First-principles calculations of Auger recombination rates (Beta)

We have tried to make the code as user friendly as possible. If you have any trouble getting things to work, or if you have any questions, do not hesitate to message me on github.

Direct Auger recombination

• Obtain the eigenenergies and wavefunctions on a irreducible wedge on a dense k-point grid
• The user sets carrier concentration and the program will apply a windowing routine to obtain the Fermi-level
• Once the Fermi-level is calculated, we compute the all momentum conserving 4-body interactions (considering Umklapp) to get all of the k-points outside of the IBZ that need to be calculated.
• Compute the eigenenergies and wavefunctions at the new k-points
• Finally compute the Auger recombination rate as a function of the band gap.

Phonon-assisted Auger recombination

• Since the phonon-assisted process does not require momentum conservation (the phonon can provide arbitrary amount of momentum), the combinatorice will be prohibatively large if we are considering k-dependent filling of the of the band edges.
• We have to overcome this by assuming that all of the states are at a single point at the band-edge (or a few if they are degenerate).
• Then we compute the electron-phonon matrix elements and Coulomb matrix element
• Note that use use a patched QE to print the electron-phonon matrix elements within QE because it's important for the phase of all wavefunctions to be consistent.

Prerequisites

Make sure that cray-FFTW is installed on the cluster you are running on and make sure the module is loaded.

Installing

On cori computing cluster, first run:

module load cray-fftw

then:

make all

Do this for both the direct and indirect versions of the code.

Examples

The inputs and outputs of two runs for GaAs (on an extremely corse grid) are included.

For the direct calculation:

• Obtain the charge density in the scf directory
• Obtain the kpoints file in the following the format of the kpoints.elec and kpoints.hole examples in the nscf directory
• Run the klist.x program in the directory with the kpoints files to generate the klist.elec.irr file. Which lists of kpoints in the irreducible zone
• In folders named k_# where # is the index from the kpoints.elec file, perform nscf calculations for each k-point. (examples in ./GaAs-direct/nscf-3x3x3)
• After completing the run on the irreducible zone we can run the klists.x program again to get the Fermi filling, and generate the additional klist files to for other points that are need from the BZ.
• After completing QE runs for all of those directories, we can finally run the auger program to obtain the rates

For the indirect calculations:

• First use the patch file to update your quantum espresso install (testes for QE 6.2.1) by running:

patch -s -p0 < [bf_auger]/qe_auger_patch.diff

In the PHonon/PH subdirectory

• Obtain the irreducible q-point files: kirr_cartesian.dat and klist_weights.dat. The kirr_cartesian.dat contains the q-point list written in cartesian coordinates, which will be used for the phonon and electron-phonon coupling calculations. The klist_weights.dat is written in relative coordinates and contains the normalized weight for each q-point.
• Run the makedirs.tsch script to create the directories (phonon_#, where # is the index of q-point) and input files for each q-point contained in kirr_cartesian.dat.
• Run ph.x < ph1.in > ph1.out to compute the phonon frequencies for each q-point. Run the extract-freq.sh to extract the phonon frequencies written into a file named omega.
• Run pw.x < nscf.in > nscf.out to perform a non-selfconsistent calculation for the kpoint where the band gap is located.
• Run ph.x < ph2.in > ph2.out to compute the electron-phonon coupling matrix elements between k and k+q.
• Run the makennkp.sh script inside each phonon_# directory. This will take ph2.out as input to generate the GaAs.nnkp file, which will be used by pw2wannier.x. Move the generated GaAs.nnkp file to the _ph0 directory.
• Run pw2wannier90.x < pw2wannier.in > pw2wannier.out to extract the eigenvalues (GaAs.eig) and wavefunctions (UNK00001.1 and UNK00002.1) for k and k+q. After completion, move GaAs.eig, UNK00001.1 and UNK00002.1 files to the directory one level above.
• Run the indirect Auger executables with the auger.in file as input to compute the indirect Auger recombination rates.

Acknowledgments

• Original code by Emmanouil Kioupakis, Daniel Steiauf, Patrick Rinke and Kris T Delaney
• Developed in the group of Chris G. Van de Walle at UC Santa Barbara

Structure of code

├── README.md
└── src
    ├── direct
    │   ├── base.F90
    │   ├── bf_auger.F90
    │   ├── bf_auger_sub_hhe.F90
    │   ├── check_kind.f90
    │   ├── energies.F90
    │   ├── inpfile.f90
    │   ├── kgrids.f90
    │   ├── klists.F90
    │   ├── make.depend
    │   ├── Makefile
    │   ├── me_direct.F90
    │   ├── me_fft_direct.F90
    │   └── me_test.f90
    └── indirect
        ├── base.F90
        ├── calculate_auger_phonon.F90
        ├── fftw3.f
        ├── inpfile.f90
        ├── Makefile
        ├── me_fft.F90
        └── tableio.f90