O2

Figure 30. The binding energy as a function of impurity position along the (a) x-axis of the square wire (L = sfñ2a*B) and (b) radius of the cylindrical wire (r0 = 2a*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.

Figure 30. The binding energy as a function of impurity position along the (a) x-axis of the square wire (L = sfñ2a*B) and (b) radius of the cylindrical wire (r0 = 2a*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.

Figure 30b shows the binding energy as a function of impurity position along the radius of the cylindrical wire (r0 = 2a*B) for different electric fields. In this case also, the binding energy becomes generally smaller for the same reason.

The Al concentration (x) dependence of the binding energy is shown in Figure 31. As expected, increasing the potential barrier increases the binding energy, because the electron is better pushed toward the Coulomb center when the walls are at a higher potential.

In conclusion, the variational method employed in this context is capable of giving all the correct trends for impurity binding energies as a function of the applied electric field, impurity position, and wire geometry.

3.6. Hydrogenic Impurities in a Spherical Quantum Dot in the Presence of a Magnetic Field

The ground state and binding energies for a hydrogenic impurity in a spherical quantum dot in the presence of a uniform magnetic field are calculated by a variational method within the effective mass approximation [99]. The simple hydrogenic trial wavefunctions used in this calculation are flexible enough to treat on-center, off-center, and edge states of impurities in a quantum dot. Overall results are in reasonable agreement when compared to other calculations. Interestingly enough, in the case of an off-center

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