def solve_for_fermi_energy(self, temperature, chemical_potentials,
bulk_dos):
"""
Solve for the Fermi energy self-consistently as a function of T
Observations are Defect concentrations, electron and hole conc
Args:
temperature: Temperature to equilibrate fermi energies for
chemical_potentials: dict of chemical potentials to use for calculation fermi level
bulk_dos: bulk system dos (pymatgen Dos object)
Returns:
Fermi energy dictated by charge neutrality
"""
fdos = FermiDos(bulk_dos, bandgap=self.band_gap)
_, fdos_vbm = fdos.get_cbm_vbm()
def _get_total_q(ef):
qd_tot = sum([
d['charge'] * d['conc'] for d in self.defect_concentrations(
chemical_potentials=chemical_potentials,
temperature=temperature,
fermi_level=ef)
])
qd_tot += fdos.get_doping(fermi_level=ef + fdos_vbm,
temperature=temperature)
return qd_tot
return bisect(_get_total_q, -1., self.band_gap + 1.)
def solve_for_fermi_energy(self, temperature, chemical_potentials, bulk_dos):
"""
Solve for the Fermi energy self-consistently as a function of T
Observations are Defect concentrations, electron and hole conc
Args:
temperature: Temperature to equilibrate fermi energies for
chemical_potentials: dict of chemical potentials to use for calculation fermi level
bulk_dos: bulk system dos (pymatgen Dos object)
Returns:
Fermi energy dictated by charge neutrality
"""
fdos = FermiDos(bulk_dos, bandgap=self.band_gap)
_,fdos_vbm = fdos.get_cbm_vbm()
def _get_total_q(ef):
qd_tot = sum([
d['charge'] * d['conc']
for d in self.defect_concentrations(
chemical_potentials=chemical_potentials, temperature=temperature, fermi_level=ef)
])
qd_tot += fdos.get_doping(fermi=ef + fdos_vbm, T=temperature)
return qd_tot
return bisect(_get_total_q, -1., self.band_gap + 1.)
def test_doping_fermi(self):
T = 300
fermi0 = self.dos.efermi
frange = [fermi0 - 0.5, fermi0, fermi0 + 2.0, fermi0 + 2.2]
dopings = [self.dos.get_doping(fermi_level=f, temperature=T) for f in frange]
ref_dopings = [3.48077e21, 1.9235e18, -2.6909e16, -4.8723e19]
for i, c_ref in enumerate(ref_dopings):
self.assertLessEqual(abs(dopings[i] / c_ref - 1.0), 0.01)
calc_fermis = [self.dos.get_fermi(concentration=c, temperature=T) for c in ref_dopings]
for j, f_ref in enumerate(frange):
self.assertAlmostEqual(calc_fermis[j], f_ref, 4)
sci_dos = FermiDos(self.dos, bandgap=3.0)
self.assertEqual(sci_dos.get_gap(), 3.0)
old_cbm, old_vbm = self.dos.get_cbm_vbm()
old_gap = old_cbm - old_vbm
new_cbm, new_vbm = sci_dos.get_cbm_vbm()
self.assertAlmostEqual(new_cbm - old_cbm, (3.0 - old_gap) / 2.0)
self.assertAlmostEqual(old_vbm - new_vbm, (3.0 - old_gap) / 2.0)
for i, c_ref in enumerate(ref_dopings):
if c_ref < 0:
self.assertAlmostEqual(sci_dos.get_fermi(c_ref, temperature=T) - frange[i], 0.47, places=2)
else:
self.assertAlmostEqual(sci_dos.get_fermi(c_ref, temperature=T) - frange[i], -0.47, places=2)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(-1e26, 300), 7.5108, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(1e26, 300), -1.4182, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(0.0, 300), 2.9071, 4)
def solve_for_non_equilibrium_fermi_energy(self, temperature, quench_temperature,
chemical_potentials, bulk_dos):
"""
Solve for the Fermi energy after quenching in the defect concentrations at a higher
temperature (the quench temperature),
as outlined in P. Canepa et al (2017) Chemistry of Materials (doi: 10.1021/acs.chemmater.7b02909)
Args:
temperature: Temperature to equilibrate fermi energy at after quenching in defects
quench_temperature: Temperature to equilibrate defect concentrations at (higher temperature)
chemical_potentials: dict of chemical potentials to use for calculation fermi level
bulk_dos: bulk system dos (pymatgen Dos object)
Returns:
Fermi energy dictated by charge neutrality with respect to frozen in defect concentrations
"""
high_temp_fermi_level = self.solve_for_fermi_energy(quench_temperature, chemical_potentials,
bulk_dos)
fixed_defect_charge = sum([
d['charge'] * d['conc']
for d in self.defect_concentrations(
chemical_potentials=chemical_potentials, temperature=quench_temperature,
fermi_level=high_temp_fermi_level)
])
fdos = FermiDos(bulk_dos, bandgap=self.band_gap)
_, fdos_vbm = fdos.get_cbm_vbm()
def _get_total_q(ef):
qd_tot = fixed_defect_charge
qd_tot += fdos.get_doping(fermi_level=ef + fdos_vbm, temperature=temperature)
return qd_tot
return bisect(_get_total_q, -1., self.band_gap + 1.)
def test_doping_fermi(self):
T = 300
fermi0 = self.dos.efermi
frange = [fermi0 - 0.5, fermi0, fermi0 + 2.0, fermi0 + 2.2]
dopings = [self.dos.get_doping(fermi=f, T=T) for f in frange]
ref_dopings = [3.48077e+21, 1.9235e+18, -2.6909e+16, -4.8723e+19]
for i, c_ref in enumerate(ref_dopings):
self.assertLessEqual(abs(dopings[i] / c_ref - 1.0), 0.01)
calc_fermis = [self.dos.get_fermi(c=c, T=T) for c in ref_dopings]
for j, f_ref in enumerate(frange):
self.assertAlmostEqual(calc_fermis[j], f_ref, 4)
sci_dos = FermiDos(self.dos, bandgap=3.0)
self.assertEqual( sci_dos.get_gap(), 3.)
old_cbm, old_vbm = self.dos.get_cbm_vbm()
old_gap = old_cbm - old_vbm
new_cbm, new_vbm = sci_dos.get_cbm_vbm()
self.assertAlmostEqual( new_cbm - old_cbm, (3. - old_gap) / 2.)
self.assertAlmostEqual( old_vbm - new_vbm, (3. - old_gap) / 2.)
for i, c_ref in enumerate(ref_dopings):
if c_ref < 0:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, T=T) - frange[i], 0.47, places=2)
else:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, T=T) - frange[i], -0.47, places=2)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(-1e26, 300),
7.5108, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(1e26, 300),
-1.4182, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(0.0, 300),
2.5226, 4)
class FermiDosTest(unittest.TestCase):
def setUp(self):
with open(
os.path.join(PymatgenTest.TEST_FILES_DIR, "complete_dos.json"),
"r") as f:
self.dos = CompleteDos.from_dict(json.load(f))
self.dos = FermiDos(self.dos)
def test_doping_fermi(self):
T = 300
fermi0 = self.dos.efermi
frange = [fermi0 - 0.5, fermi0, fermi0 + 2.0, fermi0 + 2.2]
dopings = [
self.dos.get_doping(fermi_level=f, temperature=T) for f in frange
]
ref_dopings = [3.48077e21, 1.9235e18, -2.6909e16, -4.8723e19]
for i, c_ref in enumerate(ref_dopings):
self.assertLessEqual(abs(dopings[i] / c_ref - 1.0), 0.01)
calc_fermis = [
self.dos.get_fermi(concentration=c, temperature=T)
for c in ref_dopings
]
for j, f_ref in enumerate(frange):
self.assertAlmostEqual(calc_fermis[j], f_ref, 4)
sci_dos = FermiDos(self.dos, bandgap=3.0)
self.assertEqual(sci_dos.get_gap(), 3.0)
old_cbm, old_vbm = self.dos.get_cbm_vbm()
old_gap = old_cbm - old_vbm
new_cbm, new_vbm = sci_dos.get_cbm_vbm()
self.assertAlmostEqual(new_cbm - old_cbm, (3.0 - old_gap) / 2.0)
self.assertAlmostEqual(old_vbm - new_vbm, (3.0 - old_gap) / 2.0)
for i, c_ref in enumerate(ref_dopings):
if c_ref < 0:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, temperature=T) - frange[i],
0.47,
places=2)
else:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, temperature=T) - frange[i],
-0.47,
places=2)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(-1e26, 300),
7.5108, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(1e26, 300),
-1.4182, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(0.0, 300),
2.5226, 4)
def featurize(self, dos, bandgap=None):
"""
Args:
dos (pymatgen Dos, CompleteDos or FermiDos):
bandgap (float): for example the experimentally measured band gap
or one that is calculated via more accurate methods than the
one used to generate dos. dos will be scissored to have the
same electronic band gap as bandgap.
Returns ([float]): features are fermi levels in eV at the given
concentrations and temperature + eref in eV if return_eref
"""
dos = FermiDos(dos, bandgap=bandgap)
feats = []
eref = 0.0
for c in self.dopings:
fermi = dos.get_fermi(concentration=c,
temperature=self.T,
nstep=50)
if isinstance(self.eref, str):
if self.eref == "dos_fermi":
eref = dos.efermi
elif self.eref in ["midgap", "vbm", "cbm"]:
ecbm, evbm = dos.get_cbm_vbm()
if self.eref == "midgap":
eref = (evbm + ecbm) / 2.0
elif self.eref == "vbm":
eref = evbm
elif self.eref == "cbm":
eref = ecbm
elif self.eref == "band center":
eref = self.BC.featurize(dos.structure.composition)[0]
else:
raise ValueError('Unsupported "eref": {}'.format(
self.eref))
else:
eref = self.eref
if not self.return_eref:
fermi -= eref
feats.append(fermi)
if self.return_eref:
feats.append(eref)
return feats
def featurize(self, dos, bandgap=None):
"""
Args:
dos (pymatgen Dos, CompleteDos or FermiDos):
bandgap (float): for example the experimentally measured band gap
or one that is calculated via more accurate methods than the
one used to generate dos. dos will be scissored to have the
same electronic band gap as bandgap.
Returns ([float]): features are fermi levels in eV at the given
concentrations and temperature + eref in eV if return_eref
"""
dos = FermiDos(dos, bandgap=bandgap)
feats = []
eref = 0.0
for c in self.dopings:
fermi = dos.get_fermi(c=c, T=self.T, nstep=50)
if isinstance(self.eref, str):
if self.eref == "dos_fermi":
eref = dos.efermi
elif self.eref in ["midgap", "vbm", "cbm"]:
ecbm, evbm = dos.get_cbm_vbm()
if self.eref == "midgap":
eref = (evbm + ecbm) / 2.0
elif self.eref == "vbm":
eref = evbm
elif self.eref == "cbm":
eref = ecbm
elif self.eref == "band center":
eref = self.BC.featurize(dos.structure.composition)[0]
else:
raise ValueError('Unsupported "eref": {}'.format(self.eref))
else:
eref = self.eref
if not self.return_eref:
fermi -= eref
feats.append(fermi)
if self.return_eref:
feats.append(eref)
return feats
class FermiDosTest(unittest.TestCase):
def setUp(self):
with open(os.path.join(test_dir, "complete_dos.json"), "r") as f:
self.dos = CompleteDos.from_dict(json.load(f))
self.dos = FermiDos(self.dos)
def test_doping_fermi(self):
T = 300
fermi0 = self.dos.efermi
frange = [fermi0 - 0.5, fermi0, fermi0 + 2.0, fermi0 + 2.2]
dopings = [self.dos.get_doping(fermi=f, T=T) for f in frange]
ref_dopings = [3.48077e+21, 1.9235e+18, -2.6909e+16, -4.8723e+19]
for i, c_ref in enumerate(ref_dopings):
self.assertLessEqual(abs(dopings[i] / c_ref - 1.0), 0.01)
calc_fermis = [self.dos.get_fermi(c=c, T=T) for c in ref_dopings]
for j, f_ref in enumerate(frange):
self.assertAlmostEqual(calc_fermis[j], f_ref, 4)
sci_dos = FermiDos(self.dos, bandgap=3.0)
self.assertEqual( sci_dos.get_gap(), 3.)
old_cbm, old_vbm = self.dos.get_cbm_vbm()
old_gap = old_cbm - old_vbm
new_cbm, new_vbm = sci_dos.get_cbm_vbm()
self.assertAlmostEqual( new_cbm - old_cbm, (3. - old_gap) / 2.)
self.assertAlmostEqual( old_vbm - new_vbm, (3. - old_gap) / 2.)
for i, c_ref in enumerate(ref_dopings):
if c_ref < 0:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, T=T) - frange[i], 0.47, places=2)
else:
self.assertAlmostEqual(
sci_dos.get_fermi(c_ref, T=T) - frange[i], -0.47, places=2)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(-1e26, 300),
7.5108, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(1e26, 300),
-1.4182, 4)
self.assertAlmostEqual(sci_dos.get_fermi_interextrapolated(0.0, 300),
2.5226, 4)
def solve_for_non_equilibrium_fermi_energy(self, temperature, quench_temperature,
chemical_potentials, bulk_dos):
"""
Solve for the Fermi energy after quenching in the defect concentrations at a higher
temperature (the quench temperature),
as outlined in P. Canepa et al (2017) Chemistry of Materials (doi: 10.1021/acs.chemmater.7b02909)
Args:
temperature: Temperature to equilibrate fermi energy at after quenching in defects
quench_temperature: Temperature to equilibrate defect concentrations at (higher temperature)
chemical_potentials: dict of chemical potentials to use for calculation fermi level
bulk_dos: bulk system dos (pymatgen Dos object)
Returns:
Fermi energy dictated by charge neutrality with respect to frozen in defect concentrations
"""
high_temp_fermi_level = self.solve_for_fermi_energy( quench_temperature, chemical_potentials,
bulk_dos)
fixed_defect_charge = sum([
d['charge'] * d['conc']
for d in self.defect_concentrations(
chemical_potentials=chemical_potentials, temperature=quench_temperature,
fermi_level=high_temp_fermi_level)
])
fdos = FermiDos(bulk_dos, bandgap=self.band_gap)
_,fdos_vbm = fdos.get_cbm_vbm()
def _get_total_q(ef):
qd_tot = fixed_defect_charge
qd_tot += fdos.get_doping(fermi=ef + fdos_vbm, T=temperature)
return qd_tot
return bisect(_get_total_q, -1., self.band_gap + 1.)
return
