Donor Impurity in CdS/ZnS Spherical Quantum Dots under Applied Electric and Magnetic Fields

Abstract

This article presents a theoretical study of the electronic, impurity-related, and nonlinear optical properties of CdS/ZnS quantum dots subjected to electric and magnetic fields. The magnetic field is applied along the z-axis, with the donor impurity always located in the center of the quantum dot. In the case of the electric field, two situations have been considered: applied along the z-axis and applied in the radial direction (central electric field). In both cases, the azimuthal symmetry (around the z-axis) is preserved. In the absence of a magnetic field and considering a central electric field, the system preserves its spherical symmetry both in the presence and in the absence of the donor impurity. The study is carried out in the effective mass approximation and it uses the finite element method to find the eigenfunctions and their corresponding energies, both in the presence and in the absence of the impurity. This work investigates the optical absorption coefficient and the relative change of the refractive index, considering only intraband transitions between l = 0 states (states with azimuthal symmetry concerning the z-axis). Calculations are for z-polarized incident radiation. The study shows that the combined effects of a central electric field and a z-directed magnetic field can give rise to a typical core/shell-like quantum confinement with oscillations of the electron ground state. Additionally, it is shown that the presence of the donor impurity suppresses such oscillations and it is responsible for blue shifts in the optical properties and magnifications of the corresponding resonances.

Keywords: binding energy; core/shell quantum dot; donor impurity; electric field; magnetic field; nonlinear optical properties.

Figure 1

(color online) Pictorial view of the CdS/ZnS spherical QD studied in this work. The QD size, the z-directed applied EF and MF ($F_z$ and B), and the central EF ($F_r$) are indicated, together with the r-dependent confinement potential.

Figure 2

(color online) The lowest confined electron states in a CdS/ZnS spherical QD as functions of the $R_1$-inner radius. Results are without (a) and with (b) on-center donor impurity, with $R_2=30$ nm, for several values of the l-quantum number, and without EF and MF effects.

Figure 3

(color online) The lowest confined electron states in a CdS/ZnS spherical QD as functions of the central (a,b) and z-directed (c,d) EFs. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm, for several values of the l-quantum number and without MF effects.

Figure 4

(color online) The lowest confined electron states in a CdS/ZnS spherical QD as functions of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm, for several values of the l-quantum number. Calculations are with no EF in (a,b), whereas in (c,d) the results are for a central EF $F=-20$ kV/cm.

Figure 5

(color online) The lowest confined electron states in a CdS/ZnS spherical QD as functions of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm, for several values of the l-quantum number. Calculations in (a,b) are for zero EF, whereas in (c,d) the results are for $F=-20$ kV/cm, z-directed EF.

Figure 6

(color online) The squared matrix elements for transitions from the ground state to the first fourteen excited states with $l=0$ ($|1\rangle \to |n\rangle$, with $n=2,3,\dots ,15$) of a confined electron in a CdS/ZnS spherical QD as functions of the $R_1$-inner radius. Results are without (a) and with (b) on-center donor impurity, with $R_2=30$ nm, and without EF and MF effects.

Figure 7

(color online) The squared matrix elements of the transitions from the ground state to the first fourteen excited states with $l=0$ ($|1\rangle \to |n\rangle$, with $n=2,3,...,15$) for a confined electron in a CdS/ZnS spherical QD as functions of the central (a,b) and z-directed (c,d) EF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm.

Figure 8

(color online) The squared matrix elements of the transitions from the ground state to the first fourteen excited states with $l=0$ ($|1\rangle \to |n\rangle$, with $n=2,3,\dots ,15$) for a confined electron in a CdS/ZnS spherical QD as functions of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm. Calculations are for zero EF (a,b) whereas in (c,d) the results are for $F=-20$ kV/cm, central EF.

Figure 9

(color online) The squared matrix elements of the transitions from the ground state to the first fourteen excited states with $l=0$ ($|1\rangle \to |n\rangle$, with $n=2,3,\dots ,15$) for a confined electron in a CdS/ZnS spherical QD as functions of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm. Calculations are for zero EF (a,b) whereas in (c,d) the results are for $F=-20$ kV/cm, z-directed EF.

Figure 10

(color online) The total optical absorption coefficient (a,b) and the total relative changes of the refraction index coefficient (c,d) as functions of the incident photon energy in a CdS/ZnS spherical QD with several values of the $R_1$-inner radius. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_2=30$ nm. Optical transitions are between the lowest confined $l=0$ states without electric and MF effects.

Figure 11

(color online) The total optical absorption coefficient (a,b) and the total relative changes of the refraction index coefficient (c,d) as functions of the incident photon energy in a CdS/ZnS spherical QD for several values of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm. Optical transitions are between the lowest confined $l=0$ states without EF effects.

Figure 12

(color online) The total optical absorption coefficient (a,b) and the total relative changes of the refraction index coefficient (c,d) as functions of the incident photon energy in a CdS/ZnS spherical QD, for several values of the MF. Results are without (a,c) and with (b,d) on-center donor impurity, with $R_1=20$ nm and $R_2=30$ nm. Optical transitions are between the lowest confined $l=0$ states, considering a central EF $F=-20$ kV/cm.