.7 nm thickness, the thinnest h-BN resonator known to date. In addition, we fabricate circular drumhead h-BN resonators with thicknesses ranging from ~9 to 292 nm, from which we measure up to eight resonance modes in the range of ~18 to 35 MHz. Combining measurements and modeling of the rich multimode resonances, we resolve h-BN's elastic behavior, including the transition from membrane to disk regime, with built-in tension ranging from 0.02 to 2 N m^-1. The Young's modulus of h-BN is determined to be E _Y≈392 GPa from the measured resonances. The ultrasensitive measurements further reveal subtle structural characteristics and mechanical properties of the suspended h-BN diaphragms, including anisotropic built-in tension and bulging, thus suggesting guidelines on how these effects can be exploited for engineering multimode resonant functions in 2D NEMS transducers.