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

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].