First-Principles Calculations of Electron-Defect Interactions and Defect-Limited Charge Transport

Abstract

Crystallographic defects and impurities govern charge transport at low temperature, where the electron-defect (e-d) interactions limit the carrier mobility and manifest themselves in a wide range of phenomena of broad relevance in condensed matter physics. Theoretical treatments of e-d interactions have so far relied on heuristic approaches and analytic models. However, the band structure, electronic wave functions, and defect perturbation potential are far more complex in real materials than in these simplified models. First-principles calculations can provide atomistic details of the atomic and electronic structures of the material and make accurate predictions of their properties. Yet, ab initio calculations of e-d interactions are still in their infancy, mainly because they require large simulation cells and computationally expensive workflows. This thesis aims to overcome the open challenge of computing the e-d interactions and the associated e-d matrix elements, e-d relaxation times, and defect-limited mobility using first-principles methods. We develop an efficient first-principles method to compute the e-d matrix elements and apply it to neutral vacancy and interstitial defects in silicon. Using the new approach, we demonstrate systematic convergence of the e-d relaxation times with respect to supercell size, defect position, and Brillouin zone sampling. To speed up the e-d calculations, we formulate and implement an interpolation scheme to compute the e-d matrix elements using maximally-localized Wannier functions. We show for the first time fully ab initio calculations of the temperature dependent defect-limited carrier mobility and investigate its numerical convergence. To treat charged defects, we develop a different interpolation method and apply it to a charged point defect in silicon. We use this approach together with importance sampling integration to effectively compute the e-d relaxation times for charged defects. Finally, we provide technical details of the e-d routines and discuss their integration in the open source code PERTURBO developed in the Bernardi group. In summary, the methods developed in this thesis have laid a solid foundation for future ab initio e-d interaction calculations, which can be applied broadly to address materials design challenges in electronics, energy, and quantum technologies.