Biblio
Self-assembled semiconductor quantum dots possess an intrinsic geometric symmetry due to the crystal periodic structure. In order to systematically analyze the symmetric properties of quantum dots' bound states resulting only from geometric confinement, we apply group representation theory. We label each bound state for two kinds of popular quantum dot shapes: pyramid and half ellipsoid with the irreducible representation of the corresponding symmetric groups, i.e., C4v and C2v, respectively. Our study completes all the possible irreducible representation cases of groups C4v and C2v. Using the character theory of point groups, we predict the selection rule for electric dipole induced transitions. We also investigate the impact of quantum dot aspect ratio on the symmetric properties of the state wavefunction. This research provides a solid foundation to continue exploring quantum dot symmetry reduction or broken phenomena because of strain, band-mixing and shape irregularity. The results will benefit the researchers who are interested in quantum dot symmetry related effects such as absorption or emission spectra, or those who are studying quantum dots using analytical or numerical simulation approaches.
Accurate model is very important for the control of nonlinear system. The traditional identification method based on shallow BP network is easy to fall into local optimal solution. In this paper, a modeling method for nonlinear system based on improved Deep Belief Network (DBN) is proposed. Continuous Restricted Boltzmann Machine (CRBM) is used as the first layer of the DBN, so that the network can more effectively deal with the actual data collected from the real systems. Then, the unsupervised training and supervised tuning were combine to improve the accuracy of identification. The simulation results show that the proposed method has a higher identification accuracy. Finally, this improved algorithm is applied to identification of diameter model of silicon single crystal and the simulation results prove its excellent ability of parameters identification.