Studies On Electron States, Phonon States And Heat Transport In Low-Dimensional Nanostructures

Due to their novel physical properties, and prospective and potential applications, the low-dimensional nanostructures and nanostructured materials, such as superlattices (SLs), quantum wells, wires, and dots, have been received increasing attentions and become one of the frontier research topics in condensed matter physics and material science in recent years. Simultaneously, rapid progress in the synthesis and processing of materials with structures on nanometer length scales has created a demand for greater scientific understanding of the properties of nanoscale devices, individual nanostructures, and nanostructured materials. In this thesis, localized electronic states (including surface states) in semiconductor SLs with structural defects, and the acoustic phonon transmission and thermal conductance in the low dimensional nanostructures are investigated.Using an effect-barrier height method, we investigate the influence of the coupling between normal and lateral motion of an electron on the surface electron in a semi-infinite SL with a cap layer within the framework of effective-mass theory. Meanwhile, the properties of the extended states are also discussed. The results show that the existence and features of the surface electron states, especially the higher-lying surface electron state, as well as the energy positions and widths of the minibands and minigaps are strongly dependent on the transverse wave number. The influence of the thickness and concentration of the cap layer, as well as the component of the substrate, on the surface states is also obvious. By applying magnetic fields along the growth direction of the SL, the magnetic-coupling effect brings about not only the splitting of the surface electron levels but also the definite dependence of the surface levels and its localization degree on magnetic fields and Landau indices. The imaginary component of Bloch wave number can serve as a measure of the localization degree of the surface electron states. The results will be of benefit to the design of the opto-electron devices.By introducing "complex wave vector" and applying the Bloch theorem to the N-layer-based SLs, we derive general formulae to calculate the localized electronic states in the infinite SLs with structural defects. In particular, the properties of the localized electronic states in a triple SL are studied numerically and a detailed comparison of localized electronic levels between symmetric and asymmetric structures is given. The results show that the minibands are not influenced by the structural symmetry, while the localized states display different behaviors in both symmetric and asymmetric structures. With the increase of the defect layer thickness, the localized states appear periodically in each minigap, and the branch number of the localized states increases with increasing the index of the minigap. For symmetric structure, the parities of the localized states alternate between even and odd parity in...