pymatgen.electronic_structure.boltztrap module¶
This module provides classes to run and analyze boltztrap on pymatgen band structure objects. Boltztrap is a software interpolating band structures and computing materials properties from this band structure using Boltzmann semiclassical transport theory.
Boltztrap has been developed by Georg Madsen.
http://www.icams.de/content/research/softwaredevelopment/boltztrap/
You need version 1.2.3 or higher
References are:
Madsen, G. K. H., and Singh, D. J. (2006).
BoltzTraP. A code for calculating bandstructure dependent quantities.
Computer Physics Communications, 175, 6771

class
BoltztrapAnalyzer
(gap=None, mu_steps=None, cond=None, seebeck=None, kappa=None, hall=None, doping=None, mu_doping=None, seebeck_doping=None, cond_doping=None, kappa_doping=None, hall_doping=None, intrans=None, dos=None, dos_partial=None, carrier_conc=None, vol=None, warning=None, bz_bands=None, bz_kpoints=None, fermi_surface_data=None)[source]¶ Bases:
object
Class used to store all the data from a boltztrap run
Constructor taking directly all the data generated by Boltztrap. You won’t probably use it directly but instead use the from_files and from_dict methods.
 Parameters
gap – The gap after interpolation in eV
mu_steps – The steps of electron chemical potential (or Fermi level) in eV.
cond – The electronic conductivity tensor divided by a constant relaxation time (sigma/tau) at different temperature and fermi levels. The format is {temperature: [array of 3x3 tensors at each fermi level in mu_steps]}. The units are 1/(Ohm*m*s).
seebeck – The Seebeck tensor at different temperatures and fermi levels. The format is {temperature: [array of 3x3 tensors at each fermi level in mu_steps]}. The units are V/K
kappa – The electronic thermal conductivity tensor divided by a constant relaxation time (kappa/tau) at different temperature and fermi levels. The format is {temperature: [array of 3x3 tensors at each fermi level in mu_steps]} The units are W/(m*K*s)
hall – The hall tensor at different temperature and fermi levels The format is {temperature: [array of 27 coefficients list at each fermi level in mu_steps]} The units are m^3/C
doping – The different doping levels that have been given to Boltztrap. The format is {‘p’:[],’n’:[]} with an array of doping levels. The units are cm^3
mu_doping – Gives the electron chemical potential (or Fermi level) for a given set of doping. Format is {‘p’:{temperature: [fermi levels],’n’:{temperature: [fermi levels]}} the fermi level array is ordered according to the doping levels in doping units for doping are in cm^3 and for Fermi level in eV
seebeck_doping – The Seebeck tensor at different temperatures and doping levels. The format is {‘p’: {temperature: [Seebeck tensors]}, ‘n’:{temperature: [Seebeck tensors]}} The [Seebeck tensors] array is ordered according to the doping levels in doping units for doping are in cm^3 and for Seebeck in V/K
cond_doping – The electronic conductivity tensor divided by a constant relaxation time (sigma/tau) at different temperatures and doping levels The format is {‘p’:{temperature: [conductivity tensors]}, ‘n’:{temperature: [conductivity tensors]}} The [conductivity tensors] array is ordered according to the doping levels in doping units for doping are in cm^3 and for conductivity in 1/(Ohm*m*s)
kappa_doping – The thermal conductivity tensor divided by a constant relaxation time (kappa/tau) at different temperatures and doping levels. The format is {‘p’:{temperature: [thermal conductivity tensors]},’n’:{temperature: [thermal conductivity tensors]}} The [thermal conductivity tensors] array is ordered according to the doping levels in doping units for doping are in cm^3 and for thermal conductivity in W/(m*K*s)
hall_doping – The Hall tensor at different temperatures and doping levels. The format is {‘p’:{temperature: [Hall tensors]}, ‘n’:{temperature: [Hall tensors]}} The [Hall tensors] array is ordered according to the doping levels in doping and each Hall tensor is represented by a 27 coefficients list. The units are m^3/C
intrans – a dictionary of inputs e.g. {“scissor”: 0.0}
carrier_conc – The concentration of carriers in electron (or hole) per unit cell
dos – The dos computed by Boltztrap given as a pymatgen Dos object
dos_partial – Data for the partial DOS projected on sites and orbitals
vol – Volume of the unit cell in angstrom cube (A^3)
warning – string if BoltzTraP outputted a warning, else None
bz_bands – Data for interpolated bands on a kpoint line (run_type=BANDS)
bz_kpoints – kpoint in reciprocal coordinates for interpolated bands (run_type=BANDS)
fermi_surface_data – energy values in a 3D grid imported from the output .cube file.

static
check_acc_bzt_bands
(sbs_bz, sbs_ref, warn_thr=0.03, 0.03)[source]¶ Compare sbs_bz BandStructureSymmLine calculated with boltztrap with the sbs_ref BandStructureSymmLine as reference (from MP for instance), computing correlation and energy difference for eight bands around the gap (semiconductors) or fermi level (metals). warn_thr is a threshold to get a warning in the accuracy of Boltztap interpolated bands. Return a dictionary with these keys:  “N”: the index of the band compared; inside each there are:
“Corr”: correlation coefficient for the 8 compared bands
“Dist”: energy distance for the 8 compared bands
“branch_name”: energy distance for that branch
“avg_corr”: average of correlation coefficient over the 8 bands
“avg_dist”: average of energy distance over the 8 bands
“nb_list”: list of indexes of the 8 compared bands
 “acc_thr”: list of two float corresponing to the two warning
thresholds in input
 “acc_err”: list of two bools:
True if the avg_corr > warn_thr[0], and True if the avg_dist > warn_thr[1]
See also compare_sym_bands function doc

static
from_files
(path_dir, dos_spin=1)[source]¶ get a BoltztrapAnalyzer object from a set of files
 Parameters
path_dir – directory where the boltztrap files are
dos_spin – in DOS mode, set to 1 for spin up and 1 for spin down
 Returns
a BoltztrapAnalyzer object

get_average_eff_mass
(output='eigs', doping_levels=True)[source]¶ Gives the average effective mass tensor. We call it average because it takes into account all the bands and regions in the Brillouin zone. This is different than the standard textbook effective mass which relates often to only one (parabolic) band. The average effective mass tensor is defined as the integrated average of the second derivative of E(k) This effective mass tensor takes into account: nonparabolicity multiple extrema multiple bands
For more information about it. See:
Hautier, G., Miglio, A., Waroquiers, D., Rignanese, G., & Gonze, X. (2014). How Does Chemistry Influence Electron Effective Mass in Oxides? A HighThroughput Computational Analysis. Chemistry of Materials, 26(19), 5447–5458. doi:10.1021/cm404079a
or
Hautier, G., Miglio, A., Ceder, G., Rignanese, G.M., & Gonze, X. (2013). Identification and design principles of low hole effective mass ptype transparent conducting oxides. Nature Communications, 4, 2292. doi:10.1038/ncomms3292
Depending on the value of output, we have either the full 3x3 effective mass tensor, its 3 eigenvalues or an average
 Parameters
output (string) – ‘eigs’ for eigenvalues, ‘tensor’ for the full
and 'average' for an average (tensor) –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
 Returns
{temp:[]},’n’:{temp:[]}} with an array of effective mass tensor, eigenvalues of average value (depending on output) for each temperature and for each doping level. The ‘p’ links to hole effective mass tensor and ‘n’ to electron effective mass tensor.
 Return type
If doping_levels=True,a dictionary {‘p’

get_carrier_concentration
()[source]¶ gives the carrier concentration (in cm^3)
 Returns
a dictionary {temp:[]} with an array of carrier concentration (in cm^3) at each temperature The array relates to each step of electron chemical potential

get_complete_dos
(structure, analyzer_for_second_spin=None)[source]¶ Gives a CompleteDos object with the DOS from the interpolated projected band structure :param the structure: :type the structure: necessary to identify sites for projection :param analyzer_for_second_spin must be specified to have a: :param CompleteDos with both Spin components:
 Returns
a CompleteDos object
Example of use in case of spin polarized case:
BoltztrapRunner(bs=bs,nelec=10,run_type=”DOS”,spin=1).run(path_dir=’dos_up/’) an_up=BoltztrapAnalyzer.from_files(“dos_up/boltztrap/”,dos_spin=1)
BoltztrapRunner(bs=bs,nelec=10,run_type=”DOS”,spin=1).run(path_dir=’dos_dw/’) an_dw=BoltztrapAnalyzer.from_files(“dos_dw/boltztrap/”,dos_spin=1)
cdos=an_up.get_complete_dos(bs.structure,an_dw)

get_complexity_factor
(output='average', temp=300, doping_levels=False, Lambda=0.5)[source]¶ Fermi surface complexity factor respect to calculated as explained in Ref. Gibbs, Z. M. et al., Effective mass and fermi surface complexity factor from ab initio band structure calculations. npj Computational Materials 3, 8 (2017).
 Parameters
output – ‘average’ returns the complexity factor calculated using the average of the three diagonal components of the seebeck and conductivity tensors. ‘tensor’ returns the complexity factor respect to the three diagonal components of seebeck and conductivity tensors.
doping_levels – False means that the complexity factor is calculated for every value of the chemical potential True means that the complexity factor is calculated for every value of the doping levels for both n and p types
temp – temperature of calculated seebeck and conductivity.
Lambda – fitting parameter used to model the scattering (0.5 means constant relaxation time).
 Returns
a list of values for the complexity factor w.r.t the chemical potential, if doping_levels is set at False; a dict with n an p keys that contain a list of values for the complexity factor w.r.t the doping levels, if doping_levels is set at True; if ‘tensor’ is selected, each element of the lists is a list containing the three components of the complexity factor.

get_conductivity
(output='eigs', doping_levels=True, relaxation_time=1e14)[source]¶ Gives the conductivity (1/Ohm*m) in either a full 3x3 tensor form, as 3 eigenvalues, or as the average value (trace/3.0) If doping_levels=True, the results are given at different p and n doping levels (given by self.doping), otherwise it is given as a series of electron chemical potential values
 Parameters
output (string) – the type of output. ‘tensor’ give the full
tensor, 'eigs' its 3 eigenvalues and (3x3) –
the average of the three eigenvalues ('average') –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
relaxation_time (float) – constant relaxation time in secs
 Returns
{‘p’:[],’n’:[]}}. The ‘p’ links to conductivity at ptype doping and ‘n’ to the conductivity at ntype doping. Otherwise, returns a {temp:[]} dictionary. The result contains either the sorted three eigenvalues of the symmetric conductivity tensor (format=’eigs’) or a full tensor (3x3 array) (output=’tensor’) or as an average (output=’average’). The result includes a given constant relaxation time
units are 1/Ohm*m
 Return type
If doping_levels=True, a dictionary {temp

get_extreme
(target_prop, maximize=True, min_temp=None, max_temp=None, min_doping=None, max_doping=None, isotropy_tolerance=0.05, use_average=True)[source]¶ This method takes in eigenvalues over a range of carriers, temperatures, and doping levels, and tells you what is the “best” value that can be achieved for the given target_property. Note that this method searches the doping dict only, not the full mu dict.
 Parameters
target_prop – target property, i.e. “seebeck”, “power factor”, “conductivity”, “kappa”, or “zt”
maximize – True to maximize, False to minimize (e.g. kappa)
min_temp – minimum temperature allowed
max_temp – maximum temperature allowed
min_doping – minimum doping allowed (e.g., 1E18)
max_doping – maximum doping allowed (e.g., 1E20)
isotropy_tolerance – tolerance for isotropic (0.05 = 5%)
use_average – True for avg of eigenval, False for max eigenval
 Returns
{“value”, “temperature”, “doping”, “isotropic”}
 Return type
A dictionary with keys {“p”, “n”, “best”} with subkeys

get_hall_carrier_concentration
()[source]¶ gives the Hall carrier concentration (in cm^3). This is the trace of the Hall tensor (see Boltztrap source code) Hall carrier concentration are not always exactly the same than carrier concentration.
 Returns
a dictionary {temp:[]} with an array of Hall carrier concentration (in cm^3) at each temperature The array relates to each step of electron chemical potential

get_mu_bounds
(temp=300)[source]¶  Parameters
temp – Temperature.
 Returns
The chemical potential bounds at that temperature.

get_power_factor
(output='eigs', doping_levels=True, relaxation_time=1e14)[source]¶ Gives the power factor (Seebeck^2 * conductivity) in units microW/(m*K^2) in either a full 3x3 tensor form, as 3 eigenvalues, or as the average value (trace/3.0) If doping_levels=True, the results are given at different p and n doping levels (given by self.doping), otherwise it is given as a series of electron chemical potential values
 Parameters
output (string) – the type of output. ‘tensor’ give the full 3x3
'eigs' its 3 eigenvalues and (tensor,) –
the average of the three eigenvalues ('average') –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
relaxation_time (float) – constant relaxation time in secs
 Returns
{‘p’:[],’n’:[]}}. The ‘p’ links to power factor at ptype doping and ‘n’ to the conductivity at ntype doping. Otherwise, returns a {temp:[]} dictionary. The result contains either the sorted three eigenvalues of the symmetric power factor tensor (format=’eigs’) or a full tensor (3x3 array) ( output=’tensor’) or as an average (output=’average’). The result includes a given constant relaxation time
units are microW/(m K^2)
 Return type
If doping_levels=True, a dictionnary {temp

get_seebeck
(output='eigs', doping_levels=True)[source]¶ Gives the seebeck coefficient (microV/K) in either a full 3x3 tensor form, as 3 eigenvalues, or as the average value (trace/3.0) If doping_levels=True, the results are given at different p and n doping levels (given by self.doping), otherwise it is given as a series of electron chemical potential values
 Parameters
output (string) – the type of output. ‘tensor’ give the full
tensor, 'eigs' its 3 eigenvalues and (3x3) –
the average of the three eigenvalues ('average') –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
 Returns
{‘p’:[],’n’:[]}}. The ‘p’ links to Seebeck at ptype doping and ‘n’ to the Seebeck at ntype doping. Otherwise, returns a {temp:[]} dictionary The result contains either the sorted three eigenvalues of the symmetric Seebeck tensor (output=’eigs’) or a full tensor (3x3 array) ( output=’tensor’) or as an average (output=’average’).
units are microV/K
 Return type
If doping_levels=True, a dictionary {temp

get_seebeck_eff_mass
(output='average', temp=300, doping_levels=False, Lambda=0.5)[source]¶ Seebeck effective mass calculated as explained in Ref. Gibbs, Z. M. et al., Effective mass and fermi surface complexity factor from ab initio band structure calculations. npj Computational Materials 3, 8 (2017).
 Parameters
output – ‘average’ returns the seebeck effective mass calculated using the average of the three diagonal components of the seebeck tensor. ‘tensor’ returns the seebeck effective mass respect to the three diagonal components of the seebeck tensor.
doping_levels – False means that the seebeck effective mass is calculated for every value of the chemical potential True means that the seebeck effective mass is calculated for every value of the doping levels for both n and p types
temp – temperature of calculated seebeck.
Lambda – fitting parameter used to model the scattering (0.5 means constant relaxation time).
 Returns
a list of values for the seebeck effective mass w.r.t the chemical potential, if doping_levels is set at False; a dict with n an p keys that contain a list of values for the seebeck effective mass w.r.t the doping levels, if doping_levels is set at True; if ‘tensor’ is selected, each element of the lists is a list containing the three components of the seebeck effective mass.

get_symm_bands
(structure, efermi, kpt_line=None, labels_dict=None)[source]¶ Function useful to read bands from Boltztrap output and get a BandStructureSymmLine object comparable with that one from a DFT calculation (if the same kpt_line is provided). Default kpt_line and labels_dict is the standard path of high symmetry kpoint for the specified structure. They could be extracted from the BandStructureSymmLine object that you want to compare with. efermi variable must be specified to create the BandStructureSymmLine object (usually it comes from DFT or Boltztrap calc)

get_thermal_conductivity
(output='eigs', doping_levels=True, k_el=True, relaxation_time=1e14)[source]¶ Gives the electronic part of the thermal conductivity in either a full 3x3 tensor form, as 3 eigenvalues, or as the average value (trace/3.0) If doping_levels=True, the results are given at different p and n doping levels (given by self.doping), otherwise it is given as a series of electron chemical potential values
 Parameters
output (string) – the type of output. ‘tensor’ give the full 3x3
'eigs' its 3 eigenvalues and (tensor,) –
the average of the three eigenvalues ('average') –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
k_el (boolean) – True for k_0PF*T, False for k_0
relaxation_time (float) – constant relaxation time in secs
 Returns
{‘p’:[],’n’:[]}}. The ‘p’ links to thermal conductivity at ptype doping and ‘n’ to the thermal conductivity at ntype doping. Otherwise, returns a {temp:[]} dictionary. The result contains either the sorted three eigenvalues of the symmetric conductivity tensor (format=’eigs’) or a full tensor (3x3 array) ( output=’tensor’) or as an average (output=’average’). The result includes a given constant relaxation time
units are W/mK
 Return type
If doping_levels=True, a dictionary {temp

get_zt
(output='eigs', doping_levels=True, relaxation_time=1e14, kl=1.0)[source]¶ Gives the ZT coefficient (S^2*cond*T/thermal cond) in either a full 3x3 tensor form, as 3 eigenvalues, or as the average value (trace/3.0) If doping_levels=True, the results are given at different p and n doping levels (given by self.doping), otherwise it is given as a series of electron chemical potential values. We assume a constant relaxation time and a constant lattice thermal conductivity
 Parameters
output (string) – the type of output. ‘tensor’ give the full 3x3
'eigs' its 3 eigenvalues and (tensor,) –
the average of the three eigenvalues ('average') –
doping_levels (boolean) – True for the results to be given at
doping levels, False for results (different) –
different electron chemical potentials (at) –
relaxation_time (float) – constant relaxation time in secs
k_l (float) – lattice thermal cond in W/(m*K)
 Returns
{‘p’:[],’n’:[]}}. The ‘p’ links to ZT at ptype doping and ‘n’ to the ZT at ntype doping. Otherwise, returns a {temp:[]} dictionary. The result contains either the sorted three eigenvalues of the symmetric ZT tensor (format=’eigs’) or a full tensor (3x3 array) ( output=’tensor’) or as an average (output=’average’). The result includes a given constant relaxation time and lattice thermal conductivity
 Return type
If doping_levels=True, a dictionary {temp

static
parse_cond_and_hall
(path_dir, doping_levels=None)[source]¶ Parses the conductivity and Hall tensors :param path_dir: Path containing .condtens / .halltens files :param doping_levels: ([float])  doping lvls, parse outtrans to get this
 Returns
mu_steps, cond, seebeck, kappa, hall, pn_doping_levels, mu_doping, seebeck_doping, cond_doping, kappa_doping, hall_doping, carrier_conc

static
parse_intrans
(path_dir)[source]¶ Parses boltztrap.intrans mainly to extract the value of scissor applied to the bands or some other inputs
 Parameters
path_dir – (str) dir containing the boltztrap.intrans file
 Returns
 a dictionary containing various inputs that had
been used in the Boltztrap run.
 Return type
intrans (dict)

static
parse_outputtrans
(path_dir)[source]¶ Parses .outputtrans file
 Parameters
path_dir – dir containing boltztrap.outputtrans
 Returns
tuple  (run_type, warning, efermi, gap, doping_levels)

static
parse_struct
(path_dir)[source]¶ Parses boltztrap.struct file (only the volume) :param path_dir: (str) dir containing the boltztrap.struct file
 Returns
(float) volume

static
parse_transdos
(path_dir, efermi, dos_spin=1, trim_dos=False)[source]¶ Parses .transdos (total DOS) and .transdos_x_y (partial DOS) files :param path_dir: (str) dir containing DOS files :param efermi: (float) Fermi energy :param dos_spin: (int) 1 for spin down, +1 for spin up :param trim_dos: (bool) whether to postprocess / trim DOS
 Returns
tuple  (DOS, dict of partial DOS)

exception
BoltztrapError
[source]¶ Bases:
Exception
Exception class for boltztrap. Raised when the boltztrap gives an error

class
BoltztrapRunner
(**kwargs)[source]¶ Bases:
monty.json.MSONable
This class is used to run Boltztrap on a band structure object.
 Parameters
bs – A band structure object
nelec – the number of electrons
dos_type – two options for the band structure integration: “HISTO” (histogram) or “TETRA” using the tetrahedon method. TETRA typically gives better results (especially for DOSes) but takes more time
energy_grid – the energy steps used for the integration (eV)
lpfac – the number of interpolation points in the real space. By default 10 gives 10 time more points in the real space than the number of kpoints given in reciprocal space
run_type – type of boltztrap usage. by default  BOLTZ: (default) compute transport coefficients  BANDS: interpolate all bands contained in the energy range specified in energy_span_around_fermi variable, along specified kpoints  DOS: compute total and partial dos (custom BoltzTraP code needed!)  FERMI: compute fermi surface or more correctly to get certain bands interpolated
band_nb – indicates a band number. Used for Fermi Surface interpolation (run_type=”FERMI”)
spin – specific spin component (1: up, 1: down) of the band selected in FERMI mode (mandatory).
cond_band – if a conduction band is specified in FERMI mode, set this variable as True
tauref – reference relaxation time. Only set to a value different than zero if we want to model beyond the constant relaxation time.
tauexp – exponent for the energy in the nonconstant relaxation time approach
tauen – reference energy for the nonconstant relaxation time approach
soc – results from spinorbit coupling (soc) computations give typically nonpolarized (no spin up or down) results but single electron occupations. If the band structure comes from a soc computation, you should set soc to True (default False)
doping – the fixed doping levels you want to compute. Boltztrap provides both transport values depending on electron chemical potential (fermi energy) and for a series of fixed carrier concentrations. By default, this is set to 1e16 to 1e22 in increments of factors of 10.
energy_span_around_fermi – usually the interpolation is not needed on the entire energy range but on a specific range around the fermi level. This energy gives this range in eV. by default it is 1.5 eV. If DOS or BANDS type are selected, this range is automatically set to cover the entire energy range.
scissor – scissor to apply to the band gap (eV). This applies a scissor operation moving the band edges without changing the band shape. This is useful to correct the often underestimated band gap in DFT. Default is 0.0 (no scissor)
kpt_line – list of fractional coordinates of kpoints as arrays or list of Kpoint objects for BANDS mode calculation (standard path of high symmetry kpoints is automatically set as default)
tmax – Maximum temperature (K) for calculation (default=1300)
tgrid – Temperature interval for calculation (default=50)
symprec – 1e3 is the default in pymatgen. If the kmesh has been generated using a different symprec, it has to be specified to avoid a “factorization error” in BoltzTraP calculation. If a kmesh that spans the whole Brillouin zone has been used, or to disable all the symmetries, set symprec to None.
cb_cut – by default 10% of the highest conduction bands are removed because they are often not accurate. Tune cb_cut to change the percentage (0100) of bands that are removed.
timeout – overall time limit (in seconds): mainly to avoid infinite loop when trying to find Fermi levels.

run
(path_dir=None, convergence=True, write_input=True, clear_dir=False, max_lpfac=150, min_egrid=5e05)[source]¶ Write inputs (optional), run BoltzTraP, and ensure convergence (optional) :param path_dir: directory in which to run BoltzTraP :type path_dir: str :param convergence: whether to check convergence and make
corrections if needed
 Parameters
write_input – (bool) whether to write input files before the run (required for convergence mode)
clear_dir – (bool) whether to remove all files in the path_dir before starting
max_lpfac – (float) maximum lpfac value to try before reducing egrid in convergence mode
min_egrid – (float) minimum egrid value to try before giving up in convergence mode
Returns:

write_energy
(output_file)[source]¶ Writes the energy to an output file.
 Parameters
output_file – Filename

write_input
(output_dir)[source]¶ Writes the input files.
 Parameters
output_dir – Directory to write the input files.

write_intrans
(output_file)[source]¶ Writes the intrans to an output file.
 Parameters
output_file – Filename

compare_sym_bands
(bands_obj, bands_ref_obj, nb=None)[source]¶ Compute the mean of correlation between bzt and vasp bandstructure on sym line, for all bands and locally (for each branches) the difference squared (%) if nb is specified.

eta_from_seebeck
(seeb, Lambda)[source]¶ It takes a value of seebeck and adjusts the analytic seebeck until it’s equal Returns: eta where the two seebeck coefficients are equal (reduced chemical potential)

seebeck_eff_mass_from_carr
(eta, n, T, Lambda)[source]¶ Calculate seebeck effective mass at a certain carrier concentration eta in kB*T units, n in cm3, T in K, returns mass in m0 units