Low-dimensional semiconductor structures are important for a wide variety of applications, and recent advances in nanoscale fabrication are paving the way for increasingly precise nano-engineering of a wide range of materials. It is therefore essential that the physics of materials at the nanoscale are thoroughly understood to unleash the full potential of nanotechnology, requiring the development of increasingly sophisticated instrumentation and modeling. Of particular interest is the relationship between the local density of states (LDOS) of low-dimensional structures and the band structure and local electronic properties. This dissertation presents the investigation of the band structure, LDOS, and local electronic properties of nanostructures ranging from zero-dimensional (0D) quantum dots (QDs) to two-dimensional (2D) thin films, synthesizing computational and experimental approaches including Poisson-Schrodinger band structure calculations, scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and scanning thermoelectric microscopy (SThEM). A method is presented for quantifying the local Seebeck coefficient (S) with SThEM, using a quasi-3D conversion matrix approach to directly convert temperature gradient-induced voltages S. For a GaAs p-n junction, the resulting S-profile is consistent with that computed using the free carrier concentration profile. This combined computational-experimental approach is expected to enable nanoscale measurements of S across a wide variety of heterostructure interfaces.The local carrier concentration, n, is profiled across epitaxial InAs/GaAs QDs, where SThEM is used to profile the temperature gradient-induced voltage, which is converted to a profile of the local S and finally to an n profile. The S profile is converted to a conduction band-edge profile and compared with Poisson-Schrodinger band-edge simulations. The combined computational-experimental approach suggests a reduced n in the QD center in comparison to that of the 2D alloy layer. The surface composition and band structure of ordered horizontal Sb2Te3 nanowires induced by femtosecond laser irradiation of a thin film are investigated, revealing a band gap modulation between buried Sb2Te3 nanowires and the surrounding insulating material.Finally, STM and STS are used to investigate the band structure of BiSbTe alloys at room temperature, revealing both the Fermi level and Dirac point located inside the bulk bandgap, indicating bulk-like insulating behavior with accessible surface states.
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Probing the Band Structure and Local Electronic Properties of Low-dimensional Semiconductor Structures.