Thermal Mismatch Strain Research Articles

Interfacial Strength Evaluation of Oxide Films on Carbon Steel by Using the Laser Shock Adhesion Test

We investigate the adhesion strength (interfacial strength) of the oxide film formed on a carbon steel substrate by using a laser shock adhesion test (LaSAT). A rolled carbon steel (SS400) plate is first heated at high temperature (700 °C) under the atmosphere (heat treatment) to cause the formation of oxide films about 20-50 μm thick on the steel surface. The film consisted of multiple layers, including wustite (FeO), magnetite (Fe3O4), and hematite (Fe2O3). Next, the x-ray diffraction method was used to measure the residual stress in the film. We find that compression stress develops in the film because of a mismatch of thermal strain in between the film and substrate after the heat treatment. With LaSAT, strong elastic wave generates by a pulsed laser ablation of the substrate backside, and results in interfacial fractures in the oxide films. To monitor the normal (out-of-plane) displacement of the top surface film, a laser ultrasonic interferometer is simultaneously utilized, such that we detect film delamination and determine the critical laser energy for interfacial fracture to obtain the critical stress (interfacial strength). Furthermore, additional pulsed laser irradiation is conducted against a pre-delaminated specimen in order to examine the growth of delamination area and evaluate the interfacial fracture toughness. Finally, elastic wave propagation in the sample is computed using the finite element method (FEM) in order to evaluate the interfacial stress field, accurately. For the FEM, multiple layers in the oxide film are modeled, and the residual stress due to thermal strain mismatch is introduced. The FEM computations reveal the stress distribution around the interface and evaluate the critical stress and critical stress intensity factor for delamination. We thus quantitatively evaluate the interfacial strength and interfacial fracture toughness of the oxide film formed on carbon steel. The mechanism of interfacial fracture is also discussed on the basis of microstructures in a film with multiple layers. This result may be useful for understanding the adhesion quality of oxide film during the hot-rolling process.

Dysprosium substituted Ce:YIG thin films with perpendicular magnetic anisotropy for silicon integrated optical isolator applications

In this report, dysprosium substituted Ce1Y2Fe5O12 (Ce:YIG) thin films (Dy:CeYIG) with perpendicular magnetic anisotropy (PMA) are successfully deposited on silicon and silicon-on-insulator waveguides by pulsed laser deposition. The structural, magnetic, and magneto-optical properties of Dy:CeYIG films are investigated. We find that increasing dysprosium concentration leads to a decreased out-of-plane magnetic saturation field. Dy2Ce1Fe5O12 and Dy2Ce1Al0.4Fe4.6O12 thin films show PMA dominated by magnetoelastic effects due to thermal mismatch strain. These films further exhibit high Faraday rotation and low optical loss. Our work demonstrates that Dy substitution is an effective way to induce PMA in Ce:YIG thin films without compromising their magneto-optical figure of merit, making this material promising for self-biased transverse electric mode optical isolator applications.

Perpendicular magnetic anisotropy and spin mixing conductance in polycrystalline europium iron garnet thin films

Polycrystalline single-phase europium iron garnet films (EuIG, Eu3Fe5O12, a ferrimagnetic insulator), with thicknesses from 25 to 50 nm and roughness <1 nm, have been grown on various substrates using pulsed laser deposition followed by a rapid thermal anneal. The films are under strain that originates primarily from thermal mismatch and leads to a magnetoelastic anisotropy that dominates the net anisotropy. EuIG grown on quartz (0001) demonstrated perpendicular magnetic anisotropy (PMA) attributed to the in-plane (IP) compressive thermal mismatch strain, whereas films on (11 2¯ 0) quartz, Si, fused silica, and yttria-stabilized zirconia exhibited an IP easy axis due to tensile strain, consistent with the positive magnetostriction of polycrystalline EuIG. For the PMA EuIG, the saturation magnetization was close to that of bulk EuIG, and the out-of-plane coercivity ranged from 600 to 900 Oe, depending on the film thickness. Spin transport measurements on Pt/EuIG/quartz heterostructures gave an anomalous Hall effect-like spin Hall magnetoresistance similar to that of Pt/epitaxial single crystal EuIG. These results show that high quality polycrystalline garnets can be grown with PMA making them useful for applications in spintronic devices.

Suppression of wrinkle formation in graphene on Ir(111) by high-temperature, low-energy ion irradiation

Graphene on Ir(111) is irradiated with small fluences of 500 eV He ions at temperatures close to its chemical vapor deposition growth temperature. The ion irradiation experiments explore whether it is possible to suppress the formation of wrinkles in Gr during growth. It is found that the release of thermal mismatch strain by wrinkle formation can be entirely suppressed for an irradiation temperature of 880 °C. A model for the ion beam induced suppression of wrinkle formation in supported Gr is presented, and underpinned by experiments varying the irradiation temperature or involving intercalation subsequent to irradiation.

Elastomers with Microislands as Strain Isolating Substrates for Stretchable Electronics

AbstractInorganic materials cannot be deposited perfectly on soft elastomers due to wrinkles caused by thermal mismatch in deposition, which limits heterogeneous integration for stretchable inorganic electronics. Herein, a microisland strategy is proposed to isolate the thermal strain mismatch between inorganic materials and soft elastomers, to eliminate undesirable wrinkles. Theoretical model sets up the critical dimensions of microislands to avoid wrinkling. Whether wrinkles appear with different dimensions of the microislands predicted by the theoretical model is consistent with experiments of using copper film on a polydimethylsiloxane (PDMS) substrate. Another advantage of this strategy is to reduce the energy release rate between stiff film and soft substrate in a finite element analysis (FEA) study, which avoids delamination between the film and the substrate. Examples of light emitting diode array optoelectronic devices with microislands are presented to show their advantages with respect to designs without microislands. This strategy is suitable for any situation in which a stiff film is deposited on a soft elastomer substrate, providing a viable process for fabricating stretchable electronics and improving the device yield because there is no transfer printing process.

Competing thermal expansion mismatch and lattice strain engineered growth of crack free WS2 in-plane heterostructures

Formation of heterophase WS2 cancels the competing thermal mismatch and lattice strains and stabilizes crack free monolayer heterostructures while homophase monolayer suffers from severe cracking.

Shape forming by thermal expansion mismatch and shape memory locking in polymer/elastomer laminates

This paper studies a novel method to fabricate three-dimensional (3D) structure from 2D thermo-responsive shape memory polymer (SMP)/elastomer bilayer laminate. In this method, the shape change is actuated by the thermal mismatch strain between the SMP and the elastomer layers upon heating. However, the glass transition behavior of the SMP locks the material into a new 3D shape that is stable even upon cooling. Therefore, the second shape becomes a new permanent shape of the laminate. A theoretical model that accounts for the temperature-dependent thermomechanical behavior of the SMP material and thermal mismatch strain between the two layers is developed to better understand the underlying physics. Model predictions and experiments show good agreement and indicate that the theoretical model can well predict the bending behavior of the bilayer laminate. The model is then used in the optimal design of geometrical configuration and material selection. The latter also illustrates the requirement of thermomechanical behaviors of the SMP to lock the shape. Based on the fundamental understandings, several self-folding structures are demonstrated by the bilayer laminate design.

(Invited) Strain Engineered Crack-Free GaN on Si for Integrated Vertical High Power GaN Devices with Si CMOS

We demonstrated beyond 10 µm thick crack-free GaN growth on Si substrate using selective area growth technique. Systematic characterization by scanning electron and optical microscopy on the grown samples revealed that cracks nucleate and propagate on {1-1 00} planes in <1-2 10> directions. By developing {1 -101} facet planes in selective area growth, thermal mismatch strain relief at facet surfaces eliminate cracking and enable growth over 10 µm thick crack-free GaN on Si. These grown structures exhibited high crystalline quality throughout the thickness of the structure as validated by selective area diffraction in high resolution transmission electron microscopy, with a dislocation density of 2-3 x 108 cm-2 at the GaN surface. On the same Si substrate, we were able to fabricate enhancement mode CMOS devices. The overall progress reported here paves the way for monolithically integrated GaN technologies for RF and high power applications on Si CMOS devices.

Simulating the warping of thin coated Si wafers using Ansys layered shell elements

The feasibility of simulating thin-film-on-substrates behaviour of large thin coated wafers using Ansys® “layered shells” is estimated. Layered shell elements are based on Mindlin-plates with coupled intrinsic layers. These elements can be used with an update Lagrange algorithm (NLGEOM). They are of interest because they are easy to use and require a minimum of degrees of freedom to discretize a coated wafer. More traditional discretisations with two separate element layers are used for evaluating the Finite Element (FE) solution.The simulation results are further compared to results reported in the literature and to the analytical approach of Stoney (1909). For this purpose, a thorough review of the Stoney approach is done. We present an extended version with a plate stiffness for cubic anisotropic material and an additional formula to calculate the curvature from the thermal strain mismatch. It is shown that Stoney’s approach to estimate the film stress from the curvature is inadequate for large deflections. A direct comparison to bending experiments with large thin coated wafers cannot be given since the deflection of these wafers is interfered from a predominant deflection from their dead load.

Fabrication and photoluminescence of strong phase-separated InGaN based nanopillar LEDs

A strong phase-separated InGaN/GaN multiple quantum well (MQW) light-emitting diode (LED) producing a blue-green dual-wavelength spectrum has been grown, and fabricated into two nanopillar array structures with different etching depths: one fabricated only on the p-GaN layer and the other penetrating through the active layers. Micro-photoluminescence (μ-PL) spectra have shown that compared with the as-grown (planar) LED, light extraction efficiency (LEE) is improved for both the shorter and the longer nanopillar array structures due to the increased light-extracting surface area and light-guiding effect, in contrast, internal quantum efficiency (IQE) is improved for only the longer one due to the relaxation of strain in the MQWs embedded in the nanopillars. Furthermore, the strain relaxation-induced peak blue-shift value is smaller for the green emission from In-rich quantum dots (QDs) than the blue emission from the InGaN matrix, and decreases for both the emissions with increasing temperature. The former is attributed to the quantum-confined Stark effect (QCSE) in the strong localized QDs of small size being smaller than in the InGaN matrix, the latter is due to the decrease of the thermal-mismatch strain in the MQWs with increasing temperature.

Could application of column-grid-array (CGA) technology result in inelastic-strain-free state-of-stress in solder material?

Physically meaningful and easy-to-use analytical stress model is developed for a short cylinder (beam) clamped at the ends and subjected to bending caused by the ends offset. The offset is due, in its turn, to an external lateral force that has to be determined from the known offset. It is envisioned that such a beam can adequately represent the state of stress in a column-grid-array (CGA) solder joint interconnection experiencing thermal loading due to the thermal expansion/contraction mismatch of the IC package and the printed circuit board (PCB). The CGA designs are characterized by considerably higher stand-off heights than ball-grid-array (BGA) systems. The offset Δ = lΔαΔt for a CGA solder joint located at the distance l from the mid-cross-section of the package/PCB assembly (the neutral point (DNP)), can be determined, in an approximate analysis, as a product of this distance and the “external” thermal mismatch strain ΔαΔt between the IC package and the printed circuit board (PCB). Here Δα is the difference in the effective coefficients of thermal expansion (CTE) of the PCB and package materials, and Δt is the change in temperature. The objective of the analysis is to demonstrate that the application of a CGA design, in which the solder joints are configured as short clamped–clamped beams, enables one not only to significantly relieve the thermally induced stresses, compared to the BGA system, but possibly to do that to an extent that the stresses in the solder material would remain within the elastic range. If this is achieved, the low-cycle-fatigue condition for the solder material will be replaced by the elastic-fatigue condition, thereby leading to a significantly longer fatigue lifetime of the joint. The elastic fatigue lifetime can be assessed, as is known, based on the Palmgren–Miner rule of linear accumulation of damages. Our analysis is limited therefore to elastic deformations.

Analysis of a short beam with application to solder joints: could larger stand-off heights relieve stress?

Physically meaningful and easy-to-use analytical (mathematical) stress model is developed for a short beam with clamped and known-in-advance offset ends. The analysis is limited to elastic deformations. While the classical Timoshenko short-beam theory seeks the beam’s deflection caused by the combined bending and shear deformations for the given loading, an inverse problem is considered here: the lateral force is sought for the given ends offset. In short beams this force is larger than in long beams, since, in order to achieve the given displacement (offset), the applied force has to overcome both bending and shear resistance of the beam. It is envisioned that short beams could adequately mimic the state of stress in solder joint interconnections, including ball-grid-array (BGA) systems, with large, compared to conventional joints, stand-off heights. When the package/printed-circuit-board (PCB) assembly is subjected to the change in temperature, the thermal expansion (contraction) mismatch of the package and the PCB results in an easily predictable relative displacement (offset) of the ends of the solder joint. This offset can be determined from the known external thermal mismatch strain (determined as the product of the difference in the coefficients of thermal expansion and the change in temperature) and the position of the joint with respect to the mid-cross-section of the assembly. The maximum normal and shearing stresses could be viewed as suitable criteria of the beam’s (joint’s) material long-term reliability. It is shown that these stresses can be brought down by employing beam-like joints, i.e., joints with an increased stand-off height compared to conventional joints. It is imperative, of course, that, if such joints are employed, there is still enough interfacial real estate, so that the BGA bonding strength is not compromised. On the other hand, owing to the lower stress level, reliability assurance might be much less of a challenge than in the case of conventional joint configuration. By employing beam-like solder joints one can even manage to avoid inelastic deformations of the joints, thereby increasing dramatically their fatigue lifetime. Future work will include, but might not be limited to, the finite-element computations, experimental evaluations (such as, e.g., shear-off testing), and analyses of the occurrence and the role of the inelastic strains, if any. The paper is intended for materials-, reliability- and industrial- physicists and applied scientists.

Full-field measurement of surface topographies and thin film stresses at elevated temperatures by digital gradient sensing method.

Thin film stresses in thin film/substrate systems at elevated temperatures affect the reliability and safety of such structures in microelectronic devices. The stresses result from the thermal mismatch strain between the film and substrate. The reflection mode digital gradient sensing (DGS) method, a real-time, full-field optical technique, measures deformations of reflective surface topographies. In this paper, we developed this method to measure topographies and thin film stresses of thin film/substrate systems at elevated temperatures. We calibrated and compensated for the air convection at elevated temperatures, which is a serious problem for optical techniques. We covered the principles for surface topography measurements by the reflection mode DGS method at elevated temperatures and the governing equations to remove the air convection effects. The proposed method is applied to successfully measure the full-field topography and deformation of a NiTi thin film on a silicon substrate at elevated temperatures. The evolution of thin film stresses obtained by extending Stoney's formula implies the "nonuniform" effect the experimental results have shown.

Curvature Reversal and Residual Stress in Solid Oxide Fuel Cell Induced by Chemical Shrinkage and Expansion

AbstractStructural stability of layered functional ceramic composites is challenged by curvature effects and residual stresses caused by the thermal mismatch and chemical strains. In this study, a phenomenon of curvature reversal is found in the half‐cell structure of solid oxide fuel cell (SOFC) during the reduction of the half‐cell from NiO‐YSZ to Ni‐YSZ. An analytical model is derived to study the curvature and residual stress caused by the chemical shrinkage and expansion of anode. With reducing to Ni‐YSZ, the curvature of the half‐cell changes from the initial direction to an opposite direction, then back to the initial direction. This curvature reversal is inevitable during reduction while the thickness ratio of electrolyte to anode is between 0 and 0.102. The residual stress in electrolyte, calculated by the analytical model, is well agreement with the experiment result using X‐ray stress analysis. The YSZ layer is always subjected to compressive stress in despite of curvature reversal existing in half‐cell. It is impossible to get the residual stress by measuring the curvature unless the half‐cell was reduced completely.

Structure and strain relaxation effects of defects in InxGa1−xN epilayers

The formation of trench defects is observed in 160 nm-thick InxGa1−xN epilayers with x ≤ 0.20, grown on GaN on (0001) sapphire substrates using metalorganic vapour phase epitaxy. The trench defect density increases with increasing indium content, and high resolution transmission electron microscopy shows an identical structure to those observed previously in InGaN quantum wells, comprising meandering stacking mismatch boundaries connected to an I1-type basal plane stacking fault. These defects do not appear to relieve in-plane compressive strain. Other horizontal sub-interface defects are also observed within the GaN pseudosubstrate layer of these samples and are found to be pre-existing threading dislocations which form half-loops by bending into the basal plane, and not basal plane stacking faults, as previously reported by other groups. The origins of these defects are discussed and are likely to originate from a combination of the small in-plane misorientation of the sapphire substrate and the thermal mismatch strain between the GaN and InGaN layers grown at different temperatures.

On the relationship between ceramic strength and the requirements for mechanical design

Abstract During the last fifty years the mechanical properties of ceramic materials have been greatly improved, their toughness and strength have been increased and the scatter of strength decreased. Adequate statistical design procedures for brittle materials exist but cracking and brittle fracture of ceramic components still occur very often. In this review the theory of brittle fracture and the underlying assumptions are critically discussed and the measurement procedures of strength are reviewed. It is shown that the strength of materials, the strength of specimens and the strength of components are often quite different properties. Three main factors are identified which – in order to avoid unexpected failure of components – have to be considered much more than in the past: (i) hidden stresses, i.e. stresses caused by thermal strain mismatch, by contact (for example in joints) and internal stresses, (ii) the quality of the component's surfaces and edges and (iii) proper handling of ceramic materials and components. It can clearly be stated that the mechanical properties of many ceramic materials are appropriate even for applications under severe loading conditions but bad or incomplete mechanical design, insufficient surface finish and mishandling are the main reasons for unexpected failure of ceramic components.

Thermal Misfit Strain Relaxation in Ge/(001)Si Heterostructures

We used x-ray diffraction and transmission electron microscopy to study the mechanism of thermal misfit strain relaxation in epitaxial Ge films grown on Si(001) substrates by the two-step growth technique. Lattice misfit strain associated with Ge/Si(001)Si mismatched epitaxy is largely relieved by a network of Lomer edge misfit dislocations during the first step of growth. However, thermal misfit strain during growth is relieved primarily by interdiffusion at the Si/Ge heterointerface. Two SiGe compositions containing 0.5 at.% and 6.0 at.% Si detected at the interface relieve thermal mismatch strain associated with the two growth steps. A thermodynamic model has been proposed to explain the state of strain in the films.

Bistable hybrid symmetric laminates

Bistable laminates with unsymmetric lay-ups have been studied extensively. In this work a novel type of bistable hybrid laminate with symmetric lay-up is presented. The two stable configurations of the bistable hybrid symmetric laminate are doubly-curved. The two stable configurations have identical curvatures with opposite signs. The bistability of hybrid symmetric laminates derives from the thermal strain mismatch between the metal ply and the 0° composite ply. Finite element analyses (FEA) are performed using ABAQUS and results are compared with a new analytical model which employs piecewise continuous displacement functions. Two bistable hybrid symmetric laminates are manufactured and the stable configurations are measured in experiments. Both FEA and analytical results match experimental results reasonably well. In addition, the influences of various laminates’ lay-ups, dimensions and material properties are investigated to gain a thorough understanding of the bistable characteristics of bistable hybrid symmetric laminates (BHSLs).

Fatigue Crack Development in Epoxy Coatings on Steel Substrate: The Role of Coating and Substrate Properties in Determination of the Onset of Fatigue Cracks

Development of service cracks in epoxy based corrosion protective coatings limits the life of the substrate structure. If cracks develop, corrosion protection is lost and costs of repair and re-protection of large marine structures can be crippling. Factors controlling development of cracks in the coating are poorly understood, and predictions of coating lifetime approximate. For bulk tanker applications service strains imposed on coatings arise from both low frequency thermal mismatch strains and mechanical strains from wave action. In this work the number of cycles to crack initiation has been measured during strain controlled fatigue of two selected 300 μm thick coatings applied to a 5.5 mm thick steel substrate. Cycling was performed at frequencies of 1 Hz, and strain amplitudes between ±0.16% and ±0.5%. Coating crack development was monitored optically. It was found that cycles to crack initiation depended on both strain amplitude and on the static ductility of the coating. After initiation crack growth rates in the coating reduced with increasing surface crack length. The significance of the results is considered in the light of requirements for quantitative models for service life prediction of coatings on metallic substrates.

Stress analysis and fail-safe design of bilayered tubular supported ceramic membranes

Supported ceramic membranes based on mixed ionic and electronic conductors are a promising technology for oxygen separation applications. In addition to chemically induced stress under oxygen activity gradients in the materials, strain mismatch between membrane and support gives rise to considerable stress that may compromise mechanical reliability. This paper presents an analysis of stress generated in tubular supported membranes during operation. Closed-form analytical solutions for stresses due to external pressures, strain gradients, and mismatch in materials properties are derived. Stress distributions in two membrane systems have been analyzed and routes to minimize stress are proposed. For a Ba0.5Sr0.5Co0.8Fe0.2O3−δ membrane supported on a porous substrate of the same material under pressure-vacuum operation, the optimal configuration in terms of minimizing the risk of fracture by ensuring only compressive stresses in the component is achieved by placing the support on the feed side of the membrane. For a Ce0.9Gd0.1O1.95−δ membrane on a MgO support, stress due to thermal strain mismatch is as large as that due to oxygen activity gradient. Tailoring the thermal expansion coefficient of the support is an effective method to alleviate the total stress. Failure criteria for membrane fracture under compression are thereafter presented. It is found that the tolerable flaw size for fracture in compression is in the millimeter range for both membrane systems at operating conditions in the range of practical interest.