Theoretical study on the band structure of Bi1̳-x̳Sbx̳ thin films

[摘要] The study on the electronic band structures of Bi1-xSbx thin films is a very interesting topic. Recall that in bulk Bi1-xSbx, the electronic band structure can be varied as a function of temperature T, pressure P and stoichiometry. The electronic band structure does not change with T significantly in the cryogenic temperature range under the atmospherical presure. The conduction band edge and the valence band edge are very close to each other at the three L points within the first Brillouin zone such that they are strongly coupled, and the energy band at the L points is non-parabolic dispersive. At certain conditions, the conduction band edge and the valence band edge will touch each other at the three L points, and the dispersion relation at the L points will become linear, which leads to the formation of three-dimensional Dirac points. By synthesizing Bi1-xSbx thin films, we have two more parameters to control the band structure, namely film thickness and growth orientation. We have developed the iterative-two-dimensional-two-band model to study the two- dimensional L-point non-parabolically dispersive electronic band structure of the Bi1-xSbx thin films system. The Lax model based on the k - p model describes the the L-point non- parabolic dispersion relations very well consistent with experimental results for bulk bis- muth. Because the band gap is narrow, the number of bands that are needed in the per- turbation is small. A satisfactory representation over a limited region of k-space has been archived in terms of the two coupled bands, which means that the Hamiltonian could be approximately diagonalized, and which gives a very simple form for the Lax model. In the thin films system, the anylysis is more different due to the non-parabolic quantum confinement effect. The L-point band gap is increased in a thin film compared to the L-point band gap in a bulk system. As the film thickness decreases, the L-point band gap increases. The L-point band gap and the L-point inverse-effective-mass tensor are coupled together and are different from the values for the bulk materials. Thus, iterative procedures are employed for getting the accurate values of the L-point band gap and its corresponding inverse-effective-mass tensor. The iterative-two-dimensional-two-band model can be gen- eralized to study other two-dimensional narrow-gap systems, for example lead telluride thin films and silicon-germanium alloys thin films. The model can also be modified to study one-dimensional narrow-gap systems such as Bi1-xSbx nanowires. The electronic band structure of Bi1-xSbx thin films for different growth orientations are studied. The results shows that by growing the Bi1-xSbx thin film normal to a low symmetry crystalline direction other than the trigonal axis, the three-fold symmetry of the three L points in the bulk Bi1-xSbx can be broken. Specifically, by growing the Bi1-xSbx thin film along the bisectrix axis, anisotropic single-Dirac-cone can be constructed at the L point associated with this bisectrix axis. In similar ways, by choosing proper antimony compositions, growth orientations and film thicknesses, a large variety of Dirac-cone materials can be constructed based on the Bi1-xSbx thin films system, including single-Dirac-cone materials with different aisotropies, bi-Dirac-cone materials, tri-Dirac-cone materials, quasi-Dirac-cone materials and semi- Dirac-cone materials.

[发布机构] Massachusetts Institute of Technology