On thermal transport by phonons in bulk and nanostructured semiconductor materials

Student thesis: Doctoral thesis


The aim of this theoretical work is twofold. First, to contribute to a better understand- ing of phonon heat transport in bulk and nanostructured semiconductors, like thin-films or nanowires, in a wide range of temperatures, paying special attention to phonon-phonon col- lisions. Second, to improve the prediction capability of the thermal conductivity of the most common semiconductors. To achieve this, it becomes necessary the formulation of a new model allowing us to overcome the diculties associated to the existing models, with the aim to fulfill two desirable conditions: to provide a general expression for the thermal conduc- tivity, valid for several materials with di↵erent size-scales and geometries in a wide range of temperatures, and to have the smallest number of free adjustable parameters to assure the reliability of the model. The potentiality of such model would be to serve as a useful tool to design more ecient thermoelectric devices. The fruit of our study is the Kinetic-collective model which is developed in the framework of the Boltzmann transport equation as a natural generalization of the Guyer-Krumhansl model. Since phonon interactions are the source of thermal resistance, they deserve a special discussion in any thermal conductivity study. Precisely, the keystone in our work is the treatment of phonon-phonon collisions regarding their di↵erent nature. The prediction capability of the model need to be tested on several materials. In particular, we study five materials with thermoelectric interest. In first place, silicon, because it is an ideal test material due to the considerable amount of experimental data available in the literature, and because of its inherent scientific and technological importance. Secondly, we extend our study to other materials with the same lattice structure as silicon, that is the family of group IV element semiconductors (germanium, diamond, silicon and gray-tin), which also have been object of intense study, specially germanium, due to the recent and fast development of SiGe alloys and superlattices. Finally, we finish our study with a more complicated material regarding its lattice structure, bismuth telluride, which is known to be a very ecient thermoelectric material due to its high figure of merit. The Thesis is arranged in eight Chapters. The lay out is as follows: Chapter 1 con- textualizes the topic of the work and briefly introduces the basic physics related to phonon transport. In Chapter 2 the fundamental quantity necessary for considering any thermal property, the phonon dispersion relations, have been obtained for the materials under study. For this purpose, two lattice dynamics models are used: the Bond-charge model for group-IV semiconductors (silicon, germanium, diamond and gray-tin), and the Rigid-ion model for bismuth telluride (Bi2Te3). Along with their corresponding phonon dispersion relations, phonon density of states and specific heat results are also presented. The phonon relaxation times that suit these materials are discussed in Chapter 3, where new expressions to account for the phonon-phonon collisions are also presented. In the first part of Chapter 4 the most represen- tative thermal conductivity models to date are introduced and discussed, in the second part, a new model to predict the thermal conductivity, the Kinetic-collective model, is presented and its conceptual di↵erences and advantages with respect to previous similar models are discussed. In Chapter 5 the Kinetic-collective model is applied to silicon bulk samples with di↵erent isotopic composition and several nanostructured samples with di↵erent geometries (thin-films and nanowires) obtaining predictions for their thermal conductivity in a wide in- terval of temperatures. Some novel aspects of phonon transport arising from these results are discussed. In Chapter 6 the Kinetic-collective model is applied to the other group-IV materials using theoretical expressions to predict their relaxation times and, eventually, their thermal conductivity. Results for several samples with di↵erent isotopic compositions in a wide range of temperature are presented and discussed. In Chapter 7 the Kinetic-collective model is applied to Bi2Te3, providing thermal conductivity predictions for nanowires with several diameter values, and the results are discussed in view of possible applications in ther- moelectricity. Finally, in Chapter 8 the main conclusions of this Thesis are summarized and possible future lines of work stemming from its several results are discussed.
Date of Award29 Oct 2014
Original languageEnglish
Awarding Institution
  • Universitat Autònoma de Barcelona (UAB)
SupervisorAndrés Cantarero Sáez (Director) & Francesc Xavier Alvarez Calafell (Director)


  • Thermal conductivity
  • Phonons
  • Semiconductors

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