First-principles electron transport with phonon coupling: Large scale at low cost

Abstract

Phonon-assisted tunneling plays a crucial role for electronic device performance and even more so with future size down-scaling. We show how one can include this effect in large-scale first-principles calculations using a single "special thermal displacement" (STD) of the atomic coordinates at almost the same cost as elastic transport calculations, by extending the recent method of Zacharias et al. [Phys Rev. B 94, 075125 (2016)] to the important case of Landauer conductance. We apply the method to ultra-scaled silicon devices and demonstrate the importance of phonon-assisted band-toband and source-to-drain tunneling. In a diode the phonons lead to a rectification ratio suppression in good agreement with experiments, while in an ultra-thin body transistor the phonons increase offcurrents by four orders of magnitude, and the subthreshold swing by a factor of four, in agreement with perturbation theory.

Efficient First-Principles Calculation of Phonon-Assisted Photocurrent in Large-Scale Solar-Cell Devices

“…The temperature-dependent EPC is included through a single displacement of the atomic positions according to [18,20] …”

“…The configuration displaced according to Eq. (7) gives the correct thermal average of the Landauer conductance and the optical absorption for sufficiently large systems with many repetitions of the same unit cell [18,20].…”

“…In the following section, we summarize the methodology used to calculate the photocurrent using the first-order Born approximation and the inclusion of EPC through the STD approach. Exhaustive derivations of the important equations can be found in previous publications [18,[20][21][22][23].…”

Theory of the special displacement method for electronic structure calculations at finite temperature

“…[49] calculated exciton-phonon couplings in hexagonal boron nitride; and Refs. [28,29] demonstrated calculations of finite-temperature carrier mobilities in silicon n-i-n and p-n junctions using this approach. In retrospect, these successes across a broad range of applications are not too surprising, since the method of Ref.…”

“…The method of Ref. [26] was originally named 'oneshot configuration', but subsequently it has variably been referred to as the 'WL-HA' method [47] or the 'STD' method [28]. In order to avoid a proliferation of acronyms, in this manuscript we will refer to the general theory as the special displacement method (SDM), and to Eq.…”