研究目的
To develop a gradient theory of piezoelectricity for 3D analyses of quantum dots (QDs) with functionally graded lattice mismatch between the QD and the matrix, and to investigate the influence of distances between QDs on strain distribution.
研究成果
The 3D mixed finite element model developed for QDs with functionally graded lattice mismatch shows that the largest peak values of strains are observed on interfaces of the QD and the surrounding matrix for a uniform eigenstrain. The density of QDs in the matrix influences the absolute values of the elastic strain component in the center of the QD, which increases if the distance between two QDs is decreasing.
研究不足
The study is limited by the assumptions of the gradient theory of piezoelectricity and the specific geometry and material properties considered. The influence of distance between QDs is found to be weak for both fields.
1：Experimental Design and Method Selection:
The study employs the gradient theory of piezoelectricity for 3D analyses of QDs with functionally graded lattice mismatch. The mixed FEM with C0 continuous interpolation and collocation approach for kinematic constraints between strains and displacements is developed.
2：Sample Selection and Data Sources:
The representative volume element (RVE) for the quantum nanostructure solar cell is analyzed, considering a cubic geometry with side length of b = 40 nm and a cubic QD with side length of hQD = 4 nm embedded in it.
3：List of Experimental Equipment and Materials:
Material properties of the QD correspond to InAs, and the substrate is made of GaAs.
4：Experimental Procedures and Operational Workflow:
The FEM model was set up by constructing the geometry and meshing it using 195,696 elements corresponding to 339,117 nodes. The variation of the strain component and electric potential is analyzed.
5：Data Analysis Methods:
The study analyzes the variation of strain components and electric potential along specific directions, considering different power law exponents for the functional variation of eigenstrains.
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