A new technique for producing large-area as-deposited zero-stressLPCVD polysilicon films: the MultiPoly process

Polysilicon films deposited by low-pressure chemical vapor deposition (LPCVD) exhibit tensile or compressive residual stresses, depending on the deposition temperature. Polysilicon films composed of alternating tensile and compressive layers can display any overall stress value between those of the individual layers, including a state of zero overall residual stress, depending on the relative thickness of each layer. The residual stress gradient can be similarly controlled by the layer thicknesses and distribution. This has been demonstrated with a ten-layer near-zero stress (<10 MPa), near-zero stress gradient (⩽0.2 MPa/μm) polysilicon film, containing flat cantilever beams whose length-thickness ratios exceed 150. Using multilayer deposition to control the stresses and stress gradients of polysilicon films is termed the MultiPoly process     

薄膜热膨胀系数测试技术研究

热膨胀系数是薄膜的重要热学性能参数,也是薄膜热应力和残余应力计算分析过程中的关键数据.文章基于热诱导弯曲原理,分别采用单基片法和双基片法对氮化钛(TiN)和铝(Al)薄膜的热膨胀系数进行测试,并着重对双基片法的测试误差和适用性进行了分析.研究结果表明,薄膜在不同材质基底上弹性模量的差异是影响双基片法薄膜热膨胀系数测试精度的重要因素.当不同材质基片上薄膜弹性模量差异较小时,双基片法测得的热膨胀系数与单基片法所获结果基本一致;而当不同材质基片上薄膜弹性模量相差较大时,双基片法将不再适用.此外,文章结合薄膜的形貌、结构和残余应力表征测试,对TiN和Al薄膜热膨胀系数与其块体材料的差异进行了分析,结果显示残余压应力会导致薄膜热膨胀系数增大,而残余拉应力则具有相反的效果.     

Determination of residual stress in deep submicron thick films by the critical buckling technique of annular thin plates

Critical buckling of annular plates has been proposed to measure residual stress in thin films with submicron thickness and succeeds in measuring stress ranging from decades of MPa to hundreds of MPa. In this paper, critical buckling of annular plates was further researched in order to enhance their sensitivity, and improved structures were proposed to measure ultra small residual stress in scale of several MPa. Specimens of improved annular structures with thickness down to 200 nm were prepared on silicon-on-insulator wafer, and released in hydrofluoric HF solution to get the critical etching length under an on line monitoring system. The critical etching length was inputted into the ANSYS software to predict the residual stress by the eigenvalue buckling analysis. Small compressive stress of 3.07 MPa within 100 nm film was resolved successfully with this improved annular structure, but the micro rotating structures fabricated in the same die cannot generate a distinguishable deformation.     

Fracture Properties of Silicon Carbide Thin Films by Bulge Test of Long Rectangular Membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mum were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 plusmn 47 and 201 plusmn 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 plusmn 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 plusmn 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 plusmn 0.88 and 3.16 plusmn 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mum-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mum-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws. [2007-0191].     

Continuum damage model for orthotropic materials: Application to masonry

This paper contributes to the formulation of continuum damage models for orthotropic materials under plane stress conditions. Two stress transformation tensors, related to tensile and compressive stress states, respectively, are used to establish a one-to-one mapping relationship between the orthotropic behaviour and an auxiliary model. This allows the consideration of two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the mapped space makes use of two scalar variables which monitor the local damage under tension and compression, respectively. The model affords the simulation of orthotropic induced damage, while also accounting for unilateral effects, thanks to a stress tensor split into tensile and compressive contributions. The fundamentals of the method are presented together with the procedure utilized to adjust the model in order to study the mechanical behaviour of masonry material. The validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry at the material level.     

Modeling of mechanical properties and bond relationship using data mining process

Reinforced concrete is a widely used construction material. Its properties depend on the bond between the reinforcing bar and concrete as much as the compressive strength or properties of the reinforcing bar because of component of construction expose to both flexural and bond together compressive loads. In this paper, the bond properties of concretes with different mix designs were investigated according to the results of compressive, flexural, bond, and flexural-bond tests. The data mining (DM) process was used to determine relationships among the test results and DM algorithms. Seventeen modeling techniques within WEKA were applied to the experimental data for the prediction of bond properties.The results show that the implemented models were good at predicting the bond properties. The best results were obtained from the RepTree algorithm for bond strength, the Multilayer Perceptron algorithm for flexural-bond strength, the MedSq algorithm for bond slippage, and the Pace Regression for flexural-bond deformation. Bond and flexural-bond can be easily predicted using the compressive strength, flexural strength and tensile stress of the rebar. Although a relationship is also existent between these and bond slippage and flexural-bond deformation, these relationships are weaker than the others.These results suggested that the DM algorithms can be used as an alternative approach to predict the bond strength using the results of compressive, flexural, bond, and flexural-bond tests as input parameters. The predictions of the bond slippage and flexural-bond deformation models poorly agreed with the experimental results. It can be obtained more successful results for these variables, when DM models with different inputs like the rebar-concrete interface stress together the measured parameters are used.     

Effect of substrate�Ctarget distance and sputtering pressure in the synthesis of AlN thin films

In this work, we analyze the influence of the processing pressure and the substrate?Ctarget distance on the synthesis by reactive sputtering of c-axis oriented polycrystalline aluminum nitride thin films deposited on Si(100) wafers. The crystalline quality of AlN has been characterized by high-resolution X-ray diffraction (HR-XRD). The films exhibited a very high degree of c-axis orientation especially when a low process pressure was used. After growth, residual stress measurements obtained indirectly from radius of curvature measurements of the wafer prior and after deposition are also provided. Two different techniques are used to determine the curvature??an optically levered laser beam and a method based on X-ray diffraction. There is a transition from compressive to tensile stress at a processing pressure around 2?mTorr. The transition occurs at different pressures for thin films of different thickness. The degree of c-axis orientation was not affected by the target?Csubstrate distance as it was varied in between 30 and 70?mm.     

Finite element analysis of residual stress induced by shot peening process

The aircraft industry has only recently begun to explore possible application of welding as an alternative joining method for the design of future large civil airliner wing. One of the main obstacles, encountered in the past years, to welding application within the aircraft industries were due to failure in the weldments, caused by high tensile residual stresses present in the region of the weld, reducing drastically fatigue strength of welded joints. Improvement in the fatigue life of the welded joint can be obtained if compressive residual stresses are introduced at the weld region.Shot peening is a manufacturing process intended to give aircraft structures the final shape and to introduce a compressive residual state of stress inside the material in order to increase fatigue life. This paper presents the modeling and simulation of the residual stress field resulting from the shot peening process. The results achieved show that a significant decrease of welding induced tensile residual stress magnitude can be obtained. Good agreement between experimental and numerical results was achieved.     

A micro strain gauge with mechanical amplifier

A passive micro strain gauge with a mechanical amplifier has been designed, analyzed, and tested. The mechanical amplifier provides a high gain such that residual strain in thin films can be directly measured under an optical microscope. This strain gauge can be in situ fabricated with active micro sensors or actuators for monitoring residual strain effects, and both tensile and compressive residual strains can be measured via the strain gauge. It is shown that a very fine resolution of 0.001% strain readouts can be achieved for a micro strain gauge with a 500 μm-long indicator beam. Beam theories have been used to analyze the strain gauge with a mechanical amplifier, and the results were verified by a finite-element analysis. Experimental measurements of both polysilicon and silicon-riched silicon-nitride thin films fabricated by surface micromachining processes are presented     

Asymmetric buckling of bimodulus thick annular plates

An annular element with Lagrangian polynomials and trigonometric functions as shape functions is developed for asymmetric finite element stability analysis. The annular element is based on the Mindlin plate theory so that the effect of transverse shear deformation is included. Using the asymmetric finite element model, the asymmetric static buckling of bimodulus thick annular plates subjected to a combination of a pure bending stress and compressive normal stress is investigated. The obtained results of non-dimensional critical buckling coefficients are shown to be very accurate when compared with the exact solutions. The effects of various parameters on the buckling coefficients are studied. The bimodulus properties are shown to have significant influences on the buckling coefficients.     

Effect of residual stress on RF MEMS switch

Studies have been carried out on a RF MEMS shunt switch to analyze the effect of residual stress on its electromechanical characteristics. This paper presents the simulated results as well as theoretically calculated results of a shunt switch due to the presence of residual stress gradient in respect of resonant frequency, pull down voltage and switching characteristics. The effect of introduction of holes in the beam is also studied. The calculated results, corresponding to the switch (without holes) at zero residual stress, of resonant frequency, pull-down voltage and switch on and off time are 28.14 kHz, 28.2 V, 16.35 μsec and 8.6 μsec respectively. Modal analysis of the both the structures (with and without holes) are carried out for different values of residual stress gradients. Modal analysis predicted that higher values of tensile stress gradient are not favorable for switching action. The pull-down voltages and switch on and off times are simulated at different stress gradients. With the increase in compressive stress gradient, the pull-down voltage is found to increase, whereas, switch on and off times is decreased. Corresponding to −20 MPa/μm residual stress gradient, the resonant frequency, pull-down voltage and switch on and off times are found to be 74.5 kHz, 63.5 V, 7.5 μsec and 3.36 μsec respectively. Introduction holes in the structure modified these values to 63.77 kHz, 53.1 V, 8.7 μsec, 3.92 μsec respectively.     

Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage

In this paper, a novel method has been developed to control the pull-in voltage of the fixed-fixed and cantilever MEM actuators and measure the residual stress in the fixed-fixed model using of the piezoelectric layers that have been located on the upper and lower surfaces of actuator. In the developed model, the tensile or compressive residual stresses, fringing-field and axial stress effects in the fixed-fixed end type micro-electro-mechanical systems actuator have been considered. The non-linear governing differential equations of the MEM actuators have been derived by considering the piezoelectric layers and mentioned effects. The results show that due to different applied voltage to the piezoelectric layers, the pull-in voltage can be controlled and in the fixed-fixed type the unknown value of the residual stress can be obtained.     

Comparison of hybrid-stress element through-thickness distributions corresponding to a high-order plate theory

A study using the hybrid-stress model is presented to assess various through-thickness element stress distributions to be used in conjunction with a high-order plate theory. The plane-strain example problem of a semi-infinite plate under transverse sinusoidal loading is chosen so that a computationally efficient comparison of the stress assumptions can be made using 2-D plane-strain elements. The displacement assumption for all elements allows for inplane and transverse displacements which are cubic and quadratic, respectively. On the basis of results obtained in this pilot study, recommendations are made for extensions to single- or multi-layer thick plate elements.     

A new technique for measuring the mechanical properties of thinfilms

Accurate measurement of mechanical properties is very difficult for films that are only a few microns thick. Previously, these properties have been determined by indirect methods such as cantilever beam and diaphragm bulge tests. This paper presents a new technique to measure the Young's modulus of thin films in a direct manner consistent with its definition. Strain is measured by a laser-based technique that enables direct and accurate recording of strain on a thin-film specimen. Load is recorded with a 1-lb load cell, and an air bearing is used to eliminate friction in the loading system. The specimen is phosphorus-doped polysilicon that has a gage cross section of 3.5 μm thick by 600 μm wide. All 29 uniaxial tensile tests show brittle behavior, and the average values of Young's modulus and fracture strength are measured to be 170±6.7 GPa and 1.21±0.16 GPa, respectively. One fatigue test is also reported in this paper     

纳米压痕法对304不锈钢残余应力的研究

利用纳米压痕法研究了304不锈钢的残余应力,采用Suresh理论模型恒定载荷时的公式计算残余应力,最大加载载荷依次为500μN、1 000μN、1 500μN、2 000μN、2500μN。结果表明,不锈钢硬度和弹性模量为定值,退火前后的硬度分别为5.3GPa和4.0 GPa,弹性模量分别为110 GPa和100 GPa。利用Ansys分析软件模拟了压痕过程,发现不锈钢在受压过程中有Sink-in现象发生。纳米压痕法测得了未退火不锈钢存在残余压应力,大小为381 MPa;用XRD测得了未退火不锈钢中有350 MPa±23 MPa的残余压应力,两种测量结果吻合良好,说明了纳米压痕法在残余应力测试时的准确性与可靠性。     

Focused ion beam core hole drilling for stress detection in thin-films

Since excessive stress in deposited thin-films may result in a delamination of these films, a low internal stress level is desirable. State of technology for measuring internal stress in bulk materials is the hole-drilling method. This paper investigates the application of the hole-drilling method to thin-films using a focused ion beam (FIB) for creating micro holes. With the FIB, a hole of about 20 μm in diameter is cut into a thin-film structure. The film thickness may be up to a couple of micrometers. By comparing the FIB cutting geometry and the resulting hole diameter, the stress level of the thin-film may be derived. This typically fails in the case of compressive stress. For films under tensile stress, the feasibility of the detection is shown.     

Geometrically non-linear free vibrations of clamped simply supported rectangular plates. Part I: the effects of large vibration amplitudes on the fundamental mode shape

The geometrically non-linear free vibrations of thin isotropic and laminated rectangular composite plates with fully clamped edges have been successfully investigated in previous series of works using a theoretical model based on Hamilton’s principle and spectral analysis. The objective of this work is the extension of the above model to the case of clamped clamped simply supported simply supported rectangular plates, denoted by CCSSSSRP, in order to determine their fundamental non-linear mode shape, and associated amplitude-dependent resonant frequencies, and flexural stress distribution. Numerical data are given for both linear and non-linear analysis, for various plate aspect ratios and vibration amplitudes. Good agreement was found with previous published results.     

Process Temperature–Dependent Mechanical Properties of Polysilicon Measured Using a Novel Tensile Test Structure

A new test structure was developed to measure three major unknown mechanical parameters of deposited thin films, i.e., fracture strength, Young's modulus, and residual stress. The structure was designed to have plural specimens of a deposited thin film bridging the gap of the silicon substrate and enables the easy and efficient tensile testing of the film. It was used to measure those parameters of various polysilicon films. Polysilicon is commonly used as a structural material of microelectromechanical systems (MEMS) after being deposited at a temperature below 600 degC and annealed at a temperature around 1000 degC to remove the residual stress. On the other hand, polysilicon can be also deposited at a temperature higher than 600 degC. The three parameters of polysilicon films depend on process temperature and were evaluated using the new test structure. Concerning the strength, films deposited at 560 degC had the highest strength when annealed at 850 degC. Films deposited at 625 degC and annealed at 1050 degC were weaker than those deposited at 560 degC and annealed at 1050 degC. Young's modulus was found to behave in a similar way. The trend of the residual stress was the same as already reported, but its local evaluation was possible in combination with the tensile strength determination     

Optical micro-paddle beam deflection measurement for electrostatic mechanical testing of nano-scale thin film application to MEMS

The authors describe their design for a paddle-like cantilever beam sample to relieve non-uniform stress distribution in beam-bending tests of the mechanical properties of thin film applications to MEMS. We added the sample to a custom-designed system equipped with an electrostatic panel and optical interferometer. The system overcomes problems associated with using nano-indentation for testing, and reduces errors tied to the amount of contact force required to bend the beam. Accurate paddle cantilever beam deflection was obtained using a four-step phase-shifting process with a Michelson interferometer. Film strain was determined using a simple force equilibrium equation. Residual stresses were measured at −41.3 MPa for 150 nm silver film, −3.2 MPa for 150 nm gold film, and −16.8 MPa for 150 nm copper film. We observed residual stresses for copper films at different thicknesses. The results indicate high tensile stress forms during the early deposition stage for thin copper film due to grain coalescence, and a decrease in stress with an increase in film thickness. In copper films with thicknesses greater than 153 nm, lattice relaxation associated with the surface mobility of metallic atoms changed residual stress from tension to compression.     

Mechanical characterization of post-buckled micro-bridge beams by micro-tensile testing

A micro-tensile testing system has been developed to measure the mechanical properties of post-buckled silicon dioxide micro-bridge beams. A kind of vernier-groove carrier is presented to improve alignment precision and repeatability of the measurement, and the stiffness coefficient of the tensile system is calibrated in situ in order to obtain the deformation of the tensile beams. Through analyzing a series of stress states in the beam over film preparation, post-buckling and unfolding of the beam, the initial residual stress in the film is obtained from the original load–displacement curves. The residual stress of 354 MPa is consistent with that calculated from the theory of finite deflection of buckled beams. Young’s modulus and tensile fracture strength are also obtained from the load–displacement curves. The measured modulus and strength are 64.6 ± 3 GPa and 332–489 MPa respectively. The measured properties of the thermal silicon dioxide film are reasonably coherent with other reports.