transport module¶

This module, transport.py contains the setup and checks necessary to execute the calculation of the transport coefficients. It also execute those routines.

Contains routines to set up the calculation of the charge carrier transport coefficients.

class transport.Transport(bs)¶

Bases: object

Involves all transport related routines.

Parameters:	bs : object A Band() object. lattice : object A Lattice() object. param : object A Param() object.

calc_carrier_concentration(self, temperature, chempot, dos=None, dos_energies=None, band_decomp=False, defect_ionization=False)¶

Returns the charge carrier concentration.

Parameters:

Parameters:	temperature : float The temperature in K. chempot : float The chemical potential in eV. dos : ndarray, optional Dimension: (N,M) Contains the band decomposed density of states for each band N and energy M. If not supplied, set to the dos_partial parameter of the current Bandstructure() object. dos_energies : ndarray, optional Dimension: (M) The energies in eV where the density of states are sampled. band_decomp : boolean Return a band decomposed carrier concentration or not. defect_ionization : boolean Selects if defect ionization compensation should be included. The donor_number, donor_energy, donor_degen_fact, acceptor_number, acceptor_energy and acceptor_degen_fact need to be set in the general configuration file.
Returns:	n_type : ndarray Dimension: (N) Contains the n-type carrier concentration for each band index N in units of $10^{21} \mathrm{cm}^{-3}$ . p_type : ndarray Dimension: (N) Contains the p-type carrier concentration for each band index N in units of $10^{21} \mathrm{cm}^{-3}$ .

temperature : float: The temperature in K.
chempot : float: The chemical potential in eV.
dos : ndarray, optional: Dimension: (N,M)

Contains the band decomposed density of states for each band N and energy M. If not supplied, set to the dos_partial parameter of the current Bandstructure() object.
dos_energies : ndarray, optional: Dimension: (M)

The energies in eV where the density of states are sampled.
band_decomp : boolean: Return a band decomposed carrier concentration or not.
defect_ionization : boolean: Selects if defect ionization compensation should be included. The donor_number, donor_energy, donor_degen_fact, acceptor_number, acceptor_energy and acceptor_degen_fact need to be set in the general configuration file.

Returns:

n_type : ndarray: Dimension: (N)

Contains the n-type carrier concentration for each band index N in units of $10^{21} \mathrm{cm}^{-3}$ .
p_type : ndarray: Dimension: (N)

Contains the p-type carrier concentration for each band index N in units of $10^{21} \mathrm{cm}^{-3}$ .

calc_transport_tensors(self, bs=None, temperatures=None, chempots=None, method=None)¶

Selects which method to use when calculating the transport coefficients.

Parameters:

Parameters:	bs : A Band() object containing the band structure. temperatures : ndarray, optional Dimension: (N) Contains N different temperatures in K. If not supplied the temperature from the active Transport() object is used. chempots : ndarray, optional Dimension: (M) Contains M different chemical potentials in eV. If not supplied the chempot from the active Transport() object is used. method : {“closed”, “numeric”, “numerick”} If method is not supplied is defaults to “numeric” unless bandstructure data is read numerically or generated (all cases where the closed Fermi Dirac integrals cannot be used) when it defaults to “numerick”. “closed” evaluates the closed Fermi integrals where only one scattering mechanism is possible per band. Only valid for systems where one can strictly rely on a parametrized parabolic bandstructure based on effective mass models. Parameters (e.g. effective masses for each band) are set in the bandstructure configuration file. The driver routine is `lbtecoeff.parabolic_closed()` “numeric” similar to “closed, but evaluates the Fermi integrals in an open form (e.g. it is possible to concatenate the scattering mechanisms, which is not possible for the closed Fermi integrals). The driver routine is `lbtecoeff.parabolic_numeric()` “numerick” evaluates the transport integrals more generally as an integral over the k-points. It is less restrictive than the two other options, but also more prone to convergence issues etc. However, for bandstructures read from datafiles, this is the only option. The driver routine is `lbtecoeff.numerick()`
Returns:	sigma, seebeck, lorenz : ndarray, ndarray, ndarray Dimension: (N,M,3,3), (N,M,3,3), (N,M,3,3) Returns the electrical condcutivity, Seebeck coefficient and Lorenz tensor for N temperature and M chemical potential steps in units of $\\mathrm{S}/\\mathrm{m}$ , $\\mu \\mathrm{V}/\\mathrm{K}$ , $\\mathrm{V^2}/\\mathrm{K^2}$ . These are stored in the current Transport() object.

bs : A Band() object containing the band structure.
temperatures : ndarray, optional: Dimension: (N)

Contains N different temperatures in K. If not supplied the temperature from the active Transport() object is used.
chempots : ndarray, optional: Dimension: (M)

Contains M different chemical potentials in eV. If not supplied the chempot from the active Transport() object is used.
method : {“closed”, “numeric”, “numerick”}: If method is not supplied is defaults to “numeric” unless bandstructure data is read numerically or generated (all cases where the closed Fermi Dirac integrals cannot be used) when it defaults to “numerick”.

“closed” evaluates the closed Fermi integrals where only

one scattering mechanism is possible per band. Only valid

for systems where one can strictly rely on a parametrized

parabolic bandstructure based on effective mass models.

Parameters (e.g. effective masses for each band) are set

in the bandstructure configuration file.

The driver routine is lbtecoeff.parabolic_closed()

“numeric” similar to “closed, but evaluates the Fermi

integrals in an open form (e.g. it is possible to

concatenate the scattering mechanisms, which is not

possible for the closed Fermi integrals).

The driver routine is lbtecoeff.parabolic_numeric()

“numerick” evaluates the transport integrals more generally

as an integral over the k-points. It is less restrictive

than the two other options, but also more prone to

convergence issues etc. However, for bandstructures

read from datafiles, this is the only option.

The driver routine is lbtecoeff.numerick()

Returns:

sigma, seebeck, lorenz : ndarray, ndarray, ndarray: Dimension: (N,M,3,3), (N,M,3,3), (N,M,3,3)

Returns the electrical condcutivity, Seebeck coefficient and Lorenz tensor for N temperature and M chemical potential steps in units of $\\mathrm{S}/\\mathrm{m}$ , $\\mu \\mathrm{V}/\\mathrm{K}$ , $\\mathrm{V^2}/\\mathrm{K^2}$ . These are stored in the current Transport() object.

See also

lbtecoeff.parabolic_closed
lbtecoeff.parabolic_numeric
lbtecoeff.numerick

fetch_chempots(self, store=True)¶

Set up the chemical potential.

Parameters:	store : boolean, optional If given and set to True, the chempot array is in addition to being returned also stored in the current Transport() object.
Returns:	chempot : ndarray Dimension: (N) Contains N chemical potential linear samplings in units of eV. The parameters transport_chempot_min, transport_chempot_max and transport_chempot_samples in param.yml set the maximum and minimum chemical potential and its number of samples.

fetch_etas(self, chempot, temperature)¶

Calculate the reduced chemical potential

Parameters:	chempot : ndarray Dimension: (N) Contains N samples of the chemical potential in units of eV. temperature : float The temperature in K.
Returns:	eta : ndarray Dimension: (N) Contains N samples of the reduced chemical potential

fetch_relevant_bands(self, tr=None)¶

Locate bands that will be included in the transport integrals.

Parameters:	tr : object, optional A Transport() object.
Returns:	None

Notes

The included bands are located by considering the input range of chemical potentials from transport_chempot_min and transport_chempot_max padded with the value transport_energycutband on each side (see the general configuration file).

fetch_temperatures(self, store=True)¶

Set up the temperatures.

Parameters:	store : boolean, optional If given and set to True, the temperature array is in addition to being returned also stored in the active Transport() object.
Returns:	temperature : (N) ndarray Contains N temperature linear samplings in units of K. The parameters temperature_min, temperature_max and temperature_steps in param.yml set the maximum and minimum temperature and its number of steps.

setup_scattering(self, dos=None, dos_energies=None, select_scattering=None)¶

Selects which how to set up the carrier scattering.

Parameters:

Parameters:	dos : ndarray Dimension: (N,M) Array containing the partial density of states in units of 1/eV/AA^3, where N is the band index and M is the energy index. dos_energies : ndarray Dimension: (M) Array containing the energy in eV at M samplings where the density of states is calculated. select_scattering : ndarray Dimension: (12) Array containing integers. Set to 1 to select the scattering, 0 to exclude. The variables in select_scattering are set in the bandstructure configuration file, one value for each scattering and band. See notes below for the currrently available scattering mechnisms.
Returns:	None

dos : ndarray: Dimension: (N,M)

Array containing the partial density of states in units of 1/eV/AA^3, where N is the band index and M is the energy index.
dos_energies : ndarray: Dimension: (M)

Array containing the energy in eV at M samplings where the density of states is calculated.
select_scattering : ndarray: Dimension: (12)

Array containing integers. Set to 1 to select the scattering, 0 to exclude. The variables in select_scattering are set in the bandstructure configuration file, one value for each scattering and band. See notes below for the currrently available scattering mechnisms.

Returns:

None

See also

scattering.scattering_dos
scattering.scattering_parabolic

transport.acceptor_ionization(number, energy, degen, e_fermi, beta)¶

Returns the number of ionized acceptors.

Parameters:	number : float Number of acceptors. energy : float The energy in eV where the acceptor compensation is to be evaluated. degen : float The acceptor degeneration number. e_fermi : float The Fermi level in eV. beta : float The beta (1/kT) factor in eV.
Returns:	float The acceptor ionization compensation.

transport.donor_ionization(number, energy, degen, e_fermi, beta)¶

Returns the number of ionized donors.

Parameters:	number : float Number of donors. energy : float The energy in eV where the donor compensation is to be evaluated. degen : float The donor degeneration number. e_fermi : float The Fermi level in eV. beta : float The beta (1/kT) factor in eV.
Returns:	float The donor ionization compensation.

transport.fermi_dist(e, e_fermi, beta)¶

Returns the Fermi Dirac distribution function (without spin degeneracy).

Parameters:	e : float The energy in eV where the Fermi Dirac distribution is to be evaluated. e_fermi : float The Fermi level in eV. beta : float The beta factor (1/kT) in eV.
Returns:	float The value of the Fermi function (without spin degeneracy).

transport.fetch_chempot_from_etas(temperature, etas)¶

Calculate the chemical potential from eta and the temperature.

Parameters:	temperature : float The temperature in K. etas : ndarray Dimension: N The unitless chemical potential, $\\eta$ for N steps.
Returns:	chempots : ndarray Dimension: N The chemical potentials in units of eV.