Pavel S. Shushpannikov

A Compact Analytic Model of the Strain Field Induced by Through Silicon Vias

The thermoelastic strains are induced by through silicon vias due to the difference of thermal expansion coefficients between the copper ( ~ 18 ppm / °C) and silicon ( ~ 2.8 ppm /°C) when the structures are exposed to a thermal ramp in the process flow. A compact analytic model (Bessel function) of the strain field is obtained using Kane-Mindlin theory, and has a good agreement with the finite-element simulations. The elastic strains in the silicon in the radial direction and angular direction are tensile and compressive, respectively. The linear superposition of the analytic model of a single via can be used in the multi-via configuration. Due to the interaction of vias, the slightly larger errors of strain occur between the two close vias when the linear superposition is used.

Simulation of stress-strain state in SiGe island heterostructures

The problem of simulation of the stress-strain state in SiGe island heterostructures is considered. The analytic-numerical method of multipole expansions is used to obtain an approximate solution. The problem of the stressed state influence on the diffusion mobility of atoms adsorbed on the heterostructure free surface is also discussed.

Identification of parameters of a plane elliptic crack in an isotropic linearly elastic body from the results of a single uniaxial tension test

The method earlier developed by one of the authors for identifying ellipsoidal defects is numerically tested for the applicability to the problem of identification of a degenerate ellipsoidal defect, i.e., an elliptic crack. The method is based on the reciprocity functional and the assumption that the displacements are measured in a uniaxial tension test of an isotropic linearly elastic body. Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data.

SiGe Quantum Rings by Ultra-high Vacuum Chemical Vapor Deposition

Fig. 4: Lateral strain distribution in an isotropic Ge-rich dot. e-mail: chee@cc.ee.ntu.edu.tw AbstractSiGe quanrum rings (QRs) with 1.1 nm height and 84 nm diameter were observed on SiGe quantum dots (QDs) capped with 2 nm Si. Si atoms diffuse to relatively strain-free regions to form ring-like structures around QDs. The wave number of Si-Ge phonon peak increases at beginning of Si coverage due to more compressive strain and decreases with increasing Si coverage due to reduction of Ge content. QRs are the metastable states and can be only observed in very limited conditions.

Study of Unloading at Lower Limbs Orthotics: Experiment and Simulation

The rate of healing and rehabilitation in fractures of the feet depends on the level and the program of loading the damaged segment. The paper studied the possibilities of efficiently controlling the unloading level of the affected area by varying the degree of orthosis tightening (lateral compression). Among others, a hypothesis was tested‚ according to which only in a slip the limb by increasing the lateral compression is pushed up and the coefficient of unloading (CU) grows. Two types of shin-orthosis system models were developed and studied numerically for different variants of parameters: conical models using the package, based on boundary integral equation method and BEM, and personalized real form models based on the technology «CT scan –> Specialized processing software (Mimics) –> FEA package». The unloading coefficient dependence on the circumferential tightness for two types of “slippery” stocking materials was measured. When using both synthetic and silk stockings‚ experimental results did not show valid growth of CU with an increase in tightening (lateral compression) neither while standing nor walking. As calculations showed, pushing the shin up due to lateral compression may be to a maximum of ~ 1.2 mm even in total slip. At the same time‚ the shift of the shin surface as a result of the piston effect can reach several mm. Thus, the additional sediment due to the so-called “piston effect” (skin stretching under a load, as well as its shift-slip over thin and soft layer of subcutaneous fat) is several times greater than the effect of ejection due to lateral compression and associated unloading, and thus completely reduces them to nothing. Further possibilities and approaches to the problem of load programming at limb orthotics are discussed.

Identification of Defects in an Elastic Body by Means of the Boundary Measurements

A problem of identification of a single defect (a crack, a cavity or an inclusion) in an anisotropic, linear elastic body using boundary measurements is considered. An analytical solution of the problem of ellipsoidal defect identification in an infinite elastic solid is presented in the conditions when arbitrary constant stresses are applied at the infinity and the loads and displacements are known on a closed surface, containing the defect inside. The problem is solved using reciprocity gap functional method. The obtained analytical solution is used for solving the problem of ellipsoidal defect identification in a bounded elastic body by means of the results of one static test. It is assumed that the loads and displacements are measured on the external boundary of the body. Numerical examples illustrating efficiency of the developed method are considered. Stability of the results relative to the noise in the data and variation of the defect shape is studied.

Identification of finitely many small defects in an anisotropic linearly elastic body from a single static test

The problem of identification of finitely many small defects (inclusions, cavities, cracks) clearly separated from each other in the arbitrarily anisotropic linearly elastic space is considered. It is assumed that the forces and displacements are measured on the outer boundary of the body in a single static experiment. A method for determining the number of defects and their center position from the available data is developed. The geometric parameters (dimensions and orientations) of defects are determined if they have ellipsoidal shapes.

Reply to “Comment on ‘A Compact Analytic Model of the Strain Field Induced by Through ilicon Vias”’

The comment adds the results of 2 × 2 TSVs which is an extension of our 2-TSV case, and the clarification of no thermal strain effect on mobility. There are no contradictions with our original paper at all. Note that for the mobility calculation, the temperature dependence can be considered by the band parameters and phonon scattering [1].

The Mechanical Modeling of Oxygen-Containing Precipitates in Silicon Wafers on Different Stages of the Getter Formation Process

The behavior of the oxygen-containing precipitate in silicon wafer on different stages of the getter formation process is considered from the mechanical point of view. The precipitate is modeled as a spheroidal inclusion undergoing inelastic eigenstrains in an anisotropic silicon matrix. The stress-strain state in the precipitate and matrix is calculated within the framework of the model. An energetic criterion of breaking the spherical shape by the coherent precipitates is obtained and analyzed. Criteria of the formation and onset of motion of the dislocation loops in the vicinity of the precipitate are also proposed. The obtained results are compared with the available experimental data.