This dissertation contains research directed at investigating the behavior and properties of a class of composite materials known as phononic crystals. Two categories of phononic crystals are explicitly investigated: (I) elastic phononic crystals and (II) nano-scale phononic crystals. For elastic phononic crystals, attention is directed at two-dimensional structures. Two specific structures are evaluated (1) a two-dimensional configuration consisting of a square array of cylindrical Polyvinylchloride inclusions in air and (2) a two-dimensional configuration consisting of a square array of steel cylindrical inclusions in epoxy. For the first configuration, a theoretical model is developed to ascertain the necessary band structure and equi-frequency contour features for the realization of phase control between propagating acoustic waves. In contrasting this phononic crystal with a reference system, it is shown that phononic crystals with equifrequency contours showing non-collinear wave and group velocity vectors are ideal systems for controlling the phase between propagating acoustic waves. For the second configuration, it is demonstrated that multiple functions can be realized of a solid/solid phononic crystal. The epoxy/steel phononic crystal is shown to behave as (1) an acoustic wave collimator, (2) a defect-less wave guide, (3) a directional source for elastic waves, (4) an acoustic beam splitter, (5) a phase-control device and (6) a k-space multiplexer. To transition between macro-scale systems (elastic phononic crystals) and nano-scale systems (nano-phononic crystals), a toy model of a one-dimensional chain of masses connected with non-linear, anharmonic springs is utilized. The implementation of this model introduces critical ideas unique to nano-scale systems, particularly the concept of phonon mode lifetime. The nano-scale phononic crystal of interest is a graphene sheet with periodically spaced holes in a triangular array. It is found through equilibrium molecular dynamics simulation techniques, that phonon-boundary collision effects and coherent phononic effects (band-folding) are two competing scattering mechanisms responsible for the reduction of acoustic and optical phonon lifetimes. Conclusions drawn about the lifetime of thermal phonons in phononic crystal patterned graphene are linked with the anharmonic, one-dimensional crystal model.

Possessing a wide band gap and large break down field, gallium nitride (GaN) is of interest for a host of high power, high frequency applications including next generation cellular base stations, advanced military radar, and WiMAX networks. Much of this interest stems from the continued development of the AlGaN/GaN high electron mobility transistor (HEMT) that is capable of operating at sizable power densities and switching speeds. The same fields responsible for this performance, however, also elicit acute device heating and elastic loads. These induced thermomechanical loads limit both performance and reliability thus necessitating continued improvement in the management and characterization of the coupled environments. In response, this study establishes a new implementation of Raman spectroscopy capable of simultaneously measuring the operational temperature and stress in a HEMT using only the Stokes response. First, the linewidth (FWHM) of the Stokes signal is utilized to quantify the operating temperature of a HEMT independent to the influences of stress. Second, a new method, incorporating the use of the linewidth and peak position in tandem, is developed to estimate the biaxial thermoelastic stress that arises during device operation. With this capability, the HEMT's resultant load is assessed, highlighting the large role of the residual stress on the total mechanical state of the device. Subsequently, this same linewidth is leveraged to identify the distinct effect that electrical carriers have on the thermally relevant decay of longitudinal optical phonon modes. Further investigation of the lattice transport then concludes the study by way of an analytical treatment describing the significant influence of interfacial disorder on the energy transport at GaN/substrate boundaries.