Elsevier

Microelectronics Journal

Volume 39, Issues 3–4, March–April 2008, Pages 450-454
Microelectronics Journal

Effects of geometry, applied hydrostatic pressure and magnetic field on the electron–hole transition energy in a GaAs–Ga1−xAlxAs pillbox immersed in a system of Ga1−yAlyAs

https://doi.org/10.1016/j.mejo.2007.07.020Get rights and content

Abstract

In this work, we study the behavior of the electron–hole transition energy in a GaAs–Ga1−xAlxAs pillbox immersed in a system of Ga1−yAlyAs as a function of thickness of the ladder barrier potential for a fixed length of the pillbox, length of the pillbox, thickness of the ladder barriers and pillbox position in the host of Ga1−yAlyAs. The behavior of the electron–hole transition energy as a function of an applied hydrostatic pressure and an applied magnetic field is also studied. For both electron and hole we found that in the strong confinement regime (L⩽10 Å) energy of the ground state as function of the position of the pillbox relative to the ladder barrier potential presents a behavior similar to the binding energy of a hydrogenic impurity in quantum wells, quantum wires and quantum dots [L. Esaki, R. Tsu, IBM J. Res. Dev. 14 (1970) 61; G. Bastard, Phys. Rev. B 24 (1981) 4714; N. Porras-Montenegro, J. López-Gondar, L.E. Oliveira, Phys. Rev. B 43 (1991) 1824]. Electron–heavy hole transition energies increase with the applied magnetic field. Also, we have found that these transition energies, as a function of the applied hydrostatic pressure, present an excellent agreement with experimental reports by Venkateswaran et al. [phys. Rev. B 33 (1986) 8416].

Introduction

Due to the development of experimental techniques such as the molecular beam epitaxy (MBE) and metal-organic chemical-vapor deposition (MOCVD), there has appeared a great interest in semiconductor heterostructures of low dimensionality such as quantum wells (QWs), quantum well wires (QWWs), and quantum dots (QDs), in which the charge carriers are, respectively, free to move in one and two dimensions completely confined.

Bastard [2] calculated the binding energy of the ground state of a hydrogenic impurity in a QW finding a strong dependence of the energy on the impurity position when it moves along the growth axis of the system. Porras-Montenegro et al. [3] calculated the ground state energy, the binding energy, and the density of states for shallow hydrogenic impurities in cylindrical, infinite-length, GaAs–GaAlAs quantum well wires. Perez-Merchancano and Porras Montenegro [4] calculated the ground state energy and binding energy of shallow hydrogenic impurities in spherical GaAs–GaAlAs quantum dot as a functions of the dot radius. Shu-Shen et al. [5] studied the electronic structures in the hierarchical self-assembly of GaAs/Ga1−xAlxAs quantum dots. In this work, we are concerned with the study of electron and hole states in a GaAs pillbox determined by a confinement potential due to a layer of Ga0.7Al0.3As surrounded by Ga1−yAlyAs with y>0.3. In Section 2, we propose the theoretical model. In Section 3, we present our results and, finally, in Section 4, we remark our conclusions.

Section snippets

Theoretical framework

In Fig. 1, we display the diagram for the pillbox showing both, the layers of the different materials in the growth direction and the energy scheme.

The Hamiltonian of an electron (hole) in GaAs pillbox determined by a confinement potential due to a layer of Ga0.7Al0.3As surrounded by Ga1−yAlyAs may be written asH=pe,h22me,h*+Ve,h(z,ρ),where the first term is the kinetic energy for the electron (hole), me*(mh*) is the corresponding effective mass, and the second term is the confinement potential

Results

In our results, we first explore the role of the width of the first barrier confining potential on the electron and hole energy in the pillbox structure. Second, we look at the hydrostatic pressure effects on the carrier first energy level.

In our calculations, without applied hydrostatic pressure and in the regime of low temperature, we have used me*=0.0665m0, mh*=0.3m0, and for the dielectric constant ε=12.58. We assumed that the band gap discontinuity in a GaAs–Ga1−xAlxAs QD pillbox

Conclusions

In this work using the effective mass approximation, we have calculated the ground state energy for the electron and hole in a Ga1−xAlxAs pillbox immersed in a host of Ga1−yAlyAs as a function of the thickness of the barrier potential for a fixed length of the pillbox, as a function of the length of the pillbox when the thickness of the barriers remained constant, and as a function of the pillbox position in the host of Ga1−yAlyAs. We have examined the behavior of the energy of the ground state

Acknowledgments

The authors want to thank the Colombian Scientific Agency (Colciencias, Grant no. 1106-05-13828), the CENM (Excellence Center for Novel Materials), and to the Comisión Mixta de Cooperación Científica y Técnica México-Colombia for the financial support.

References (10)

  • L. Esaki et al.

    IBM J. Res. Dev.

    (1970)
  • G. Bastard

    Phys. Rev. B

    (1981)
  • N. Porras-Montenegro et al.

    Phys. Rev. B

    (1991)
  • N. Porras-Montenegro et al.

    Phys. Rev. B

    (1992)
  • L. Shu-Shen et al.

    Phys. Rev. B

    (2005)
There are more references available in the full text version of this article.

Cited by (3)

  • Effects of temperature on binding energy and the nonlinear optical properties of a hydrogenic donor in a GaAs/Ga<inf>0.8</inf>Al<inf>0.2</inf>As pillbox immersed in a Ga<inf>0.6</inf>Al<inf>0.4</inf>As material

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    Kasapoglu [33] has studied the combined effects of hydrostatic pressure and temperature on donor impurity binding energy in GaAs/Ga0.7Al0.3As double quantum well. Ramos-Arteaga et al. [34] have examined the effects of hydrostatic pressure and magnetic field on electron–hole transition energy in GaAs/Ga1 − xAlxAs immersed in a system of Ga1 − yAlyAs. Duque et al. [35] have investigated the effects of applied magnetic field and hydrostatic pressure on the optical transitions in self-assembled QDs.

1

On sabbatical leave from IFUNAM.

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