Theoretical study on the band structure of Bi1̳-x̳Sbx̳ thin films
Author(s)Tang, Shuang, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Materials Science and Engineering.
Mildred S. Dresselhaus.
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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 A satisfactory representation over a limited region of k-space has been archived in terms of the two coupled bands, which means that the Hamiltonian could be approximately diagonalized, and which gives a very simple form for the Lax model.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.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.In title on title page, "1̳", "-x̳" and "x̳" in "Bi1̳-x̳Sbx̳" appear as subscript script. Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 56-61).
DepartmentMassachusetts Institute of Technology. Dept. of Materials Science and Engineering.
Massachusetts Institute of Technology
Materials Science and Engineering.