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EPIC STAR

Energy-dependent Phonon- and Impurity- limited Carrier Scattering Time AppRoximation (EPIC STAR) is an approximation for Boltzmann transport properties simulation.

The theoretical and implementation details are described in: Deng, T., Wu, G., Sullivan, M.B. et al. EPIC STAR: a reliable and efficient approach for phonon- and impurity-limited charge transport calculations. npj Comput Mater 6, 46 (2020). https://doi.org/10.1038/s41524-020-0316-7

Currently the code only works for three-dimensional systems, and care should be taken in special cases, such as those extreme anisotropy, soft phonons, or flat bands.

Knowledge of Quantum Espresso (especially ph.x) and BoltzTraP is needed, and please consult their manuals for input explanation.

Installation

Apply the corresponding patches for BoltzTraP and QE and compile as usual.

BoltzTraP:

  1. Download and unpack BoltzTraP 1.2.5 as boltztrap-1.2.5: tar -jxvf boltztrap-1.2.5.tar.bz2
  2. Apply patch: patch -p0 < ./epicstar/src/boltztrap-1.2.5-EPIC.patch
  3. Configure and compile BoltzTraP as usual

QE 6.3:

  1. Download and unpack QE 6.3 as q-e-qe-6.3: tar -zxvf q-e-qe-6.3.tar.gz
  2. Apply patch: patch -p0 < ./epicstar/src/qe-6.3-EPIC.patch
  3. Configure and compile ph as usual

Workflow

  1. Run SCF calculation using pw.x ('fixed' occupation is needed for polar correction).

  2. Run DFPT calculation using ph.x to obtain dV_scf (phonon perturbation potential).

      1. optional: run frohlich.x with lfroh = .true. to obtain Frohlich interaction strength file prefix.dyn1.froh. This requires running ph.x with 'fixed' occupation and epsil = .true., and q=0 Gamma point should be the first q-point.

  3. Re-run SCF calculation using pw.x with sufficient empty bands in order to compute el-ph matrix for conduction bands.

  4. Run DFPT calculation with trans = .false. and electron_phonon = 'epa' to obtain el-ph matrix elements file (prefix.epa.k).

  5. Run NSCF calculation on a denser k-grid to obtain band structure needed by BoltzTraP. Then use qe2boltz-epic.py to generated BoltzTraP input.

  6. Run modified BoltzTraP program for prefix.transdos, prefix.sigxx, and prefix.curv.

  7. Run epic.x to compute the generalized Eliashberg function which describes the short-range el-ph interaction.

  8. Run tau.epic.x to compute transport properties at arbitrary condition (temperature, doping, etc.).

Input file for epic.x, frohlich.x and tau.epic.x

epic.x

The input for epic.x is rather similar to epa.x, as it reads the epa.k file originally generated for EPA.

Lines Description
Si.epa.k epa.k file produced by ph.x with electron_phonon = 'epa'
Si prefix for output files, including generalized Eliashberg function
epic job type. Currently only 'epic' is used.
6.2586 -0.0027211 200 1 4 VBM, dE_v, N_E_v, nbnd_min_v, nbnd_max_v
6.6992 0.0027211 200 5 8 CBM, dE_c, N_E_c, nbnd_min_c, nbnd_max_c
0.2 0.005 Electron and phonon smearing paramters in eV

For line 4 and 5:

Symbol Explanation
VBM(CBM) valence (conduction) band edge energy in eV
dE_v(dE_c) valence (conduction) band energy sampling step in eV, for generalized Eliashberg function
N_E_v(N_E_c) number of energy sampling points for valence (conduction) band
nbnd_min_v,nbnd_max_v(nbnd_min_c, nbnd_max_c) min and max indices of valence (conduction) bands to include

frohlich.x

The input file for frohlich.x is largely identical to dynmat.x of QE. Only the following two optionas are added:

Options Description
lfroh .true. to compute Frohlich interaction strength. If .false. frohlich.x is identical to dynmat.x
nmesh number of angular sampling point for numerical integration, needed to compute spherically averaged Frohlich interaction strength

tau.epic.x

The input for tau.epic.x:

Lines Description
Si prefix, same as QE, BoltzTraP and epic.x
2 spin degeneracy (2 for nspin = 1, 1 for nspin = 2)
300 temperature in K
6.5 6.51 lowest and highest chemical potential (Fermi level) in eV
2 number of chemical potential to sample. Optional: an extra number to define a desired carrier density in m^-3 (positive for n-dope)
imp scattering mechanisms: eph for el-ph only, tf-eph for Thomas-Fermi screened el-ph, imp for TF-screened el-ph + el-imp
39.14770475 unit-cell volume in Ang^3
`` filename of .froh file generated by frohlich.x. Leave blank to neglect Frohlich correction.
0.0 14.323856554 Impurity density and averaged dielectric constant. If impurity density is zero, n_imp == abs(n_doping)

Note if .froh file is provided, averaged dielectric constant is read from .froh and overwrite the option here.

If desired carrier density is provided in line 5 after number of chemical potential sample, one single chemical potential corresponding to this density is used.

Output files

epic.x is used to generate the following files:

prefix.epic.g2: containing generalized Eliashberg function prefix.epic.invq2: containing information for Frohlich correction

tau.epic.x is used to generate the following files:

prefix.{data}.dat: containing transport data (conductivity sigma, mobility, Seebeck coefficient, power factor PF etc.) prefix.e.{data}.dat: same as above, with only conduction band contribution prefix.h.{data}.dat: same as above, with only valence band contribution

Examples

Simple examples for silicon and gallium arsenide are provided. See their respective test.sh for details.

Licenses

Patches to Quantum ESPRESSO and BoltzTraP are distributed under GPL-2.0 and LGPL-3.0+ licenses, respectively.