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. ^

Synthesis and electron emission properties of aligned carbon nanotube arrays

Carbon nanotubes (CNTs) have become one of the most interesting allotropes of carbon due to their intriguing mechanical, electrical, thermal and optical properties. The synthesis and electron emission properties of CNT arrays have been investigated in this work. Vertically aligned CNTs of different densities were synthesized on copper substrate with catalyst dots patterned by nanosphere lithography. The CNTs synthesized with catalyst dots patterned by spheres of 500 nm diameter exhibited the best electron emission properties with the lowest turn-on/threshold electric fields and the highest field enhancement factor. Furthermore, CNTs were treated with NH3 plasma for various durations and the optimum enhancement was obtained for a plasma treatment of 1.0 min. CNT point emitters were also synthesized on a flat-tip or a sharp-tip to understand the effect of emitter geometry on the electron emission. The experimental results show that electron emission can be enhanced by decreasing the screening effect of the electric field by neighboring CNTs. In another part of the dissertation, vertically aligned CNTs were synthesized on stainless steel (SS) substrates with and without chemical etching or catalyst deposition. The density and length of CNTs were determined by synthesis time. For a prolonged growth time, the catalyst activity terminated and the plasma started etching CNTs destructively. CNTs with uniform diameter and length were synthesized on SS substrates subjected to chemical etching for a period of 40 minutes before the growth. The direct contact of CNTs with stainless steel allowed for the better field emission performance of CNTs synthesized on pristine SS as compared to the CNTs synthesized on Ni/Cr coated SS. Finally, fabrication of large arrays of free-standing vertically aligned CNT/SnO2 core-shell structures was explored by using a simple wet-chemical route. The structure of the SnO2 nanoparticles was studied by X-ray diffraction and electron microscopy. Transmission electron microscopy reveals that a uniform layer of SnO2 is conformally coated on every tapered CNT. The strong adhesion of CNTs with SS guaranteed the formation of the core-shell structures of CNTs with SnO2 or other metal oxides, which are expected to have applications in chemical sensors and lithium ion batteries.

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.