def compute_properties_doping(self, doping, temp_r=None):
"""
Calculate all the properties w.r.t. the doping levels in input.
Args:
doping: numpy array specifying the doping levels
When executed, it add the following variable at the BztTransportProperties
object:
Conductivity_doping, Seebeck_doping, Kappa_doping, Power_Factor_doping,
cond_Effective_mass_doping are dictionaries with 'n' and 'p' keys and
arrays of dim (len(temp_r),len(doping),3,3) as values.
Carriers_conc_doping: carriers concentration for each doping level and T.
mu_doping_eV: the chemical potential corrispondent to each doping level.
"""
if temp_r is None:
temp_r = self.temp_r
(
self.Conductivity_doping,
self.Seebeck_doping,
self.Kappa_doping,
self.Carriers_conc_doping,
) = ({}, {}, {}, {})
self.Power_Factor_doping, self.Effective_mass_doping = {}, {}
mu_doping = {}
doping_carriers = [
dop * (self.volume / (units.Meter / 100.0)**3) for dop in doping
]
for dop_type in ["n", "p"]:
sbk = np.zeros((len(temp_r), len(doping), 3, 3))
cond = np.zeros((len(temp_r), len(doping), 3, 3))
kappa = np.zeros((len(temp_r), len(doping), 3, 3))
hall = np.zeros((len(temp_r), len(doping), 3, 3, 3))
dc = np.zeros((len(temp_r), len(doping)))
if dop_type == "p":
doping_carriers = [-dop for dop in doping_carriers]
mu_doping[dop_type] = np.zeros((len(temp_r), len(doping)))
for t, temp in enumerate(temp_r):
for i, dop_car in enumerate(doping_carriers):
mu_doping[dop_type][t, i] = BL.solve_for_mu(
self.epsilon,
self.dos,
self.nelect + dop_car,
temp,
self.dosweight,
True,
False,
)
# mu_doping[dop_type][t, i] = self.find_mu_doping(
# self.epsilon, self.dos, self.nelect + dop_car, temp,
# self.dosweight)
N, L0, L1, L2, Lm11 = BL.fermiintegrals(
self.epsilon,
self.dos,
self.vvdos,
mur=mu_doping[dop_type][t],
Tr=np.array([temp]),
dosweight=self.dosweight,
)
cond[t], sbk[t], kappa[t], hall[
t] = BL.calc_Onsager_coefficients(
L0,
L1,
L2,
mu_doping[dop_type][t],
np.array([temp]),
self.volume,
Lm11,
)
dc[t] = self.nelect + N
self.Conductivity_doping[dop_type] = cond * self.CRTA # S / m
self.Seebeck_doping[dop_type] = sbk * 1e6 # microVolt / K
self.Kappa_doping[dop_type] = kappa * self.CRTA # W / (m K)
# self.Hall_doping[dop_type] = hall
self.Carriers_conc_doping[dop_type] = dc / (
self.volume / (units.Meter / 100.0)**3)
self.Power_Factor_doping[dop_type] = (
sbk @ sbk) @ cond * self.CRTA * 1e3
cond_eff_mass = np.zeros((len(temp_r), len(doping), 3, 3))
for t in range(len(temp_r)):
for i, dop in enumerate(doping):
try:
cond_eff_mass[t, i] = np.linalg.inv(
cond[t,
i]) * dop * units.qe_SI**2 / units.me_SI * 1e6
except np.linalg.LinAlgError:
pass
self.Effective_mass_doping[dop_type] = cond_eff_mass
self.doping = doping
self.mu_doping = mu_doping
self.mu_doping_eV = {
k: v / units.eV - self.efermi
for k, v in mu_doping.items()
}
self.contain_props_doping = True
erange=[data.fermi - ecut, data.fermi + ecut],
npts=round(2 * ecut / deltae),
scattering_model='uniform_tau')
# Define the temperatures and chemical potentials we are interested in
#Tr = np.arange(deltat, tmax + deltat / 2, deltat)
#mur_indices = np.logical_and(epsilon > data.fermi - efcut, epsilon < data.fermi + efcut)
#mur = epsilon[mur_indices]
Tr = np.arange(deltat, tmax + deltat / 2, deltat)
mur = np.empty_like(Tr)
_nelect = data.nelect
for iT, T in enumerate(Tr):
mur[iT] = BL.solve_for_mu(epsilon,
dos,
_nelect - doping_level,
T,
data.dosweight,
refine=True)
# The flow from this point is again similar to that in parse_integrate,
# with the exception that the chemical potentials are different for
# each temperature.
N = np.empty_like(Tr)
L0, L1, L2 = (np.empty((Tr.shape[0], 3, 3)) for ii in range(3))
Lm11 = np.empty((Tr.shape[0], 3, 3, 3))
# Obtain the Fermi integrals required to get the Onsager coefficients
for iT, T in enumerate(Tr):
(N[iT], L0[iT], L1[iT], L2[iT],
Lm11[iT]) = BL.fermiintegrals(epsilon,
dos,
def boltztrap(dirname, bt2file, title, T):
print(("\n\nWorking in %s for %s at %i K" % (dirname, title, T)))
# If a ready-made file with the interpolation results is available, use it
# Otherwise, create the file.
if not os.path.exists(bt2file):
# Load the input
data = BTP.DFTData(dirname)
# Select the interesting bands
nemin, nemax = data.bandana(emin=data.fermi - .2, emax=data.fermi + .2)
# Set up a k point grid with roughly five times the density of the input
equivalences = sphere.get_equivalences(data.atoms,
len(data.kpoints) * 5)
# Perform the interpolation
coeffs = fite.fitde3D(data, equivalences)
# Save the result
serialization.save_calculation(
bt2file, data, equivalences, coeffs,
serialization.gen_bt2_metadata(data, data.mommat is not None))
# Load the interpolation results
print("Load the interpolation results")
data, equivalences, coeffs, metadata = serialization.load_calculation(
bt2file)
# Reconstruct the bands
print("Reconstruct the bands")
lattvec = data.get_lattvec()
eband, vvband, cband = fite.getBTPbands(equivalences, coeffs, lattvec)
# Obtain the Fermi integrals for different chemical potentials at
# room temperature.
TEMP = np.array([T])
epsilon, dos, vvdos, cdos = BL.BTPDOS(eband, vvband, npts=4000)
margin = 9. * units.BOLTZMANN * TEMP.max()
mur_indices = np.logical_and(epsilon > epsilon.min() + margin,
epsilon < epsilon.max() - margin)
mur = epsilon[mur_indices]
N, L0, L1, L2, Lm11 = BL.fermiintegrals(epsilon,
dos,
vvdos,
mur=mur,
Tr=TEMP,
dosweight=data.dosweight)
# Compute the Onsager coefficients from those Fermi integrals
print("Compute the Onsager coefficients")
UCvol = data.get_volume()
sigma, seebeck, kappa, Hall = BL.calc_Onsager_coefficients(
L0, L1, L2, mur, TEMP, UCvol)
fermi = BL.solve_for_mu(epsilon, dos, data.nelect, T, data.dosweight)
savedata[title + '-%s' % T] = {
"sigma": sigma,
"seebeck": seebeck,
"kappa": kappa,
"Hall": Hall,
"mu": (mur - fermi) / BL.eV,
"temp": T,
"n": N[0] + data.nelect
}
mur_indices = np.logical_and(epsilon > epsilon.min() + margin,
epsilon < epsilon.max() - margin)
mur = epsilon[mur_indices]
N, L0, L1, L2, Lm11 = BL.fermiintegrals(epsilon,
dos,
vvdos,
mur=mur,
Tr=TEMP,
dosweight=data.dosweight)
# Compute the Onsager coefficients from those Fermi integrals
UCvol = data.get_volume()
sigma, seebeck, kappa, Hall = BL.calc_Onsager_coefficients(
L0, L1, L2, mur, TEMP, UCvol)
fermi = BL.solve_for_mu(epsilon, dos, data.nelect, 300, data.dosweight)
# Plot the results
fig1, ax1 = pl.subplots(1, figsize=(6, 3))
ax1.set_xlim([-1, 1])
ax1.set_ylim([-300, 300])
ax1.plot((mur - fermi) / BL.eV,
seebeck[0, :, 0, 0] * 1e6,
"k-",
label="xx \n seebeck[0, 0:0, 0, 0] * 1e6")
ax1.plot((mur - fermi) / BL.eV, seebeck[0, :, 2, 2] * 1e6, "k--", label="zz")
ax1.set_xlabel("$\mu$ [eV]")
ax1.set_ylabel("$S$ [$\mu$V/K]")
ax1.legend()
fig1.tight_layout(pad=1.)
fig1.savefig("seebeck.pdf")