Matching Items (26)
Description
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
ContributorsVega-Guzmán, José Manuel, 1982- (Author) / Sulov, Sergei K (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Platte, Rodrigo (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2013
Description
Photodetectors in the 1.7 to 4.0 μm range are being commercially developed on InP substrates to meet the needs of longer wavelength applications such as thermal and medical sensing. Currently, these devices utilize high indium content metamorphic Ga1-xInxAs (x > 0.53) layers to extend the wavelength range beyond the 1.7 μm achievable using lattice matched GaInAs. The large lattice mismatch required to reach the extended wavelengths results in photodetector materials that contain a large number of misfit dislocations. The low quality of these materials results in a large nonradiative Shockley Read Hall generation/recombination rate that is manifested as an undesirable large thermal noise level in these photodetectors. This work focuses on utilizing the different band structure engineering methods to design more efficient devices on InP substrates. One prospective way to improve photodetector performance at the extended wavelengths is to utilize lattice matched GaInAs/GaAsSb structures that have a type-II band alignment, where the ground state transition energy of the superlattice is smaller than the bandgap of either constituent material. Over the extended wavelength range of 2 to 3 μm this superlattice structure has an optimal period thickness of 3.4 to 5.2 nm and a wavefunction overlap of 0.8 to 0.4, respectively. In using a type-II superlattice to extend the cutoff wavelength there is a tradeoff between the wavelength reached and the electron-hole wavefunction overlap realized, and hence absorption coefficient achieved. This tradeoff and the subsequent reduction in performance can be overcome by two methods: adding bismuth to this type-II material system; applying strain on both layers in the system to attain strain-balanced condition. These allow the valance band alignment and hence the wavefunction overlap to be tuned independently of the wavelength cutoff. Adding 3% bismuth to the GaInAs constituent material, the resulting lattice matched Ga0.516In0.484As0.970Bi0.030/GaAs0.511Sb0.489superlattice realizes a 50% larger absorption coefficient. While as, similar results can be achieved with strain-balanced condition with strain limited to 1.9% on either layer. The optimal design rules derived from the different possibilities make it feasible to extract superlattice period thickness with the best absorption coefficient for any cutoff wavelength in the range.
ContributorsSharma, Ankur R (Author) / Johnson, Shane (Thesis advisor) / Goryll, Michael (Committee member) / Roedel, Ronald (Committee member) / Arizona State University (Publisher)
Created2013
Description
Dual-wavelength laser sources have various existing and potential applications in wavelength division multiplexing, differential techniques in spectroscopy for chemical sensing, multiple-wavelength interferometry, terahertz-wave generation, microelectromechanical systems, and microfluidic lab-on-chip systems. In the drive for ever smaller and increasingly mobile electronic devices, dual-wavelength coherent light output from a single semiconductor laser diode would enable further advances and deployment of these technologies. The output of conventional laser diodes is however limited to a single wavelength band with a few subsequent lasing modes depending on the device design. This thesis investigates a novel semiconductor laser device design with a single cavity waveguide capable of dual-wavelength laser output with large spectral separation. The novel dual-wavelength semiconductor laser diode uses two shorter- and longer-wavelength active regions that have separate electron and hole quasi-Fermi energy levels and carrier distributions. The shorter-wavelength active region is based on electrical injection as in conventional laser diodes, and the longer-wavelength active region is then pumped optically by the internal optical field of the shorter-wavelength laser mode, resulting in stable dual-wavelength laser emission at two different wavelengths quite far apart. Different designs of the device are studied using a theoretical model developed in this work to describe the internal optical pumping scheme. The carrier transport and separation of the quasi-Fermi distributions are then modeled using a software package that solves Poisson's equation and the continuity equations to simulate semiconductor devices. Three different designs are grown using molecular beam epitaxy, and broad-area-contact laser diodes are processed using conventional methods. The modeling and experimental results of the first generation design indicate that the optical confinement factor of the longer-wavelength active region is a critical element in realizing dual-wavelength laser output. The modeling predicts lower laser thresholds for the second and third generation designs; however, the experimental results of the second and third generation devices confirm challenges related to the epitaxial growth of the structures in eventually demonstrating dual-wavelength laser output.
ContributorsGreen, Benjamin C (Author) / Zhang, Yong-Hang (Thesis advisor) / Ning, Cun-Zheng (Committee member) / Tao, Nongjian (Committee member) / Roedel, Ronald J (Committee member) / Arizona State University (Publisher)
Created2011
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
In 2022, integrated circuit interconnects will approach 10 nm and the diffusion barrier layers needed to ensure long lasting devices will be at 1 nm. This dimension means the interconnect will be dominated by the interface and it has been shown the interface is currently eroding device performance. The standard interconnect system has three layers - a Copper metal core, a Tantalum Adhesion layer and a Tantalum Nitride Diffusion Barrier Layer. An alternate interconnect schema is a Tantalum Nitride barrier layer and Silver as a metal. The adhesion layer is removed from the system along with changing to an alternate, low resistivity metal. First principles are used to assess the interface of the Silver and Tantalum Nitride. Several stoichiometric 1:1 Tantalum Nitride polymorphs are assessed and it is found that the Fe2P crystal structure is actually the most stable crystal structure which is at odds with the published phase diagram for ambient crystal structure. The surface stability of Fe2P-TaN is assessed and the absorption enthalpy of Silver adatoms is calculated. Finally, the thermodynamic stability of the TaN-Ag interconnect system is assessed.
ContributorsGrumski, Michael (Author) / Adams, James (Thesis advisor) / Krause, Stephen (Committee member) / Alford, Terry (Committee member) / Arizona State University (Publisher)
Created2012
Description
In mesoscopic physics, conductance fluctuations are a quantum interference phenomenon that comes from the phase interference of electron wave functions scattered by the impurity disorder. During the past few decades, conductance fluctuations have been studied in various materials including metals, semiconductors and graphene. Since the patterns of conductance fluctuations is related to the distributions and configurations of the impurity scatterers, each sample has its unique pattern of fluctuations, which is considered as a sample fingerprint. Thus, research on conductance fluctuations attracts attention worldwide for its importance in both fundamental physics and potential technical applications. Since early experimental measurements of conductance fluctuations showed that the amplitudes of the fluctuations are on order of a universal value (e2/h), theorists proposed the hypothesis of ergodicity, e.g. the amplitudes of the conductance fluctuations by varying impurity configurations is the same as that from varying the Fermi energy or varying the magnetic field. They also proposed the principle of universality; e.g., that the observed fluctuations would appear the same in all materials. Recently, transport experiments in graphene reveal a deviation of fluctuation amplitudes from those expected from ergodicity.
Thus, in my thesis work, I have carried out numerical research on the conductance fluctuations in GaAs nanowires and graphene nanoribbons in order to examine whether or not the theoretical principles of universality and ergodicity hold. Finite difference methods are employed to study the conductance fluctuations in GaAs nanowires, but an atomic basis tight-binding model is used in calculations of graphene nanoribbons. Both short-range disorder and long-range disorder are considered in the simulations of graphene. A stabilized recursive scattering matrix technique is used to calculate the conductance. In particular, the dependence of the observed fluctuations on the amplitude of the disorder has been investigated. Finally, the root-mean-square values of the amplitude of conductance fluctuations are calculated as a basis with which to draw the appropriate conclusions. The results for Fermi energy sweeps and magnetic field sweeps are compared and effects of magnetic fields on the conductance fluctuations of Fermi energy sweeps are discussed for both GaAs nanowires and graphene nanoribbons.
Thus, in my thesis work, I have carried out numerical research on the conductance fluctuations in GaAs nanowires and graphene nanoribbons in order to examine whether or not the theoretical principles of universality and ergodicity hold. Finite difference methods are employed to study the conductance fluctuations in GaAs nanowires, but an atomic basis tight-binding model is used in calculations of graphene nanoribbons. Both short-range disorder and long-range disorder are considered in the simulations of graphene. A stabilized recursive scattering matrix technique is used to calculate the conductance. In particular, the dependence of the observed fluctuations on the amplitude of the disorder has been investigated. Finally, the root-mean-square values of the amplitude of conductance fluctuations are calculated as a basis with which to draw the appropriate conclusions. The results for Fermi energy sweeps and magnetic field sweeps are compared and effects of magnetic fields on the conductance fluctuations of Fermi energy sweeps are discussed for both GaAs nanowires and graphene nanoribbons.
ContributorsLiu, Bobo (Author) / Ferry, David K. (Thesis advisor) / Akis, Richard (Committee member) / Saraniti, Marco (Committee member) / Goryll, Michael (Committee member) / Arizona State University (Publisher)
Created2015
Description
High-performance III-V semiconductors based on ternary alloys and superlattice systems are fabricated, studied, and compared for infrared optoelectronic applications. InAsBi is a ternary alloy near the GaSb lattice constant that is not as thoroughly investigated as other III-V alloys and that is challenging to produce as Bi has a tendency to surface segregate and form droplets during growth rather than incorporate. A growth window is identified within which high-quality droplet-free bulk InAsBi is produced and Bi mole fractions up to 6.4% are obtained. Photoluminescence with high internal quantum efficiency is observed from InAs/InAsBi quantum wells. The high structural and optical quality of the InAsBi materials examined demonstrates that bulk, quantum well, and superlattice structures utilizing InAsBi are an important design option for efficient infrared coverage.
Another important infrared material system is InAsSb and the strain-balanced InAs/InAsSb superlattice on GaSb. Detailed examination of X-ray diffraction, photoluminescence, and spectroscopic ellipsometry data provides the temperature and composition dependent bandgap of bulk InAsSb. The unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattice is measured and found to significantly impact the analysis of the InAs/InAsSb band alignment. In the analysis of the absorption spectra, the ground state absorption coefficient and transition strength of the superlattice are proportional to the square of the electron-hole wavefunction overlap; wavefunction overlap is therefore a major design parameter in terms of optimizing absorption in these materials. Furthermore in addition to improvements through design optimization, the optical quality of the materials studied is found to be positively enhanced with the use of Bi as a surfactant during molecular beam epitaxy growth.
A software tool is developed that calculates and optimizes the miniband structure of semiconductor superlattices, including bismide-based designs. The software has the capability to limit results to designs that can be produced with high structural and optical quality, and optimized designs in terms of maximizing absorption are identified for several infrared superlattice systems at the GaSb lattice constant. The accuracy of the software predictions are tested with the design and growth of an optimized mid-wave infrared InAs/InAsSb superlattice which exhibits superior optical and absorption properties.
Another important infrared material system is InAsSb and the strain-balanced InAs/InAsSb superlattice on GaSb. Detailed examination of X-ray diffraction, photoluminescence, and spectroscopic ellipsometry data provides the temperature and composition dependent bandgap of bulk InAsSb. The unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattice is measured and found to significantly impact the analysis of the InAs/InAsSb band alignment. In the analysis of the absorption spectra, the ground state absorption coefficient and transition strength of the superlattice are proportional to the square of the electron-hole wavefunction overlap; wavefunction overlap is therefore a major design parameter in terms of optimizing absorption in these materials. Furthermore in addition to improvements through design optimization, the optical quality of the materials studied is found to be positively enhanced with the use of Bi as a surfactant during molecular beam epitaxy growth.
A software tool is developed that calculates and optimizes the miniband structure of semiconductor superlattices, including bismide-based designs. The software has the capability to limit results to designs that can be produced with high structural and optical quality, and optimized designs in terms of maximizing absorption are identified for several infrared superlattice systems at the GaSb lattice constant. The accuracy of the software predictions are tested with the design and growth of an optimized mid-wave infrared InAs/InAsSb superlattice which exhibits superior optical and absorption properties.
ContributorsWebster, Preston Thomas (Author) / Johnson, Shane R (Thesis advisor) / Zhang, Yong-Hang (Committee member) / Menéndez, Jose (Committee member) / Vasileska, Dragica (Committee member) / Arizona State University (Publisher)
Created2016
Description
InAsBi is a narrow direct gap III-V semiconductor that has recently attracted considerable attention because its bandgap is tunable over a wide range of mid- and long-wave infrared wavelengths for optoelectronic applications. Furthermore, InAsBi can be integrated with other III-V materials and is potentially an alternative to commercial II-VI photodetector materials such as HgCdTe.
Several 1 μm thick, nearly lattice-matched InAsBi layers grown on GaSb are examined using Rutherford backscattering spectrometry and X-ray diffraction. Random Rutherford backscattering measurements indicate that the average Bi mole fraction ranges from 0.0503 to 0.0645 for the sample set, and ion channeling measurements indicate that the Bi atoms are substitutional. The X-ray diffraction measurements show a diffraction sideband near the main (004) diffraction peak, indicating that the Bi mole fraction is not laterally uniform in the layer. The average out of plane tetragonal distortion is determined by modeling the main and sideband diffraction peaks, from which the average unstrained lattice constant of each sample is determined. By comparing the Bi mole fraction measured by random Rutherford backscattering with the InAsBi lattice constant for the sample set, the lattice constant of zinc blende InBi is determined to be 6.6107 Å.
Several InAsBi quantum wells tensilely strained to the GaSb lattice constant with dilute quantities of Bi are characterized using photoluminescence spectroscopy. Investigation of the integrated intensity as a function of carrier excitation density spanning 5×1025 to 5×1026 cm-3 s-1 indicates radiative dominated recombination and high quantum efficiency over the 12 to 250 K temperature range. The bandgap of InAsBi is ascertained from the photoluminescence spectra and parameterized as a function of temperature using the Einstein single oscillator model. The dilute Bi mole fraction of the InAsBi quantum wells is determined by comparing the measured bandgap energy to that predicted by the valence band anticrossing model. The Bi mole fraction determined by photoluminescence agrees reasonably well with that estimated using secondary ion mass spectrometry.
Several 1 μm thick, nearly lattice-matched InAsBi layers grown on GaSb are examined using Rutherford backscattering spectrometry and X-ray diffraction. Random Rutherford backscattering measurements indicate that the average Bi mole fraction ranges from 0.0503 to 0.0645 for the sample set, and ion channeling measurements indicate that the Bi atoms are substitutional. The X-ray diffraction measurements show a diffraction sideband near the main (004) diffraction peak, indicating that the Bi mole fraction is not laterally uniform in the layer. The average out of plane tetragonal distortion is determined by modeling the main and sideband diffraction peaks, from which the average unstrained lattice constant of each sample is determined. By comparing the Bi mole fraction measured by random Rutherford backscattering with the InAsBi lattice constant for the sample set, the lattice constant of zinc blende InBi is determined to be 6.6107 Å.
Several InAsBi quantum wells tensilely strained to the GaSb lattice constant with dilute quantities of Bi are characterized using photoluminescence spectroscopy. Investigation of the integrated intensity as a function of carrier excitation density spanning 5×1025 to 5×1026 cm-3 s-1 indicates radiative dominated recombination and high quantum efficiency over the 12 to 250 K temperature range. The bandgap of InAsBi is ascertained from the photoluminescence spectra and parameterized as a function of temperature using the Einstein single oscillator model. The dilute Bi mole fraction of the InAsBi quantum wells is determined by comparing the measured bandgap energy to that predicted by the valence band anticrossing model. The Bi mole fraction determined by photoluminescence agrees reasonably well with that estimated using secondary ion mass spectrometry.
ContributorsShalindar Christraj, Arvind Joshua Jaydev (Author) / Johnson, Shane R (Thesis advisor) / Alford, Terry L. (Committee member) / Goryll, Michael (Committee member) / Arizona State University (Publisher)
Created2016
Description
Conductance fluctuations associated with quantum transport through quantumdot systems are currently understood to depend on the nature of the corresponding classical dynamics, i.e., integrable or chaotic. There are a couple of interesting phenomena about conductance fluctuation and quantum tunneling related to geometrical shapes of graphene systems. Firstly, in graphene quantum-dot systems, when a magnetic field is present, as the Fermi energy or the magnetic flux is varied, both regular oscillations and random fluctuations in the conductance can occur, with alternating transitions between the two. Secondly, a scheme based on geometrical rotation of rectangular devices to effectively modulate the conductance fluctuations is presented. Thirdly, when graphene is placed on a substrate of heavy metal, Rashba spin-orbit interaction of substantial strength can occur. In an open system such as a quantum dot, the interaction can induce spin polarization. Finally, a problem using graphene systems with electron-electron interactions described by the Hubbard Hamiltonian in the setting of resonant tunneling is investigated.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
ContributorsYing, Lei (Author) / Lai, Ying-Cheng (Thesis advisor) / Vasileska, Dragica (Committee member) / Chen, Tingyong (Committee member) / Yao, Yu (Committee member) / Arizona State University (Publisher)
Created2016
Description
In this work, transport in nanowire materials and nanowire field effect transistors is studied using a full band Monte Carlo simulator within the tight binding basis. Chapter 1 is dedicated to the importance of nanowires and nanoscale devices in present day electronics and the necessity to use a computationally efficient tool to simulate transport in these devices. Chapter 2 discusses the calculation of the full band structure of nanowires based on an atomistic tight binding approach, particularly noting the use of the exact same tight binding parameters for bulk band structures as well as the nanowire band structures. Chapter 3 contains the scattering rate formula for deformation potential, polar optical phonon, ionized impurity and impact ionization scattering in nanowires using Fermi’s golden rule and the tight binding basis to describe the wave functions. A method to calculate the dielectric screening in 1D systems within the tight binding basis is also described. Importantly, the scattering rates of nanowires tends to the bulk scattering rates at high energies, enabling the use of the same parameter set that were fitted to bulk experimental data to be used in the simulation of nanowire transport. A robust and efficient method to model interband tunneling is discussed in chapter 4 and its importance in nanowire transport is highlighted. In chapter 5, energy relaxation of excited electrons is studied for free standing nanowires and cladded nanowires. Finally, in chapter 6, a full band Monte Carlo particle based solver is created which treats confinement in a full quantum way and the current voltage characteristics as well as the subthreshold swing and percentage of ballistic transport is analyzed for an In0.7Ga0.3As junctionless nanowire field effect transistor.
ContributorsHathwar, Raghuraj (Author) / Goodnick, Stephen M (Committee member) / Saraniti, Marco (Committee member) / Vasileska, Dragica (Committee member) / Ferry, David K. (Committee member) / Arizona State University (Publisher)
Created2016