<p>Within the past decade, advances in small-scale electronics have reduced power consumption requirements such that mechanisms for harnessing ambient kinetic energy for self-sustenance are a viable technology. Such devices, known as energy harvesters, may enable self-sustaining wireless sensor networks for applications ranging from Tsunami warning detection to environmental monitoring to cost-effective structural health diagnostics in bridges and buildings. In particular, flexible electroelastic materials such as lead-zirconate-titanate (PZT) are sought after in designing such devices due to their superior efficiency in transforming mechanical energy into the electrical domain in comparison to induction methods. To date, however, material and dynamic nonlinearities within the most popular type of energy harvester, an electroelastically laminated cantilever beam, has received minimal attention in the literature despite being readily observed in laboratory experiments. </p><p>In the first part of this dissertation, an experimentally validated first-principles based modeling framework for quantitatively characterizing the intrinsic nonlinearities and moderately large amplitude response of a cantilevered electroelastic generator is developed. Nonlinear parameter identification is facilitated by an analytic solution for the generator's dynamic response alongside experimental data. The model is shown to accurately describe amplitude dependent frequency responses in both the mechanical and electrical domains and implications concerning the conventional approach to resonant generator design are discussed. Higher order elasticity and nonlinear damping are found to be critical for correctly modeling the harvester response while inclusion of a proof mass is shown to invigorate nonlinearities a much lower driving amplitudes in comparison to electroelastic harvesters without a tuning mass.</p><p>The second part of the dissertation concerns dynamical systems design to purposefully engage nonlinear phenomena in the mechanical domain. In particular, two devices, one exploiting hysteretic nonlinearities and the second featuring homoclinic bifurcation are investigated. Both devices exploit nonlinear magnet interactions with piezoelectric cantilever beams and a first principles modeling approach is applied throughout. The first device is designed such that both softening and hardening nonlinear resonance curves produces a broader response in comparison to the linear equivalent oscillator. The second device makes use of a supercritical pitchfork bifurcation wrought by nonlinear magnetic repelling forces to achieve a bistable electroelastic dynamical system. This system is also analytically modeled, numerically simulated, and experimentally realized to demonstrate enhanced capabilities and new challenges. In addition, a bifurcation parameter within the design is examined as a either a fixed or adaptable tuning mechanism for enhanced sensitivity to ambient excitation. Analytical methodologies to include the method of Harmonic Balance and Melnikov Theory are shown to provide superior insight into the complex dynamics of the bistable system in response to deterministic and stochastic excitation.</p> / Dissertation

Multiscale computational simulations are performed to investigate how electronic structure and optical absorption characteristics of recently reported nanostructured III-nitride core-shell MQW solar cells are governed by an intricate coupling of size-quantization, atomicity, and built-in structural and polarization fields. The core computational framework, as available in our in-house QuADS 3-D simulator, is divided into four coupled phases: 1) Geometry construction for the wurtzite lattice having hexagonal crystal symmetry and non-conventional crystal orientations; 2) Structural relaxation and calculation of atomistic strain distributions using the VFF Keating molecular-mechanics model, which employs a conjugate gradient energy minimization scheme; 3) Obtaining the induced polarization and internal potential distributions using a 3-D atomistic Poisson solver; 4) Computing the single-particle electronic structure and optical transition rates using a 10- band sp3 s*-spin tight-binding framework; and 5) Using a TCAD toolkit, study the carrier transport and obtain the device terminal characteristics. Special care was taken in incorporating the nonpolar m-plane crystallographic orientation within the simulator via appropriate lattice vectors, rotational matrices, neighboring atom co-ordinates and sp3-hybridized passivation scheme. Numerical calculations of electronic structure properties are generally based on non-primitive rectangular unit cell. The rectangular geometry approximation is still valid and can be considered even in the presence of strain in nanostructures such as quantum wells, nanowires, and even in self-assembled quantum dots with varying composition. With this approximation, atoms are grouped into traditional unit cells resulting in simpler analysis and better storage scheme, which results in more dynamic and easily debugged algorithms. Note that the contribution of the second-order piezoelectric polarization is small in the nonpolar m-plane structure (as compared to the polar c-plane counterpart) and was neglected in this study. Besides, the spontaneous polarization is non-existent in m-plane structure. The polarization fields are incorporated in the Hamiltonian as an external potential within a non-self-consistent approximation. From the simulations, it is found that, even without the inclusion of any internal fields, the crystal symmetry is lowered compared to ideal geometries, which is due mainly to the fundamental atomicity and interface discontinuities. However, with the inclusion of internal polarization fields, although the symmetry is lowered further, the m-plane structure exhibits a stronger overlap and localization of the wavefunctions, as compared to the c-plane counterpart. Importantly, strain, in the m-plane structure, causes a larger splitting of the topmost valence band and the interband transition probability involving the 4th valence band was found to be highest. Overall, the m-plane structure offers higher spontaneous emission rate and internal quantum efficiency (IQE) as well as an improved fill-factor.