def _log_results_summary(amset_data, output_parameters):
results_summary = []
doping = [d * (1 / bohr_to_cm)**3 for d in amset_data.doping]
temps = amset_data.temperatures
if output_parameters["calculate_mobility"] and not amset_data.is_metal:
logger.info("Average conductivity (σ), Seebeck (S) and mobility (μ)"
" results:")
headers = ("conc [cm⁻³]", "temp [K]", "σ [S/m]", "S [µV/K]",
"μ [cm²/Vs]")
for c, t in np.ndindex(amset_data.fermi_levels.shape):
results = (
doping[c],
temps[t],
tensor_average(amset_data.conductivity[c, t]),
tensor_average(amset_data.seebeck[c, t]),
tensor_average(amset_data.mobility["overall"][c, t]),
)
results_summary.append(results)
else:
logger.info("Average conductivity (σ) and Seebeck (S) results:")
headers = ("conc [cm⁻³]", "temp [K]", "σ [S/m]", "S [µV/K]")
for c, t in np.ndindex(amset_data.fermi_levels.shape):
results = (
doping[c],
temps[t],
tensor_average(amset_data.conductivity[c, t]),
tensor_average(amset_data.seebeck[c, t]),
)
results_summary.append(results)
table = tabulate(
results_summary,
headers=headers,
numalign="right",
stralign="center",
floatfmt=(".2e", ".1f", ".2e", ".2e", ".1f"),
)
logger.info(table)
if output_parameters["separate_mobility"] and not amset_data.is_metal:
labels = amset_data.scattering_labels
logger.info("Mobility breakdown by scattering mechanism, in cm²/Vs:")
headers = ["conc [cm⁻³]", "temp [K]"] + labels
results_summary = []
for c, t in np.ndindex(amset_data.fermi_levels.shape):
results = [doping[c], temps[t]]
results += [
tensor_average(amset_data.mobility[s][c, t]) for s in labels
]
results_summary.append(results)
table = tabulate(
results_summary,
headers=headers,
numalign="right",
stralign="center",
floatfmt=[".2e", ".1f"] + [".2e"] * len(labels),
)
logger.info(table)
def calculate_fd_cutoffs(
self,
fd_tolerance: Optional[float] = 0.01,
cutoff_pad: float = 0.0,
max_moment: int = 2,
mobility_rates_only: bool = False,
):
energies = self.dos.energies
vv = {
s: v.transpose((0, 3, 1, 2))
for s, v in self.velocities_product.items()
}
_, vvdos = self.tetrahedral_band_structure.get_density_of_states(
energies, integrand=vv, sum_spins=True, use_cached_weights=True)
vvdos = tensor_average(vvdos)
# vvdos = np.array(self.dos.get_densities())
# three fermi integrals govern transport properties:
# 1. df/de controls conductivity and mobility
# 2. (e-u) * df/de controls Seebeck
# 3. (e-u)^2 df/de controls electronic thermal conductivity
# take the absolute sum of the integrals across all doping and
# temperatures. this gives us the energies that are important for
# transport
if fd_tolerance:
def get_min_max_cutoff(cumsum):
min_idx = np.where(cumsum < fd_tolerance / 2)[0].max()
max_idx = np.where(cumsum > (1 - fd_tolerance / 2))[0].min()
return energies[min_idx], energies[max_idx]
min_cutoff = np.inf
max_cutoff = -np.inf
for n, t in np.ndindex(self.fermi_levels.shape):
ef = self.fermi_levels[n, t]
temp = self.temperatures[t]
dfde = -dfdde(energies, ef, temp * boltzmann_au)
for moment in range(max_moment + 1):
weight = np.abs((energies - ef)**moment * dfde)
weight_dos = weight * vvdos
weight_cumsum = np.cumsum(weight_dos)
weight_cumsum /= np.max(weight_cumsum)
cmin, cmax = get_min_max_cutoff(weight_cumsum)
min_cutoff = min(cmin, min_cutoff)
max_cutoff = max(cmax, max_cutoff)
# import matplotlib.pyplot as plt
# ax = plt.gca()
# plt.plot(energies / units.eV, weight / weight.max())
# plt.plot(energies / units.eV, vvdos / vvdos.max())
# plt.plot(energies / units.eV, weight_dos / weight_dos.max())
# plt.plot(energies / units.eV, weight_cumsum / weight_cumsum.max())
# ax.set(xlim=(4, 7.5))
# plt.show()
else:
min_cutoff = energies.min()
max_cutoff = energies.max()
if mobility_rates_only:
vbm = get_vbm_energy(self.energies, self.vb_idx)
cbm = get_cbm_energy(self.energies, self.vb_idx)
mid_gap = (cbm + vbm) / 2
if np.all(self.doping < 0):
# only electron mobility so don't calculate valence band rates
min_cutoff = max(min_cutoff, mid_gap)
elif np.all(self.doping < 0):
# only hole mobility so don't calculate conudction band rates
max_cutoff = min(max_cutoff, mid_gap)
min_cutoff -= cutoff_pad
max_cutoff += cutoff_pad
logger.info("Calculated Fermi–Dirac cut-offs:")
log_list([
"min: {:.3f} eV".format(min_cutoff * hartree_to_ev),
"max: {:.3f} eV".format(max_cutoff * hartree_to_ev),
])
self.fd_cutoffs = (min_cutoff, max_cutoff)
def test_tensor_average(tensor, expected):
assert tensor_average(tensor) == expected