Elastic and piezoelectric fields around a quantum dot: Fully coupled or semicoupled model?

In the study of elastic and piezoelectric fields in semiconductors due to buried quantum dots (QDs), the semicoupled piezoelectric model is commonly adopted. However, its accuracy and suitability have never been studied. In this article, by developing a fully coupled piezoelectric model and deriving the analytical elastic and piezoelectric fields based on this and the semicoupled models, we are able to verify that when the piezoelectric coupling is weak, like GaAs with the electromechanical coupling factor $g=0.04,$ the semicoupled model predicts very accurate results as compared to those based on the fully coupled model. However, if the piezoelectric coupling is relatively strong, like AlN with $g=0.32,$ we have shown that the semicoupled model gives very serious errors or even totally wrong results. Applying these two models to a uniformly strained AlN layer grown along the polar axis has also confirmed our observation. Therefore, for semiconductors like AlN, the fully coupled model presented in this article must be employed in order to give a reliable and accurate prediction for the elastic and piezoelectric fields. Also presented in this article is the distribution of the piezoelectric field on the surface of a half-space GaAs due to a buried QD located at 2 nm below the surface with a volume 4π/3 $(nm)3.$ It is observed that the horizontal electric field on the traction-free and insulating surface shows some special features and its maximum magnitude can be as high as $3.5×107$ V/m when the uniform mismatch eigenstrain is 0.07. Furthermore, the piezoelectric field on the traction-free and conducting surface exhibits different characters as compared to the traction-free and insulating case.