Theoretical Study On The Electronic Properties In Semiconductor Quantum Wires And Quantum Dots

Quantum theory has gotten significant achievements in practice. Quantum component is the forefront of field in electron component manufacture, which has great potential application in low-dimensional semiconductor quantum material especially. And it stimulates greatly people to study on quantum material theoretically and experimentally.In this thesis, we focus on theoretical studies on properties related to electron in semiconductor quantum wires and dots. Stark effect in cross-sectional area of the rectangular quantum wires is investigated in the presence of electric field. Binding energies of hydrogenic impurities in cylindrical quantum dots are also studied in the presence of external electric and magnetic fields.In chapter 2, Stark shift of electron in semiconductor cross-sectional area of the rectangular quantum wires is studied by variational method and effective mass approximation. 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, we discuss the Stark shift is related to both the electric field and the quantum sizes. The electric field direction has little effect on Stark shift in the cross-sectional area of square quantum wires for low electric fields while Stark shift is largest when the electric field direction is along the diagonal of the square for high electric fields. Stark shift is largest when the electric field direction is along a side of the cross-sectional area of the rectangular quantum wires. But the largest Stark shift is found when the high electric field direction is along the diagonal of the cross-sectional area in the quantum wire with the length nearly being equal to width. Stark shift is only related to the length of side along the x axis rather than the y axis when the electric field is parallel to the x axis.In chapter 3, we study the binding energies of hydrogenic impurities in cylindrical quantum dots by finite-difference method. 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 electric field and magnetic field. We have studied the influences of the electric field, the magnetic field and the positions of impurities on the binding energies. When the impurity is located at the center of a quantum dot, the binding energies decrease for the electric field and effective radius increasing. When the impurity is located at the plane through the axis of QD center, the binding energy changes symmetrically as the location is far away from the QD center, however, when the impurity is located at the z axis, the symmetry vanishes for the electric field affection.