Elsevier

Microelectronics Journal

Volume 36, Issues 3–6, March–June 2005, Pages 244-246
Microelectronics Journal

The effects of magnetic field on the energy levels of shallow donor impurities in GaAs/AlxGa1−x as quantum dots

https://doi.org/10.1016/j.mejo.2005.02.013Get rights and content

Abstract

In the present work, we report a calculation of the electron energy levels (1s,2p−,2p+) and the binding energies of a shallow impurity placed in the center of a circular quantum dot of a GaAs surrounded by AlGaAs in the presence of a uniform magnetic field applied perpendicularly to the plane of the dot. We also present results for the 1s−2p+ transition energy as a function of the magnetic field.

Introduction

In the last few years the semiconductor quantum dot (QD) systems have attracted much attention, because of their potential applications in electronic and optoelectronic devices.

In these quasi-zero-dimensional electronic systems the confinement in all three direction, increases greatly the Coulomb interaction. Thus the presence of a donor impurity plays an important role in the electronic properties of these structures. The donor binding energies have been studied theoretically in quantum dots of different geometric forms: cylindrical, rectangular, spherical, pyramidal, etc. [1], [2], [3], [4], [5], [6].

In the present work we report a calculation of the electron energy levels (1s, 2p−, 2p+) and the binding energies of a shallow impurity placed in the center of a circular QD of GaAs surrounded by AlxGa1−xAs in the presence of a uniform magnetic field applied perpendicularly to the plane of the dot. First, without the magnetic field, the electron wave functions are obtained analytically by solving the Schrödinger equation and the donor impurity levels are determined through the numerical solution of the transcendental equation obtained from the boundary conditions imposed to the QD interfaces. When a magnetic field is applied to the system, analytic solutions of the Schrödinger equation are not possible and a variational method is used in order to calculate the impurity binding energies as a function of the magnetic field strength and of the QD radius.

Section snippets

Theory

Let us consider a impurity donor located in the center of a circular QD of GaAs surrounded by AlxGa1−xAs in the presence of a uniform magnetic field applied in the z-direction perpendicular to the QD plane. The electron-confinement potential V(r) is assumed as zero inside the QD (r<R), where R is the QD radius, and outside of the QD (r>R) as Vo=0.6[1047x+470x2] meV, where x is the aluminium concentration in the barrier material. The electron effective mass depends on the electron position r=(x,y

Results and discussion

Our numerical calculations are for a QD composed of GaAs and surrounded by AlxGa1−xAs with aluminium concentration x=0.3 corresponding to a confining potential barrier height of Vo=214 meV. The GaAs physical parameters used in the calculation were the effective Bohr radius, ao*=98.69 Å, and the effective Rydberg, R*=5.83 meV. The results obtained with the trial wave function are in a great agreement with the analytical results obtained from the solution of the transcendental Eq. (5) in the absence

Conclusion

In summary we have studied the magnetic field effects on the impurity energies levels 1s and 2p+ as a function of a uniform magnetic field applied perpendicularly to a circular GaAs–AlGaAs quantum dot. The impurity is located in the center of the QD. The magnetic field effects on the binding energies and on the 1s−2p+ transition energies were also studied.

Acknowledgements

We thank the Fundação de Apoio à Pesquisa FUNAPE-UFG and Pró-Reitoria de Pesquisa e Pós-Graduação (PROPE) da UCG for financial support.

References (6)

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