Periodically Grown Quantum Nanostructures with Arbitrary Geometries: Periodicity Effects on the Induced Electro-elastic Fields

Quantum nanostructures (QNSs), due to their widespread and attractive physical, optical, and electronic properties, have been at the center of attention of many nanoscience and nanotechnology researches. In order to predict the electro-mechanical behavior of QNSs, accurate determination of the electro-elastic fields induced by quantum wells (QWs), quantum wires (QWRs), and quantum dots (QDs) in such nanostructures would be of great importance and particular interest. In this study, by utilization of the electro-mechanical eigenfield concept in conjunction with the Fourier series technique, an analytical solution is presented which gives the electro-elastic fields induced by one-, two-, and three-dimensional periodic distribution of QWs, QWRs, and QDs, respectively. This methodology takes into account the electro-mechanical couplings of elastic and electric fields within the piezoelectric barrier as well as the interaction between periodically grown QWRs and QDs. The latter would be so important since the density of the periodically grown QNSs will have significant effects on the induced electro-elastic fields within both the QNSs and the surrounding barrier; this issue is addressed precisely in the present study by measuring the induced electro-elastic fields due to different periodicities of pyramidal QDs. Furthermore, the current formulation is capable of treating arbitrary geometries of QWRs and QDs which makes the solution more interesting and powerful.