PSI - Issue 42

Neha Duhan et al. / Procedia Structural Integrity 42 (2022) 863–870 Duhan et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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devices. The alloying leads to unique properties of band-gap and strain/lattice parameters different than individual components Si and Ge. The semiconductors are crystalline materials (cubic/hexagonal close packed) and slightly imperfect lattice arrangement can result in defects. The lattice defects, such as point or line (dislocation) defects, can result in performance degradation and failure. To restrict the defects in the materials along with properties control, the alloying of different semiconductor materials is helpful. The alloy is a solid solution that is not completely defect-free and possesses some defects (dislocations) in it. The dislocations succeeding motion can annihilate and result in cracks which can result in failure of the component/structure. This indicates the necessity to study the behavior of dislocation in semiconductors. The strain in Si x Ge 1-x alloy semiconductor has useful effects however the plastic deformation due to strain relaxation can result in defect formation. The Si x Ge 1-x crystals, when grown on the substrate layer, generate dislocations at different locations in it. The material properties of Si x Ge 1-x alloy semiconductor, such as lattice constant, thermal and electrical conductivity, along with thermal expansion coefficient, are dependent on the mole fraction (x Si ) of silicon as given by Dismukes et al. (1964a), (1964b). The temperature also has a role to play on the change in material properties of semiconductor alloys. The existence of dislocation can result in scattering, which will impact the electrical conductivity, thermal conductivity and Seebeck coefficient (Watling and Paul (2011)). The motion of dislocations in Si x Ge 1-x crystals has already been studied experimentally by Iunin et al. (1996). For a given alloy, the velocity of individual dislocation was studied with respect to temperature and stress. Also, Abrosimov et al. (1997) performed experiments to understand dislocation mobility and kink motion in Si x Ge 1-x alloy crystals under conventional and intermittent loadings. Two different models were used with the experimental data to describe the interaction of dislocation with point defects. Moreover, the experiments to understand the dislocation motion in Si x Ge 1-x with recombination were also performed in a high voltage transmission electron microscope (TEM) (Yonenaga et al. (1999)). The velocities of dislocations were found to be increased due to the recombination-assisted kink formation. A review of experimental investigation of the dislocation motion in compound semiconductors is available in the literature to understand the dislocation behavior at the microscopic scale (Vanderschaeve et al. (2001)). Huang et al. (2005) used the transmission ion channeling technique to map misfit dislocations between Si x Ge 1-x layer and silicon. 60° misfit dislocations cause crystal plane bending, which is observed experimentally. Then the dislocation network formed by edge type dislocations in Si x Ge 1-x layers was analyzed at the interface between Si x Ge 1-x and Si substrate using TEM (Sakai et al. (2005)). The dislocation network was found as it is even after Si and Ge intermixing. The dislocation dynamics in SiGe alloys was studied by Yonenaga (2013) to know the dislocation velocity and mechanical strength of the Si x Ge 1-x alloy crystal. The dislocation velocity was found to be decreasing with an increase in Si content (from 0.004 to 0.08) in Si x Ge 1-x alloys and first increasing then decreasing and again increasing for Si content between 0.92 to 1. Other than the experimental studies of dislocations in semiconductors, we can see different numerical studies also available in the literature. Recently, the finite element modeling (FEM) of semiconductor thermoelectric generator made of Si x Ge 1-x alloys has been done by Big-Alabo (2021) without considering dislocations in it. The dislocations in semiconductors have discontinuity and singularity related to the presence of the glide plane and core. The modeling of discontinuity and singularity is a difficult task with FEM hence the XFEM has been adopted to simulate dislocations (Gracie et al. (2007)). The linear elastic (Gracie et al . (2008)), electromechanical (Skiba et al. (2013)) and thermo elastic studies of dislocations (Duhan et al. (2021)) are available in the literature. Recently, Duhan et al. (2022) considered the nonlinearity due to temperature dependent material properties of the semiconductors while analyzing the thermo-elastic fields with consideration of internal heat due to Joule Heat. From the literature, it is found that the dislocation simulation is not yet done for the alloy semiconductors where material properties are changing with the concentration of one of the alloy components. Here, the Si x Ge 1-x alloy having edge dislocation with Joule heat generation at the core is considered for the simulation of the Peach-Koehler force used in different electronic devices. The present paper is structured in four segments, namely: (1) Introduction, (2) Problem Formulation, (3) Numerical Example and (4) Conclusion. In section 1, a brief review of the literature studies is present where the available experimental and numerical studies related to the presence of dislocation in semiconductors specially Si x Ge 1-x alloys are discussed. In section 2, the equations related to the formulation of the dislocation problem using XFEM is