Development of an eight-band theory for quantum-dot heterostructures
نویسندگان
چکیده
We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantumdot heterostructures (QDHs) in Burt’s envelope-function representation. The 8×8 radial Hamiltonian and the boundary conditions for the Schrödinger 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 k ·p 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 8×8 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. PACS numbers: 73.20.Dx, 73.40.Kp, 73.40.Lq
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