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Date of Award

Summer 8-15-2016

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



Recently, a new semiconducting 2D material, black phosphorus, has piqued the interest of research groups in the field. In its bulk form, black phosphorus was synthesized over a century ago and in 2014 devices based on thin flakes of black phosphorus were successfully realized. This was a crucial step towards the exploration and characterization of this material. However, because this material was virtually ignored until this point, many open questions needed to be quickly addressed. Fundamental properties such as the band gap, carrier mobility, optical spectrum, and thermal transport had not been established. Furthermore, the effect of extrinsic factors such as the number of layers, external electric fields, and applied strain had not been explored. How these extrinsic factors affect the tunability of the aforementioned physical properties is of utmost importance for device engineers. Using first principle computations based on density functional theory and the GW approximation including many-electron effects, we calculate the fundamental electronic and optical properties of few-layer black phosphorus. Beyond basic calculations, such as the band structure, quasiparticle band gap, and optical absorption spectrum, we dig deeper to explore the origin and nature of some of black phosphorus' unusual and surprising properties. These properties include the existence of relativistic Dirac fermions as charge carriers, a highly anisotropic band structure, an anisotropic optical absorption spectrum, quasi-1D excitonic features, and an ultra-high sensitivity to a gate electric field. In the first chapter, we discuss the properties of few-layer black phosphorus. We calculate the quasiparticle band gap, and excitonic optical spectra for 1-4 layers. We provide an empirical formula in the form of a power law to fit the calculated results and predict the values for larger layer numbers. We also propose an effective mass hydrogenic model to describe the excitonic spectra calculated. We use a symmetry analysis of the wavefunctions to determine the optical selection rules present in black phosphorus and use the rules to explain the observed anisotropic absorption spectra. Finally, we employ a Wannier function decomposition of the valence bands to illuminate the origin of the anisotropic band dispersion in black phosphorus. In the fourth chapter, we discuss the electronic and optical properties of phosphorene nanoribbons. Using first principles calculations, we find that due to the anisotropic band dispersion present in monolayer phosphorene, nanoribbons cut along the armchair and zigzag directions differ drastically in their properties. We show that the band gap of armchair nanoribbons obeys the usual quantum confinement law of mass particles, while the band gap of zigzag nanoribbons obey a law consistent with Dirac fermions. We show that this is a manifestation of the unique relativistic dispersion in phosphorene. Finally, we discuss the effect of interlayer interactions in few-layer and multilayer black phosphorus. We determine that tunneling through the van der Walls interlayer barrier plays a key role in determining the band gap behavior with respect to the number of layers. We use this to create a model that accurately describes the band gap evolution with the number of layers and the band gap under the application of a gate electric field. Our results show that the strength of the interlayer interaction is in a unique range compared with other layered materials. The interlayer interaction leads to a very large sensitivity of the band gap to a gate electric field. This ultra-high tunability could be very useful for future devices.


English (en)

Chair and Committee

Li Yang

Committee Members

Parag Banerjee, Anders Carlsson, Erik Henriksen, Zohar Nussinov, Michael Ogilvie


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