def _get_fd(energy, fermi_levels, temperatures):
f = np.zeros(fermi_levels.shape)
for n, t in np.ndindex(fermi_levels.shape):
f[n, t] = fd(energy, fermi_levels[n, t],
temperatures[t] * boltzmann_au)
return f
def _get_weighted_dos(energies,
dos,
fermi_level,
temperature,
atomic_units=True):
if temperature == 0.0:
occ = np.where(energies < fermi_level, 1.0, 0.0)
occ[energies == fermi_level] = 0.5
else:
kbt = temperature * boltzmann_au
if atomic_units:
occ = fd(energies, fermi_level, kbt)
else:
occ = fd(energies * ev_to_hartree, fermi_level * ev_to_hartree,
kbt)
wdos = dos * occ
return wdos
def _get_fd(energy, amset_data):
f = np.zeros(amset_data.fermi_levels.shape)
for n, t in np.ndindex(amset_data.fermi_levels.shape):
f[n, t] = fd(
energy,
amset_data.fermi_levels[n, t],
amset_data.temperatures[t] * boltzmann_au,
)
return f
def fermiintegrals(epsilon, dos, sigma, mur, Tr, dosweight=2.0, cdos=None):
"""Compute the moments of the FD distribution over the band structure.
Args:
epsilon: array of energies at which the DOS is available
dos: density of states
sigma: transport DOS
mur: array of chemical potential values
Tr: array of temperature values
dosweight: maximum occupancy of an electron mode
cdos: "curvature DOS" if available
Returns:
Five numpy arrays, namely:
1. An (nT, nmu) array with the electron counts for each temperature and
each chemical potential.
2. An (nT, nmu, 3, 3) with the integrals of the 3 x 3 transport DOS
over the band structure taking the occupancies into account.
3. An (nT, nmu, 3, 3) with the first moment of the 3 x 3 transport DOS
over the band structure taking the occupancies into account.
4. An (nT, nmu, 3, 3) with the second moment of the 3 x 3 transport DOS
over the band structure taking the occupancies into account.
5. If the cdos argument is provided, an (nT, nmu, 3, 3, 3) with the
integrals of the 3 x 3 x 3 "curvature DOS" over the band structure
taking the occupancies into account.
where nT and nmu are the sizes of Tr and mur, respectively.
"""
kBTr = np.array(Tr) * BOLTZMANN
nT = len(Tr)
nmu = len(mur)
N = np.empty((nT, nmu))
L0 = np.empty((nT, nmu, 3, 3))
L1 = np.empty((nT, nmu, 3, 3))
L2 = np.empty((nT, nmu, 3, 3))
if cdos is not None:
L11 = np.empty((nT, nmu, 3, 3, 3))
else:
L11 = None
de = epsilon[1] - epsilon[0]
for iT, kBT in enumerate(kBTr):
for imu, mu in enumerate(mur):
N[iT, imu] = -(dosweight * dos * fd(epsilon, mu, kBT)).sum() * de
int0 = -dosweight * dfdde(epsilon, mu, kBT)
intn = int0 * sigma
L0[iT, imu] = intn.sum(axis=2) * de
intn *= epsilon - mu
L1[iT, imu] = -intn.sum(axis=2) * de
intn *= epsilon - mu
L2[iT, imu] = intn.sum(axis=2) * de
if cdos is not None:
cint = int0 * cdos
L11[iT, imu] = -cint.sum(axis=3) * de
return N, L0, L1, L2, L11
def calculate_inverse_screening_length_sq(amset_data, dielectric):
inverse_screening_length_sq = np.zeros(amset_data.fermi_levels.shape)
tdos = amset_data.dos.tdos
energies = amset_data.dos.energies
fermi_levels = amset_data.fermi_levels
vol = amset_data.structure.volume
for n, t in np.ndindex(inverse_screening_length_sq.shape):
ef = fermi_levels[n, t]
temp = amset_data.temperatures[t]
f = fd(energies, ef, temp * boltzmann_au)
integral = np.trapz(tdos * f * (1 - f), x=energies)
inverse_screening_length_sq[n, t] = (
integral * 4 * np.pi / (dielectric * boltzmann_au * temp * vol))
return inverse_screening_length_sq