Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

Critical Analysis on the Structural and Magnetic Properties of Bulk and Nanocrystalline Cu-Fe-O

Nanocrystalline and bulk samples of “Fe”-doped CuO were prepared by coprecipitation and ceramic methods. Structural and compositional analyses were performed using X-ray diffraction, SEM, and EDAX. Traces of secondary phases such as CuFe2O4, Fe3O4, and α-Fe2O3 having peaks very close to that of the host CuO were identified from the Rietveld profile analysis and the SAED pattern of bulk and nanocrystalline Cu0.98Fe0.02O samples. Vibrating Sample Magnetometer (VSM) measurements show hysteresis at 300 K for all the samples. The ferrimagnetic Neel transition temperature () was found to be around 465°C irrespective of the content of “Fe”, which is close to the value of cubic CuFe2O4. High-pressure X-Ray diffraction studies were performed on 2% “Fe”-doped bulk CuO using synchrotron radiation. From the absence of any strong new peaks at high pressure, it is evident that the secondary phases if present could be less than the level of detection. Cu2O, which is diamagnetic by nature, was also doped with 1% of “Fe” and was found to show paramagnetic behavior in contrast to the “Fe” doped CuO. Hence the possibility of intrinsic magnetization of “Fe”-doped CuO apart from the secondary phases is discussed based on the magnetization and charge state of “Fe” and the host into which it is substituted.

A precise measurement of the two -photon exchange effect

The two-photon exchange phenomenon is believed to be responsible for the discrepancy observed between the ratio of proton electric and magnetic form factors, measured by the Rosenbluth and polarization transfer methods. This disagreement is about a factor of three at Q 2 of 5.6 GeV2. The precise knowledge of the proton form factors is of critical importance in understanding the structure of this nucleon. The theoretical models that estimate the size of the two-photon exchange (TPE) radiative correction are poorly constrained. This factor was found to be directly measurable by taking the ratio of the electron-proton and positron-proton elastic scattering cross sections, as the TPE effect changes sign with respect to the charge of the incident particle. A test run of a modified beamline has been conducted with the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. This test run demonstrated the feasibility of producing a mixed electron/positron beam of good quality. Extensive simulations performed prior to the run were used to reduce the background rate that limits the production luminosity. A 3.3 GeV primary electron beam was used that resulted in an average secondary lepton beam of 1 GeV. As a result, the elastic scattering data of both lepton types were obtained at scattering angles up to 40 degrees for Q2 up to 1.5 GeV2. The cross section ratio displayed an &epsis; dependence that was Q2 dependent at smaller Q2 limits. The magnitude of the average ratio as a function of &epsis; was consistent with the previous measurements, and the elastic (Blunden) model to within the experimental uncertainties. Ultimately, higher luminosity is needed to extend the data range to lower &epsis; where the TPE effect is predicted to be largest.

A nanoliter volume nuclear magnetic resonance (NMR) system using tunneling magneto-resistive (TMR) sensors to recognize biomolecules

The need to incorporate advanced engineering tools in biology, biochemistry and medicine is in great demand. Many of the existing instruments and tools are usually expensive and require special facilities.^ With the advent of nanotechnology in the past decade, new approaches to develop devices and tools have been generated by academia and industry. ^ One such technology, NMR spectroscopy, has been used by biochemists for more than 2 decades to study the molecular structure of chemical compounds. However, NMR spectrometers are very expensive and require special laboratory rooms for their proper operation. High magnetic fields with strengths in the order of several Tesla make these instruments unaffordable to most research groups.^ This doctoral research proposes a new technology to develop NMR spectrometers that can operate at field strengths of less than 0.5 Tesla using an inexpensive permanent magnet and spin dependent nanoscale magnetic devices. This portable NMR system is intended to analyze samples as small as a few nanoliters.^ The main problem to resolve when downscaling the variables is to obtain an NMR signal with high Signal-To-Noise-Ratio (SNR). A special Tunneling Magneto-Resistive (TMR) sensor design was developed to achieve this goal. The minimum specifications for each component of the proposed NMR system were established. A complete NMR system was designed based on these minimum requirements. The goat was always to find cost effective realistic components. The novel design of the NMR system uses technologies such as Direct Digital Synthesis (DDS), Digital Signal Processing (DSP) and a special Backpropagation Neural Network that finds the best match of the NMR spectrum. The system was designed, calculated and simulated with excellent results.^ In addition, a general method to design TMR Sensors was developed. The technique was automated and a computer program was written to help the designer perform this task interactively.^

Step and flash imprint lithography: Fabrication of patterned media for extremely high density magnetic data storage devices

Currently the data storage industry is facing huge challenges with respect to the conventional method of recording data known as longitudinal magnetic recording. This technology is fast approaching a fundamental physical limit, known as the superparamagnetic limit. A unique way of deferring the superparamagnetic limit incorporates the patterning of magnetic media. This method exploits the use of lithography tools to predetermine the areal density. Various nanofabrication schemes are employed to pattern the magnetic material are Focus Ion Beam (FIB), E-beam Lithography (EBL), UV-Optical Lithography (UVL), Self-assembled Media Synthesis and Nanoimprint Lithography (NIL). Although there are many challenges to manufacturing patterned media, the large potential gains offered in terms of areal density make it one of the most promising new technologies on the horizon for future hard disk drives. Thus, this dissertation contributes to the development of future alternative data storage devices and deferring the superparamagnetic limit by designing and characterizing patterned magnetic media using a novel nanoimprint replication process called "Step and Flash Imprint lithography". As opposed to hot embossing and other high temperature-low pressure processes, SFIL can be performed at low pressure and room temperature. Initial experiments carried out, consisted of process flow design for the patterned structures on sputtered Ni-Fe thin films. The main one being the defectivity analysis for the SFIL process conducted by fabricating and testing devices of varying feature sizes (50 nm to 1 μm) and inspecting them optically as well as testing them electrically. Once the SFIL process was optimized, a number of Ni-Fe coated wafers were imprinted with a template having the patterned topography. A minimum feature size of 40 nm was obtained with varying pitch (1:1, 1:1.5, 1:2, and 1:3). The Characterization steps involved extensive SEM study at each processing step as well as Atomic Force Microscopy (AFM) and Magnetic Force Microscopy (MFM) analysis.