Determination of the Elastic Properties of Au5Sn and AuSn from Ab Initio Calculations

Elastic constants of single-crystal Au₅Sn and AuSn were determined through ab␣initio calculations to characterize their polycrystalline elastic behavior and elastic anisotropy. The ideal bulk (K = 127 GPa), shear (G = 28 GPa), and Young’s modulus (E = 78 GPa), as well as Poisson’s ratio (v = 0.398), of Au₅Sn were determined using the Voigt–Reuss–Hill method and were very close to the range of experimental results; the values of AuSn were 88 GPa, 15 GPa, 42 GPa, and 0.420, but its ideal Young’s modulus was much smaller than the experimentally obtained values. This unusual discrepancy in the Young’s modulus of AuSn is probably attributed to its extraordinarily high anisotropy in Young’s modulus, with a 95 GPa difference between its maximum and minimum values. Au₅Sn exhibits relatively low anisotropy in Young’s modulus with a maximum-minimum difference of 38 GPa.     

Determination of the Elastic Properties of Cu<Subscript>3</Subscript>Sn Through First-Principles Calculations

Nine elastic constants of single-crystal Cu₃Sn were determined from first-principles calculations to characterize its polycrystalline elastic behavior and elastic anisotropy. The ideal elastic (E = 147 GPa), shear (G = 56 GPa) and bulk modulus (K = 132 GPa), and Poisson’s ratio (v = 0.315), were determined using the Voigt–Reuss–Hill method and were very close to the range of experimental results. Cu₃Sn exhibits distinct anisotropy in Young’s modulus, with a 44 GPa difference between its maximum and minimum values, which may be partially responsible for the discrepancy in the reported experimental results.     

Nanoindentation on SnAgCu lead-free solder joints and analysis

The lead-free SnAgCu (SAC) solder joint on copper pad with organic solderability preservative (Cu-OSP) and electroless nickel and immersion gold (ENIG) subjected to thermal testing leads to intermetallic growth. It causes corresponding reliability concerns at the interface. Nanoindentation characterization on SnAgCu solder alloy, intermetallic compounds (IMCs), and the substrates subjected to thermal aging is reported. The modulus and hardness of thin IMC layers were measured by nanoindentation continuous stiffness measurement (CSM) from planar IMC surface. When SAC/Ni(Au) solder joints were subject to thermal aging, the Young’s modulus of the NiCuSn IMC at the SAC/ENIG specimen changed from 207 GPa to 146 GPa with different aging times up to 500 h. The hardness decreased from 10.0 GPa to 7.3 GPa. For the SAC/Cu-OSP reaction couple, the Young’s modulus of Cu₆Sn₅ stayed constant at 97.0 GPa and hardness about 5.7 GPa. Electron-probe microanalysis (EPMA) was used to thermal aging. The creep effect on the measured result was analyzed when measuring SnAgCu solder; it was found that the indentation penetration, and thus the hardness, is loading rate dependent. With the proposed constant P/P experiment, a constant indentation strain rate h/h and hardness could be achieved. The log-log plot of indentation strain rate versus hardness for the data from the constant P/P experiments yields a slope of 7.52. With the optimized test method and CSM Technique, the Modulus of SAC387 solder alloy and all the layers in a solder joint were investigated.     

Mechanical integrity of polysilicon films exposed to hydrofluoric acid solutions

This paper presents the results from a comparative study of Young’s modulus, residual stress, and membrane burst pressure of undoped LPCVD polysilicon films exposed to various concentrations of hydrofluoric acid (HF). Load deflection measurements on square membranes of polysilicon with residual tensile stress were used to obtain estimates of Young’s modulus, residual stress and burst pressure. The polysilicon membranes were exposed to four different solutions of the 49% by weight reagent HF including 10:1 DI water and HF, 1:1 DI water the HF, commercial 10:1 buffered oxide etchant, or pure HF (i.e. 49% by weight reagent). Two control groups were studied composed of membranes with no treatment and membranes exposed to DI water. Young’s modulus changed from an average of 190 GPa for the control groups to an average of 240 GPa for films exposed to pure HF. Residual stress values exhibited a less pronounced and opposite change, with an average of 42 MPa for the control groups and an average of 27 MPa for films exposed to pure HF. Similarly, burst pressure was seen to decrease with increasing HF concentration, ranging in value from an average of 96.5 kPa (14 psi) for the control groups to an average of 34.5 kPa (5 psi) for films exposed to pure HF. It was found that the change in the investigated mechanical properties of polysilicon was approximately equal for HF:DI solutions of HF concentration above 10%. Furthermore, for solutions of equal HF concentration, the addition of the buffering agent decreases the effect on membrane burst pressures significantly.     

Tensile properties of aluminum/alumina multi-layered thin films

Thin, free standing aluminum and alumina films were produced by physical vapor deposition and tensile properties were measured. Young’s modulus of the aluminum was microstructure insensitive, but the plastic behavior was very structure sensitive. The natural surface oxide of the aluminum had no apparent affect on the measured value ofYoung’s modulus. The alumina films showed true brittle behavior, but Young’s modulus was lower than bulk. Impurities residing at the grain boundaries were observed in the aluminum films using transverse Auger electron spectroscopy (AES). The films were well characterized using AES, transmission electron microscopy, Rutherford backscattering spectroscopy, and secondary electron microscopy. Well characterized, thin three-layered aluminum/alumina compositionally modulated films were produced by alternate depositions and tensile properties were measured. Young’s modulus was found to be less than a weighted thickness average of Young’s modulus of the individual constituents. Otherwise, the mechanical measurements yielded typical bulk behavior.     

Measurement of Young’s modulus of GaAs nanowires growing obliquely on a substrate

A convenient and fast method for measuring Young’s modulus of semiconductor nanowires obliquely standing on the growth substrate is presented. In this method, the nanowire is elastically bent under the force exerted by the probe of an atomic-force microscope, and the load-unload dependences for the bending of the probe cantilever are recorded. Next, these curves are used to find the bending stiffness of the tilted nanowires, after which, taking into account the nanowire dimensions, Young’s modulus is obtained. The implementation of this method is demonstrated for tilted GaAs nanowires growing on a GaAs (111) substrate. Young’s modulus is determined by applying finite-element analysis to the problem of the stationary elastic bending of a nanowire taking into account the actual nanowire shape and faceting. It proves that a fairly accurate estimate of Young’s modulus can be obtained even if the nanowire shape is approximated by a circular cylinder with a single cross-sectional area. The values of Young’s modulus obtained for GaAs nanowires of cubic lattice symmetry are 2 to 3 times smaller than its value for bulk GaAs. This difference is attributed to the presence of stacking faults in the central part of the nanowires.     

Elastic modulus measurement of thin film using a dynamic method

A two layer composite model was developed using a beam vibration theory and the model was applied for measuring the Young’s modulus of thin films. The Ti coated Si wafer composites were produced by radio frequency magnetron sputtering and used to test the developed model. The measured film modulus using a dynamic method was checked with that using the static method utilizing the pure bending of a cantilever composite beam. The film modulus values measured in both methods were in good agreement. The film modulus values for the specimens with different film thicknesses were also in good agreement when they were measured by the same method.     

Developing an analytic methodology to accurately predict probing depth in integrated circuit structures

This work designs an analytic methodology for applying the probe-before-bump procedure to predict probing depth and proposes feasible probing design parameters to avoid excessive probing of the bump pad. Two kinds of multi-level wafers were used to implement the probing experiment, with a single touch down, and an overdrive of 70 μm, 100 μm, 130 μm, and 150 μm by using a vertical probe card. The Young’s modulus and hardness of the two multilevel structures are measured on which the first bump pads are produced by sputtering aluminum onto the SiO₂, while the second bump pads are produced by sputtering aluminum onto the copper, creating a pad metal of approximately 1-μm thickness by using the nanoindenter. The test results indicate that the Young’s modulus of the thin film material exceeds that of bulk material by 20–30 GPa. The difference between analytic and experimental probing depth ranges from 2.3% to 8.9%, revealing that the proposed novel analytic model is extremely accurate. Engineers or researchers can use the analytic methodology to accurately predict probing depth and acquire probing parameters that are accurate, cost effective, and efficient, thus eliminating the need to use focused ion beam (FIB) or other measurement instruments to determine the probing depth.     

Structural,Elastic, and Electronic Properties of Al-Cu Intermetallics from First-Principles Calculations

The structural, elastic, and electronic properties of Al-Cu intermetallics were investigated using first-principles calculations. The polycrystalline elastic modulus and Poisson’s ratio were deduced from calculated single-crystal elastic constants, and the calculated structural properties agreed well with previous experimental results. Meanwhile, the elastic anisotropy of Al-Cu intermetallics was analyzed based on the directional dependence of the Young’s modulus and its origin explained based on the electronic nature of the crystals.     

Time-independent mechanical and physical properties of the ternary 95.5Sn-3.9Ag-0.6Cu solder

The development of a constitutive model for predicting the thermal-mechanical fatigue (TMF) of 95.5Sn-3.9Ag-0.6Cu (wt.%) Pb-free solder interconnects requires the measurement of time-independent mechanical and physical properties. Yield stress was measured over the temperature range of −25–160°C using strain rates of 4.2 × 10⁻⁵ s⁻¹ and 8.3 × 10⁻⁴ s⁻¹. The yield-stress values ranged from approximately 40 MPa at −25°C to 10 MPa at 160°C for tests performed at 4.2 × 10⁻⁵ s⁻¹. The faster strain rate and specimen aging had a limited impact on the yield stress. The true stress/true strain curves indicated that dynamic-recovery and dynamic-recrystallization processes took place in as-cast samples exposed to temperatures of 125°C and 160°C, respectively, while tested at a strain rate of 4.2 × 10⁻⁵ s⁻¹. Aging the sample prior to testing, as well as a faster strain rate, mitigated both phenomena. Dynamic Young’s modulus values ranged from 55 GPa at −50°C to 35 GPa at 200°C, while the coefficient of thermal expansion (CTE) increased from approximately 12 × 10⁻⁶°C⁻¹ to 24 × 10⁻⁶°C⁻¹ for the same temperature range. The aging treatment had little effect on either Young’s modulus or the CTE.     

Characterization study of time- and temperature-dependent mechanical behavior of polyimide materials in electronic packaging applications

The thermo-mechanical testing of the type HPP ST polyimide films with high performance, supplied by Dupont, was realized under different strain rates and temperature effects. Therefore, the rate-temperature-dependent stress-strain behavior of materials was investigated and the dependence of the Young’s modulus on temperature and strain rate was reported. In view of the uncertainty of the Young’s modulus determination, the specimens were tested with the unloading-reloading technique to verify the test results. The constant strain rate uniaxial tensile test and long-time creep test at various temperatures were performed to characterize the time-temperature-dependent mechanical property precisely. The cyclic loading test was also implemented on the specimen to investigate cyclic stress-strain behavior. In addition, the nanoindentation test was carried out at room temperature to validate the elastic modulus derived from the uniaxial tensile test. This research is expected to investigate the time-temperature-dependent mechanical behavior of the polyimide materials for different service regimes including tensile and cyclic mechanical loading under elevated temperature in a systematic manner.     

Effect of Microstructural Development on Mechanical and Electrical Properties of Inkjet-Printed Ag Films

The microstructural characterization of inkjet-printed Ag films sintered at various conditions was carried out to analyze the effect of microstructure on mechanical and electrical properties. As expected, the films became denser with grain growth with increasing sintering time and temperature, which resulted in improvement in mechanical properties. However, the resistivity of the films reached a minimum value of 3.0 μΩ cm before full densification. In order to improve the mechanical properties, pressure-assisted sintering was introduced. As a result, inkjet-printed Ag films sintered at 250°C under 5 MPa showed a tensile strength of 550 MPa, elongation of 2.4%, Young’s modulus of 55 GPa, and resistivity of ~3.0 μΩ cm.     

Predicting tensile properties of the bulk 96.5Sn-3.5Ag lead-free solder

Equations are presented for predicting tensile properties as functions of temperature and strain rate for the bulk-eutectic 96.5Sn-3.5Ag lead-free solder. At 25°C, we obtained 49.0 GPa for Young’s modulus based on acoustic measurements, which is higher than most of those measured by tensile tests that are subject to viscoelastic creep; 23.1 MPa and 26.3 MPa for yield stress and ultimate tensile strength (UTS) of specimens that are cast, annealed, and aged at a strain rate of 2.0×10⁻⁴ s⁻¹; 48.7% for total elongation, which is larger than most of the reported values. The presence of “initial defects” in the specimens, such as porosity and void, might cause the reduction in measured total elongations. Contribution of NIST, an agency of the U.S. government, not subject to copyright in the United States.     

Microstructure evaluation and mechanical properties of nanolayered chromium nitride/tungsten nitride coating

Chromium nitride (CrN) and tungsten nitride (WN) multilayer coating were fabricated by radiofrequency (rf) magnetron reactive sputtering technique. These two nitride coatings were deposited sequentially with a dual-gun system, and an alternating nanolayered CrN/WN coating was derived. The bilayer period, one CrN and one WN layer, of the multilayer was controlled at 10 nm and 24 nm, respectively. The microstructure of the CrN/WN nanolayered coatings was inspected by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Elemental distribution and periodic feature of the nanolayered coatings were revealed by the Auger electron depth profiling analysis. Nanoindentation technique was employed to evaluate the mechanical properties, including hardness and Young’s modulus. The nanolayered CrN/WN coatings exhibited a high hardness around 30 GPa, which was superior to that of the CrN single-layer coating. The nanolayered structure with confined grains of the nitrides in the nano range was beneficial to the enhancement of the mechanical performance for the multilayer coating.     

On solution schemes for time-independent thermomechanical analysis for structures containing polymeric materials

Contradicting ideas about implementing temperature-dependent Young’s modulus in a time-independent quasi-static thermomechanical analysis can be found regularly in the literature. The incremental (quasi-static evolution) and the non-incremental (Hookean) solution schemes represent simplifications of the viscoelastic behavior of polymeric materials according to different theoretical disciplines. These two schemes lead to completely different solutions when Young’s modulus is a function of the temperature. In this paper we review the ideas about implementing temperature-dependent Young’s modulus in a time-independent quasi-static thermomechanical analysis. Differences of the ideologies are highlighted using bimaterial beam solutions. Thermomechanical deformations of a bimaterial structure, which resembles a plastic ball grid array package assembly, at different temperatures are measured using shadow Moiré interferometry. Numerical solutions from different schemes are compared with measurement results.     

Simulation and optimization on the squeeze-film damping of a novel high-g accelerometer

The damping characteristics of a packaged high-g accelerometer have been investigated in this paper. Firstly, a multi-segments-plates-approximate (MSPA) model on curved surface damping suitable for this component has been established to obtain the relationship between the parallel-shift-distance (PSD) of curved stop and the damping of component. Subsequently, not only the effect of the PSD of curved protection but also the impact of the characteristics of damping media on the dynamic shock response of the component has been studied with ANSYS FEM technology. Results show that the dynamic output responses of component were in reality the superposition of both the forced vibration under acceleration shock and the vibration of cantilever in its inherent frequency. With the increase of PSD, the inherent frequency vibration became outstanding in output response and both the peak output voltage and displacement of beam end increased linearly whereas its corresponding time decreased nonlinearly. The effects of damping media on the dynamic response characteristics of the component were attributed to the difference of viscosity coefficient of damping medium. Under the same other conditions, with increment of viscosity coefficient, the output response curve become smoother except for lower peak voltage. Therefore, the PSD of curved stop should be controlled between 0.5 and 0.65 μm during the fabrication of chip and if the PSD was about 0.5 μm, air would be the most suitable damping media in the packaging of the component.     

Low noise accelerometer microsystem with highly configurable capacitive interface

This paper presents a low noise accelerometer microsystem with a highly configurable capacitive interface circuit. A programmable capacitive readout circuit is designed to minimize the offset and gain error due to the parasitic capacitance mismatch and the process variations. The interface circuit is implemented in a 0.5 μm 2P3M CMOS technology with EEPROM. The interface circuit and MEMS sensing element are integrated in a single package, and consist the accelerometer microsystem. The supply voltage and supply current of the system are 5 V and 1.17 mA, respectively. The input range and gain are 2.5 V and 0.5 V/g, respectively. The max–min gain error and max–min offset error after calibration was measured to be 1.2% FSO and 3.3% FSO, respectively. The signal to noise ratio (SNR) and noise equivalent resolution (NER) are measured to be 93.1 dB and 110.6 μg/√Hz, respectively, when a 40 Hz, 5 g sinusoidal input acceleration is applied.     

Tensile and Fatigue Behavior of Al-1Si Wire Used in Wire Bonding

In this work, the mechanical properties of Al-1Si microelectronic wire were studied. The microstructure of the wire was examined to characterize the distribution of Al-Si inclusions and grain size. The wires had a diameter of 63.3 ± 0.1 μm and an elongated grain structure due to the hot extrusion process used to fabricate them. The transverse grain size was measured to be 1.1 ± 0.3 μm. The anisotropy in grain structure was characterized by dual-beam focused ion beam (FIB). The Young’s modulus was measured by conducting experiments at various gage lengths. The measured modulus was 71.7 ± 6.1 GPa, similar to that of bulk Al-Si. Strength data were measured for many wires, and the variability evaluated by Weibull statistics. The wires had a strength slightly less than 200 MPa and strain to failure of over 2%. A Weibull modulus of 110 was obtained, indicating very low variability in the data. Stress versus fatigue cycles was also conducted. Specimens that survived 10⁶ cycles exhibited a significant decrease in strength over the as-processed material. Fractographic analysis showed a significant amount of plastic flow and fracture by necking to a single point.     

Electromigration effect on intermetallic growth and Young’s modulus in SAC solder joint

Solid-state intermetallic compound (IMC) growth behavior plays and important role in solder joint reliability of electronic packaging assemblies. The directional impact of electromigration (EM) on the growth of interfacial IMCs in Ni/SAC/Ni, Cu/SAC/Ni single BGA ball solder joint, and fine pitch ball-grid-array (FPBGA) at the anode and cathode sides is reported in this study. When the solder joint was subjected to a current density of 5,000 A/cm² at 125°C or 150°C, IMC layer growth on the anode interface was faster than that on the cathode interface, and both were faster than isothermal aging due to the Joule heating effect. The EM affects the IMC growth rate, as well as the composition and mechanical properties. The Young’s modulus and hardness were measured by the nanoindentation continuous stiffness measurement (CSM) from planar IMC surfaces after EM exposure. Different values were observed at the anode and cathode. The energy-dispersive x-ray (EDX) line scan analysis was conducted at the interface from the cathode to anode to study the presence of species; Ni was found in the anode IMC at SAC/Cu in the Ni/SAC/Cu joint, but not detected when the current was reverse. Electron-probe microanalysis (EPMA) measurement on the Ni/SAC/Ni specimen also confirmed the polarized Ni and Cu distributions in cathode and anode IMCs, which were (Ni_0.57Cu_0.43)₃Sn₄ and (Cu_0.73Ni_0.27)₆Sn₅, respectively. Thus, the Young’s moduli of the IMC are 141 and 175 GPa, respectively.     

微机械气流式加速度计敏感机理的有限元分析

揭示了微机械气流式加速度计的敏感机理。采用有限元方法,分析了在不同加速度输入时敏感元件内的流场分布。结果表明,无加速度输入时,两热敏电阻处的气流速度相等,两热敏电阻上的电流相等,电桥输出为0;有加速度输入时,两热敏电阻处的气流速度之差随加速度变化而变化,引起两热敏电阻上电流之差也随之变化,电桥输出一个对应于加速度的电压。所述的方法为微机械气流式加速度计的结构优化设计提供了简单有效的途径。