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Power modules are utilized for electric power control and play a key role in efficient energy conversion. A structural reliability problem of wire bonding, wire-liftoff, in power modules becomes important at high-temperature operation. Wire-liftoff is a thermal fatigue phenomenon caused by thermal stress due to mismatch of coefficients of thermal expansion between a wire and a chip material. According to experimental studies, a saturation phenomenon of wire-liftoff lifetime was observed in power modules above the maximum junction temperature of 200 °C. In this paper, we examine the failure models for predicting wire-liftoff lifetime proposed in the previous studies and also propose a new failure model based on the nonlinear fracture mechanics parameter $T^\ast $ -integral range $\Delta T^\ast $ . Among various failure models, the proposed model is the best to represent a saturation phenomenon of wire-liftoff lifetime. For practical use of the failure model based on $\Delta T^\ast $ -integral range, we propose a simple calculation method of $\Delta T^\ast $ -integral range that can be calculated by using the commercial finite element computer code such as Marc, Ansys, and so on.

This paper reviews the previous research on the methodologies for evaluating structural integrity of wire bonds and die-attachments in power modules. Under power module operation, these parts are subjected to repeated temperature variations which induce repeated thermal stress due to the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. Thus, thermal fatigue phenomena are critical issues for the structural integrity of power modules. In the present paper, we also deal with the evaluation methodologies for thermal fatigue in the temperatures over 200 °C, which are expected operational temperatures for wide bandgap semiconductor power modules. The failure models based on the temperature range ΔT widely used in the power electronics community are critically reviewed from a mechanical engineering viewpoint. Detailed discussion is given concerning the superiority of failure models based on the physical quantities such as the inelastic strain range Δεin, the inelastic strain energy density range ΔWin, and the nonlinear fracture mechanics parameter range ΔT* over the conventional ΔT-based failure models. It is also pointed out that the distributed state concept (DSC) approaches based on the unified constitutive modeling and the unified mechanics theory are promising for evaluating the structural integrity of power modules. Two kinds of test methods, a power cycling test (PCT) and a thermal cycling test (TCT), are discussed in the relation to evaluating the lifetimes of wire-liftoff and die attach cracking.

One of the common reliability concern on most of power modules is a failure of its bonding. Stress, strain, and displacement fields around those bonding in power modules are required for highly-reliable design based on physically/mechanically based failure model. They can be accurately obtained from CAE tools such as finite element computer codes for stress analysis with mechanical properties of materials not only in the elastic region but also in the inelastic region. In this paper, for the reliability study of an aluminum bonding wire, an experimental study was performed to acquire its plastic and creep characteristics. The temperature-dependent constitutive equations for plastic and creep behavior of an aluminum wire are presented based on the isothermal tensile test data. These constitutive equations can be used at the temperatures ranging from 20 °C to 250°C, and are useful for estimating fatigue life predictions of bonding wires, when we utilize the failure models based on the physical quantities such as the inelastic strain range, the inelastic strain energy density range, the nonlinear fracture mechanics parameter T* range and so on.

The J-integral range or the cyclic J-integral, Δ J , is frequently utilized to deal with the fatigue crack growth of ductile materials with large scale yielding. Δ J was originally defined as a line integral similar to the J-integral proposed by Rice. Many researchers correlated fatigue crack growth rate of ductile materials with Δ J defined by J m a x − J m i n . Although it is theoretically shown that the latter definition of Δ J , that is, Δ J = J m a x − J m i n , is not equivalent to the former defined by a line integral, why is the latter definition of Δ J utilized so frequently? This question is main concern of the present paper. To answer this question, we derive the expression of Δ J represented by a line integral for HRR singular fields, which govern the vicinity of a crack tip under large scale yielding, then formulate the difference between the Δ J represented by a line integral and Δ J = J m a x − J m i n . We perform the error estimation for three-point bending specimens to clarify how accurately ( J m a x − J m i n ) predicts the Δ J -value, compared with the Δ J represented by a line integral, which is supposed to provide the exact Δ J -value. As a result, the Δ J -value calculated from ( J m a x − J m i n ) is identical to the Δ J -value calculated from a line integral in the case of the zero-tension cyclic loading conditions, and the deviation between the former and latter values is small under near zero-tension and large cyclic loading amplitude conditions. The use of the Δ J defined by ( J m a x − J m i n ) should be limited to the cases where near zero-tension and large cyclic loading amplitude conditions are satisfied.

Asymptotic solutions around an interfacial corner can be obtained by a combination of the Stroh formalism and the Williams eigenfunction method. The H -integral method, which is derived from Betti’s reciprocal theorem, is useful for analyzing the stress intensity factors (SIFs) of cracks and corners. By expanding these theories for a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials, we develop a modified H -integral method. This method has high generality that can deal with a jointed corner with a varied number of materials and boundary conditions on corner surfaces. We proposed a new definition for the SIFs of an interfacial corner between anisotropic piezoelectric multi-materials, which is compatible with the SIF definitions of a crack in a homogeneous material and an interfacial crack, as well as applicable in various coordinate systems. The accuracy of obtained SIFs was confirmed by comparing the asymptotic solutions obtained from the SIFs with the stress/electric-displacement field directly obtained by the finite element method (FEM). We also propose a numerical method for degenerate materials, which cause numerical problems in the Stroh formalism.

This article presents a critical review of papers dealing with solid particle erosion characteristics of polymer matrix composites, metal matrix composites, and ceramic matrix composites. In addition, the solid particle erosion characteristics of coatings for composite materials are also reviewed. Attention was paid to type of a reinforcement material (fiber/filler), amount of fiber/filler, fiber orientation, and interfacial strength between fiber/filler and matrix, which affect the solid particle erosion in addition to the variables affecting the solid particle erosion of monolithic materials, that is, impact angle, particle velocity, temperature, particle flux, and erodent properties such as shape, size, hardness, and so on. General characteristics of solid particle erosion for composites are extracted from the review of the papers.

This paper focuses on the stress-induced changes of the direct-current (dc) characteristics on p-type metal-oxide-semiconductor (MOS) field-effect-transistors (FETs). First, the uniaxial-stress effects on dc characteristics of pMOSFETs are evaluated experimentally. Then, the experimental results are simulated using a device simulation including an exiting hole mobility model for considering the effects of mechanical stress. The hole mobility model is able to consider the stress-induced variations of the transport mass of holes. It is demonstrated that the device simulation can qualitatively produce the effects of uniaxial-stress on dc characteristics of pMOSFETs.

In order to clarify hydrogen embrittlement mechanisms and to estimate structural strength of machine components under a hydrogen environment, it is essential to know the hydrogen concentration and its existing state in materials. Solute-hydrogen atoms change the behavior and stability of lattice defects and trigger strength degradation. This paper proposes a method for quantitatively evaluating hydrogen concentrations in metals under various conditions on the basis of first-principles calculations and lattice vibration analysis, to consider the influence of thermal vibrations. First, we give a formulation that yields the hydrogen concentration at interstitial sites and at vacancies and vacancy concentration. We then evaluate the influence of the hydrogen concentration at interstitial sites and sites around vacancies in α-Fe for the total hydrogen concentration. We show that the influence of the hydrogen around vacancies is small, and that the interstitial hydrogen concentration is the dominant influence when materials are well annealed. We also investigate hydrogen concentrations in various metals (Al, Ni, Cu, Pd, Mo, α-Ti, Mg, and α-Zr) and show that the calculated concentrations agree with the experimental data, given that interactions between solute-hydrogen atoms are not significant.

Numerical methods like the finite element (FE) method are often used to evaluate the reliability of electronic packages. However, the accuracy of non-linear numerical analyses should be confirmed by experimental measurements. In this study, we evaluated the strain distribution in flip chip (FC) packages with multi-layered printed circuit boards (PCBs) by combining the digital image correlation method (DICM) and the non-linear FE method, considering the viscoelasticity of resins and the elastoplasticity and creep of solder alloy. Four types of FC package consisting of two types of buildup (BU) resin and two types of underfill (UF) resin were evaluated. The distributions of strain on the cutting sections of FC packages were measured using the DICM with microphotographs obtained by a confocal laser scanning microscope (CLSM). The strain measurements showed that the UF resin with the low coefficient of thermal expansion (CTE) reduced thermal strain around a solder bump, and the BU resin with the low CTE reduced the strain concentration along the interface between a Si chip and a solder bump. We performed the non-linear FE analyses while taking into account the viscoelastic Poisson’s ratio of the UF resin and the constant instantaneous Poisson’s ratio. The result of the FE analyses with the constant instantaneous Poisson’s ratio did not correspond with the strain measurements using the DICM. The normal strain in a solder bump was less than that obtained by the measurement, and the direction of a shear strain band in a solder bump was different from that measured using the DICM. On the other hand, the FE analyses considering the viscoelastic Poisson’s ratio showed good agreement with the strain measurements using the DICM. The strain measurement using the DICM improved the accuracy of the non-linear FE analysis of microelectronic packages effectively.

Magnesium alloys containing long-period-stacking ordered (LPSO) phases have attracted considerable attention because they have been reported to exhibit excellent mechanical properties, including high strength and reasonable ductility. It is thought that the LPSO phase plays a critical role in producing these favorable mechanical properties. We analyze the deformation behavior of the LPSO phases with different stacking sequences using molecular dynamics simulations. To highlight the specific deformation behavior of the LPSO phases, we also perform deformation analyses of hexagonal-close-packed and face-centered-cubic (FCC) structures. We focus on the influence of the stacking order rather than the segregated atoms around the FCC-structured layers, and we model an LPSO structure by single element composition where the interatomic interaction is described by a smoothed Lennard-Jones potential. Our simulations indicate that an LPSO structure with a shorter stacking sequence tends to exhibit a higher compressive flow stress, because FCC-structured layers inhibit twinning deformations and non-basal slips. Kinking deformation is observed for an LPSO structure when both compression and shear deformation are present. It is shown that the first-order pyramidal-< c + a> dislocation disarranges the stacking of an LPSO structure and leaves behind many lattice defects. In addition, those lattice defects activate numerous basal slips. Finally, basal dislocations arrange in a line and generate a misorientation angle. Furthermore, this angle originates the compressive deformation. We also observed some prismatic-< a> dislocations and cross slips to the basal plane. These results suggest the importance of non-basal slips for kinking deformation.

Kink deformation is one of the possible principal deformation modes of alloys with a long-period stacking ordered structure under compression parallel to the basal plane. In this deformation, dislocation pairs are massively nucleated, and these dislocations align in a line to form kink bands. In this study, we investigated the nucleation of a dislocation pair in a pure magnesium single crystal by molecular dynamics simulations. We also evaluated the activation free energy of nucleation of a dislocation pair and investigated the dependence of the activation free energy on the applied shear stress and temperature. [doi:10.2320/matertrans.MI201213]

A numerical method for evaluating the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials subjected to thermal and mechanical stresses is proposed. The M1-integral method was applied to an interfacial crack between three-dimensional anisotropic bimaterials under thermal stress. The moving least square approximation was utilized to calculate the value of the M1-integral. The M1-integral in conjunction with the moving least square approximation can be used to calculate the SIFs from nodal displacements obtained by finite element analysis. SIF analyses were performed for double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load. Excellent agreement was achieved between the numerical results obtained by the present method and the exact solution. In addition, we computed the SIFs of an external circular interfacial crack in jointed dissimilar anisotropic solids under thermal stress and showed the distributions of SIFs along the crack front. The distribution of stress and the crack opening displacement obtained by the asymptotic solution using the computed SIFs were compared with those obtained by the finite element analysis with fine mesh. They were almost identical to each other, except for the minor component of SIFs that is much smaller than the major component of SIFs. These results indirectly demonstrate the accuracy of the obtained SIFs.

A numerical method is proposed for evaluating the stress intensity factors of a three-dimensional bimaterial interfacial crack using tetrahedral finite elements. This technique is based on the M1-integral method and employs the moving least-squares approximation. Stress or strain in the M1-integral equation is automatically approximated from the nodal displacements obtained by the finite element analysis using the moving least-squares method. Therefore, the presented method needs no elemental information from the finite element analysis. In this study, stress intensity factor analyses of some typical three-dimensional interface crack problems using the tetrahedral finite elements are demonstrated.

Asymptotic solutions around the interfacial corner between piezoelectric bimaterials can be obtained by the combination of the Stroh formalism and the Williams eigenfunction expansion method. Based on an extension of the Stroh formalism and the H -integral derived from Betti’s reciprocal principle for piezoelectric problems, we analyzed the stress intensity factors (SIFs) and asymptotic solutions of piezoelectric bimaterials. The eigenvalues and eigenvectors of an interfacial corner between dissimilar piezoelectric anisotropic materials are determined using the key matrix. The H -integral for piezoelectric problems is introduced to obtain the scalar coefficients, which are related to the SIFs. We propose a new definition of the SIFs of an interfacial corner for piezoelectric materials, and we demonstrated the accuracy of the SIFs by comparing the asymptotic solutions with the results obtained by the finite element method (FEM) with very fine meshes.

Numerous studies have reported that solute hydrogen atoms and lattice defects have strong interactions, and that hydrogen atoms significantly change the stability and/or mobility of lattice defects. Although molecular dynamics (MD) simulations can treat complicated interactions of various lattice defects, the time scale is insufficient to treat hydrogen diffusion so as to influence the lattice-defect generation and cooperative motion of hydrogen atoms and lattice defects. Here we developed an interatomic potential for Fe with pseudo-hydrogen effects on lattice-defect energies and performed MD simulations of tensile loading. First, we estimated the lattice-defect energies of Fe and hydrogen-trap energies of lattice defects by using first-principle calculations and evaluated the lattice-defect energies under a practical gaseous hydrogen environment. Second, we refitted the existing embedded-atom-method potential for Fe to represent the lattice-defect energies amended by hydrogen effects. Finally, we confirmed that our potential is applicable for various phenomena by estimating the reproducibility of grain-boundary energies that are not employed for potential fitting. Our tensile-loading simulations of a nano specimen show that hydrogen reduces elongation at rupture.

Highly accurate predictions of hydrogen’s influence on material strength and development of materials with minimal hydrogen effects are essential to prevent failure under various hydrogen environments. Here, we investigated the influence of misorientation angle and solute elements (carbon and nitrogen) on the cohesive energy of symmetrical tilt grain boundaries (STGBs) in bcc Fe under a gaseous hydrogen environment by using density functional theory. We found a good correlation among GB energy, GB free volume, and the hydrogen concentration at GBs under hydrogen environments: high-energy GBs have large gaps, and many hydrogen atoms are captured at these spaces. Thus, higher-energy GBs are more influenced by hydrogen. It is also shown that the binding energy between hydrogen and a GB is negligible when nitrogen or carbon atoms exist at the GB at their solubility limit. Therefore, carbon and nitrogen atoms exclude hydrogen atoms from GBs and improve the cohesive energy of GBs under hydrogen environments.

This paper presents a practical method of drift-diffusion device simulation for evaluating the effects of mechanical stress on n-type silicon semiconductor devices. The device simulation incorporates an electron mobility model for considering the effects of stress. In this paper, we focus on stress effects that are induced by applying inplane biaxial stress to the devices. Therefore, two physical phenomena that are attributed to mechanical stress are modeled in the electron mobility model, i.e., the changes in relative population and the momentum relaxation time (intervalley scattering) of electrons in conduction-band valleys. Stress-induced variations of direct-current characteristics on n-type metal-oxide-semiconductor (MOS) field-effect transistors are evaluated using a device simulation including the proposed electron mobility model. Then, the electron mobility model and the simulation method are verified by comparing with experimental results. It is demonstrated that experimental results can be reasonably estimated using this device simulation method. From discussions regarding the electron mobility model, it is suggested that the comprehensive stress sensitivity of MOS devices is larger than that of lightly doped silicon.

The interaction between a dislocation and hydrogen is considered to play an important role in hydrogen-related fractures for metals; it has been experimentally reported that hydrogen affects the dislocation mobility. These studies, however, show different macroscopic softening and/or hardening effects in iron, and the interaction between the dislocation and hydrogen remains unclear. In this study, we investigated the occurrence of interactions between a {112} edge dislocation and a hydrogen atom via the estimation of the stress-dependent energy barriers for the dislocation motion and hydrogen diffusion in alpha iron using atomistic calculations. Our results show the existence of boundary stress conditions: dislocation mobility increment (softening) occurs at a lower applied stress, dislocation mobility decrement (hardening) occurs at an intermediate stress, and no effects occur for the steady motion of a dislocation at a higher stress in this analysis condition.

実装応力に起因した半導体デバイスの電気特性変動について，応力効果を考慮したデバイスシミュレーションによる評価を行った。その際，ゲート長さが異なる3種類（ゲート長さ：24 μm，0.8 μm，85 nm）のnMOSFETに対して，デバイス内部の微細構造に起因する応力分布の影響を考慮した。DC特性値の変動をシミュレーションした結果，デバイス内部の応力分布を考慮した場合の変動率の方が，公称応力値（チップ表面の応力値）に対する変動率よりも小さくなった。デバイスの微細構造に起因するチャネル領域の残留応力が，デバイスの電気特性に有意な影響を及ぼすことを示した。

2011年3月11日の東日本大震災に伴い，福島第一原子力発電所の事故が発生した。この事故後から東京都内(世田谷区深沢)で大気浮遊塵，農畜水産物，浄水の放射能濃度及びγ線の空間線量率のモニタリングを行ってきた。5月31日までの測定結果を基に132Te，131I，132I，134Cs，137Csの5核種による内部被ばく線量及び空間線量率による外部被ばく線量を試算した。その結果，測定開始から1年間の積算線量は425.1μSvとなり，ICRPの定める一般公衆の年間被ばく限度(1mSv)を超えないものと推定された。

In hydrogen diffusion in metals, we have to consider not only the hydrogen flux driven by the gradient of hydrogen concentration but also the hydrogen flux driven by the gradient of hydrostatic stress. Such hydrogen diffusion is a multi-physics problem coupled hydrogen diffusion with a stress field. We performed such hydrogen diffusion analyses for a steel pipe with a crack on an inner surface under internal pressure. On the inner surface of the pipe, the hydrogen concentration calculated using the fugacity of the hydrogen molecules was used as a boundary condition for a hydrogen diffusion equation. The finite element method was employed both for a hydrogen diffusion analysis and for a stress analysis. We obtained the hydrogen concentration around a crack tip by varying the magnitude of internal pressure and the crack length, and examined the relationship between the maximum hydrogen concentration and a nonlinear fracture mechanics parameter CTOD ( C rack T ip O pening D isplacement). Good correlation is found between the maximum hydrogen concentration and CTOD.

Stress-induced shifts of the direct current characteristics on n-type metal oxide semiconductor field effect transistors (nMOSFETs) were investigated experimentally. The stress sensitivities of nMOSFET characteristics were measured by the 4-point bending method, and the gate-length dependence of transconductance shifts caused by uniaxial stress was evaluated. As a result, it is shown that the gate-length dependence of transconductance shifts is attributed to parasitic resistance of the nMOSFETs. Also, this paper verified the electron-mobility model proposed in the previous study that includes stress effects in comparison with the experimental results. As a result, several improvements for the electron-mobility model are proposed in this paper. We describe the change of the conduction-band energy induced by the shear deformation of silicon. The shear deformation with a uniaxial stress along the direction of silicon should be considered in the change of the conduction-band energy.