Thermal Mismatch Strain Research Articles

Realizing strain enhanced dielectric properties in BaTiO3 films by liquid phase assisted growth

The addition of a liquid-forming flux to barium titanate thin films promotes densification and grain growth, improves nonlinear dielectric properties, and allows residual strain to be sustained in polycrystalline films without cracking at thicknesses relevant to device fabrication. Relative tuning, an excellent indicator of crystalline quality and an important material property for tunable microwave devices, increases from 20% to 70%. Films exhibit 0.15% residual differential thermal expansion mismatch strain, resulting in a shift to the paraelectric-ferroelectric phase transition of 50 °C. This result is in excellent agreement with theory, demonstrating the ability to tune ferroic transitions without epitaxial approaches.

Structural optimization of the micro-membrane for a novel surface stress-based capacitive biosensor

Thin membrane transducer can be used for detecting the surface stress induced by the bio-molecular reactions. Designing research of the capacitive thin membrane transducer is proposed in the paper. The relationship between the sensitivity of the surface stress-based biosensors and the geometrical parameters of membrane was analyzed using the finite element method. The thermal strain mismatch resulting from the CTE difference of the two-layers of the membrane was also studied. The structure characteristics were analyzed systematically, including shape, size, gold coverage, which are normally considered in the design of the biosensors. Furthermore, a novel bi-membrane structure, which has high signal-to-noise ratio and can minimize the influence of the environment, is proposed.

Dislocation Reduction by Glide in Epitaxial IV–VI Layers on Si Substrates

It is explained with a simple model why the reduction of threading dislocation (TD) densities in epitaxial lattice and thermal expansion mismatched IV–VI layers such as PbSe(111) on Si(111) substrates follows a 1/h 2 dependence where h is the thickness of the layer. This is in contrast to the 1/h dependence for III–V and II–VI layers grown on mismatched substrates. The 1/h 2 dependence results since the thermal mismatch strain is mainly reduced by glide and reactions of the TD in their main {100}-type glide system of the NaCl-type IV–VI semiconductors. In addition, multiple thermal cycles lead to further reduction of the TD densities by glide and fusion since fusion does not cause dislocation blocking.

Determination of the Creep Properties of Pb-free Solders for Harsh Environments Using Meso-scale Testing

Solder joints in electronic packages are prone to failure due to the evolution of thermal expansion mismatch strains during thermal cycling. The comparatively wide operating temperature range and long lifetimes of aerospace electronics require high reliability solder joints. Since 2006, high reliability industries (aerospace and military amongst others) that are exempt from lead-free RoHS regulation on account of concerns over the reliability of Pb-free solders have found it increasingly difficult and expensive to continue using traditional Sn-Pb-based solders. Hence there is a pressing need to find a suitable alternative that can match the manufacturing and reliability performance of Sn-Pb. There remains a dearth of data for the constitutive behaviour of Pb-free solders under harsh environment scenarios. Unfortunately, conventional test approaches, particularly in the case of creep behaviour which is critical to solder lifetimes, are expensive and time-consuming. High temperature nanoindentation has been recently developed as a quick method for the determination of creep properties of solder alloys. This paper compares and contrasts nanoindentation creep results for bulk Pb-Sn and lead-free solders. However, there are limits to nanoindentation creep, in particular the load-dependence of the technique. A new meso-scale test approach that lies between nanoindentation and bulk creep testing has been developed. Real ball grid arrays using Pb-free solders have been creep tested in the temperature and stress ranges of operating solder joints. High temperature creep constitutive data has been obtained. The technique offers promising time and materials savings in obtaining important mechanical property data for subsequent use in life-prediction models.

Role of buried cracks in mitigating strain in crack free GaN grown on Si (1 1 1) employing AlN interlayer schemes

This paper investigates the effect of buried cracks in the AlN interlayer buffer on mitigation of the large, tensile, thermal expansion mismatch strain in the GaN/Si system, which is a key hurdle for achieving crack free GaN epitaxy on silicon. The thermally induced strain is determined by temperature-dependent, high-resolution X-ray diffraction measurements carried out from room temperature up to the growth temperature. It is found that in addition to the balancing effect of compressive lattice-mismatch strain induced by the AlN interlayers, buried cracks in the AlN interlayer region can also relax some of the thermal expansion mismatch strain through elastic distortion at crack edges. The degree of relaxation is dependent on the spacing-to-height aspect ratio of the buried cracks, consistent with prediction of crack-edge-induced relaxation models.

Curvature and stresses for bi-layer functional ceramic materials

The technical application of layered functional ceramic components is challenged by curvature effects and residual stresses originating mostly from the thermal mismatch or chemical strains of the joined materials. Based on the general solution for elastic deformation of monolithic and multilayered materials the determination of curvature and residual stress for linear elastic bi-material specimens with chemical strains, chemical reduction in stiffness, shape variations, gradients in elastic modulus or thermal expansion is outlined. The use of the relationships is exemplified for ceramic solid oxide fuel cell (SOFC) and ceramic membrane materials. For SOFCs curvature changes are considered resulting from the reduction of the anode and crystallization of a glass–ceramic sealant with semi-spherical shape. For gas separation membranes which currently under development for fossil power plants the effect of chemical strains is assessed. The limits of using analytical relationships are addressed for the warpage of thin, rectangular SOFCs.

Crystallization kinetics, mineralization and crack propagation in partially crystallized bioactive glass 45S5

Thermal treatment of bioactive glass ceramics dictates many important features such as microstructure, degree of crystallinity, mechanical properties, and biological response. This report investigates the heat treating conditions and the Avrami crystallization kinetics of melt cast bioactive glass 45S5 at 680 °C. Glass discs were found to follow three dimensional bulk crystallization kinetics (Avrami exponent n = 3). Partially crystallized bioactive glass samples were subjected to in vitro immersion testing to assist a comparative study of the adhesion capabilities of the mineralized layer formed on crystalline and amorphous regions. Higher adhesion of the mineralized layer to the amorphous region was observed as compared to its crystalline counterpart. Furthermore, Palmqvist crack propagation in amorphous and partially crystallized bioactive glass was studied. The crack paths in amorphous bioactive glass were straight, yet crack deflections were observed in the crystalline regions, likely attributed to different crystallographic orientations of crystals or residual thermal mismatch strains present in the bioglass ceramic. Hence, the mineralized layer interfacial fracture toughness and bulk fracture toughness of bioglass ceramics are different from their amorphous counterpart.

The absence of thermal expansion mismatch strengthening in nanostructured metal–matrix composites

A bulk particulate reinforced nanostructured metal–matrix composite (MMC) was synthesized via cryomilling and consolidation. The effect of thermal expansion mismatch strain on strengthening was investigated in detail. The results indicate that, unlike in conventional coarse-grained MMCs, thermal expansion mismatch strengthening does not occur. Transmission electron microscopy demonstrates that formation of geometrically necessary dislocations is constrained to a nanostructured interfacial layer with grains ∼30–50 nm in size, thus limiting strain hardening in the bulk region of the matrix.

In situ flow stress of pure aluminium constrained by tightly packed alumina fibres

The in situ matrix flow stress of continuous fibre-reinforced aluminium is measured in tension along the fibre axis. We use a new, tighter, estimate for the effect of differential Poisson contraction between fibres and matrix and take into consideration nonlinear elastic fibre behaviour; these improvements remove inconsistencies found in earlier work. Resulting in situ matrix flow stress curves are characterized by a substantial gain in hardness of the matrix as compared to the unreinforced alloy, and a strong Bauschinger effect. These effects are caused by dislocation emission during cooldown by matrix/fibre thermal strain mismatch. The surprising insensitivity of hardening to the prior rate of composite cooldown suggests that thermal dislocational hardening starts already at temperatures where unreinforced pure aluminium would creep rapidly. The absence of significant recovery during furnace cooldown is attributed to a small amount of iron in supersaturated solution, and/or to subgrain boundary pinning at the fibres.

Coupled Finite Element–Potts Model Simulations of Grain Growth in Copper Interconnects

AbstractThe paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and the height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.

Spatially resolved strain measurements in Mo-alloy micropillars by differential aperture x-ray microscopy

Spatially resolved strain distributions in the NiAl matrix and the ∼550–1000 nm Mo fibers of a NiAl–Mo eutectic were investigated by microbeam x-ray diffraction. Position sensitive d-spacings for the individual phases were obtained from spatially resolved and energy-resolved Laue patterns. For embedded Mo fibers, the measured elastic strain is consistent with the predicted thermal mismatch strain between the NiAl and Mo phases. However, when the NiAl matrix is etched back to expose Mo micropillars, the d-spacing increases to that of unconstrained Mo, indicating release of the compressive residual strain in the Mo fibers.

In-plane anisotropic strain in a-ZnO films grown on r-sapphire substrates

We deposited (112¯0) nonpolar a-plane ZnO (a-ZnO) films on (011¯2) r-sapphire substrates using metalorganic chemical vapor deposition. Unit cell deformation due to interfacial strain in films was determined by triple-axis x-ray diffraction. Due to low symmetry of a-plane, anisotropic strain is observed along the [0001] (c-axis) and [11¯00] (m-axis) in-plane axes. Out-of-plane strain along [112¯0] (a-axis) is tensile and relaxes for film thickness ⩾2μm. The in-plane m-axis is under tensile strain and c-axis is under compressive strain. Increase in film thickness increases in-plane strain anisotropy due to faster relaxation along the m-axis. Thermal and lattice mismatch strains are separated by curve fitting.

Comparative finite element analysis of the stress–strain states in three different bonded solid oxide fuel cell seal designs

One of the critical issues in designing and fabricating a high performance planar solid oxide fuel cell (pSOFC) stack is the development of the appropriate materials and techniques for hermetically sealing the metal and ceramic components. A second critical issue is ensuring that the brittle ceramic cell constituents, i.e. the electrodes and electrolyte, exhibit high mechanical reliability by mitigating potential sources of thermal-mechanically induced stresses that can lead to fracture during operation and/or shutdown. A foil-based sealing approach is currently being developed that appears to offer good hermeticity and mechanical integrity, while minimizing the generation of high stresses in either of the joint's substrate materials. Based on the concept's viability, demonstrated in prior experimental work, numerical analyses were conducted to evaluate the behavior and benefits of the seal in a configuration prototypic of current pSOFC stack designs. This paper presents recent results from finite element (FE) simulations of a planar cell using the foil-based seal, along with companion analyses of the more conventionally employed glass-ceramic and brazed joints. The stresses and deformations of the components were evaluated at isothermal operating and shutdown temperatures. The results indicate that the foil seal is able to accommodate a significant degree of thermal mismatch strain between the metallic support structure and the ceramic cell via elastic deformations of the foil and plasticity in the foil-to-cell braze layer. Consequently the cell stresses in this type of seal are predicted to be much lower than those in the glass-ceramic and brazed designs, which is expected to lead to improved stack reliability. This ability to accommodate large thermal strain mismatches allows the design requirement of thermal expansion matching between ceramic and metal stack components to be relaxed and expands the list of candidate materials that can be considered for the metal frames and interconnects.

Damage evaluation in discontinuously reinforced aluminum matrix composites subjected to thermal cycling

A comparative study of the damage in the powder metallurgy processed Al–Cu–Mg alloy–SiC (as-extruded and solution-treated) and Al–SiC (hot rolled), and in situ cast Al–TiC (as-extruded) composites, each with 15 vol.% particulate reinforcements, has been carried out. Repeated thermal cycling of the composites between 500 and 0 °C was followed by evaluation of damage by examination of microstructure using scanning electron microscopy, determination of changes in dynamic Young's modulus, and measurement of microhardness near the reinforcement–matrix interfaces. The thermally cycled Al alloy–SiC composites have exhibited reduction in Young's modulus and microhardness adjacent to reinforcement–matrix interfaces, due to decohesion caused by thermal mismatch strains. In contrast, the SiC or TiC reinforced Al composites subjected to thermal cycling, have shown only a marginal reduction in the Young's modulus, and cracks in the Al matrix rather than at interfaces, near which microhardness increment by strain-hardening through dislocation generation has been noticed.

Surface and interfacial structure of epitaxial SrTiO 3 thin films on (0 0 1) Si grown by molecular beam epitaxy

Effects of relaxation of interfacial misfit strain and non-stoichiometry on surface morphology and surface and interfacial structures of epitaxial SrTiO 3 (STO) thin films on (0 0 1) Si during initial growth by molecular beam epitaxy (MBE) were investigated. In situ reflection high-energy electron diffraction (RHEED) in combination with X-ray diffraction (XRD), atomic force microscopy (AFM), X-ray photoelectron spectrometry (XPS) and transmission electron microscopy (TEM) techniques were employed. Relaxation of the interfacial misfit strain between STO and Si as measured by in situ RHEED indicates initial growth is not pseudomorphic, and the interfacial misfit strain is relaxed during and immediately after the first monolayer (ML) deposition. The interfacial strain up to 15 ML results from thermal mismatch strain rather than lattice mismatch strain. Stoichiometry of STO affects not only surface morphology but interfacial structure. We have identified a nanoscale Sr 4Ti 3O 10 second phase at the STO/Si interface in a Sr-rich film.

Advances in pulsed-laser-deposited AIN thin films for high-temperature capping, device passivation, and piezoelectric-based RF MEMS/NEMS resonator applications

In this paper we report recent advances in pulsed-laser-deposited AIN thin films for high-temperature capping of SiC, passivation of SiC-based devices, and fabrication of a piezoelectric MEMS/NEMS resonator on Pt-metallized SiO2/Si. The AlN films grown using the reactive laser ablation technique were found to be highly stoichiometric, dense with an optical band gap of 6.2 eV, and with a surface smoothness of less than 1 nm. A low-temperature buffer-layer approach was used to reduce the lattice and thermal mismatch strains. The dependence of the quality of AlN thin films and its characteristics as a function of processing parameters are discussed. Due to high crystallinity, near-perfect stoichiometry, and high packing density, pulsed-laser-deposited AlN thin films show a tendency to withstand high temperatures up to 1600°C, and which enables it to be used as an anneal capping layer for SiC wafers for removing ion-implantation damage and dopant activation. The laser-deposited AlN thin films show conformal coverage on SiC-based devices and exhibit an electrical break-down strength of 1.66 MV/cm up to 350°C when used as an insulator in Ni/AlN/SiC metal-insulator-semiconductor (MIS) devices. Pulsed laser deposition (PLD) AlN films grown on Pt/SiO2/Si (100) substrates for radio-frequency microelectrical and mechanical systems and nanoelectrical and mechanical systems (MEMS and NEMS) demonstrated resonators having high Q values ranging from 8,000 to 17,000 in the frequency range of 2.5–0.45 MHz. AlN thin films were characterized by x-ray diffraction, Rutherford backscattering spectrometry (in normal and oxygen resonance mode), atomic force microscopy, ultraviolet (UV)-visible spectroscopy, and scanning electron microscopy. Applications exploiting characteristics of high bandgap, high bond strength, excellent piezoelectric characteristics, extremely high chemical inertness, high electrical resistivity, high breakdown strength, and high thermal stability of the pulsed-laser-deposited thin films have been discussed in the context of emerging developments of SiC power devices, for high-temperature electronics, and for radio frequency (RF) MEMS.

A sintering model for thermal barrier coatings

A mathematical model is developed for the progressive sintering of ceramic columns in a thermal barrier coating made using the electron beam–physical vapour deposition route. The model assumes that inter-columnar sintering is driven by changes in the interface energy and elastic stored energy of the columns. The analysis reveals the sensitivity of the sintering rate to the in-plane elastic modulus as well as to an imposed thermal mismatch strain, interfacial energies and diffusivities. It is shown that mud-cracking of the coating leads to a drop in in-plane stress within the coating and thereby to accelerated sintering. Explicit calculations are reported for the evolution of sintering within an array of mud-cracked columns, and for the density of mud cracks.

Microstructure and Dielectric Properties of Textured SrTiO3 Thin Films

We investigate the relationship between microstructure and dielectric properties of textured SrTiO3 thin films deposited by radio‐frequency magnetron sputtering on epitaxial Pt electrodes on sapphire substrates. The microstructures of Pt electrodes and SrTiO3 films are studied by transmission electron microscopy, atomic force microscopy, and X‐ray diffraction. SrTiO3 films grown on as‐deposited and annealed Pt electrodes, respectively, consist of a mixture of (111)‐ and (110)‐oriented grains. Temperature‐dependent dielectric measurements show that differences in texture and microstructure are reflected in the Curie–Weiss behavior of the SrTiO3 films. Phenomenological models that account for the effects of thermal mismatch strain on the dielectric behavior are developed for different film textures. The models predict that at a given temperature, paraelectric (111)‐oriented films of SrTiO3 on tensile substrates will have a higher Curie–Weiss temperature and a greater dielectric constant than (110)‐oriented films or bulk SrTiO3. The experimental dielectric behavior is compared with the predictions from theory, and different contributions, such as interfacial layers, film stress, and microstructure, to the Curie–Weiss behavior are discussed.

Study on models of strain and stress distribution in heterostructures

Based on the equilibrium of combined girders, a set of models for the strain a nd stress distributions in heterostructures introduced by lattice mismatch, ther mal mismatch and the combination of the two factors are set up, and the analyti c solutions, including lattice mismatch strain, thermal mismatch strain, bending strain and the radius of curvature of the system, are also given. Furthermore, by using the models given here, strain and stress distributions in HgCdTe/CdZnTe heterostructures are calculated. The results show that both the maximum stress in HgCdTe films and the maximum stress in CdZnTe always appear at the interface between them, and that the neutral axis as a function of thickness and elastic parameters in the heterostructures are not related to lattice mismatch, lattice relaxation, thermal mismatch, and so on. In addition, the radius of curvature of HgCdTe/CdZnTe decreases with decreasing thickness of CdZnTe. In order to avoid cracking of HgCdTe/CdZnTe device at 77K, the thickness of CdZnTe must b e larger than the limited value.

Characterization of Hygroscopic Swelling Behavior of Mold Compounds and Plastic Packages

Hygroscopic swelling behavior of mold compounds is analyzed by a novel experimental procedure using a whole-field displacement technique. Large variation in moisture content at the virtual equilibrium state is observed, while the coefficient of hygroscopic swelling is shown to not vary significantly. An investigation on an actual package is also performed to determine the hygroscopic swelling mismatch strains at the chip/mold compound interface. The results are compared with the thermal expansion mismatch strains at the same interface and reveal much higher hygroscopic swelling mismatch strains. The hygroscopic strains must be considered for reliability assessment when a package is subjected to environments where the relative humidity fluctuates.