First-principles calculations of electron mobilities in silicon: Phonon and Coulomb scattering

Abstract

Electron mobilities limited by phonon and ionized impurity scattering have traditionally been modeled by suppressing atomic-scale detail, relying on empirical deformation potentials and either effective-mass theory or bulk energy bands to describe electron velocities. Parameter fitting to experimental data is needed. As modern technologies require modeling of transport at the nanoscale and unprecedented materials are introduced, predictive parameter-free mobility modeling becomes necessary. Here we report the development of first-principles quantum-mechanical methods to calculate scattering rates and electronic mobilities limited by phonon and ionized-impurity scattering. We report results for n-doped silicon that are in good agreement with experiment.

Assessing the Thermoelectric Properties of Sintered Compounds via High-ThroughputAb-InitioCalculations

“…However, due to the size of the materials library, this task is not computationally feasible within the current HT approach. Furthermore, the optimized power factors typically occur for the Fermi level about 0.02 eV into the band, in a regime in which the RBA is expected to be applicable [14,15,31,32]. Hence, we consider the RBA to be a reasonable compromise between efficiency and accuracy.…”

“…[13] for SiGe, and Refs. [14,15] or [16] for mobility or of Si, respectively). The approach is accurate, but it is limited to perfect crystals and simple alloys: it is computationally very expensive and usually difficult to transfer to other systems.…”

Fröhlich Electron-Phonon Vertex from First Principles

“…In contrast to this fast-paced progress, in the case of polar semiconductors and insulators the study of EPIs from first principles has not gone very far, owing to the prohibitive computational costs of EPI calculations for polar materials. For example, a fully ab initio calculation of the carrier mobility of a polar semiconductor has not been performed yet, while such calculations have recently been reported for non-polar semiconductors such as silicon [13] and graphene [14]. Given the fast-growing technological importance of polar semiconductors, from light-emitting devices to transparent electronics, solar cells and photocatalysts [15][16][17], developing accurate and efficient computational methods for studying EPIs in these systems is of primary importance.…”

“…This quantity has the meaning of probability amplitude for the scattering between the initial electronic state |ψ nk and the final state |ψ mk+q via the perturbation ∆ qν V due to a phonon with crystal momentum q, branch ν and frequency ω qν . The matrix elements g mnν (k, q) can be calculated starting from density functional perturbation arXiv:1510.06373v1 [cond-mat.mtrl-sci] 21 Oct 2015 theory [21], and have been employed to investigate many properties involving EPIs, for example the electron velocity renormalization [22] and lifetimes [23,24], phonon softening [3] and lifetimes [25,26], phonon-assisted absorption [27,28], critical temperature in conventional superconductors [10,29,30], and resistivity [13,14]. The key ingredient of all these calculations is the evaluation of g mnν (k, q) on extremely dense Brillouin zone grids, which is computationally prohibitive.…”

Full First-Principles Theory of Spin Relaxation in Group-IV Materials

“…Within the Born approximation, the EY spin relaxation time can be related to the momentum relaxation time (which is proportional to the carrier mobility) [13]. The underlying theory to connect them exists on a phenomenological level for III-V semiconductors with direct gap [14,15], but not within a first principles framework that includes indirect band gap semiconductors [11].Since a methodology based on density-functional theory (DFT) to calculate electron mobilities (and thus momentum relaxation times) has been recently developed by one of us [16], what is left to show here is establishing the relationship between the spin-flip and momentum scattering matrix elements. Other than most previous work, we do not employ a semiempirical k·p representation of the band structure to model the effect of spin-orbit coupling on the electronic wave functions [17], but rather use the spin-dependent DFT wave functions directly.…”