Nanoscale Thermal and Electro-Thermal Transport: Lévy Flights and Percolation Networks
Huge development in the synthesis and processing of materials with nanostructures on nanometer length scales has created a demand for a deeper understanding of thermal and electro-thermal transport in nanoscale devices and nanostructured materials. Besides, heterogeneity of nanocomposite materials and devices has brought the need to assess the validity of conventional theories of transport and/or develop new theories for these devices. First, considering the problem of heat transfer, it is surprising that the theory we use dates back to Joseph Fourier, and he developed it to explain how the temperature of the Earth changes. However, we still use the same theory at the smallest size scale; say tens of nanometers, and the fastest time scale of hundreds of picoseconds. Developing models that account accurately for ballistic heat transport becomes essential to enable innovative device designs for thermoelectrics as well as ultrafast thermal management of high power electronics and optoelectronics. This can also be used for advanced phonon spectroscopy. A new model based on Truncated Lévy (TL) flight is introduced to describe the phonon random walk. We can extract the fractal diffusion exponent for several alloys as evidence for anomalous diffusion (superdiffusion) at early times. This approach captures the ballistic heat transport at early time/ short length scales. The truncation at a characteristic length/time to converge to normal diffusion is necessary for consistency with bulk solution. Finally, developing new materials with engineered non-diffusive heat transport is investigated. In analogy with light superdiffusion in Levy glass, we studied heat transport in semiconductors alloys with different embedded nanoparticles concentration. It is shown theoretically and experimentally that, even when the volume concentration of embedded nanoparticles changes by two orders of magnitude, the fractal exponent of heat superdiffusion remains constant. In a second example, we use Monte Carlo Boltzmann transport equation to simulate heat transport in non-periodic multilayer structure with power-law layer thickness distribution. The idea is to introduce fractal structure with high thermal conductivity contrast between the host material and island material through which one can tune the phonon jump length distribution. The heterogeneity of nanocomposite devices can give rise to anomalous transport behavior even in steady state. The technological importance of 2D materials (e.g., graphene, carbon nanotube (CNT) network, MoS2) has encouraged fundamental exploration into the electro-thermal properties of these systems. In this work, we use ultra-high resolution thermo-reflectance imaging to map the spatial distribution of temperature rise due to self-heating in two types of 2D transparent electrodes (percolating and co-percolating networks). We experimentally demonstrate a spatially-resolved, reversible nonlinear electro-thermal percolation transport in network structures. A novel algorithm for temperature data extraction is proposed using a binary masking algorithm, followed by quantitative statistical data analysis of self-heating of nanowire networks. We establish a universal scaling function (Weibull) that describes the nonlinear percolation transport for network structures. A phenomenological model is also proposed providing interesting insights regarding both experimental and theoretical studies of nonlinear percolation transport in the networks.
Shakouri, Purdue University.
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