Full space elastic field of heterogeneous structures with an ellipsoidal inhomogeneity
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Abstract:
Heterogeneous semiconductors usually have better performance than homogeneous semiconductors, but the eigenstrain caused by lattice mismatch or thermal expansion of the embedded inhomogeneity has a serious impact on the overall performance of the material. Therefore, it is necessary to study the effect of inhomogeneity on the full space elastic field of heterogeneous structures. According to the classical inclusion theory of Eshelby and considering the anisotropy and heterogeneity of practical semiconductor materials, an analytical model of heterogeneous structure with an ellipsoidal inhomogeneity is established based on the equivalent inclusion method and Green’s function method. In order to solve the model, the exact numerical integration of Green’s function and its derivatives in real space are derived by Fourier transform and inverse transformation, and the numerical integration expression of the elastic field in full space is obtained. The comparison of the results obtained by the proposed model with those by the finite element method and those reported in literature verifies the correctness of the model and shows the necessity of the anisotropy hypothesis. The results show that the shape change of heterogeneous inclusions changes the internal elastic field from the plane stress state to the plane strain state, and affects the strain magnitude and attenuation degree near the interface. Interestingly, when the eigenstrain only contains normal components, the final elastic field does not change with shear elastic constants of the inhomogeneity with orthotropic or higher symmetry, but it is only related to tensile elastic constants with the same changing trend.
