Descripción microscópica del transporte térmico en dieléctricos con efectos de memoria y no locales
- Autores: Lluc Sendra Molins
- Directores de la Tesis: Francesc Xavier Àlvarez Calafell (dir. tes.), Juan Camacho (codir. tes.)
- Lectura: En la Universitat Autònoma de Barcelona ( España ) en 2023
- Idioma: español
- Tribunal Calificador de la Tesis: José Miguel Alonso Pruneda (presid.), Javier Rodríguez Viejo (secret.), Carla de Tomás Andrés (voc.)
- Programa de doctorado: Programa de Doctorado en Física por la Universidad Autónoma de Barcelona
- Materias:
- Enlaces
- Tesis en acceso abierto en: TDX
- Resumen
This thesis provides a new formalism to solve the phonon Boltzmann transport equation for finite Knudsen numbers that supplies a hydrodynamic heat transport equation, the Guyer-Krumhansl equation, similar to the Navier-Stokes equation for general semiconductors. This generalization of Fourier's law is obtained in general cases, from systems dominated by momentum-preserving normal collisions, as is well known, to kinetic materials dominated by resistive collisions, where it captures nonlocal effects. The key feature of our framework is to assume that the nonequilibrium phonon distribution function is described in terms of the heat flux and its first derivatives. We obtain explicit expressions for the nonequilibrium phonon distribution and for the geometry-independent macroscopic parameters as a function of phonon properties that can be calculated from first principles.
This formalism is validated from two different perspectives: theoretical and experimental. From the theoretical perspective, we recover two well-known results in thermal transport. First, we obtain Fourier's law with a general collisions operator. Second, we exactly recover the original results for the Guyer and Krumhansl equation, where it is used that normal collisions dominate. From an experimental point of view, the ab initio model predictions agree with a wide range of experiments in silicon and germanium, considering different geometries, temperatures, sizes, or time-dependent and independent situations. Furthermore, in contrast to approaches directly based on the Boltzmann transport equation, the hydrodynamic equation can be solved in arbitrary geometries, thus providing a powerful tool for nanoscale heat modeling at a low computational cost.
Finally, this formalism opens the door to improving its applicability to larger Knudsen numbers by including higher-order derivatives or using effective parameters in the description.
