Size dependence of Young's modulus in ZnO nanowires

Young's Modulus of Wurtzite and Zinc Blende InP Nanowires

The Young's modulus of thin conical InP nanowires with either wurtzite or mixed "zinc blende/wurtzite" structures was measured. It has been shown that the value of Young's modulus obtained for wurtzite InP nanowires (E_[0001] = 130 ± 30 GPa) was similar to the theoretically predicted value for the wurtzite InP material (E_[0001] = 120 ± 10 GPa). The Young's modulus of mixed "zinc blende/wurtzite" InP nanowires (E_[111] = 65 ± 10 GPa) appeared to be 40% less than the theoretically predicted value for the zinc blende InP material (E_[111] = 110 GPa). An advanced method for measuring the Young's modulus of thin and flexible nanostructures is proposed. It consists of measuring the flexibility (the inverse of stiffness) profiles 1/k(x) by the scanning probe microscopy with precise control of loading force in nanonewton range followed by simulations.

Adhesion contact deformation in nanobridge tests

An accurate grasp of the mechanical properties, especially Young's moduli, of one dimensional nanomaterials plays a crucial role in the design and safe service of flexible electronic devices and implanted biomedical sensors. Nanobridge tests are widely used in the characterization of the mechanical properties of nanowires. In these tests, an atomic force microscope (AFM), functioning as a test machine, exerts a force to bend a nanowire suspended across a trench or a hole with the two ends fixed on a template or substrate. Adhesion contact deformation occurs inevitably during nanobridge testing between the AFM tip and the tested sample, thereby underestimating the Young's modulus of the tested nanowire and causing a pseudo-size effect in the determined Young's modulus. The present work systematically investigates the adhesion contact deformation in nanobridge tests and provides an analytical approach to evaluate the contact deformation and to determine the Young's modulus. To illustrate the developed methodology, AFM nanobridge tests were conducted on gold nanowires (180-340 nm wide, 3.6-5.1 μm long and 90 nm thick). The results indicate that when the contact deformation was taken into consideration, the average Young's modulus increased by 4.63%. Guidelines for minimizing the impact of contact deformation in practical experiments are presented. Furthermore, the results provide insight into the probable causes of the variation in experimentally obtained size-dependencies of Young's moduli of nanowires.

Manipulating Surface States of III-V Nanowires with Uniaxial Stress

III-V compound semiconductors are indispensable materials for today's high-end electronic and optoelectronic devices and are being explored for next-generation transistor logic and quantum technologies. III-V surfaces and interfaces play the leading role in determining device performance, and therefore, methods to control their electronic properties have been developed. Typically, surface passivation studies demonstrated how to limit the density of surface states. Strain has been widely used to improve the electronic transport properties and optoelectronic properties of III-Vs, but the potential of this technology to modify the surface properties still remains to be explored. Here we show that uniaxial stress induces a shift in the energy of the surface states of III-V nanowires, modifying their electronic properties. We demonstrate this phenomenon by modulating the conductivity of InAs nanowires over 4 orders of magnitude with axial strain ranging between -2.5% in compression and 2.1% in tension. The band bending at the surface of the nanostructure is modified from accumulation to depletion reversibly and reproducibly. We provide evidence of this physical effect using a combination of electrical transport measurement, Raman spectroscopy, band-structure modeling, and technology computer aided design (TCAD) simulations. With this methodology, the deformation potentials for the surface states are quantified. These results reveal that strain technology can be used to shift surface states away from energy ranges in which device performance is negatively affected and represent a novel route to engineer the electronic properties of III-V devices.

An open-source platform to study uniaxial stress effects on nanoscale devices

We present an automatic measurement platform that enables the characterization of nanodevices by electrical transport and optical spectroscopy as a function of the uniaxial stress. We provide insights into and detailed descriptions of the mechanical device, the substrate design and fabrication, and the instrument control software, which is provided under open-source license. The capability of the platform is demonstrated by characterizing the piezo-resistance of an InAs nanowire device using a combination of electrical transport and Raman spectroscopy. The advantages of this measurement platform are highlighted by comparison with state-of-the-art piezo-resistance measurements in InAs nanowires. We envision that the systematic application of this methodology will provide new insights into the physics of nanoscale devices and novel materials for electronics, and thus contribute to the assessment of the potential of strain as a technology booster for nanoscale electronics.

On the wurtzite to tetragonal phase transformation in ZnO nanowires

There is a long standing contradiction on the tensile response of zinc oxide nanowires between theoretical prediction and experimental observations. Although it is proposed that there is a ductile behavior dominated by phase transformation, only an elastic deformation and brittle fracture was witnessed in experiments. Using molecular dynamics simulations, we clarified that, as the lateral dimension of zinc oxide nanowires increases to a critical value, an unambiguous ductile-to-brittle transition occurs. The critical value increases with decreasing the strain rate. Factors including planar defects and surface contamination induce brittle fracture prior to the initiation of phase transformation. These findings are consistent with previous atomistic standpoints and experimental results.

The Mechanical Properties of Nanowires

Applications of nanowires into future generation nanodevices require a complete understanding of the mechanical properties of the nanowires. A great research effort has been made in the past two decades to understand the deformation physics and mechanical behaviors of nanowires, and to interpret the discrepancies between experimental measurements and theoretical predictions. This review focused on the characterization and understanding of the mechanical properties of nanowires, including elasticity, plasticity, anelasticity and strength. As the results from the previous literature in this area appear inconsistent, a critical evaluation of the characterization techniques and methodologies were presented. In particular, the size effects of nanowires on the mechanical properties and their deformation mechanisms were discussed.

Facile synthesis of silicon nitride nanowires with flexible mechanical properties and with diameters controlled by flow rate

Ultralong Si₃N₄ nanowires (NWs) were successfully synthesized with size controlled in N₂ gas by using an efficient method. The diameters of the Si₃N₄ NWs increased when the flow rate of N₂ gas increased, with average diameters of 290 nm from flow rates of 100 ml/min, 343 nm from flow rates of 200 ml/min and 425 nm from flow rates of 400 ml/min. Young's modulus was found to rely strongly on the diameters of the Si₃N₄ NWs, decreasing from approximately 526.0 GPa to 321.9 GPa; as the diameters increased from 360 nm to 960 nm. These findings provide a promising method for tailoring these mechanical properties of the NWs in a controlled manner over a wide range of Young's modulus values. Vapour-liquid-solid (VLS) mechanisms were used to model the growth of Si₃N₄ NWs on the inner wall of an alumina crucible and on the surface of the powder mixture. Alumina may be an effective mediator of NW growth that plays an important role in controlling the concentrations of Si-containing reactants to support the growth of NWs on the inner wall of the alumina crucible. This approach offers a valuable means for preparing ultralong Si₃N₄ NWs doped with Al with unique properties.

Defect Engineering: A Path toward Exceeding Perfection

Moving to nanoscale is a path to get perfect materials with superior properties. Yet defects, such as stacking faults (SFs), are still forming during the synthesis of nanomaterials and, according to common notion, degrade the properties. Here, we demonstrate the possibility of engineering defects to, surprisingly, achieve mechanical properties beyond those of the corresponding perfect structures. We show that introducing SFs with high density increases the Young's Modulus and the critical stress under compressive loading of the nanowires above those of a perfect structure. The physics can be explained by the increase in intrinsic strain due to the presence of SFs and overlapping of the corresponding strain fields. We have used the molecular dynamics technique and considered ZnO as our model material due to its technological importance for a wide range of electromechanical applications. The results are consistent with recent experiments and propose a novel approach for the fabrication of stronger materials.

In situ thermomechanical testing methods for micro/nano-scale materials

The advance of micro/nanotechnology in energy-harvesting, micropower, electronic devices, and transducers for automobile and aerospace applications has led to the need for accurate thermomechanical characterization of micro/nano-scale materials to ensure their reliability and performance. This persistent need has driven various efforts to develop innovative experimental techniques that overcome the critical challenges associated with precise mechanical and thermal control of micro/nano-scale specimens during material characterization. Here we review recent progress in the development of thermomechanical testing methods from miniaturized versions of conventional macroscopic test systems to the current state of the art of in situ uniaxial testing capabilities in electron microscopes utilizing either indentation-based microcompression or integrated microsystems. We discuss the major advantages/disadvantages of these methods with respect to specimen size, range of temperature control, ease of experimentation and resolution of the measurements. We also identify key challenges in each method. Finally, we summarize some of the important discoveries that have been made using in situ thermomechanical testing and the exciting research opportunities still to come in micro/nano-scale materials.

A closed form large deformation solution of plate bending with surface effects

We study the effect of surface stress on the pure bending of a finite thickness plate under large deformation. The surface is assumed to be isotropic and its stress consists of a part that can be interpreted as a residual stress and a part that stiffens as the surface increases its area. Our results show that residual surface stress and surface stiffness can both increase the overall bending stiffness but through different mechanisms. For sufficiently large residual surface tension, we discover a new type of instability - the bending moment reaches a maximum at a critical curvature. Effects of surface stress on different stress components in the bulk of the plate are discussed and the possibility of self-bending due to asymmetry of the surface properties is also explored. The results of our calculations provide insights into surface stress effects in the large deformation regime and can be used as a test for implementation of finite element methods for surface elasticity.

A finite-element approach to evaluating the size effects of complex nanostructures

The size effects that reveal the dramatic changes of mechanical behaviour at nanoscales have traditionally been analysed for regular beam systems. Here, the method of using finite-element analysis is explored with the intention of evaluating the size effects for complex nanostructures. The surface elasticity theory and generalized Young-Laplace equation are integrated into a beam element to account for the size effects in classical Euler-Bernoulli and Timoshenko beam theories. Computational results match well with the theoretical predictions on the size effect for a cantilever beam and a cubic unit cell containing 24 horizontal/vertical ligaments. For a simply supported nanowire, it is found that the results are very close to the experimental data. With the assumption that nanoporous gold is composed of many randomly connected beams, for the first time, the size effect of such a complex structure is numerically determined.

Mechanical test method and properties of a carbon nanomaterial with a high aspect ratio

Superior nanomaterials have been developed and applied to many fields, and improved characteristic of nanomaterials have been studied. Measurement of the mechanical properties for nanomaterials is important to ensure the reliability and predict the service life times of products containing nanomaterials. However, it is challenging to measure the mechanical properties of nanomaterials due to their very small dimensions. Moreover, macro-scale measurement systems are not suitable for use with nanomaterials. Therefore, various methods have been developed and used to in an effort to measure the mechanical properties of nanomaterials. This paper presents a review of various evaluation systems and the measurement methods which are used to determine the mechanical properties of carbon nanotube (CNT) and carbon nanofiber (CNF), representatively. In addition, we measured the tensile strength and elastic modulus of the CNT and CNF in the scanning electron microscope (SEM) installed the nano-manipulator and the force sensor and this measurement system and results would be introduced in detail.

Progress in piezo-phototronic effect modulated photovoltaics

Wurtzite structured materials, like ZnO, GaN, CdS, and InN, simultaneously possess semiconductor and piezoelectric properties. The inner-crystal piezopotential induced by external strain can effectively tune/control the carrier generation, transport and separation/combination processes at the metal-semiconductor contact or p-n junction, which is called the piezo-phototronic effect. This effect can efficiently enhance the performance of photovoltaic devices based on piezoelectric semiconductor materials by utilizing the piezo-polarization charges at the junction induced by straining, which can modulate the energy band of the piezoelectric material and then accelerate or prevent the separation process of the photon-generated electrons and vacancies. This paper introduces the fundamental physics principles of the piezo-phototronic effect, and reviews recent progress in piezo-phototronic effect enhanced solar cells, including solar cells based on semiconductor nanowire, organic/inorganic materials, quantum dots, and perovskite. The piezo-phototronic effect is suggested as a suitable basis for the development of an innovative method to enhance the performance of solar cells based on piezoelectric semiconductors by applied extrinsic strains, which might be appropriate for fundamental research and potential applications in various areas of optoelectronics.

Atomic Defects Influenced Mechanics of II-VI Nanocrystals

Mechanical properties of nanocrystals are influenced by atomic defects. Here, we demonstrate the effect of planar defects on the mechanics of ZnO nanorods using atomic force microscopy, high-resolution transmission electron microscopy, and large-scale atomistic simulation. We study two different conditionally grown single nanorods. One contains extended I₁-type stacking fault (SF) and another is defect free. The SF containing nanorods show buckling behaviors with reduced critical loading, whereas the other kinds show linear elastic behavior. We also studied the size dependence of elastic modulus and yield strength. The elastic modulus in both nanorods is inversely proportional to their size. Similar trend is observed for yield strength in the SF containing nanorods; however, the opposite is observed in the SF-free nanorods. This first experimental and theoretical study will guide toward the development of reliable electromechanical devices.

The role of confinement and corona crystallinity on the bending modulus of copolymer micelles measured directly by AFM flexural tests

We present an approach which makes it possible to directly determine the bending modulus of single elongated block copolymer micelles. This is done by forming arrays of suspended micelles onto microfabricated substrates and by performing three-point bending flexural tests, using an atomic force microscope, on their suspended portions. By coupling the direct atomic force microscopy measurements with differential scanning calorimetry data, we show that the presence of a crystalline corona strongly increases the modulus of the copolymer elongated micelles. This large increase suggests that crystallites in the corona are larger and more uniformly oriented due to confinement effects. Our findings together with this hypothesis open new interesting avenues for the preparation of core-templated polymer fibres with enhanced mechanical properties.

Complex tribomechanical characterization of ZnO nanowires: nanomanipulations supported by FEM simulations

In the present work, we demonstrate a novel approach to nanotribological measurements based on the bending manipulation of hexagonal ZnO nanowires (NWs) in an adjustable half-suspended configuration inside a scanning electron microscope. A pick-and-place manipulation technique was used to control the length of the adhered part of each suspended NW. Static and kinetic friction were found by a 'self-sensing' approach based on the strain profile of the elastically bent NW during manipulation and its Young's modulus, which was separately measured in a three-point bending test with an atomic force microscope. The calculation of static friction from the most bent state was completely reconsidered and a novel more realistic crack-based model was proposed. It was demonstrated that, in contrast to assumptions made in previously published models, interfacial stresses in statically bent NW are highly localized and interfacial strength is comparable to the bending strength of NW measured in respective bending tests.

Automated circuit fabrication and direct characterization of carbon nanotube vibrations

Since their discovery, carbon nanotubes have fascinated many researchers due to their unprecedented properties. However, a major drawback in utilizing carbon nanotubes for practical applications is the difficulty in positioning or growing them at specific locations. Here we present a simple, rapid, non-invasive and scalable technique that enables optical imaging of carbon nanotubes. The carbon nanotube scaffold serves as a seed for nucleation and growth of small size, optically visible nanocrystals. After imaging the molecules can be removed completely, leaving the surface intact, and thus the carbon nanotube electrical and mechanical properties are preserved. The successful and robust optical imaging allowed us to develop a dedicated image processing algorithm through which we are able to demonstrate a fully automated circuit design resulting in field effect transistors and inverters. Moreover, we demonstrate that this imaging method allows not only to locate carbon nanotubes but also, as in the case of suspended ones, to study their dynamic mechanical motion.

Integrating carbon nanotubes into electronic devices requires quick and non-invasive imaging of the nanostructures for precision positioning. Here, the authors use the base of the nanotubes to nucleate the growth of optically visible organic nanocrystals, which thus enables simple microscopy.

Effect of a High Density of Stacking Faults on the Young's Modulus of GaAs Nanowires

Stacking faults (SFs) are commonly observed crystalline defects in III-V semiconductor nanowires (NWs) that affect a variety of physical properties. Understanding the effect of SFs on NW mechanical properties is critical to NW applications in nanodevices. In this study, the Young's moduli of GaAs NWs with two distinct structures, defect-free single crystalline wurtzite (WZ) and highly defective wurtzite containing a high density of SFs (WZ-SF), are investigated using combined in situ compression transmission electron microscopy and finite element analysis. The Young's moduli of both WZ and WZ-SF GaAs NWs were found to increase with decreasing diameter due to the increasing volume fraction of the native oxide shell. The presence of a high density of SFs was further found to increase the Young's modulus by 13%. This stiffening effect of SFs is attributed to the change in the interatomic bonding configuration at the SFs.

Flexible, transparent and exceptionally high power output nanogenerators based on ultrathin ZnO nanoflakes

Novel nanogenerator structures composed of ZnO nanoflakes of less than 10 nm thickness were fabricated using a novel method involving a facile synthetic route and a rational design. The fabricated nanogenerators exhibited a short-circuit current density of 67 μA cm(-2), a peak-to-peak open-circuit voltage of 110 V, and an overall output power density exceeding 1.2 mW cm(-2), and to the best of our knowledge, these are the best values that have been reported so far in the literature on ZnO-based nanogenerators. We demonstrated that our nanogenerator design could instantaneously power 20 commercial green light-emitting diodes without any additional energy storage processes. Both the facile synthetic route for the ZnO nanoflakes and the straightforward device fabrication process present great scaling potential in order to power mobile and personal electronics that can be used in smart wearable systems, transparent and flexible devices, implantable telemetric energy receivers, electronic emergency equipment, and other self-powered nano/micro devices.

Determination of Young's modulus of Sb2S3 nanowires by in situ resonance and bending methods

In this study we address the mechanical properties of Sb2S3 nanowires and determine their Young's modulus using in situ electric-field-induced mechanical resonance and static bending tests on individual Sb2S3 nanowires with cross-sectional areas ranging from 1.1·10(4) nm(2) to 7.8·10(4) nm(2). Mutually orthogonal resonances are observed and their origin explained by asymmetric cross section of nanowires. The results obtained from the two methods are consistent and show that nanowires exhibit Young's moduli comparable to the value for macroscopic material. An increasing trend of measured values of Young's modulus is observed for smaller thickness samples.

Nanostructured conducting polymers for stiffness controlled cell adhesion

We propose a facile and reproducible method, based on ultra thin porous alumina membranes, to produce cm(2) ordered arrays of nano-pores and nano-pillars on any kind of substrates. In particular our method enables the fabrication of conducting polymers nano-structures, such as poly[3,4-ethylenedioxythiophene]:poly[styrene sulfonate] (

PEDOT

PSS). Here, we demonstrate the potential interest of those templates with controlled cell adhesion studies. The triggering of the eventual fate of the cell (proliferation, death, differentiation or migration) is mediated through chemical cues from the adsorbed proteins and physical cues such as surface energy, stiffness and topography. Interestingly, as well as through material properties, stiffness modifications can be induced by nano-topography, the ability of nano-pillars to bend defining an effective stiffness. By controlling the diameter, length, depth and material of the nano-structures, one can possibly tune the effective stiffness of a (nano) structured substrate. First results indicate a possible change in the fate of living cells on such nano-patterned devices, whether they are made of conducting polymer (soft material) or silicon (hard material).

Mechanics of aligned carbon nanotube polymer matrix nanocomposites simulated via stochastic three-dimensional morphology

The promise of enhanced and tailored properties motivates the study of one-dimensional nanomaterials, especially aligned carbon nanotubes (A-CNTs), for the reinforcement of polymeric materials. While CNTs have remarkable theoretical properties, previous work on aligned CNT polymer matrix nanocomposites (A-PNCs) reported mechanical properties that are orders of magnitude lower than those predicted by rule of mixtures. This large difference primarily originates from the morphology of the CNTs, because the CNTs that comprise the A-PNCs have significant local curvature commonly referred to as waviness. Here we present a simulation framework capable of analyzing 10(5) wavy CNTs with realistic three-dimensional morphologies to quantify the impact of waviness on the effective elastic modulus contribution of wavy CNTs. The simulation results show that due to the low shear modulus of the reinforcing CNT 'fibers', and large ([Formula: see text]) compliance contribution of the shear deformation mode, waviness reduces the effective stiffness contribution of the A-CNTs by two to three orders of magnitude. Also, the mechanical property predictions resulting from the simulation framework outperform those previously reported using finite element analysis since representative descriptions of the morphology are required to accurately predict properties of the A-PNCs. Further work to quantify the morphology of A-PNCs in three-dimensions, simulate their full non-isotropic constitutive relations, and predict their failure mechanisms is planned.

Young's modulus and Poisson's ratio for TiO2-based nanotubes and nanowires: modelling of temperature dependence

The temperature dependence of the Young's modulus and Poisson's ratio of a number of TiO₂-based four-facetted nanotubes and nanowires are predicted through the calculation of the Helmholtz free energy.

Atomistic investigation into the mechanical behaviour of crystalline and amorphous TiO2 nanotubes

The mechanical properties of titanium dioxide (TiO₂) nanotubes are studied based on molecular dynamics simulations.

Size- and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient of thin films

Surfaces of nanomaterials play an essential role in size-dependent material properties.

Mechanochemical stability of sub-nm ZnO chains

Formation of monoatomic chains by axial stretching of zinc oxide nanowires is investigated using molecular dynamics and supported by density functional calculations.

Strain Loading Mode Dependent Bandgap Deformation Potential in ZnO Micro/Nanowires

The electronic-mechanical coupling in semiconductor nanostructures under different strain loading modes can modulate their photoelectric properties in different manners. Here, we report the systematic investigation on the strain mode dependent bandgap deformation potential of ZnO micro/nanowires under both uniaxial tensile and bending strains at room temperature. Uniaxial stretching-photoluminescence results show that the deformation potential of the smaller ZnO nanowire (with diameter d = 260 nm) is -30.6 meV/%, and is close to the bulk value, whereas it deviates the bulk value and becomes to be -10.6 meV/% when the wire diameter is increased to d = 2 μm. This unconventional size dependence stems from surface effect induced inhomogeneous strain in the surface layer and the core of the ZnO micro/nanowires under uniaxial tension. For bending load mode, the in situ high-resolution transmission electron microscope analysis reveals that the local strain distributes linearly in the bending cross section. Further cathodoluminescence measurements on a bending ZnO microwire (d = 1.8 μm) demonstrate that the deformation potential is -27 meV/%, whose absolute value is much larger than that of the ZnO microwire under uniaxial tension. Further analysis reveals that the distinct deformation potentials originate from the different deforming modes in ZnO micro/nanowires under bending or uniaxial tensile strains. Our results should facilitate the design of flexible optoelectronic nanodevices.

Growth Conditions Control the Elastic and Electrical Properties of ZnO Nanowires

Great efforts have been made to synthesize ZnO nanowires (NWs) as building blocks for a broad range of applications because of their unique mechanical and mechanoelectrical properties. However, little attention has been paid to the correlation between the NWs synthesis condition and these properties. Here we demonstrate that by slightly adjusting the NW growth conditions, the cross-sectional shape of the NWs can be tuned from hexagonal to circular. Room temperature photoluminescence spectra suggested that NWs with cylindrical geometry have a higher density of point defects. In situ transmission electron microscopy (TEM) uniaxial tensile-electrical coupling tests revealed that for similar diameter, the Young's modulus and electrical resistivity of hexagonal NWs is always larger than that of cylindrical NWs, whereas the piezoresistive coefficient of cylindrical NWs is generally higher. With decreasing diameter, the Young's modulus and the resistivity of NWs increase, whereas their piezoresistive coefficient decreases, regardless of the sample geometry. Our findings shed new light on understanding and advancing the performance of ZnO-NW-based devices through optimizing the synthesis conditions of the NWs.

Piezoelectric Size Effects in a Zinc Oxide Micropillar

In this work, the dependence of piezoelectric coefficients (PE) on the size of artificial fabricated ZnO micropillars on Si substrate is investigated. ZnO full film is grown with c-axis orientation and an average grain size of 20 nm at a substrate temperature of 500 °C by pulsed laser ablation. The micropillars with the size range of 1.5 to 7 μm are formed by top-down semiconductor device processing. The PE, characterized by piezoelectric force microscopy (PFM), is found to increase from 18.2 to 46.9 pm/V, when the ZnO pillar size is reduced from 7 to 1.5 μm. The strong PE dependence on ZnO pillar size can be explained by local changes in polarization and reduction of unit cell volume with respect to bulk values. These results have strong implications in the field of energy harvesting, as piezoelectric voltage output scales with the piezoelectric coefficient.

Dependence of Young's modulus on the sodium content within the structural tunnels of a one-dimensional Na-ion battery cathode

We report on the Young's modulus (YM) of single-crystalline Na4Mn9O18 (or Na0.44MnO2) nanowires (NWs), which have shown promise as reversible sodium-ion (Na(+)) intercalation cathodes with high capacity and excellent cyclability. In addition, acid treatment of this material yielded proton stabilized Na(0.44-y)MnO2 (y ∼ 0.23) NWs with a 74% increase in the YM. The tight correlation between YM and ionic content within the crystalline tunnels is particularly significant, since it points to the strong dependence of elastic properties on state-of-charge (SOC) within battery materials.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.

Effects of loading misalignment and tapering angle on the measured mechanical properties of nanowires

Loading misalignment and tapering of nanowires are usually unavoidable factors in compression and tensile mechanical property testing of nanowires. Herein, we report quantitative finite element analyses and experimental measurements on how these two factors affect the measured compression and tensile mechanical properties if they are not included in the data analysis. The results obtained show that ignoring these two factors leads to different degrees of underestimation of the critical load, Young's modulus and tensile fracture strength.

Tunable micro- and nanomechanical resonators

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

Determination of Young's Modulus of Ultrathin Nanomaterials

Determination of the elastic modulus of nanostructures with sizes at several nm range is a challenge. In this study, we designed an experiment to measure the elastic modulus of amorphous Al2O3 films with thicknesses varying between 2 and 25 nm. The amorphous Al2O3 was in the form of a shell, wrapped around GaAs nanowires, thereby forming an effective core/shell structure. The GaAs core comprised a single crystal structure with a diameter of 100 nm. Combined in situ compression transmission electron microscopy and finite element analysis were used to evaluate the elastic modulus of the overall core/shell nanowires. A core/shell model was applied to deconvolute the elastic modulus of the Al2O3 shell from the core. The results indicate that the elastic modulus of amorphous Al2O3 increases significantly when the thickness of the layer is smaller than 5 nm. This novel nanoscale material can be attributed to the reconstruction of the bonding at the surface of the material, coupled with the increase of the surface-to-volume ratio with nanoscale dimensions. Moreover, the experimental technique and analysis methods presented in this study may be extended to measure the elastic modulus of other materials with dimensions of just several nanometers.

Large anelasticity and associated energy dissipation in single-crystalline nanowires

Anelastic materials exhibit gradual full recovery of deformation once a load is removed, leading to dissipation of internal mechanical energy. As a consequence, anelastic materials are being investigated for mechanical damping applications. At the macroscopic scale, however, anelasticity is usually very small or negligible, especially in single-crystalline materials. Here, we show that single-crystalline ZnO and p-doped Si nanowires can exhibit anelastic behaviour that is up to four orders of magnitude larger than the largest anelasticity observed in bulk materials, with a timescale on the order of minutes. In situ scanning electron microscope tests of individual nanowires showed that, on removal of the bending load and instantaneous recovery of the elastic strain, a substantial portion of the total strain gradually recovers with time. We attribute this large anelasticity to stress-gradient-induced migration of point defects, as supported by electron energy loss spectroscopy measurements and also by the fact that no anelastic behaviour could be observed under tension. We model this behaviour through a theoretical framework by point defect diffusion under a high strain gradient and short diffusion distance, expanding the classic Gorsky theory. Finally, we show that ZnO single-crystalline nanowires exhibit a high damping merit index, suggesting that crystalline nanowires with point defects are promising materials for energy damping applications.

Young's Modulus, Residual Stress, and Crystal Orientation of Doubly Clamped Silicon Nanowire Beams

Initial or residual stress plays an important role in nanoelectronics. Valley degeneracy in silicon nanowires (SiNWs) is partially lifted due to built-in stresses, and consequently, electron-phonon scattering rate is reduced and device mobility and performance are improved. In this study we use a nonlinear model describing the force-deflection relationship to extract the Young's modulus, the residual stress, and the crystallographic growth orientation of SiNW beams. Measurements were performed on suspended doubly clamped SiNWs subjected to atomic force microscopy (AFM) three-point bending constraints. The nanowires comprised different growth directions and two SiO2 sheath thicknesses, and underwent different rapid thermal annealing processes. Analysis showed that rapid thermal annealing introduces compressive strains into the SiNWs and may result in buckling of the SiNWs. Furthermore, the core-shell model together with the residual stress analysis accurately describe the Young's modulus of oxide covered SiNWs and the crystal orientation of the measured nanowires.

Band-gap deformation potential and elasticity limit of semiconductor free-standing nanorods characterized in situ by scanning electron microscope-cathodoluminescence nanospectroscopy

Modern field-effect transistors or laser diodes take advantages of band-edge structures engineered by large uniaxial strain εzz, available up to an elasticity limit at a rate of band-gap deformation potential azz (= dEg/dεzz). However, contrary to aP values under hydrostatic pressure, there is no quantitative consensus on azz values under uniaxial tensile, compressive, and bending stress. This makes band-edge engineering inefficient. Here we propose SEM-cathodoluminescence nanospectroscopy under in situ nanomanipulation (Nanoprobe-CL). An apex of a c-axis-oriented free-standing ZnO nanorod (NR) is deflected by point-loading of bending stress, where local uniaxial strain (εcc = r/R) and its gradient across a NR (dεcc/dr = R(-1)) are controlled by a NR local curvature (R(-1)). The NR elasticity limit is evaluated sequentially (εcc = 0.04) from SEM observation of a NR bending deformation cycle. An electron beam is focused on several spots crossing a bent NR, and at each spot the local Eg is evaluated from near-band-edge CL emission energy. Uniaxial acc (= dEg/dεcc) is evaluated at regulated surface depth, and the impact of R(-1) on observed acc is investigated. The acc converges with -1.7 eV to the R(-1) = 0 limit, whereas it quenches with increasing R(-1), which is attributed to free-exciton drift under transversal band-gap gradient. Surface-sensitive CL measurements suggest that a discrepancy from bulk acc = -4 eV may originate from strain relaxation at the side surface under uniaxial stress. The nanoprobe-CL technique reveals an Eg(εij) response to specific strain tensor εij (i, j = x, y, z) and strain-gradient effects on a minority carrier population, enabling simulations and strain-dependent measurements of nanodevices with various structures.

The smallest resonator arrays in atmosphere by chip-size-grown nanowires with tunable Q-factor and frequency for subnanometer thickness detection

A chip-size vertically aligned nanowire (NW) resonator arrays (VNRs) device has been fabricated with simple one-step lithography process by using grown self-assembled zinc oxide (ZnO) NW arrays. VNR has cantilever diameter of 50 nm, which breakthroughs smallest resonator record (>100 nm) functioning in atmosphere. A new atomic displacement sensing method by using atomic force microscopy is developed to effectively identify the resonance of NW resonator with diameter 50 nm in atmosphere. Size-effect and half-dimensional properties of the NW resonator have been systematically studied. Additionally, VNR has been demonstrated with the ability of detecting nanofilm thickness with subnanometer (<10(-9)m) resolution.

Time-domain investigation of the acoustic vibrations of metal nanoparticles: size and encapsulation effects

The acoustic vibrations of single-metal and multi-material nanoparticles are studied by ultrafast pump-probe optical spectroscopy and described in the context of the continuous elastic model. The applicability of this model to the small size range, down to one nanometer, is discussed in the light of recent experimental data and ab initio calculations. Investigations of multi-material nano-objects stress the impact of the intra-particle interface on the characteristics of their vibrational modes, also yielding information on the composition and spatial distribution of the constituting materials.

In situ bending of an Au nanowire monitored by micro Laue diffraction

This article reports on the first successful combination of micro Laue (µLaue) diffraction with an atomic force microscope for in situ nanomechanical tests of individual nanostructures. In situ three-point bending on self-suspended gold nanowires was performed on the BM32 beamline at the ESRF using a specially designed atomic force microscope. During the bending process of the self-suspended wire, the evolution of µLaue diffraction patterns was monitored, allowing for extraction of the bending angle of the nanowire. This bending compares well with finite element analysis taking into account elastic constant bulk values and geometric nonlinearities. This novel experimental setup opens promising perspectives for studying mechanical properties at the nanoscale.

Elastic properties of GaN nanowires: revealing the influence of planar defects on young's modulus at nanoscale

The elastic properties of gallium nitride (GaN) nanowires with different structures were investigated by in situ electron microscopy in this work. The electric-field-induced resonance method was utilized to reveal that the single crystalline GaN nanowires, along [120] direction, had the similar Young's modulus as the bulk value at the diameter ranging 92-110 nm. Meanwhile, the elastic behavior of the obtuse-angle twin (OT) GaN nanowires was disclosed both by the in situ SEM resonance technique and in situ transmission electron microscopy tensile test for the first time. Our results showed that the average Young's modulus of these OT nanowires was greatly decreased to about 66 GPa and indicated no size dependence at the diameter ranging 98-171 nm. A quantitative explanation for this phenomenon is proposed based on the rules of mixtures in classical mechanics. It is revealed that the elastic modulus of one-dimensional nanomaterials is dependent on the relative orientations and the volume fractions of the planar defects.

Size dependence and UV irradiation tuning of the surface potential in single conical ZnO nanowires

Kelvin probe force microscopy (KPFM) is used to measure the surface potential of single conical ZnO nanowires with different diameters.

Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory

Free vibration and mass detection of carbon nanotube-based sensors are studied in this paper. Since the mechanical properties of carbon nanotubes possess a size effect, the nonlocal beam model is used to characterize flexural vibration of nanosensors carrying a concentrated nanoparticle, where the size effect is reflected by a nonlocal parameter. For nanocantilever or bridged sensor, frequency equations are derived when a nanoparticle is carried at the free end or the middle, respectively. Exact resonance frequencies are numerically determined for clamped-free, simply-supported, and clamped-clamped resonators. Alternative approximations of fundamental frequency are given in closed form within the relative error less than 0.4%, 0.6%, and 1.4% for cantilever, simply-supported, and bridged sensors, respectively. Mass identification formulae are derived in terms of the frequency shift. Identified masses via the present approach coincide with those using the molecular mechanics approach and reach as low as 10(-24)kg. The obtained results indicate that the nonlocal effect decreases the resonance frequency except for the fundamental frequency of nanocantilever sensor. These results are helpful to the design of micro/nanomechanical zeptogram-scale biosensor.

Asymmetric surface effect on the configuration of bilayer Si/SiGe nanosprings

This study investigates the asymmetric surface effect on nanosprings composed of Si/SiGe bilayer thin films.

Growth, structure, luminescence and mechanical resonance of Bi2O3nano- and microwires

The growth, morphology, structure and luminescence properties of α-Bi₂O₃hierarchical architectures are reported. The Young moduli and quality factors of the microwires as micromechanical resonators were determined from their resonance frequencies.

Mechanical stability of zinc oxide nanowires under tensile loading: is wurtzite stable at the nanoscale?

New theoretical evidence suggests that ZnO wurtzite nanowires transform to a body-centered-tetragonal structure under tensile loading at 600 K.

Design Concepts, Fabrication and Advanced Characterization Methods of Innovative Piezoelectric Sensors Based on ZnO Nanowires

Micro- and nano-scale materials and systems based on zinc oxide are expected to explode in their applications in the electronics and photonics, including nano-arrays of addressable optoelectronic devices and sensors, due to their outstanding properties, including semiconductivity and the presence of a direct bandgap, piezoelectricity, pyroelectricity and biocompatibility. Most applications are based on the cooperative and average response of a large number of ZnO micro/nanostructures. However, in order to assess the quality of the materials and their performance, it is fundamental to characterize and then accurately model the specific electrical and piezoelectric properties of single ZnO structures. In this paper, we report on focused ion beam machined high aspect ratio nanowires and their mechanical and electrical (by means of conductive atomic force microscopy) characterization. Then, we investigate the suitability of new power-law design concepts to accurately model the relevant electrical and mechanical size-effects, whose existence has been emphasized in recent reviews.