Session X10: Invited Session: Thermal Properties and Electron-Phonon Coupling from First Principles

Phonon Raman scattering from first principles

Light propagating through a crystal can be inelastically scattered by lattice vibrations. Thereby the exciting light beam experiences a frequency shift which is detected in the Raman experiment. This {\it Raman shift} is caused by the modulation of the material's polarizability upon time-dependent ionic displacements. Experimental Raman data thus contain a wealth of information about phonons, electronic structure, as well as their interplay. For instance, temperature-dependent lineshapes and overtone spectra can be related to the extent of anharmonic effects, and strong electron-phonon interaction is expressed in terms of large scattering intensities. The assignment of frequencies to specific vibrations typically relies on comparison with reference systems by considering atomic masses and the symmetry of the crystal. For an in-depth understanding of the measured features and an unambiguous assignment of modes, {\it ab initio} theory can provide valuable insight. In the Raman spectra, the peak positions correspond to the phonon frequencies and thus can be solely determined from frozen-phonon or linear-response calculations. The scattering intensities, however, involve the change of the frequency-dependent complex dielectric tensor with atomic displacements along the phonon eigenvector. All these quantities can be obtained from density-functional theory (DFT) in combination with time-dependent DFT or many-body perturbation theory. In this talk, I will review how to compute Raman spectra from first principles. Selected examples will demonstrate the effects of isotope substitution, anharmonicity, temperature, and excitation energy, as well as the role of symmetry. They reveal that Raman scattering is a beautiful technique as it reflects basic principles of quantum mechanics as much as complex excitations of complex matter.   

Pushing the limits of first-principles electron-phonon calculations: from photoemission kinks to band gaps

The electron-phonon interaction is key to some of the most intriguing and technologically important phenomena in condensed matter physics, ranging from superconductivity to charge density waves, electrical resistivity, and thermoelectricity. Starting from the late nineties first-principles calculations of electron-phonon interactions in metals have become increasingly popular, mainly in connection with the study of conventional superconductors and with the interpretation of angle-resolved photoemission experiments. In contrast, progress on first-principles calculations of electron-phonon interactions in insulators has been comparatively slower. This delay is arguably due to the conventional wisdom that the signatures of electron-phonon interactions in semiconductor band structures are so small that they fall within the error bar of the most accurate electronic structure calculations. In order to fill this gap we developed, within the context of state-of-the-art density-functional techniques, a theory proposed by Allen and Heine for calculating the temperature dependence of band gaps in semiconductors [P. B. Allen, V. Heine, J. Phys. C: Solid State Phys. 69, 2305 (1976)]. This methodology allows us to calculate both the temperature dependence of the quasiparticle energies and the renormalization due to zero-point quantum fluctuations. In order to demonstrate this technique an application to the intriguing case of diamond will be discussed [F. Giustino, S. G. Louie, M. L. Cohen, Phys. Rev. Lett. 105, 265501 (2010)]. In this case the calculated temperature dependence of the direct band gap agrees well with spectroscopic ellipsometry data, and the renormalization due to the electron-phonon interaction is found to be spectacularly large ($>$0.6 eV). This unexpected finding might be only the tip of the iceberg in a research area which remains largely unexplored and which, from a first glimpse, appears rich of surprises.   

Phonon-assisted Auger recombination and optical absorption in semiconductors

The coupling of charge carriers to lattice vibrations is an important process in materials that enables higher-order electronic transitions. We employed first-principles methods based on density functional theory to study various phonon-assisted electronic processes in semiconductors, such as Auger recombination and optical absorption. Auger recombination is a three-particle non-radiative recombination process that affects optoelectronic devices at high carrier densities. Phonon-assisted Auger recombination, in particular, is expected to be important in wide-band-gap materials. We describe the computational formalism to study phonon-assisted Auger recombination in semiconductors. We show that these indirect Auger processes are strong in the group-III nitrides and affect the high-power performance of visible light-emitting diodes. Moreover, the electron-phonon interaction facilitates the absorption of light by free carriers in doped semiconductors and transparent conducting oxides, which limits the output power of optoelectronic devices. We describe how first-principles techniques can be used to calculate the phonon-assisted free-carrier absorption coefficient in semiconductors and discuss our results for the group-III nitrides. In addition, the electron-phonon coupling enables indirect interband optical transitions in indirect-gap materials such as silicon. These processes are instrumental for the absorption of visible light and the operation of silicon solar cells. We present our first-principles formalism and calculated results for the phonon-assisted absorption of visible light in silicon. Our calculated results are in very good agreement with experiment. Our work highlights the significance of first-principles methods in understanding key microscopic quantum phenomena in technologically important materials and devices. Work done in collaboration with C. G. Van de Walle, P. Rinke, K. Delaney, A. Schleife, F. Bechstedt, D. Steiauf, H. Peelaers, J. Noffsinger, S. G. Louie, and M. L. Cohen. Support was provided by CEEM, SSLEC, NERSC, and Teragrid.   

Large scale atomistic approaches to thermal transport and phonon scattering in nanostructured materials

Decreasing the thermal conductivity of bulk materials by nanostructuring and dimensionality reduction, or by introducing some amount of disorder represents a promising strategy in the search for efficient thermoelectric materials [1]. For example, considerable improvements of the thermoelectric efficiency in nanowires with surface roughness [2], superlattices [3] and nanocomposites [4] have been attributed to a significantly reduced thermal conductivity. In order to accurately describe thermal transport processes in complex nanostructured materials and directly compare with experiments, the development of theoretical and computational approaches that can account for both anharmonic and disorder effects in large samples is highly desirable. We will first summarize the strengths and weaknesses of the standard atomistic approaches to thermal transport (molecular dynamics [5], Boltzmann transport equation [6] and Green's function approach [7]) . We will then focus on the methods based on the solution of the Boltzmann transport equation, that are computationally too demanding, at present, to treat large scale systems and thus to investigate realistic materials. We will present a Monte Carlo method [8] to solve the Boltzmann transport equation in the relaxation time approximation [9], that enables computation of the thermal conductivity of ordered and disordered systems with a number of atoms up to an order of magnitude larger than feasible with straightforward integration. We will present a comparison between exact and Monte Carlo Boltzmann transport results for small SiGe nanostructures and then use the Monte Carlo method to analyze the thermal properties of realistic SiGe nanostructured materials. This work is done in collaboration with Davide Donadio, Francois Gygi, and Giulia Galli from UC Davis.\\[4pt] [1] See e.g. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, Energy Environ. Sci. 2, 466 (2009).\\[0pt] [2] A. I. Hochbaum et al, Nature 451, 163 (2008).\\[0pt] [3] R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Nature 413, 597 (2001).\\[0pt] [4] B. Poudel et al, Science 320, 634 (2008).\\[0pt] [5] See e.g. Y. He, D. Donadio, and G. Galli, Nano Lett. 11, 3608 (2011).\\[0pt] [6] See e.g. A. Ward and D. A. Broido, Phys. Rev. B 81, 085205 (2010).\\[0pt] [7] See e.g. I. Savic, N. Mingo, and D. A. Stewart, Phys. Rev. Lett. 101, 165502 (2008).\\[0pt] [8] I. Savic, D.Donadio, F.Gygi, and G.Galli (in preparation).\\[0pt] [9] See e.g. J. E. Turney, E. S. Landry, A. J. H. McGaughey, and C. H. Amon, Phys. Rev. B, 79, 064301 (2009).