This award supports theoretical research and education that aims to investigate the transport of heat by phonons and mechanical oscillations in fabricated structures of GaAs and silicon on the 10-100 nm length scale. Recent advances in microfabrication techniques have allowed the construction of suspended, free-standing structures of insulating or doped GaAs or silicon. Portions of these structures are isolated from the substrate so that the only thermal pathway to the environment is through the suspension "beams." These beams are defined lithographically, so they can be designed to allow measurements of thermal transport at the mesoscopic scale. Thermal pathways of rectangular cross-section 200 X 300 nm and length 5m have already been constructed, and much smaller widths seem feasible. The mechanical oscillations of these structures can also be studied experimentally. These advances promise the first systematic investigation of heat transport by phonons in mesoscopic systems, and further development in the study of mechanical oscillations in mesoscopic systems which is poorly understood. The PI proposes a theoretical attack on these problems. The PI plans to extend their recent work based on the Landuaer-Buttiker formalism. Realistic models of phonons that will allow the quantitative prediction of thermal transport will be used and the effects of scattering by geometry, surface roughness, and material disorder will be included. Electron-phonon interaction effects, which can also be studied in experimental geometries, will be investigated. At low temperatures, the modes containing the thermal energy become the mechanical oscillation modes of the suspended structures, so that studies of heat transport and dissipation in mechanical oscillators becomes closely related. Thus it is possible to extend the theoretical investigation to mesoscopic oscillators, and in particular the Q of such oscillators. %%% This award supports research and education in an area that is both fundamental science and related to MEMS (microelectromechanical systems). The PI will use state of the art techniques to study vibrations and oscillations and the flow of heat in mechanical systems fabricated from silicon and other materials on micron and sub-micron length scales. ***
