## Info

Figure 31. The binding energy as a function of Al concentration for hydrogenic impurities in a cylindrical wire (r0 = a*B). Same electric field values as in Figure 28. Reprinted with permission from [205], J. L. Marín et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

impurity, a critical point from which bulk states change their nature (edge states) is also found.

Semiconductors composed of III-V materials usually have small effective masses, which means that the Bohr radius associated with the impurity is large compared with achievable quantum dot sizes. The binding energy of the impurity increases as the size of the confining region becomes of the order of Bohr radius, which makes possible, for instance, the fabrication of a low-threshold laser diode [100].

In this section a variational study about the effect of a magnetic field on the ground state and binding energies of a hydrogenic impurity within spherical quantum dot is made. The impurity can be located on (off) the center of symmetry to get a symmetric (asymmetric) situation, or near the boundary of quantum dot to get surfacelike states (edge states) of this system.

### 3.6.1. Theory and Model

Within the framework of the effective mass approximation, the Hamiltonian of a hydrogenic impurity located at the center of symmetry of a spherical quantum dot of radius r0, in the presence of magnetic field, can be written as

where k is the dielectric constant of materia^ inside the quantum dot, m*e is the electron effective mass, A is the vector potential, and Vh(r) is the confining potential defined by

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