Electron-phonon scattering rates in complex polar crystals

The thermalization of fast electrons by phonons is studied in CsI, NaI, ${\mathrm{SrI}}_2$, and ${\mathrm{YAlO}}_3$. This numerical study uses an improvement to a recently developed method based on a density functional perturbation description of the phonon modes that provides a way to go beyond widely used phonon models based on binary crystals. The method is compared to standard ab initio approaches to the electron-phonon interaction. Improvements to this method are described, and scattering rates are presented and discussed. The relative activity of the numerous phonon modes in materials with complicated structures is discussed, and a simple criterion for finding the modes that scatter strongly is presented.

Figure 1

Computed electronic first-order density response (smooth lines) and the corresponding effective charge approximation (decorated lines) in CsI. The imaginary part of the induced density in response to displacing Cs is in blue (the real part vanishes by symmetry); the real part of the response to I displacements is in yellow; the imaginary part of the I response is in purple.

Figure 2

Computed phonon density of states.

Figure 3

Computed phonon band structure (in ${\mathrm{cm}}^{-1}$) along high-symmetry directions in NaI compared to the experimental data of Melvin [55] (+'s) and Woods [56] (x's).

Figure 4

Phonon band structure (in ${\mathrm{cm}}^{-1}$) along high-symmetry directions in YAP. The color of the lines indicates the degree to which the mode is longitudinal: Red corresponds to longitudinal modes and black to purely transverse modes.

Figure 5

Phonon band structure (in ${\mathrm{cm}}^{-1}$) along high-symmetry directions in ${\mathrm{SrI}}_2$. The color of the lines indicates the degree to which the mode is longitudinal: Red corresponds to longitudinal modes and black to purely transverse modes.

Figure 6

Total phonon scattering rates in CsI and NaI and the contribution of the acoustic modes at zero and room temperature.

Figure 7

Scattering rates from the single LO mode in CsI and NaI at room temperature from the current work and the usual phenomenological model evaluated at parameters from our DFT calculations (i.e., $m^{*}=1$ and ${\epsilon }_0$, ${\epsilon }_{\infty }$ listed in Table 2).

Figure 8

Scattering rates from the acoustic and transverse optical modes in CsI and NaI at room temperature. The current semiclassical results are compared to phenomenological models following the work of Sparks [20] and Llacer and Garwin [19]. Models are shown with and without the correction proposed by Bradford and Woolf [62].

Figure 9

Average cosine of the scattering angle as a function of particle energy. Results from the phenomenological model for the LO modes of Ref. [51] are also shown.

Figure 10

Total phonon emission rate in inverse seconds at $T=0$ in a suite of polar crystals.

Figure 11

Contributions to the phonon scattering rate by the three strongest modes in YAP as a function of the energy of the thermalizing particle.

Figure 12

Contributions to the phonon scattering rate by the three strongest modes in ${\mathrm{SrI}}_2$ as a function of the energy of the thermalizing particle for particles moving in the $yz$ plane with a $y$ component of the velocity twice the $z$ component.