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Figure 25. Binding energy of the ground state (s0B) and the first excited (e1B) states of a donor in a spherical quantum dot versus the dot radius r0. The curves a, ab, and b represent s0B of the dot of V0 = 80, 60, and 40Ry, and the curves c, cd, and d represent s1B of V0 = 80, 60, and 40Ry, respectively. Arrows indicate the relevant vertical scales. Reprinted with permission from [205], J. L. Marin et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

their maxima and that the increase of the binding energies is always much less than the increase of the energies of the corresponding states of an electron only confined by the spherical quantum dot, although the binding energies can be much larger than those in the corresponding two-dimensional quantum well and quantum well wire. It means that confinement effects [95, 96] are dominant in the range of r0. Further, it is also true for the higher excited states. Therefore we can know what kind of quantum-level sequence we will have if the motion of an electron is confined by both a spherical quantum well and a Coulomb field with the same center. The level sequence is similar to that of a three-dimensional hydrogenic donor if r0 is much larger and quantum confinement due to the spherical quantum dot is very weak. However, it is similar to that of the electron in the spherical quantum dot if the quantum confinement of the spherical quantum dot is stronger than that of the Coulomb potential. Based on what we have mentioned, we can understand why the quantum level structure of GaAs-Ga1—x Alx As superatoms [93, 97] is similar to that of an electron in a spherical quantum dot and quite different from those of ordinary atoms and why the electronic structure of the superatoms is dominated by no-radial-node states of 1s, 1p(2p), 1d(3d), and so on.

In Figure 26, the maximum binding energies ebmax for the hydrogenic donor ground and first excited states in a spherical quantum dot as a function of the barrier height V0 were plotted. It is shown that the enhancement of the maximum is greater in a spherical quantum dot (quasi-zero-dimensional) than in the corresponding quantum well wire and two-dimensional quantum well as V0 is increased. This is because of the enhancement of the electron confinement in three dimensions in the spherical quantum dot. In Figure 27, it was shown that the maximum binding energy ebmax of ground states of a donor at the center of a different kind of quantum well depends on the well dimensionality and barrier height V0 and presents quasi-two-, one-, and zero-dimensional features of the hydrogenic donor, respectively. It is interesting to note that the mean values of

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