Efficientab initiocalculations of electron-defect scattering and defect-limited carrier mobility

Abstract

Electron-defect (e-d) interactions govern charge carrier dynamics at low temperature, where they limit the carrier mobility and give rise to phenomena of broad relevance in condensed matter physics. Ab initio calculations of e-d interactions are still in their infancy, mainly because they require large supercells and computationally expensive workflows. Here we develop an efficient ab initio approach for computing elastic e-d interactions, their associated e-d relaxation times (RTs), and the lowtemperature defect-limited carrier mobility. The method is applied to silicon with simple neutral defects, such as vacancies and interstitials. Contrary to conventional wisdom, the computed e-d RTs depend strongly on carrier energy and defect type, and the defect-limited mobility is temperature dependent. These results highlight the shortcomings of widely employed heuristic models of e-d interactions in materials. Our method opens new avenues for studying e-d scattering and lowtemperature charge transport from first principles.

Atomistic T -matrix theory of disordered two-dimensional materials: Bound states, spectral properties, quasiparticle scattering, and transport

“…26 In comparison with analytic and tight-binding based T -matrix studies of defects in, e.g., graphene [27][28][29][30][31][32][33][34] and black phosphorus, 35 our first-principles method permits for parameter-free modeling of realistic defects in disordered materials. It furthermore goes beyond other first-principles studies of defects and their transport-limiting effects based on the Born approximation, [36][37][38][39][40] which we here demonstrate breaks down for point defects in 2D materials. The first-principles T -matrix method introduced in the present work is therefore of high relevance for the further development of first-principles transport methodologies with high predictive power.…”

Ab initio electron-defect interactions using Wannier functions

“…where |nk is the Bloch state with band index n and crystal momentum k. To handle these e-d interactions, one needs to store and manipulate a matrix M mn of size N 2 b (N b is the number of bands) for each pair of crystal momenta k and k in the BZ. Within DFT, the perturbation potential ∆V e−d can be computed as the difference between the Kohn-Sham potential of a defect-containing supercell and that of a pristine supercell with no defect [18]. We compute the e-d matrix elements in Eq.…”

“…The method for directly computing the e-d matrix elements we developed in Ref. [18] and the interpolation method shown here are general, and can be applied to metals, semiconductors and insulators. As an example, we show a calculation on a metal, copper, containing vacancy defects (see Methods).…”

“…The methods to directly compute the e-d matrix elements and from them obtain the RTs, mobility, and conductivity (or resistivity) are described in detail in Ref. [18]. Briefly, we compute the coarse-grid e-d matrix elements using the wave functions of the primitive cell, and obtain the perturbation potential due to a vacancy defect using a 6 × 6 × 6 supercell.…”

“…Several properties have been computed with this approach, including the magnetoresistance due to impurity scattering [7], the residual resistivity of metals and alloys [8], and spin relaxation [9][10][11][12] and the spin Hall effect [13][14][15]. In contrast, ab initio e-d calculations using pseudopotentials or projector augmented waves [16][17][18] have seen slower progress, mainly due to the high computational cost of obtaining the e-d interaction matrix elements needed for perturbative calculations [19].…”