Theoretical Studies On The Electronic Properties In Semiconductor Quantum Dots

Low-dimensional quantum dots material has great potential application in nanoelectronics at 21st century, which stimulates greatly people to study on this subject. Studies on properties related to electron in such material understand easily the principle of quantum component, which is useful, such as emission and absorption in quantum lasers.In this thesis, we focus on theoretical studies on properties related to electron in semiconductor quantum dots. Stark effect in rectangular quantum dots is investigated and binding energies of hydrogenic impurities in cylindrical quantum dots are studied in the presence of external fields.In chapter 2, Stark shift of electron in GaAs semiconductor rectangular quantum dots is studied. The asymptotic expansions of the Stark shift are given in the limits of low and high fields, respectively, they clearly indicate that the Stark shift is quadratic function of the electric field for low electric fields and is an approximate linear function of the electric field for high electric fields. Likewise, our results show also that the largest Stark shift is obtained for the field directed along the diagonal in a cubic box, and is found for the low field directed along a side of the box and for the high field along the diagonal in a rectangular one. Within the effective-mass approximation, the numerical results from the effects of the electric fields and quantum sizes on Stark shift are given. It can be clearly seen that quantum sizes have a demonstrable effect on the shift.In chapter 3, we study the binding energies of hydrogenic impurities in cylindrical quantum dots. The QD is modeled by superposing a square-well potential and a strong lateral confinement potential by the combining of a parabolic potential and a changeable magnetic field. Under the strong lateral confinement, we may replace three dimensional Coulomb potential with quasi-one-dimensional effective potential.The influences of the electric field, magnetic field and the positions of impurities on the binding energies are studied. When the impurity is located at the center of a quantum dot, the electric field pushes the electron away from the center of impurity while the magnetic field takes the electron to close to the center. This fact leads an interesting compete between electric field and magnetic field. Meanwhile, one finds that the binding energies highly depend on the impurity positions under the applied transverse fields. When the impurity is located.at the right half of the cylinder, the electric field pushes the electron to left side, then the binding energy decreases; when the impurity is located at the left, the binding energy first increases and reaches a peak value, then deceases with the electric field.