Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN

Abstract

First-principles calculations of e-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) e-ph interaction, a long-range scattering mechanism due to acoustic phonons in noncentrosymmetric polar materials, is not accurately described at present. Current calculations include short-range e-ph interactions (obtained by interpolation) and the dipolelike Frölich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the long-range e-ph interaction due to dynamical quadrupoles, and apply this framework to investigate e-ph interactions and the carrier mobility in the PE material wurtzite GaN. We show that the quadrupole contribution is essential to obtain accurate e-ph matrix elements for acoustic modes and to compute PE scattering. Our work resolves the outstanding problem of correctly computing e-ph interactions for acoustic modes from first principles, and enables studies of e-ph coupling and charge transport in PE materials.

Long-range quadrupole electron-phonon interaction from first principles

“…Our results demonstrate that both dipole and quadrupole terms are essential for accurate acoustic mode e-ph interactions in piezoelectric materials [37]. The relative magnitude of the strain and quadrupole contributions is material dependentthe two terms can nearly cancel each other out, as we have shown elsewhere for GaN [29], or their ratio can be mode and phonon wave-vector dependent, as we find in PbTiO 3 .…”

“…Our results clearly show that the quadrupole interactions are crucial for obtaining accurate e-ph matrix elements, scattering rates, and electronic transport properties. The quadrupole effect is particularly apparent in piezoelectric materials such as wurtzite GaN [29] and PbTiO 3 , in which neglecting the quadrupole interaction leads to large and uncontrolled errors. The method introduced in this work enables accurate calculations of electrical transport, thermoelectric properties and superconductivity in a wide range of materials.…”

“…We investigate the effect of the quadrupole e-ph interaction in silicon, a nonpolar semiconductor, and tetragonal PbTiO 3 , a polar piezoelectric material. Calculations on GaN are shown in the companion work [29]. The ground state and band structure are obtained using DFT in the local density approximation with a plane-wave basis using the QUANTUM ESPRESSO code [30].…”

“…The quadrupole term gives a larger correction at lower temperatures, reaching values up to ∼25% at 100 K. This result is due to the dominant acoustic mode contribution at low temperatures together with the large quadrupole correction for acoustic modes in piezoelectric materials. At higher temperatures, where optical mode scattering is dominant and acoustic scattering less important, the quadrupole contribution is smaller, only about 10% at 400 K. Due to differences in the quadrupole interaction for different phonon modes and to varying mode contributions to the mobility as a function of temperature, including the quadrupole term corrects the temperature dependence of the mobility [29] and is essential in piezoelectric materials.…”

Phonon-limited electron mobility in Si, GaAs, and GaP with exact treatment of dynamical quadrupoles

“…Note added. Recently, we became aware of a related work by another group that reaches similar conclusions about the importance of the dynamical quadrupole term to obtain an accurate physical description of e-ph interactions [89,90]. = e ik•S −1 (r+R−f ) u nk (S −1 (r − f )) = e i t S −1 k•R ψ nk (S −1 (r − f )) = e i Sk•RŜ f ψ nk (r),…”