Estudo dos efeitos da orientação do campo magnético sobre a estrutura eletrônica de poços quânticos semicondutores

Abstract

This work is aimed to theoretically determine, based on the k p method, the energy spectrum of the minimum of conduction band and the top of valence band, in a quantum well heterostructure based on gallium arsenide, in the presence of a tilted magnetic eld. In this work, conduction and valence bands are independently treated. For the conduction band, it is employed the e ective-mass Hamiltonian when the magnetic eld is parallel, perpendicular, and tilted in relation to the con nement direction of the quantum well, de ned here as ^z. The basis that solves the orbital problem for = 0o is also employed to perpendicular ( = 90o) and tilted magnetic eld cases through two approaches: (i) expansion and diagonalization of orbital part of Hamiltonian and (ii) non-degenerate perturbation theory. The problem for = 90o is also analytically treated, through a basis composed of con uent hypergeometric functions. Results obtained by approach (i) are shown to be equivalent to those extracted from the analytical treatment, for a broad range of magnetic eld intensity and quantum well thickness. Such a result motivates the employment of the basis, determined for = 0o, to deal with tilted eld in the conduction band and with the treatment of valence band, based on the Luttinger model. The Luttinger Hamiltonian is expanded and diagonalized, in parallel and tilted magnetic eld con gurations, with respect to ^z. The energy branches as a function of the magnetic eld intensity are computed for the valence band when = 0o, = 35o, and = 70o. The two topmost states are selected, whose spin characters indicate that both predominantly have a heavy hole type with either spin-up or spin-down. From these levels, it is calculated the electron-hole pair spin splitting EZ, for quantum wells of di erent thickness and for angles 0o, 35o and 70o with respect to ^z. The connection with experimental results is performed by using the data of the Zeeman splitting obtained from a sample of multiple quantum wells made of gallium-aluminium arsenide, on which a magnetic eld is applied in = 0o and in = 70o. The calculated EZ show a reasonable agreement with the experimental data in both cases when = 0o and = 70o.