Charge and Heat Transport in Non-Metallic Crystals Using First-Principles Boltzmann Transport Theory

Citation

Cheng, Peishi Stephen (2022) Charge and Heat Transport in Non-Metallic Crystals Using First-Principles Boltzmann Transport Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/45fv-ja45. https://resolver.caltech.edu/CaltechTHESIS:05082022-230903229

Abstract

Phonon-phonon and electron-phonon interactions underlie many fundamental transport properties like thermal conductivity and electrical mobility, and models of these properties provide information about the underlying microscopic interactions present in the materials. Many of these models use the Boltzmann transport equation where the choice of the expression for the collision integral is the most important and challenging aspect since it should capture all of the relevant interactions. In the past the expressions were semi-empirical, but in recent decades first principles models with no fitting parameters have become more commonplace, leading to discovery of new materials or providing deeper insights into the relevant mechanisms governing transport. This thesis presents first-principles calculations of thermal conductivity in polymer crystals, and charge transport at high electric fields in semiconductors in the Boltzmann transport framework.

Polymers are thermally insulating in their typical amorphous form, but it is known that their thermal conductivity can be enhanced through drawing and aligning of their polymer chains. With perfect chain alignment, the structures can be described as polymer crystals, which tend to contain many atoms per unit cell. However, the conventional understanding of thermal transport in crystals predicts low thermal conductivity for complex, many atom unit cells. It is known from simple models that phonon focusing redirects the heat flow into the polymer chain direction, but the extent to which phonon focusing plays a role in setting the intrinsic upper limits of polymer thermal conductivity has not been assessed from a first principles standpoint. We calculate the ab initio lattice conductivity of polythiophene, a complex molecular crystal with 28 atoms per unit cell, using the temperature dependent effective potential (TDEP) method to obtain finite temperature phonon properties taking into account the large quantum nuclear motion of hydrogen atoms present in polymers. We find a high thermal conductivity due to phonon focusing and stiff branches that overcome the expected low phonon lifetimes. The phonon focusing aligns group velocities along the chain axis throughout the Brillouin zone, even for states with wave vector almost orthogonal to the chain axis.

For charge transport, ab initio calculations focus almost exclusively on low field mobility, but technologically relevant phenomena like negative differential resistance manifest only at high fields far from equilibrium. Further, there are no ab initio calculations of non-equilibrium electronic noise, which differs qualitatively from transport observables at high fields. We report a methodological advance that obtains both the high-field transport properties and the non-equilibrium noise using an ab initio Boltzmann transport approach. Our method extends the collision integral to high fields by making physically motivated approximations to account for the non-linearities at high fields.

Using our method, we calculate the high-field noise and transport properties in GaAs and find that the 1ph level of theory is inadequate. Thus, we implement an approximate form of higher order interactions where electrons are scattered consecutively by two phonons (2ph) and find that these 2ph processes qualitatively alter the energy relaxation of the electron system compared to 1ph scattering, resolving a long-standing discrepancy in the strength of intervalley scattering inferred from different experiments. We also calculate non-equilibrium electronic noise from first principles for the first time. However, we are not able to reproduce experimental trends, and we suggest that 2ph processes beyond our approximation may be necessary to obtain experimental agreement. Our calculation shows how noise provides a new observable against which the accuracy of first-principles methods can be measured.

Thesis Files