Error in POP calculation using AMSET

Gurudayal93 · September 21, 2021, 12:21pm

Hii, I am calculating the transport properties of beta-arsenene (2d material) including all the scattering mechanisms ADP, IMP, PIE, and POP. But there are certain errors are coming when I include the POP tag. Here I am attaching the amset.log file below which shows the error. Please help me to resolve this error.

Thanks in advance.
##################################################################################

     /$$$$$$  /$$      /$$  /$$$$$$  /$$$$$$$$ /$$$$$$$$
    /$$__  $$| $$$    /$$$ /$$__  $$| $$_____/|__  $$__/
   | $$  \ $$| $$$$  /$$$$| $$  \__/| $$         | $$
   | $$$$$$$$| $$ $$/$$ $$|  $$$$$$ | $$$$$      | $$
   | $$__  $$| $$  $$$| $$ \____  $$| $$__/      | $$
   | $$  | $$| $$\  $ | $$ /$$  \ $$| $$         | $$
   | $$  | $$| $$ \/  | $$|  $$$$$$/| $$$$$$$$   | $$
   |__/  |__/|__/     |__/ \______/ |________/   |__/

                                                v0.4.11

  A. Ganose, J. Park, A. Faghaninia, R. Woods-Robinson,
  A. Jain, in prep.

amset starting on 21 Sep 2021 at 17:11


Run parameters:
  - scattering_type: ['IMP', 'ADP', 'POP', 'PIE']
  - doping: [1.e+20]
  - temperatures: [300]
  - bandgap: 2.28
  - soc: False
  - zero_weighted_kpoints: prefer
  - interpolation_factor: 10
  - wavefunction_coefficients: wavefunction.h5
  - use_projections: False
  - free_carrier_screening: False
  - high_frequency_dielectric: 
      [[  4.43   0.00   0.00]
       [  0.00   4.43   0.00]
       [  0.00   0.00   2.39]]
  - static_dielectric: 
      [[  4.17   0.00   0.00]
       [  0.00   4.17   0.00]
       [  0.00   0.00   1.27]]
  - elastic_constant: 
      [[  28.0    5.0    0.1    0.0    0.0    0.0]
       [   5.0   28.0    0.1    0.0   -0.0    0.0]
       [   0.1    0.1   -0.5    0.0    0.0    0.0]
       [   0.0    0.0    0.0   11.5    0.0    0.0]
       [   0.0   -0.0    0.0    0.0    0.0    0.0]
       [   0.0    0.0    0.0    0.0    0.0    0.0]]
  - deformation_potential: deformation.h5
  - piezoelectric_constant: 
      [[-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000]
       [-0.0000 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000]
       [-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000]]
  - defect_charge: 1
  - compensation_factor: 2
  - pop_frequency: 8.35
  - energy_cutoff: 1.5
  - fd_tol: 0.05
  - dos_estep: 0.01
  - symprec: 0.01
  - nworkers: -1
  - cache_wavefunction: True
  - calculate_mobility: True
  - separate_mobility: True
  - mobility_rates_only: False
  - file_format: json
  - write_input: False
  - write_mesh: False
  - print_log: True
  - write_log: True


~~~~~~~~~~~~~~~~~~~~~~~~~~~~ STRUCTURE ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Structure information:
  - formula: As
  - # sites: 2
  - space group: P3-m1

Lattice:
  - a, b, c [angstrom]: 3.61, 3.61, 18.54
  - a, b, y [deg]: 90, 90, 120


~~~~~~~~~~~~~~~~~~~~~~~~~~ BAND STRUCTURE ~~~~~~~~~~~~~~~~~~~~~~~~~

Input band structure information:
  - # bands: 20
  - # k-points: 19
  - Fermi level: -3.592 eV
  - spin polarized: False
  - metallic: False

Band gap:
  - indirect band gap: 2.248 eV
  - direct band gap: 2.681 eV
  - direct k-point: [0.00, 0.00, 0.00]

Valence band maximum:
  - energy: -3.807 eV
  - k-point: [0.00, 0.00, 0.00]
  - band indices: 4, 5

Conduction band minimum:
  - energy: -1.559 eV
  - k-point: [0.33, 0.00, 0.00]
  - band indices: 6


~~~~~~~~~~~~~~~~~~~~~~~~~~ INTERPOLATION ~~~~~~~~~~~~~~~~~~~~~~~~~~

Getting band interpolation coefficients
  - time: 0.0311 s

Interpolation parameters:
  - k-point mesh: 31x31x5
  - energy cutoff: 1.5 eV

Interpolating spin-up bands 3-6
  - time: 0.1420 s

bandgap set to 2.280 eV, applying scissor of 0.052 eV

Generating tetrahedron mesh vertices
  - time: 0.0411 s

Initializing tetrahedron band structure
  - time: 0.0524 s

Initializing momentum relaxation time factor calculator

Initializing wavefunction overlap calculator

Desymmetrizing k-point mesh
  - Found initial mesh: 12.000 x 12.000 x 1.000
  - Integer mesh: 12 x 12 x 1
  - Using 12 symmetry operations

Desymmetrizing wavefunction coefficients
  - time: 0.0456 s


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ DOS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

DOS parameters:
  - emin: -8.57 eV
  - emax: -0.10 eV
  - dos weight: 2
  - n points: 847

Generating tetrahedral DOS:
  - time: 0.4171 s

Intrinsic DOS Fermi level: -2.6932 eV

DOS contains 5.941 electrons

Calculated Fermi levels:

numpy.linalg.LinAlgError: SVD did not converg
  conc [cm-3]    temp [K]    E_fermi [eV]
-------------  ----------  --------------
     1.00e+20       300.0         -3.9407

Calculated Fermi-Dirac cut-offs:
  - min: -4.183 eV
  - max: -3.844 eV


~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SCATTERING ~~~~~~~~~~~~~~~~~~~~~~~~~~~

Scattering mechanisms to be calculated: IMP, ADP, POP, PIE

Inverse screening length (b) and impurity concentration (N_i):

  conc [cm-3]    temp [K]    b2 [a^-2]    N_i [cm-3]
-------------  ----------  -----------  ------------
     1.00e+20       300.0     1.97e-02      2.00e+20

Initializing deformation potential interpolator

Initializing POP scattering
  - average N_po: 0.3568
  - w_po: 52.46 2pi THz
  - hbar.omega: 0.0345 eV

Forking 12 processes to calculate scattering
  - time: 0.1990 s

Scattering information:
  - # ir k-points: 448

Calculating rates for spin-up band 1
  - # k-points within Fermi-Dirac cut-offs: 0
  - time: 0.0307 s

Calculating rates for spin-up band 2
  - # k-points within Fermi-Dirac cut-offs: 77
  - time: 6.7124 s

Calculating rates for spin-up band 3
  - # k-points within Fermi-Dirac cut-offs: 479
  - time: 4.5993 s

Calculating rates for spin-up band 4
  - # k-points within Fermi-Dirac cut-offs: 0
  - time: 0.0007 s

Interpolating missing scattering rates
  - time: 0.0022 s

Filling scattering rates [s⁻¹] outside FD cutoffs with:

  conc [cm-3]    temp [K]       IMP       ADP       PIE    POP
-------------  ----------  --------  --------  --------  -----
     1.00e+20       300.0  1.27e+14  7.29e+14  3.70e+07    nan


~~~~~~~~~~~~~~~~~~~~~~~~~~~~ TRANSPORT ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Calculating conductivity, Seebeck, and electronic thermal 
conductivity


  ERROR: amset exiting on 21 Sep 2021 at 17:11
Traceback (most recent call last):
  File "/home/gurudayal/y/bin/amset", line 8, in <module>
    sys.exit(cli())
  File "/home/gurudayal/y/lib/python3.7/site-
packages/click/core.py", line 829, in __call__
    return self.main(*args, **kwargs)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/click/core.py", line 782, in main
    rv = self.invoke(ctx)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/click/core.py", line 1259, in invoke
    return _process_result(sub_ctx.command.invoke(sub_ctx))
  File "/home/gurudayal/y/lib/python3.7/site-
packages/click/core.py", line 1066, in invoke
    return ctx.invoke(self.callback, **ctx.params)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/click/core.py", line 610, in invoke
    return callback(*args, **kwargs)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/tools/run.py", line 139, in run
    runner.run()
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/run.py", line 68, in run
    multiprocess=True,
  File "/home/gurudayal/y/lib/python3.7/site-
packages/memory_profiler.py", line 336, in memory_usage
    returned = f(*args, **kw)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/run.py", line 121, in _run_wrapper
    amset_data, timing = self._do_fd_tol(amset_data, directory, 
prefix, timing)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/run.py", line 132, in _do_fd_tol
    amset_data, transport_time = self._do_transport(amset_data)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/run.py", line 282, in _do_transport
    progress_bar=self.settings["print_log"],
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/transport.py", line 40, in 
solve_boltzman_transport_equation
    amset_data, progress_bar=progress_bar
  File "/home/gurudayal/y/lib/python3.7/site-
packages/amset/core/transport.py", line 187, in 
_calculate_transport_properties
    l0, l1, l2, fermi, temp, volume
  File "/home/gurudayal/y/lib/python3.7/site-
packages/BoltzTraP2/bandlib.py", line 505, in 
calc_Onsager_coefficients
    pL11 = np.linalg.pinv(L11[iT, imu])
  File "<__array_function__ internals>", line 6, in pinv
  File "/home/gurudayal/y/lib/python3.7/site-
packages/numpy/linalg/linalg.py", line 2002, in pinv
    u, s, vt = svd(a, full_matrices=False, hermitian=hermitian)
  File "<__array_function__ internals>", line 6, in svd
  File "/home/gurudayal/y/lib/python3.7/site-
packages/numpy/linalg/linalg.py", line 1660, in svd
    u, s, vh = gufunc(a, signature=signature, extobj=extobj)
  File "/home/gurudayal/y/lib/python3.7/site-
packages/numpy/linalg/linalg.py", line 97, in 
_raise_linalgerror_svd_nonconvergence
    raise LinAlgError("SVD did not converge")
numpy.linalg.LinAlgError: SVD did not converge
########################################################################

alex · September 21, 2021, 12:57pm

Your static dielectric tensor is smaller than the high-frequency dielectric tensor. This is impossible since static dielectric = high-frequency dielectric + ionic contributions. Please see this answer for more details: What is the high_frequency_dielectric - #2 by alex

Once you have the right dielectric constants your calculation should work fine. Although I have a couple of other notes on your calculation:

You don’t need to include “PIE” scattering in the calculation as your piezoelectric coefficient is basically zero.
Because you are at a relatively large carrier concentration, I can recommend that you set free_carrier_screening: true in your settings file. You can read more about this option here: Settings - AMSET Documentation

Best,
Alex

Gurudayal93 · September 21, 2021, 2:16pm

Hii Alex,
Thanks a lot for your clarifications. Now it is working fine. One more doubt I have regarding the carrier concentration.
How much carrier concentration should be sufficient enough to calculate scattering rates? is there any thumb rule to choose the carrier concentration values for a particular system?

Thanks and Regards,
Guru

alex · September 21, 2021, 2:34pm

The realistic carrier concentrations will depend on the doping (intrinsic or extrinsic) of the system which is controlled by the synthesis conditions. There are two approaches:

If you are comparing against experiment you should use the experimentally determined carrier concentrations.
If there are no experiments you can report the results for a range of reasonable doping concentrations, say 10^{15}-10^{19}\,\mathrm{cm}^{-3}. Larger doping concentrations typically require extrinsic dopants.

LLei · February 27, 2022, 6:07am

hello,There is always a problem when calculating pop, I would like to ask you, When I calculate pop, the result is always0.35Thz, but it’s actually 10.5Thz, could you help me solve this queastion ,very thank