Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems

Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental rule of heat transfer in solids. It states that the thermal conductivity is independent of sample scale and geometry. Although Fourier's law has received great success in describing macroscopic thermal transport in the past two hundreds years, its validity in low dimensional systems is still an open question. Here we give a brief review of the recent developments in experimental, theoretical and numerical studies of heat transport in low dimensional systems, include lattice models, nanowires, nanotubes and graphenes. We will demonstrate that the phonon transports in low dimensional systems super-diffusively, which leads to a size dependent thermal conductivity. In other words, Fourier's law is breakdown in low dimensional structures

Study of the temperature distribution in Si nanowires under microscopic laser beam excitation

The use of laser beams as excitation sources for the characterization of semiconductor nanowires (NWs) is largely extended. Raman spectroscopy and photoluminescence (PL) are currently applied to the study of NWs. However, NWs are systems with poor thermal conductivity and poor heat dissipation, which result in unintentional heating under the excitation with a focused laser beam with microscopic size, as those usually used in microRaman and microPL experiments. On the other hand, the NWs have subwavelength diameter, which changes the optical absorption with respect to the absorption in bulk materials. Furthermore, the NW diameter is smaller than the laser beam spot, which means that the optical power absorbed by the NW depends on its position inside the laser beam spot. A detailed analysis of the interaction between a microscopic focused laser beam and semiconductor NWs is necessary for the understanding of the experiments involving laser beam excitation of NWs. We present in this work a numerical analysis of the thermal transport in Si NWs, where the heat source is the laser energy locally absorbed by the NW. This analysis takes account of the optical absorption, the thermal conductivity, the dimensions, diameter and length of the NWs, and the immersion medium. Both free standing and heat-sunk NWs are considered. Also, the temperature distribution in ensembles of NWs is discussed. This analysis intends to constitute a tool for the understanding of the thermal phenomena induced by laser beams in semiconductor NWs