Usage

A typical usage will consist of about three steps; 1. preparation, 2. building Potential, and 3. computing capture coefficient. Find more detail for step 2 and step 3 in example notebooks. The command line interface is depreciated and not recommended.

1. Preparation

Before CarrierCapture, you need to calculate potential energy surfaces of atomic vibrations (one-dimensional Configuration Coordinate diagram; 1D-CC) and e-ph coupling matrix element (W_if). Prepare a sequence of structures with displacements which interpolate between two defect states. Run single-point energy calculations on these structures, and extract the total energies. Scripts for preprocessing can be found in /script which require the pymatgen python library.

1. Generate 1D-CC

   1. Calculate equilibrium geometries and total energies of defective supercells with charge states q(initial) and q±1(final) denoted Conf.(q) and Conf.(q±1), respectively.

   2. Generate interpolated and extrapolated structures between Conf.(q) (POSCAR_i) and Conf.(q±1) (POSCAR_f). You may use gen_cc_struct.py:

      $ gen_cc_struct.py -i POSCAR_i -f POSCAR_f -d -1 -0.6 -0.4 -0.2 -0.1 0 0.1 0.2 0.4 0.6 1.0
      $ ls
      disp_dir_i
      disp_dir_f

   3. Run total-energy calculations for each structure. Example of the directory tree (template) contains all input files for DFT calculations. Make sure DFT-program writes wavefunctions (e.g. LWAVE=.TRUE. in VASP) for the next stage W_if):

      ├── 00_q2q±1
      │   ├── 00_q
      │   │   ├── DISP_000
      │   │   ├── DISP_001
      │   │   ├── ...
      │   │   ├── disp_dir -> ../../90_DISPLACEMENT/disp_dir_i
      │   │   └── template
      │   └── 01_q±1
      │       ├── DISP_000
      │       ├── DISP_001
      │       ├── ...
      │       ├── disp_dir -> ../../90_DISPLACEMENT/disp_dir_f
      │       └── template
      ├── 90_DISPLACEMENT
      │   ├── disp_dir_f
      │   │   ├── POSCAR_000
      │   │   ├── ...
      │   ├── disp_dir_i
      │   │   ├── POSCAR_000
      │   │   ├── ...

      You can submit jobs for all calculations using a following script in a high-performance computer with a batch system.

      #!/bin/bash -l
      
      for NUM in {-14,-13,-12,-11,-10,-09,-08,-07,-06,-05,-04,-03,-02,-01,000,001,002,003,004,005,006,007,008,009,010,011,012,013,014}
      do
         #if [ ! -d DISP_$NUM ]
         #then
           echo DISP_$NUM
           cp -r template DISP_$NUM
           cp disp_dir/POSCAR_$NUM DISP_$NUM/POSCAR
           cd  DISP_$NUM
           qsub run.pbs
           cd ../
         #fi
      done

   4. Calculate 𝛥Q using get_del_Q.py. Generate notential.csv using following script.<a name="qe_data"></a>

      #!/bin/bash -l
      
      echo Q, E
      for NUM in {-14,-13,-12,-11,-10,-09,-08,-07,-06,-05,-04,-03,-02,-01,000,001,002,003,004,005,006,007,008,009,010,011,012,013,014}
      do
         en=`tail -n 1 DISP_$NUM/OSZICAR|awk '{print $3};'|sed  's/-./-0./' `
         del_Q=`get_del_Q.py -i $1 -f  DISP_$NUM/POSCAR`
         echo ${del_Q}, ${en}
      done

      Example potential.csv file:

      Q, E
      5.034147844442521, -0.28566871E+03
      4.027331082104984, -0.28581530E+03
      ...
      1.0068515567113572, -0.28581699E+03
      0.0, -0.28566641E+03

1. Calcuate e-ph coupling matrix element W_if <a name="wif"></a>

   You already have eigenvalues, wavefunctions and configurations. Read Work by Alkauskas and coworkers carefully.

   1. Find initial and final eigenvalues (ϵ_i and ϵ_f).

   2. Calculate overlap initial and final wavefunctions. For VASP, you can use get_wf.py:

      $ python get_wf.py   -d 288 -b 291  -D DISP_000 -i DISP_-02 DISP_-01 DISP_001 DISP_002
      
      GRID ENCUT 918.2911873931497
      finished making projector list
      --------------
      ran get_projector_list in 0.033210 seconds
      ---------------
      STARTING PROJSETUP
      started setup_proj
      calculating projector_values
      onto_projector calcs
      Done
      --------------
      
      ...
      
      =================================
      ----------- Overlaps ------------
      =================================
      [[0.0574]
       [0.0267]
       [0.0345]
       [0.0643]]

   3. Calculate the rate of change in overlap between initial and final wavefunctions <ψ_i0|ψ_f(𝛥Q)> as the geometry changes 𝛥Q: W_if = (ϵ_f - ϵ_i) d<ψ_i0|ψ_f(𝛥Q)> / d𝛥Q. See more detail in this example.

2. Building Potential

See Example.

1. Use fit_pot! to find a best fit to the data of Q and E.
2. Use solve_pot! to solve 1D Shrödinger equation for the potential energy surface (PES).

3. Computing capture rates

See Example.

1. Use calc_overlap! to calculate the overlap between phonon wave functions.
2. Use calc_capt_coeff! to calculate the capture coefficient as a function of temperature.

High-Throughput Usage

High-throughput usage is possible by preparing files in a similar method to the examples, useParamScan_Harmonic.jl and useParamScan_Anharmonic.jl. It is recommended that a high-performance computer rather than a personal machine is used, depending on how many calculations are performed. The code can then be run remotely using nohup julia useParamScan_Harmonic &.

The steps are as follows,

1. Define the parameters for which capture coefficient C will be calculated.

2. Calculate C for these parameters, in parallel over the largest parameter range (usually ΔQ)

3. Find ccArray.npz to analyse the capture coefficient as a function of its parameters.