Quantum semiconductor structure has been considered to be a promising nanostructure with certain unique electronic and optical features as compared to its traditional counterpart. Because of the lattice difference between different materials in the structure, a misfit strain field is introduced. Furthermore, other external sources, such as far-field loading, may introduce a superposing strain field. These strain fields then in turn induce elastic and piezoelectric fields in the system. In the physical community, a semicoupled model is usually adopted to calculate these induced fields. In such a simplified model, the elastic field is first solved based on the purely elastic model. The piezoelectric field then is obtained from the elastic field through the polarization equation. In this article, we derive the elastic and piezoelectric fields in the AlN plate subjected to a uniaxial far-field strain based on a fully coupled piezoelectric model. We show that in this strongly coupled piezoelectric material, the elastic and piezoelectric fields predicted based on the semicoupled model can be in serious error, as compared to those based on the fully coupled model.
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