Heat transfer in rough nanofilms and nanowires using Full Band Ab Initio Monte Carlo simulation
Résumé
I. Abstract The Boltzmann transport equation is one of the most relevant framework to study the heat transport at the nanoscale, beyond the diffusive regime and up to the micrometer-scale. In the general case of three-dimensional devices, the particle Monte Carlo approach of phonon transport is particularly powerful and convenient, and requires reasonable computational resources. In this work, we propose an original and versatile particle Monte Carlo approach parametrized by using ab-initio data. Both the phonon dispersion and the phonon-phonon scattering rates have been computed by DFT calculation in the entire 3D Brillouin zone. To treat the phonon transport at rough interfaces, a combination of specular and diffuse reflections has been implemented in phase space. Thermal transport has been investigated in nanowires and thin films made of cubic and hexagonal Silicon, including edge roughness, in terms of effective thermal conductivity, phonon band contributions and heat flux orientation. It is shown that the effective thermal conductivity in quasi-ballistic regime obtained from our Monte Carlo simulation cannot be accurately fitted by simple semi-analytical Matthiessen-like models and that spectral approaches are mandatory to get good results. Our Full Band approach shows that some phonon branches exhibiting a negative group velocity in some parts of the Brillouin zone may contribute negatively to the total thermal flux. Besides, the thermal flux clearly appears to be oriented along directions of high density of states. The resulting anisotropy of the heat flux is discussed together with the influence of rough interfaces. II. Introduction The optimization of the thermoelectric conversion is an active subject of research. The main applications are related to energy harvesting for power supply autonomous systems as well as heat management in CPU cooling. Yet, common and efficient thermoelectric materials such as Bismuth Telluride, Lead Telluride, etc., often rely on unfortunately rare and toxic compounds. Their replacement by Silicon and Germanium which are more abundant and widely used in microelectronics would be appealing if their naturally poor thermoelectric properties could be significantly improved, especially close to room temperature. The thermoelectric efficiency of a material is characterized by a unitless thermoelectric figure of merit í µí±í µí± = í µí± 2 í µí¼í µí±/í µí¼ that depends on the electrical conductivity í µí¼, the Seebeck coefficient S and the thermal conductivity í µí¼. To improve the conversion efficiency, í µí±í µí± has to be increased. Consequently, í µí¼ must be reduced while í µí¼ must be preserved as far as possible. As these two parameters are strongly interdependent in common bulk materials, ZT optimization remained very limited for decades[1]. However, nanotechnologies provide new routes to optimize the thermoelectric conversion[2] For instance, nanostructures with a characteristic width í µí± both larger than the mean free path of electrons í µí± í µí±í µí±í µí± í µí± and smaller than the mean free path of phonons í µí± í µí±í µí±í µí± í µí±ℎ (í µí± í µí±í µí±í µí± í µí± < í µí± < í µí± í µí±í µí±í µí± í µí±ℎ) can be used to specifically control and limit the effective phonon mean free path. This way, since heat transfer in non-degenerate semiconductors is mainly due to phonons, higher ratios í µí¼/í µí¼ can be achieved and finally ZT can be significantly higher in such nanomaterials than in their bulk counterpart. For instance, experimental measurements in Silicon nanowires of appropriate diameters[3] i.e. on the order of 100 nm, have demonstrated a large reduction of the effective thermal
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