Development of an eight-band theory for quantum-dot heterostructures

Details Development of an eight-band theory for quantum-dot heterostructures Development of an eight-band theory for quantum-dot heterostructures

2001-09-14

arxiv.org/abs/cond-mat/0109275v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

36 pages, 10 figures, E-mail addresses: devreese@uia.ua.ac.be, fomin@uia.ua.ac.be

Scientific paper

10.1103/PhysRevB.64.245328

We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot heterostructures (QDHs) in Burt's envelope-function representation. The 8x8 radial Hamiltonian and the boundary conditions for the Schroedinger equation are obtained for spherical QDHs. Boundary conditions for symmetrized and nonsymmetrized radial Hamiltonians are compared with each other and with connection rules that are commonly used to match the wave functions found from the bulk kp Hamiltonians of two adjacent materials. Electron and hole energy spectra in three spherical QDHs: HgS/CdS, InAs/GaAs, and GaAs/AlAs are calculated as a function of the quantum dot radius within the approximate symmetrized and exact nonsymmetrized 8x8 models. The parameters of dissymmetry are shown to influence the energy levels and the wave functions of an electron and a hole and, consequently, the energies of both intraband and interband transitions.

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