from cached_property import cached_property
import dolfin
import ufl
from ..fem import expm1
from ..util import SetattrInitMixin
__all__ = [
'ElectroOpticalProcess',
'NonOverlappingTopHatBeerLambert',
'NonOverlappingTopHatBeerLambertIB',
'SRHRecombination',
'NonRadiativeTrap',
'DarkEOPMixin',
'TrapEOPMixin',
'TwoBandEOPMixin',
'RadiativeEOPMixin',
'AbsorptionAndRadiativeRecombinationEOPMixin',
]
[docs]class ElectroOpticalProcess(SetattrInitMixin):
'''This class exists to represent both electro-optical process and
purely electronic (dark) processes, such as nonradiative
recombination.
Attributes
----------
pdd: PoissonDriftDiffusion
Instance of :class:`.PoissonDriftDiffusion`.
optical: Optical
Instance of :class:`.Optical`.
pre_iteration_hook: callable
Implement this method in order to run code before each PDD Newton
iteration. Useful for processes that need procedural code (cannot
be expressed as UFL form).
pre_first_iteration_hook: callable
This method is called before the *first* PDD Newton iteration.
post_iteration_hook: callable
This method is called after each PDD Newton iteration.
'''
pre_iteration_hook = None
pre_first_iteration_hook = None
post_iteration_hook = None
@property
def unit_registry(self):
return self.mesh_util.unit_registry
@property
def mesh_util(self):
return self.pdd.mesh_util
[docs] def get_optical_generation_by_optical_field(self, optical_field):
'''Exists as a separate method to make anisotropy possible.
By default just calls :code:`self.get_optical_generation`, and
multiplies by :py:attr:`~.optical.OpticalField.solid_angle`.'''
return (self.get_optical_generation(optical_field.photon_energy) *
optical_field.solid_angle)
[docs] def get_optical_generation(self, photon_energy):
''' Override for luminescent coupling. By default returns zero. '''
return 0 * self.unit_registry("1/cm^3/s")
[docs] def get_alpha_by_optical_field(self, optical_field):
'''Exists as a separate method to make anisotropy possible.
By default just calls ``self.get_alpha``.'''
return self.get_alpha(optical_field.photon_energy)
[docs] def get_alpha(self, photon_energy):
'''This method is called to get Beer-Lambert absorption
coefficient alpha at a particular photon energy. Must return a UFL
quantity on the PDD mesh, or :code:`None`.
**User class must implement this.**
'''
raise NotImplementedError()
[docs] def get_quantum_yield_by_optical_field(self, optical_field):
'''Exists as a separate method to make anisotropy possible.
By default just calls ``self.get_quantum_yield``.'''
return self.get_quantum_yield(optical_field.photon_energy)
[docs] def get_quantum_yield(self, photon_energy):
''' Default ``quantum_yield=1``. '''
return 1.0
[docs] def get_band_generation_sign(self, band):
'''As the generation process intensifies (e.g., light
intensity increases), does :code:`band` lose or gain more carriers?
The default implementation always returns :code:`None`. User classes
are expected to override this method.
Note: If you are implementing a two-band process, you almost certainly
want to inherit from :py:class:`TwoBandEOPMixin`.
Returns
-------
sign: object
If the band participates in the process, returns :code:`+1` or
:code:`-1` if it gains or loses carriers,
respectively. Otherwise, return :code:`None`.'''
return None
@cached_property
def _zero_generation(self):
'''Constant for zero generation, with the right units.'''
return self.unit_registry("1/mesh_unit^3/s") * 0.0
[docs] def get_generation(self, band):
return self.get_generation_user(band)
[docs] def get_generation_user(self, band):
'''This method is called to get the generation contribution to
band :code:`band`. Must return a UFL quantity on the PDD mesh.
**User class may override this.** By default, this method just calls
:py:meth:`get_generation_optical`.
Sign convention: **The returned value is positive or negative if
the band gains or loses carriers respectively.**
This method will be called for *every* band in the system. You are strongly
encouraged to use :py:meth:`get_band_generation_sign` to determine
whether the process causes a gain or a loss of carriers in band
:code:`band`, and whether the band participates in the process at all.
'''
return self.get_generation_optical(band)
[docs] def get_generation_optical(self, band):
'''Compute carrier generation due to optical absorption, using
absorption coefficient given by :py:meth:`get_alpha_by_optical_field`
and quantum yield given by :py:meth:`get_quantum_yield`.'''
sign = self.get_band_generation_sign(band)
if sign is None:
return self._zero_generation
g = self._zero_generation
for field in self.optical.fields:
Phi = self.get_photon_flux_on_pdd_mesh(field)
alpha = self.get_alpha_by_optical_field(field)
if alpha is not None:
g = g + Phi*alpha*self.get_quantum_yield(field)*sign
return g
[docs] def get_photon_flux_on_pdd_mesh(self, optical_field):
'''Returns optical photon flux, adapted onto PDD mesh. Use this
accessor instead of reaching inside :py:class:`.optical.OpticalField`
yourself.
Parameters
----------
optical_field: :py:class:`.optical.OpticalField`
Optical field whose photon flux (clipped to be nonnegative) to get.
'''
return optical_field.Phi_pddproj_clipped
[docs]class DarkEOPMixin():
[docs] def get_alpha(self, photon_energy):
return None
[docs]class TwoBandEOPMixin():
'''Convenience mixin representing a generation process across
two bands.
Sign convention: **As the generation process intensifies, the
destination band gains more carriers.** The source band may gain or
lose carriers depending on its carrier type.
Attributes
----------
src_band: Band
Source band (which may gain or lose a carrier depending on the sign).
dst_band: Band
Destination band (which always gains a carrier).
'''
[docs] def get_band_generation_sign(self, band):
'''Provides a non-trivial implementation of
:py:meth:`ElectroOpticalProcess.get_band_generation_sign()` in the
case of two active bands.
See :py:class:`TwoBandEOPMixin` for the sign convention.'''
if band == self.dst_band:
return +1 # destination band gains carriers
elif band == self.src_band:
# what happens to source band depends on bands' carrier types
return -(self.dst_band.sign * self.src_band.sign)
else: # irrelevant band
return None
[docs]class TrapEOPMixin():
''' Calculates properties involved in trapping, such as u1, tau, etc.
Attributes
----------
trap_band: Band
Band doing the trapping.
reg_band: Band
Non-trap band. e.g. CB or VB.'''
[docs] @classmethod
def easy_add_two_traps_to_pdd(
cls, pdd, name_prefix, top_band, bottom_band, trap_band, **kwargs):
CB = top_band
VB = bottom_band
IB = trap_band
pdd.easy_add_electro_optical_process(
cls, dst_band=CB, src_band=IB, trap_band=IB,
name=name_prefix + '_top', **kwargs)
pdd.easy_add_electro_optical_process(
cls, dst_band=IB, src_band=VB, trap_band=IB,
name=name_prefix + '_bottom', **kwargs)
@cached_property
def reg_band(self):
if self.dst_band == self.trap_band:
return self.src_band
elif self.src_band == self.trap_band:
return self.dst_band
else:
return None
[docs] def get_trap_process_name(self, band):
if band is None:
name = self.name
elif band == self.src_band:
name = self.name + '_top'
elif band == self.dst_band:
name = self.name + '_bottom'
else:
raise ValueError()
return name
[docs] def trap_spatial_get(self, name, band=None):
pname = self.get_trap_process_name(band)
return self.pdd.spatial.get('/'.join((pname, name)))
[docs] def get_trap_concentration(self, band=None):
trap_band = self.trap_band
if trap_band is None: # pull from spatial parameters
return self.pdd.spatial.get('/'.join((self.name, 'N_t')))
else: # just use trap band number of states
return trap_band.number_of_states
[docs] def get_tau(self, band=None):
N_t = self.get_trap_concentration(band)
c = self.get_capture_coefficient(band)
return 1/(c * N_t)
[docs] def get_sigma_th(self, band=None):
return self.trap_spatial_get('sigma_th', band=band)
[docs] def get_v_th(self, band=None):
return self.trap_spatial_get('v_th', band=band)
[docs] def get_capture_coefficient(self, band=None):
'''See [Shockley1952a] (3.5).'''
sigma_th = self.get_sigma_th(band)
v_th = self.get_v_th(band)
return sigma_th * v_th
[docs] def get_trap_energy_level(self):
trap_band = self.trap_band
if trap_band is None:
return self.pdd.spatial.get('/'.join((self.name, 'energy_level')))
else:
return trap_band.effective_energy_level # handle trap degeneracy
[docs] def get_u1(self, band):
E_I = self.get_trap_energy_level()
u1 = band.phiqfl_to_u(E_I)
return u1
[docs] def get_shockley_read_trap_generation(self, capture_coeff):
IB = self.trap_band
RB = self.reg_band
if IB.sign == RB.sign:
# same signs for trap and regular band, need other type of
# carrier in the trap because we're look for empty states
# to get trapped in
trap_filling_factor = IB.number_of_states - IB.u
else:
# opposite signs, just return trap carrier concentration
trap_filling_factor = IB.u
kT = self.pdd.kT
x = (RB.sign * (RB.qfl - IB.qfl)/kT).m_as('dimensionless')
r = (-expm1(x)) * RB.u * trap_filling_factor * capture_coeff
return -r
[docs]class RadiativeEOPMixin():
''' Calculates properties involved in radiative processes, such as
trapping or recombination.
Only works in non-degenerate condition
:code:`exp((E_photon_min - mu_fi)/kT) >> 1`. See [Strandberg2011],
page 3, under Eq. 6.
'''
[docs] def get_strandberg_I(self):
u = self.unit_registry
h = u('1 planck_constant')
c = u('1 speed_of_light')
kT = self.pdd.kT
mu = self.pdd.mesh_util
n_r = 1
K = (8 * dolfin.pi * n_r **2) / (h**3 * c**2)
E_L, E_U = self.get_absorption_bounds()
# equivalent to flipping integration bounds if E_U < E_L
sign = dolfin.conditional(dolfin.gt(
E_U.magnitude,
E_L.m_as(E_U.units)), +1, -1)
# antiderivative of `E^2 exp(E/kT)`
def F(E):
return -kT*(2*kT**2 + 2*E*kT + E**2) * mu.exp(-E/kT)
I = F(E_U) - F(E_L)
ans = K * I * sign
# to evaluate integrals
# ans = (ans.m((0.0, 0.0)) * ans.units).to("1 / centimeter ** 2 / second")
# print(self.src_band.key, self.dst_band.key, ans)
return ans
[docs] def get_absorption_bounds(self):
from .optical import AbsorptionRangesHelper
ab = AbsorptionRangesHelper(problem_data=self.pdd.problem_data)
keyname = frozenset((self.src_band.key, self.dst_band.key))
return ab.get_transition_bounds().get(keyname)
[docs] def inside_absorption_bounds_conditional(self, E, value):
E_L, E_U = self.get_absorption_bounds()
E_L = E_L.m_as('eV')
E_U = E_U.m_as('eV')
E = E.m_as('eV')
return value.units * dolfin.conditional(
ufl.And(E_L <= E, E < E_U), value.magnitude, 0)
[docs]class AbsorptionAndRadiativeRecombinationEOPMixin():
enable_radiative_recombination = True
[docs] def get_generation_user(self, band):
'''Call :py:meth:`get_generation_optical` and
:py:meth:`get_radiative_recombination` and add together their results
accordingly.
Only include the radiative recombination process if
:py:attr:`enable_radiative_recombination` is true.
'''
sign = self.get_band_generation_sign(band)
if sign is None:
return self._zero_generation
g_abs = self.get_generation_optical(band) # absorption
if self.enable_radiative_recombination:
g_rad = self.get_radiative_recombination() * sign
else:
g_rad = self._zero_generation
return g_abs - g_rad
[docs]class NonOverlappingTopHatBeerLambert(
AbsorptionAndRadiativeRecombinationEOPMixin,
RadiativeEOPMixin,
TwoBandEOPMixin,
ElectroOpticalProcess):
'''Absorption or radiative recombination between src_band and dst_band.
For absorption, src_band=VB and dst_band=CB, and vice versa for
recombination.
Includes radiative recombination by default.
'''
name = 'beer_lambert'
[docs] def get_constant_alpha(self):
return self.pdd.spatial.get('/'.join((self.name, 'alpha')))
[docs] def get_alpha(self, photon_energy):
'''Return constant alpha, clipped by absorption bounds.'''
return self.inside_absorption_bounds_conditional(
photon_energy, self.get_constant_alpha())
[docs] def get_radiative_recombination(self):
alpha = self.get_constant_alpha()
strb_I = self.get_strandberg_I()
beta = 1/self.pdd.kT
CB = self.dst_band
VB = self.src_band
x = (beta * (CB.qfl - VB.qfl)).m_as('dimensionless')
return alpha * strb_I * expm1(x)
[docs]class NonOverlappingTopHatBeerLambertIB(
AbsorptionAndRadiativeRecombinationEOPMixin,
RadiativeEOPMixin,
TrapEOPMixin,
TwoBandEOPMixin,
ElectroOpticalProcess):
'''Absorption between intermediate band and regular band.
Includes radiative recombination by default.
Based on [Strandberg2011].'''
name = 'beer_lambert_IB'
[docs] def get_radiative_recombination(self):
# pseudo capture coefficient
capture_coeff = self.get_radiative_pseudo_capture_coefficient()
g = self.get_shockley_read_trap_generation(capture_coeff)
return -g
[docs] def get_constant_sigma_opt(self):
return self.pdd.spatial.get('/'.join((self.name, 'sigma_opt')))
[docs] def get_sigma_opt(self, photon_energy):
'''Return constant sigma_opt, clipped by absorption bounds.'''
return self.inside_absorption_bounds_conditional(
photon_energy, self.get_constant_sigma_opt())
[docs] def get_alpha(self, photon_energy):
IB = self.trap_band
RB = self.reg_band
sigma = self.get_sigma_opt(photon_energy)
if IB.sign == RB.sign:
# same signs for trap and regular band, the more carriers
# in trap band the more this absorption process will
# happen
trap_filling_factor = IB.u
else:
# opposite signs, need complementary carrier type for trap
trap_filling_factor = IB.number_of_states - IB.u
return sigma*trap_filling_factor
[docs] def get_radiative_pseudo_capture_coefficient(self):
''' See `eq:rad-u-form` in `doc/ib.lyx`. '''
RB = self.reg_band
sigma_opt = self.get_constant_sigma_opt()
strandberg_I = self.get_strandberg_I()
u1 = self.get_u1(RB)
return sigma_opt * strandberg_I / u1
[docs]class SRHRecombination(
DarkEOPMixin,
TrapEOPMixin,
TwoBandEOPMixin,
ElectroOpticalProcess):
'''SRH recombination. The destination band is the one *losing*
carriers through recombination.
Typically, dst_band=CB and src_band=VB.'''
name = 'SRH'
trap_band = None
tau_from_spatial = True
[docs] def get_tau(self, band):
if self.tau_from_spatial:
return self.pdd.spatial.get('/'.join((
self.name, band.name, 'tau')))
else:
return super().get_tau(band)
[docs] def get_generation_user(self, band):
sign = self.get_band_generation_sign(band)
if sign is None:
return self._zero_generation
CB = self.dst_band
VB = self.src_band
CB_tau = self.get_tau(CB)
VB_tau = self.get_tau(VB)
CB_u1 = self.get_u1(CB)
VB_u1 = self.get_u1(VB)
r = ((VB.u*CB.u - VB.thermal_equilibrium_u*CB.thermal_equilibrium_u)/
((CB.u + CB_u1)*VB_tau +
(VB.u + VB_u1)*CB_tau))
g = -r
return g * sign
[docs]class NonRadiativeTrap(
DarkEOPMixin,
TrapEOPMixin,
TwoBandEOPMixin,
ElectroOpticalProcess):
'''Shockley Read Hall trapping process. Typically, trap_band = IB.
If you do not have an explicit :py:class:`Band` object for the traps
concentration, use :py:class:`SRHRecombination` instead.
See `doc/ib.lyx`.
'''
name = 'nonradiative'
[docs] def get_generation_user(self, band):
g_sign = self.get_band_generation_sign(band)
if g_sign is None:
return self._zero_generation
# capture coefficient
capture_coeff = self.get_capture_coefficient()
g = self.get_shockley_read_trap_generation(capture_coeff)
return g * g_sign