Quantum Ring Impurity States In Quantum Tunneling

Quantum rings have attracted much attention since they were first successfully grown by A.Lorke et al in 1997, and their characteristics have now been extensively studied both theoretically and experimentally.In this thesis, we examine quantum rings and Aharonov-Bohm rings in the presence of a shallow-donor atom. We treat the rings as two dimensional objects bounded by a cylindrical square-well potential (SWP) with infinite barrier in the plane of the ring. This potential geometry is used for two reasons: First, the rings are subject to a strong binding potential in the thickness direction making the two dimensional description quite appropriate, and second, this two-dimensional mode has been found to give a good description, in the absence of donor ions, of the electronic states of a quantum ring as well as the tunneling properties of an Aharonov-Bohm ring.For cases with the shallow donor at the center of a typical ring (inner radius 10nm and outer radius 50nm in this work), separation of variables and diagonalization have been used to obtain the states of the donor and the binding energy. The analytical solution for the wave function is obtained for the case where the shallow-donor appears at the center of the ring. The electronic probability is also discussed. We find all the donor states are lower than corresponding electronic states, in particular, the ground state reduces more than excited states. With the increase of inner radius (the outer radius is fixed), the effect of the donor is weaker and weaker. When the donor is moved from the center of the ring to inner edge of the ring, the ground state is lower and lower and reduction is faster and faster.Finally, we examine the transport properties of an Aharonov-Bohm (AB) ring both with and without a shallow donor atom. In particular, we find the tunneling peaks cleave both presence and absence of the donor, when the angle between the two channels changes but the inner and outer radii are fixed. The donor makes the cleft more sensitive to the change of the angle; on the other hand, the donor didn't change the restrained of the peaks. Finally, we find that when the ring radii are allowed to change with fixed ring width, the larger the ring radii, the smaller is the effect of the donor.