Some semiconductor devices such as lasers have long had critical dimensions on the nanoscale where quantum effects are critical. Others such as MOSFETs are now being scaled to within this regime. Quantum effects neglected in semiclassical models become increasing important at the nanoscale. Meanwhile, scattering remains important even in MOSFETs of 10 nm and below. Therefore, accurate quantum transport simulators with scattering are needed to explore the essential device physics at the nanoscale. The work of this dissertation is aimed at developing accurate quantum transport simulation tools for deep submicron device modeling, as well as utilizing these simulation tools to study the quantum transport and scattering effects in the nano-scale semiconductor devices. The basic quantum transport method "Schrödinger Equation Monte Carlo" (SEMC) provides a physically rigorous treatment of quantum transport and phasebreaking inelastic scattering (in 3D) via real (actual) scattering processes such as optical and acoustic phonon scattering. The SEMC method has been used previously to simulate carrier transport in nano-scaled devices in order to gauge the potential reliability of semiclassical models, phase-coherent quantum transport, and other limiting models as the transition from classical to quantum transport is approached. In this work, SEMC-1D and SEMC-2D versions with long range polar optical scattering processes have been developed and used to simulate quantum transport in tunnel injection lasers and nanoscaled III-V MOSFETs. Simulation results serve not only to demonstrate the capabilities of the developed quantum transport simulators, but also to illuminate the importance of physically accurate simulation of scattering for the predictive modeling of transport in nano-scaled devices.

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A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1980. / Microfiche copy available in Archives and Science. / Vita. / Includes bibliographical references. / by William Allan Perrie. / Ph.D.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Bibliography: leaves 198-203. / by Dick Kau-Ping Yue. / Sc.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 91-92. / by François-Marc Turpin. / M.S.

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We study ground states in the nonlinear Schrödinger equation (NLS) with an isotropic harmonic potential, in energy-critical and energy-supercritical cases. In both cases, we prove existence of a family of ground states parametrized by their amplitude, together with the corresponding values of the spectral parameter. Moreover, we derive asymptotic behavior of the spectral parameter when the amplitude of ground states tends to infinity. We show that in the energy-supercritical case the family of ground states converges to a limiting singular solution and the spectral parameter converges to a nonzero limit, where the convergence is oscillatory for smaller dimensions, and monotone for larger dimensions. In the energy-critical case, we show that the spectral parameter converges to zero, with a specific leading-order term behavior depending on the spatial dimension. Furthermore, we study the Morse index of the ground states in the energy-supercritical case. We show that in the case of monotone behavior of the spectral parameter, that is for large values of the dimension, the Morse index of the ground state is finite and independent of its amplitude. Moreover, we show that it asymptotically equals to the Morse index of the limiting singular solution. This result suggests how to estimate the Morse index of the ground state numerically. / Dissertation / Doctor of Philosophy (PhD)

The long time behavior of antisymmetric as well as symmetric waves on a two-dimensional liquid sheet is studied, the effects of the surrounding fluid being taken into account. The non-linear Schrödinger equation governing the wave motion is derived by the method of multiple scales. Modulatory stability, wave-wave interaction and non-linear stability are studied and a possible mechanism accounting for the disintegration of the sheet is found. / M.S.