Mechanical properties of silicon nanobeams with an undercut evaluated by combining the dynamic resonance test and finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications.A numerical experimental method of determining resonant frequencies and Young’s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper.Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process,which inevitably generates the undercut of the nanobeam clamping.In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut,dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L,which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data.By using a least-square fit expression including △L,we finally extract Young’s modulus from the measured resonance frequency versus effective length dependency and find that Young’s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon.This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

基于纳米压痕法的多孔硅硬度及杨氏模量与微观结构关系研究

采用电化学腐蚀制备多孔硅，利用场致发射扫描式电子显微镜(field emission scanning electron microscope，FESEM)观测多孔硅的二维微观形貌，利用Nano Indenter XP中的纳米轮廓扫描仪组件(nano profilometry, NP)得到其三维拓扑分析图像，分析了微观结构差异的原因并讨论了多孔硅内部微观结构对其机械性能的影响；利用MTS Nano Indenter XP纳米压入测量仪器，研究了多孔硅的显微硬度和杨氏模量随压入深度的变化规律，比较了不同孔隙率多孔硅的机械性能差别.实验结果测得40mA/cm²，60mA/cm²，80mA/cm²和100mA/cm²四个不同腐蚀电流密度条件下制备多孔硅样品的孔隙率在60%—80%范围内，孔隙率随着腐蚀电流密度的增加而增大；在氢氟酸(HF)浓度为20%的条件下制备出多孔硅样品的厚度在40μm—50μm范围内；测得多孔硅的平均硬度、平均杨氏模量分别在0.478GPa—1.171GPa和10.912GPa—17.15GPa范围内，并且其数值随腐蚀电流密度的增加而减小，在纳米硬度范围内随压入深度的增加而减小，在显微硬度范围内其数值保持相对恒定，分析了样品表面、厚度、微观结构，及环境对其机械性能的影响，得到了多孔硅力学性能随其微观尺度形貌的变化规律. 关键词： 多孔硅 微观结构 硬度 杨氏模量     

Study of the Anisotropic Elastoplastic Properties of β-Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> Films Synthesized on SiC/Si Substrates

The structural and mechanical properties of gallium oxide films grown on silicon crystallographic planes (001), (011), and (111) with a buffer layer of silicon carbide are investigated. Nanoindentation was used to study the elastoplastic properties of gallium oxide and also to determine the elastic recovery parameter of the films under study. The tensile strength, hardness, elasticity tensor, compliance tensor, Young’s modulus, Poisson’s ratio, and other characteristics of gallium oxide were calculated using quantum chemistry methods. It was found that the gallium oxide crystal is auxetic because, for some stretching directions, the Poisson’s ratio takes on negative values. The calculated values correspond quantitatively to the experimental data. It is concluded that the elastoplastic properties of gallium oxide films approximately correspond to the properties of bulk crystals and that a change in the orientation of the silicon surface leads to a significant change in the orientation of gallium oxide.     

Studies on morphology and molecular arrangement of pentacene on different substrates

Pentacene (C₂₂H₁₄) thin films with different thicknesses were fabricated to study the dynamic growth process and morphology of pentacene on different substrates. A discontinuous monomolecular layer was observed when a pentacene thin film is about 0.5 nm thick on native oxide silicon wafer. The terraced islands and dendritic structure gradually formed with increasing pentacene thin film thickness. The height of each layer is about 1.4 nm which corresponds well with the length of the long axis of the pentacene molecule at 1.45 nm. Experimental results show that the pentacene molecule is perpendicular to the silicon wafer surface with a slight tilted angle. However, the pentacene molecular orientation on a polymer pre-covered indium tin oxide coated substrate could not give any indication on the scale of nanometers. The surface roughness of substrates strongly influences pentacene molecular diffusion and the morphology of pentacene thin films.     

掺杂硅纳米梁谐振频率的理论模型及分子动力学模拟

通过理论计算与模拟,研究分析了P元素替代掺杂单晶硅纳米梁的谐振频率.计算模拟了两端固支单晶硅纳米梁的谐振频率随尺寸、掺杂浓度与温度的变化.通过对计算结果与模拟结果的分析得到:单晶硅纳米梁的谐振频率随着硅纳米梁长度尺寸的增大而减小;硅纳米梁的谐振频率随着掺杂浓度的增大而增大,但变化趋势并不明显;最后考虑了温度效应,发现掺杂硅纳米梁的谐振频率随着温度的增大而减小,但从谐振频率的数值来看,硅梁的谐振频率随温度的变化趋势并不明显,即温度对硅梁谐振频率基本无影响.由此得出结论:掺杂浓度与温度对硅纳米梁谐振频率的影响很小,影响单晶硅纳米梁谐振频率的主要因素是尺寸大小,掺杂单晶硅纳米梁的谐振频率具有尺寸效应.     

Erratum to: Superconductivity and spin fluctuations

Based on structure prediction method, the machine learning method is used instead of the density functional theory (DFT) method to predict the material properties, thereby accelerating the material search process. In this paper, we established a data set of carbon materials by high-throughput calculation with available carbon structures obtained from the Samara Carbon Allotrope Database. We then trained a machine learning (ML) model that specifically predicts the elastic modulus (bulk modulus, shear modulus, and the Young’s modulus) and confirmed that the accuracy is better than that of AFLOW-ML in predicting the elastic modulus of a carbon allotrope. We further combined our ML model with the CALYPSO code to search for new carbon structures with a high Young’s modulus. A new carbon allotrope not included in the Samara Carbon Allotrope Database, named Cmcm-C24, which exhibits a hardness greater than 80 GPa, was firstly revealed. The Cmcm-C24 phase was identified as a semiconductor with a direct bandgap. The structural stability, elastic modulus, and electronic properties of the new carbon allotrope were systematically studied, and the obtained results demonstrate the feasibility of ML methods accelerating the material search process.

     

Young's Modulus Characterization of Nano-Level Silicon Nanomembrane

Silicon nanomembrane (SiNM) has drawn great attention for the application in nanoelectrical devices as it shows excellent flexibility and is compatible with the integrated circuit process. The mechanical property measurement of the SiNM with nanoscale thickness is critical. A suspended SiNM (40 nm thick) for mechanical measurements is fabricated by transferring a chemically etched ultrathin monocrystalline silicon film from silicon on insulator wafer to a substrate with a multi-hole array. And then, the atomic force probe is utilized to load force on the free-standing SiNM to obtain a force deflection curve, and then the Young's modulus of such floating SiNM can be directly calculated based on the large deflection plane model. It shows that the Young's modulus of such SiNM is basically consistent with that of the bulk silicon. However, the SiNMs’ floating area significantly affects the results, i.e., the Young's modulus varies with the ratio of the suspended area diameter (i.e., hole diameter) to the film thickness. The Young's modulus is independent of hole diameter when the ratio is greater than 425. According to this relationship, the variation of Young's modulus can be predicted for arbitrary thick SiNMs and any transferable nanofilms.     

Ab initio investigation of the mechanical properties of copper

Employing the ab initio total energy method based on the density functional theory with the generalized gradient approximation, we have systematically investigated the theoretical mechanical properties of copper (Cu). The theoretical tensile strengths are calculated to be 25.3 GPa, 5.9 GPa, and 37.6 GPa for the fcc Cu single crystal in the [001], [110], and [111] directions, respectively. Among the three directions, the [110] direction is the weakest one due to the occurrence of structure transition at the lower strain and the weakest interaction of atoms between the (110) planes, while the [111] direction is the strongest direction because of the strongest interaction of atoms between the (111) planes. In terms of the elastic constants of Cu single crystal, we also estimate some mechanical quantities of polycrystalline Cu, including bulk modulus B, shear modulus G, Young’s modulus E p , and Poisson’s ratio ν.     

Ab initio investigation of the pressure influence on elastic properties of the GaS layered compound

From first principles, in the pressure range of 0–20 GPa, taking into account the structural phase transition at 3 GPa, all independent elastic constants of GaS compound have been calculated. From obtained data, the pressure dependences of the velocities of propagation of elastic waves in different symmetry directions have been determined. The values of averaged elastic moduli, Young’s modulus and Poisson’s ratio and their pressure dependence have also been calculated..     

First-principles investigation of the equation of state and elastic properties of perovskite-type SrW(O,N)<Subscript>3</Subscript> under hydrostatic pressures up to 139 GPa

Pressure dependence of the structural and elastic properties of perovskite-type cubic SrWO_2.05N_0.95 was studied using firstprinciples density functional theory (DFT) utilizing the plane wave pseudopotential and the exchange-correlation functionals within the generalized gradient approximation. The estimated bulk modulus and its pressure derivative values from the P ? V data fitted to the third-order Birch-Murnaghan equation of state were close to the data obtained from the independent elastic constants. Based on the generalized Born stability criteria, SrWO_2.05N_0.95 is mechanically stable up to 139 GPa. The influence of hydrostatic pressure (0 to 139 GPa) on the bulk modulus, shear modulus, Young’s modulus, Pugh’s modulus ratio, Poisson’s ratio, Vickers hardness, sound velocities, Debye temperature, Debye-Grüneisen parameter, minimum thermal conductivity and elastic anisotropy of SrWO_2.05N_0.95 was particularly studied in detail. It was found that SrWO_2.05N_0.95 is a ductile and hard solid with large bulk, shear and Young’s modulus and displays an extraordinary low thermal conductivity. Since there are not any experimental or theoretical data available for comparison the results of the present study have revealed an important fundamental information about the elastic properties of perovskite-type cubic SrWO_2.05N_0.95 for future experimental studies.     

Elasticity and inelasticity of the SiC/Al-13Si-9Mg biomorphic metal ceramics

The acoustic investigations of the elastic (Young’s modulus) and microplastic properties of a composite material, the SiC/Al-13Si-9Mg biomorphic metal ceramic, were performed. The ceramic was prepared by infiltration of the Al-13Si-9Mg melt into porous silicon carbide derived from wood of two species of trees, beech and sapele. The measurements were performed with a composite piezoelectric vibrator under resonance conditions, with rod-shaped samples vibrated longitudinally at about 100 kHz over a wide range of vibrational strain amplitudes, which included both the linear (amplitude-independent) and nonlinear (microplastic) regions. It was shown that the Young’s modulus and the microplastic properties of the composite are anisotropic and depend substantially on the tree species, particularly when longitudinal vibrations are excited in samples cut along the tree fibers.     

杨氏弹性模量测量的设计性实验

首先分析指出杨氏弹性模量测量作为设计性实验符合设计性实验的选题原则;然后,简介测量金属丝伸长量的几种方案,通过不确定度分析,指出进一步提高杨氏弹性模量测量精度的关键;最后,总结了本设计性实验的意义.     

Features of atomic and electronic structure of oxides on porous silicon surface according to XANES data

Based on synchrotron research of the fine structure main parameters of SiL _{2, 3} X-ray absorption edges (X-ray absorption near edge structure (XANES)) in porous silicon on boron-doped Si(100) wafers, the thickness of the surface oxide layer and the degree of distortions of the silicon-oxygen tetrahedron in this layer were estimated. The thickness of the oxide layer formed on the amorphous layer coating nanocrystals of porous silicon exceeds the thickness of the native oxide on the surface of Si(100) : P and Si(100) : B single-crystal (100) silicon wafers by several times. Distortion of the silicon-oxygen tetrahedron, i.e., the basic unit of silicon oxide, is accompanied by Si-O bond stretching and an increase in the angle between Si-O-Si bonds.     

Characterization of new cellulose sansevieria ehrenbergii fibers for polymer composites

Natural cellulose fibers were newly identified from the sources of sansevieria ehrenbergii plant. These fibers were extracted using the mechanical decortication process. The hierarchical cell structure of the plant and fibers was analyzed using scanning electron microscope, optical microscope, Fourier transforms infrared, and X-ray diffraction. The density and diameter of the fibers were found to be approximately 0.887?g/cm³ and 10–250?μm, respectively. The various chemical compositions were analyzed and compared with other natural fibers. The thermal stability of the fiber was examined through thermogravimetric analysis/differential thermogravimetric analysis (DTG). The maximum peak temperature was obtained at 333.02?°C in DTG curve. The raw fibers exhibited a tensile strength of 50–585?MPa, an elongation at break of 2.8–21.7%, a Young’s modulus of 2.5–7.5?GPa, and a corrected compliances Young’s modulus of 2.5–7.8?GPa.     

尺寸相关的弹性常数对应变硅纳米线电学性质的影响

从Keating模型出发,基于离散化思想建立了计算单晶硅纳米线弹性常数和杨氏模量的半连续原子晶格力学模型. 从微扰理论和形变势理论出发,采用有限差分方法建立了计算不同晶向应变硅纳米线价带结构的数值模型. 结合上述的两个计算模型,进而应用经典弹道传输模型研究了轴向应力和弹性常数对p型硅纳米线弹道晶体管电学特性的影响. 研究结果表明,硅纳米线的弹性常数和杨氏模量呈现尺寸效应,该结果与分子动力学的模拟结果具有很好的一致性. 同时发现尺寸相关的弹性常数对硅纳米线晶体管输运电流的影响强烈依赖于单轴应力对输运电流的影 关键词： 应变硅纳米线 弹性常数 弹道电流 价带结构模型     

钙钛矿结构ZrBeO3稳定性的第一性原理研究

基于密度泛函理论构建了钙钛矿结构ZrBeO3晶体模型,计算了该晶体模型结合能,表明了该构型热力学稳定性;计算出该结构在不同压力下的弹性常数,并据此计算了ZrBeO3的体积模量、剪切模量、杨氏模量、泊松比、BH/GH(体模量/剪切模量)等参数,结果表明该材料具有机械稳定性,随着等静压力增加,材料由脆性向韧性转变;计算了零压下ZrBeO3的硬度,为34.5 GPa,表明该结构晶体应为超硬材料;计算了ZrBeO3的声子能谱,结果表明ZrBeO3在低温零压下热动力学不稳定,为此分析比较了不同压力下的声子能谱、不同原子轨道及化学键布居值,研究表明随着压力增加,Be原子sp杂化后形成的Be-O共价键成分增强、Zr-O键离子键成分增强,晶格动力学趋于稳定。     

Modification of the Mechanical Properties of Core-Shell Liquid Gallium Nanoparticles by Thermal Oxidation at Low Temperature

Gallium nanoparticles (Ga NPs) are attracting increasing attention because of their appealing physical-chemical properties. In particular, their mechanical properties play a key role in the implementation of these core-shell structures on certain applications, such as soft and stretchable electronics. Thus, efforts are being addressed to modulate them mainly by chemical means. In contrast, this study investigates how the mechanical properties of the outer gallium thin oxide shell change when its thickness is increased through a thermal oxidation strategy. Specifically, as-deposited Ga NPs, as well as those subjected to thermal oxidation at 300 °C for three different times, are studied by performing single-particle indentations by atomic force microscopy over a wide range of NP radius. This analysis helps to confirm that the Reissner's thin-shell model for small deformations within the elastic regime is obeyed. From these data, the dependence of the shell stiffness and the Young's modulus of the gallium oxide on the thermal treatment is obtained. It is found that the shell stiffness increases with the annealing time, even by a factor of 50 under prolonged thermal oxidation, while the gallium oxide Young's modulus, close to 30 GPa, does not change significantly.     

Internal friction and Young’s modulus of a carbon matrix for biomorphic silicon carbide ceramics

The amplitude, temperature, and time dependences of the Young’s modulus and internal friction (ultrasonic attenuation) of a eucalyptus-based carbon biomatrix intended for preparing biomorphic silicon carbide ceramics were studied. Adsorption and desorption of molecules of the ambient medium (air) was shown to determine, to a considerable extent, the effective Young’s modulus and acoustic vibration decrement of a specimen. A doublet maximum in the temperature dependence of ultrasonic attenuation was observed at a temperature close to the sublimation temperature of solid CO₂. The microplastic properties of the material were estimated from acoustic measurement data.     

Measurement of the elastic moduli of dense layers of oriented carbon nanotubes by a scanning force microscope

A technique is developed for measuring the modulus of elasticity of a material with a Nanoscan scanning force microscope on the basis of measuring the dependence of probe vibration frequency on the penetration depth of the needle into the specimen. This technique makes it possible to study materials with elastic moduli from 50 to 1000 GPa. The Young moduli of dense films of carbon nanotubes oriented at angles of 45° and 90° to the quartz substrate are measured. From their ratio, the Young modulus in the direction perpendicular to the tubes and the anisotropy of the elastic moduli are determined. A comparison of these values with the corresponding values obtained for a nanotube film deposited on a silicon substrate is carried out. On the basis of this comparison, a conclusion is made concerning the interaction between single-layer nanotubes and between nanotubes in a mixture of single-layer and multilayer ones.     

Nanoindentation study of Cu52Zr37Ti8In3 bulk metallic glass

In this paper, Cu₅₂Zr₃₇Ti₈In₃ bulk metallic glass has been studied by nanoindentation. Three different ways for nanoindentation tests were employed. Load-control nanoindentation was used to investigate the effect of the loading rate on the hardness and Young’s modulus. Young’s modulus of the specimen shows a loading rate dependence. The constant-load indentation creep measurement was performed. The creep data were fitted with the generalized Kelvin model, and the compliance spectrum and retardation spectrum were derived. Furthermore, the storage compliance and loss compliance were also discussed. For characterizing the change of the hardness and Young’s modulus with increasing indentation depth, depth-control nanoindentation analysis was conducted. The results show that both the hardness and Young’s modulus decrease with nanoindentation depth.