Semiconductor Quantum Dots (nc-si/sio <sub> 2 </ Sub>) / Sio <sub> 2 </ Sub> Exciton Energy Levels

In this dissertation, based on the effective-mass approximation, the electronic structures in semiconductor quantum dots ((nc-Si/SiO₂)/ SiO₂) are investigated in detail. The aim is to explore the physical mechanisms of the new effects in low-dimensional semiconductor systems, and to supply physical models and make the theoretical validity in designing novel quantum devices with better properties.1. According to spherical model of quantum dots, and with the condition of infinite potential well and finite potential well, the exciton energy levels and wave functions of the quantum dot structure (nc-Si/SiO₂) / SiO₂ are analyzed. Furthermore, to get a closer form to actual situation, the finite potential well model was adopted.2. The silicon quantum dots dielectric limited effect (surface polarization effect) was studied with the variational method. The relationship between the scale of quantum dots and the influence of quantum dots dielectric limited effect on the ground state energy of limited exciton is theoretical illustrated. The decrement in the ratio of dielectric constant of quantum dot on the dielectric constant of substrate will lead to decrement in the ground state energy of limited exciton in the quantum dot. As the ratio of dielectric constant of quantum dot on the dielectric constant of substrate <<1, the ground state energy of limited exciton will tends to a limit value but not decrease unlimitedly. 3. In the framework of the effective mass approximation, and using variational method, the ground state energy of limited exciton in silicon quantum dots with different shape was theoretical calculated. With the same volume (i.e. the same average limited scale), the ground state energy of limited excition depends on the symmetry of the shape of quantum dots, and a better symmetry will lead to a lower ground state energy of limited exciton. Therefore, the ground state energy of limited exciton for spherical quantum dots is lowest due to the good symmetry of sphere, and the ground state energy of limited exciton for cubic quantum dots is highest due to poor symmetry of cube.4. Quantum dot Silicon corresponding to an indirect band-gap structure, and phonon plays the key role in the transition of exciton. Based on the linear combination operator and unitary transformation method, we investigate the influence of phonon on the ground state energy of exciton in silicon quantum dots. By taken into consideration of the effect of phonon, the interaction energy of electron (hole)– phonon is a negative value, and the ground state energy of exciton is lower than the situation without the consideration. It is proper to consider the effect of phonon on the ground state energy.