def equilibrium_f(self, temperature, semiconductor, fermi_level_from_conduction_band,
electron_volts=False, use_mpmath=False, debug=False):
"""
Calculates trap equilibrium filling for given Fermi level position
:param temperature: Temperature, K
:param semiconductor: Semiconductor object
:param fermi_level_from_conduction_band: distance from Conduction band to Fermi level
:param electron_volts: if True assume all energy values to be in eV
:param use_mpmath: if True integration is done using mpmath.quad function instead of numpy.trapz (default)
:param debug: if True prints out some debug information
:return: equilibrium f between 0 and 1
"""
if electron_volts:
energy_coefficient = to_numeric(q)
energy_unit = 'eV'
else:
energy_coefficient = 1
energy_unit = 'J'
energy_scale = to_numeric(k * temperature) / energy_coefficient
conduction_band = 0
fermi_level = conduction_band - fermi_level_from_conduction_band
trap_energy_level = self.energy_level(temperature, semiconductor, charge_state_idx=0,
electron_volts=electron_volts)
if debug:
print 'Et = %2.2g ' % ((conduction_band - trap_energy_level)) + energy_unit
print 'Ef =', fermi_level, energy_unit
g_ratio = self.charge_states[0][2] / self.charge_states[1][2]
if self.energy_distribution_function in energy_distribution_functions['Single Level']:
fermi_level_grid, = np.meshgrid(fermi_level)
exp_arg = (np.float(conduction_band - trap_energy_level) - fermi_level_grid) / energy_scale
exp_term = np.exp(exp_arg)
f = 1 / (1 + g_ratio * exp_term)
else:
energy = sym.symbols('E')
energy_distribution = self.energy_distribution.subs([('Et', trap_energy_level * energy_coefficient),
('Ecb', conduction_band * energy_coefficient)])
energy_distribution = energy_distribution.subs(q, to_numeric(q))
if not use_mpmath:
if debug:
print 'Numeric integration (numpy.trapz)'
energy_range = centered_linspace(conduction_band - trap_energy_level,
10 * to_numeric(self.energy_spread) / energy_coefficient,
to_numeric(self.energy_spread) / energy_coefficient / 1000)
energy_range_grid, fermi_level_grid = np.meshgrid(energy_range, fermi_level)
fermi_function = 1 / (1 + g_ratio * np.exp((energy_range_grid - fermi_level_grid) / energy_scale))
energy_distribution_function = sym.lambdify(energy, energy_distribution, 'numpy')
integrand_array = energy_distribution_function(energy_range_grid * energy_coefficient) * fermi_function
f = np.trapz(integrand_array, energy_range_grid * energy_coefficient, axis=1)
else:
if debug:
print 'Numeric integration (mpmath.quad)'
fermi_level_grid, = np.meshgrid(fermi_level)
f = np.zeros_like(fermi_level_grid)
for i, fermi_level_i in enumerate(fermi_level_grid):
fermi_function = fermi(energy, fermi_level_i * energy_coefficient, temperature, g_ratio)
fermi_function = fermi_function.subs(k, to_numeric(k))
integrand = sym.lambdify(energy, energy_distribution * fermi_function)
f[i] = mp.quad(integrand,
[to_numeric(energy_coefficient * (conduction_band - trap_energy_level)
- 10 * self.energy_spread),
to_numeric(energy_coefficient * (conduction_band - trap_energy_level)
- 0.5 * self.energy_spread),
to_numeric(energy_coefficient * (conduction_band - trap_energy_level)
+ 0.5 * self.energy_spread),
to_numeric(energy_coefficient * (conduction_band - trap_energy_level)
+ 10 * self.energy_spread)])
if debug:
print 'F =', f
if f.size == 1:
f = f[0]
return f
def emission_rate(self,
temperature,
semiconductor,
f,
poole_frenkel_e=None,
poole_frenkel_h=None,
barrier_lowering_e=None,
barrier_lowering_h=None,
use_mpmath=False,
debug=False):
"""
Calculate carriers emission rate for bot electrons and holes
:param temperature: Temperature, K
:param semiconductor: Semiconductor object
:param f: Trap occupation from 0.0 to 1.0
:param poole_frenkel_e: emission rate boost due to Poole-Frenkel effect for electron
:param poole_frenkel_h: emission rate boost due to Poole-Frenkel effect for electron
:param barrier_lowering_e: lowering of activation energy for electrons
:param barrier_lowering_h: lowering of activation energy for holes
:param use_mpmath: if True integration is done using mpmath.quad function instead of numpy.trapz (default)
:param debug: if True prints out some debug information
:return: emission_e, emission_h
"""
if barrier_lowering_e is None:
barrier_lowering_e = np.zeros_like(f, dtype=np.float)
if barrier_lowering_h is None:
barrier_lowering_h = np.zeros_like(f, dtype=np.float)
if poole_frenkel_e is None:
poole_frenkel_e = np.ones_like(f, dtype=np.float)
if poole_frenkel_h is None:
poole_frenkel_h = np.ones_like(f, dtype=np.float)
energy_scale = to_numeric(k * temperature)
conduction_band = 0
band_gap = semiconductor.band_gap(temperature,
symbolic=False,
electron_volts=False)
valence_band = conduction_band - band_gap
trap_energy_level_e = np.float(
self.energy_level(temperature,
semiconductor,
charge_state_idx=1,
electron_volts=False))
trap_energy_level_h = np.float(
self.energy_level(temperature,
semiconductor,
charge_state_idx=0,
electron_volts=False))
trap_energy_level_e_positive = conduction_band - trap_energy_level_e
trap_energy_level_h_positive = conduction_band - trap_energy_level_h
g_ratio_e = self.charge_states[0][2] / self.charge_states[1][2]
g_ratio_h = self.charge_states[1][2] / self.charge_states[0][2]
v_e = np.float(semiconductor.v_T('e', temperature, symbolic=False))
v_h = np.float(semiconductor.v_T('h', temperature, symbolic=False))
if debug:
print '<v_e> =', v_e, 'm/s'
print '<v_h> =', v_h, 'm/s'
sigma_n, sigma_p = self.capture_cross_sections(temperature)
fore_factor_n = np.float(
sigma_n * v_e * semiconductor.Nc(temperature, symbolic=False) *
g_ratio_e)
fore_factor_p = np.float(
sigma_p * v_h * semiconductor.Nv(temperature, symbolic=False) *
g_ratio_h)
fore_factor_n *= poole_frenkel_e
fore_factor_p *= poole_frenkel_h
if debug:
print 'factor_n =', fore_factor_n
print 'factor_p =', fore_factor_p
if self.energy_distribution_function in energy_distribution_functions[
'Single Level']:
activation_energy_e = conduction_band - trap_energy_level_e_positive - barrier_lowering_e
activation_energy_h = trap_energy_level_h_positive - valence_band - barrier_lowering_h
emission_rate_e = fore_factor_n * np.exp(
-activation_energy_e / energy_scale)
emission_rate_h = fore_factor_p * np.exp(
-activation_energy_h / energy_scale)
emission_time_constant_e = 1 / emission_rate_e
emission_time_constant_h = 1 / emission_rate_h
emission_e = emission_rate_e * f
emission_h = emission_rate_h * (1 - f)
else:
quasi_fermi_level = self.f_to_equilibrium_fermi_level(
temperature,
semiconductor,
f,
electron_volts=False,
use_mpmath=use_mpmath,
debug=False)
quasi_fermi_level = conduction_band - quasi_fermi_level
if debug:
print 'Eqf =', quasi_fermi_level / to_numeric(q), 'eV'
energy = sym.symbols('E')
energy_distribution_e = self.energy_distribution.subs([
('Et', trap_energy_level_e), ('Ecb', conduction_band)
])
energy_distribution_e = energy_distribution_e.subs(
q, to_numeric(q))
energy_distribution_h = self.energy_distribution.subs([
('Et', trap_energy_level_h), ('Ecb', conduction_band)
])
energy_distribution_h = energy_distribution_h.subs(
q, to_numeric(q))
energy_range_e = centered_linspace(
conduction_band - trap_energy_level_e,
10 * to_numeric(self.energy_spread),
to_numeric(self.energy_spread) / 1000)
energy_range_h = centered_linspace(
conduction_band - trap_energy_level_h,
10 * to_numeric(self.energy_spread),
to_numeric(self.energy_spread) / 1000)
energy_distribution_function_e = sym.lambdify(
energy, energy_distribution_e, 'numpy')
energy_distribution_function_h = sym.lambdify(
energy, energy_distribution_h, 'numpy')
energy_range_grid_e, barrier_lowering_grid_e = np.meshgrid(
energy_range_e, barrier_lowering_e)
energy_range_grid_h, barrier_lowering_grid_h = np.meshgrid(
energy_range_h, barrier_lowering_h)
exp_term_e = np.exp(-(conduction_band - energy_range_grid_e +
barrier_lowering_grid_e) / energy_scale)
exp_term_h = np.exp(
-(energy_range_grid_h - barrier_lowering_grid_h - valence_band)
/ energy_scale)
emission_rate_e = energy_distribution_function_e(
energy_range_e) * exp_term_e * fore_factor_n
emission_rate_h = energy_distribution_function_h(
energy_range_h) * exp_term_h * fore_factor_p
emission_rate_e_max = np.max(emission_rate_e, axis=1)
emission_rate_h_max = np.max(emission_rate_h, axis=1)
emission_time_constant_e = 1 / emission_rate_e_max
emission_time_constant_h = 1 / emission_rate_h_max
if not use_mpmath:
if debug:
print 'Numeric integration (numpy.trapz)'
energy_range_grid_e, fermi_level_grid_e = np.meshgrid(
energy_range_e, quasi_fermi_level)
energy_range_grid_h, fermi_level_grid_h = np.meshgrid(
energy_range_h, quasi_fermi_level)
fermi_function_e = 1 / (1 + g_ratio_e * np.exp(
(energy_range_grid_e - fermi_level_grid_e) / energy_scale))
fermi_function_h = 1 - 1 / (1 + g_ratio_h * np.exp(
(energy_range_grid_h - fermi_level_grid_h) / energy_scale))
exp_term_e = np.exp(-(conduction_band - energy_range_grid_e +
barrier_lowering_e) / energy_scale)
exp_term_h = np.exp(
-(energy_range_grid_h - barrier_lowering_h - valence_band)
/ energy_scale)
emission_rate_e = energy_distribution_function_e(
energy_range_grid_e) * exp_term_e
emission_rate_h = energy_distribution_function_h(
energy_range_grid_h) * exp_term_h
integrand_array_e = emission_rate_e * fermi_function_e
integrand_array_h = emission_rate_h * fermi_function_h
emission_e = np.trapz(integrand_array_e,
energy_range_grid_e,
axis=1) * fore_factor_n
emission_h = np.trapz(integrand_array_h,
energy_range_grid_h,
axis=1) * fore_factor_p
else:
if debug:
print 'Numeric integration (mpmath.quad)'
exp_term_e = sym.exp(
-(conduction_band - energy + barrier_lowering_e) /
energy_scale)
exp_term_h = sym.exp(
-(energy - barrier_lowering_h - valence_band) /
energy_scale)
quasi_fermi_level_grid, = np.meshgrid(quasi_fermi_level)
emission_e = np.zeros_like(quasi_fermi_level_grid)
emission_h = np.zeros_like(quasi_fermi_level_grid)
for i, quasi_fermi_level_i in enumerate(
quasi_fermi_level_grid):
fermi_function_e = fermi(energy, quasi_fermi_level_i,
temperature, g_ratio_e)
fermi_function_e = fermi_function_e.subs(k, to_numeric(k))
fermi_function_h = fermi(quasi_fermi_level_i, energy,
temperature, g_ratio_h)
fermi_function_h = fermi_function_h.subs(k, to_numeric(k))
integrand_e = sym.lambdify(
energy,
energy_distribution_e * fermi_function_e * exp_term_e)
integrand_h = sym.lambdify(
energy,
energy_distribution_h * fermi_function_h * exp_term_h)
emission_integral_e = mp.quad(integrand_e, [
to_numeric(trap_energy_level_e_positive -
10 * self.energy_spread),
to_numeric(trap_energy_level_e_positive -
0.5 * self.energy_spread),
to_numeric(trap_energy_level_e_positive +
0.5 * self.energy_spread),
to_numeric(trap_energy_level_e_positive +
10 * self.energy_spread)
])
emission_integral_h = mp.quad(integrand_h, [
to_numeric(trap_energy_level_h_positive -
10 * self.energy_spread),
to_numeric(trap_energy_level_h_positive -
0.5 * self.energy_spread),
to_numeric(trap_energy_level_h_positive +
0.5 * self.energy_spread),
to_numeric(trap_energy_level_h_positive +
10 * self.energy_spread)
])
emission_e[i] = np.float(emission_integral_e *
fore_factor_n)
emission_h[i] = np.float(emission_integral_h *
fore_factor_p)
if isinstance(emission_e, np.ndarray):
if emission_e.size == 1:
emission_e = emission_e[0]
emission_h = emission_h[0]
emission_time_constant_e = emission_time_constant_e[0]
emission_time_constant_h = emission_time_constant_h[0]
if debug: print 'emission_e =', emission_e
if debug: print 'emission_h =', emission_h
if debug: print 'emission_tau_e =', emission_time_constant_e
if debug: print 'emission_tau_h =', emission_time_constant_e
return emission_e, emission_h, emission_time_constant_e, emission_time_constant_h
def emission_rate(self, temperature, semiconductor, f, poole_frenkel_e=1.0, poole_frenkel_h=1.0,
barrier_lowering_e=None, barrier_lowering_h=None, use_mpmath=False, debug=False):
"""
Calculate carriers emission rate for bot electrons and holes
:param temperature: Temperature, K
:param semiconductor: Semiconductor object
:param f: Trap occupation from 0.0 to 1.0
:param poole_frenkel_e: emission rate boost due to Poole-Frenkel effect for electron
:param poole_frenkel_h: emission rate boost due to Poole-Frenkel effect for electron
:param barrier_lowering_e: lowering of activation energy for electrons
:param barrier_lowering_h: lowering of activation energy for holes
:param use_mpmath: if True integration is done using mpmath.quad function instead of numpy.trapz (default)
:param debug: if True prints out some debug information
:return: emission_e, emission_h
"""
if barrier_lowering_e is None:
barrier_lowering_e = np.zeros_like(f, dtype=np.float)
if barrier_lowering_h is None:
barrier_lowering_h = np.zeros_like(f, dtype=np.float)
energy_scale = to_numeric(k * temperature)
conduction_band = 0
band_gap = semiconductor.band_gap(temperature, symbolic=False, electron_volts=False)
valence_band = conduction_band - band_gap
trap_energy_level_e = np.float(self.energy_level(temperature, semiconductor,
charge_state_idx=1, electron_volts=False))
trap_energy_level_h = np.float(self.energy_level(temperature, semiconductor,
charge_state_idx=0, electron_volts=False))
trap_energy_level_e_positive = conduction_band - trap_energy_level_e
trap_energy_level_h_positive = conduction_band - trap_energy_level_h
g_ratio_e = self.charge_states[0][2] / self.charge_states[1][2]
g_ratio_h = self.charge_states[1][2] / self.charge_states[0][2]
v_e = np.float(semiconductor.v_T('e', temperature, symbolic=False))
v_h = np.float(semiconductor.v_T('h', temperature, symbolic=False))
if debug:
print '<v_e> =', v_e, 'm/s'
print '<v_h> =', v_h, 'm/s'
sigma_n, sigma_p = self.capture_cross_sections(temperature)
fore_factor_n = np.float(sigma_n * v_e * semiconductor.Nc(temperature, symbolic=False) * g_ratio_e)
fore_factor_p = np.float(sigma_p * v_h * semiconductor.Nv(temperature, symbolic=False) * g_ratio_h)
fore_factor_n *= poole_frenkel_e
fore_factor_p *= poole_frenkel_h
if debug:
print 'factor_n =', fore_factor_n
print 'factor_p =', fore_factor_p
if self.energy_distribution_function in energy_distribution_functions['Single Level']:
activation_energy_e = conduction_band - trap_energy_level_e_positive - barrier_lowering_e
activation_energy_h = trap_energy_level_h_positive - valence_band - barrier_lowering_h
emission_rate_e = fore_factor_n * np.exp(-activation_energy_e / energy_scale)
emission_rate_h = fore_factor_p * np.exp(-activation_energy_h / energy_scale)
emission_time_constant_e = 1 / emission_rate_e
emission_time_constant_h = 1 / emission_rate_h
emission_e = emission_rate_e * f
emission_h = emission_rate_h * (1 - f)
else:
quasi_fermi_level = self.f_to_equilibrium_fermi_level(temperature, semiconductor, f,
electron_volts=False,
use_mpmath=use_mpmath, debug=False)
quasi_fermi_level = conduction_band - quasi_fermi_level
if debug:
print 'Eqf =', quasi_fermi_level / to_numeric(q), 'eV'
energy = sym.symbols('E')
energy_distribution_e = self.energy_distribution.subs([('Et', trap_energy_level_e),
('Ecb', conduction_band)])
energy_distribution_e = energy_distribution_e.subs(q, to_numeric(q))
energy_distribution_h = self.energy_distribution.subs([('Et', trap_energy_level_h),
('Ecb', conduction_band)])
energy_distribution_h = energy_distribution_h.subs(q, to_numeric(q))
energy_range_e = centered_linspace(conduction_band - trap_energy_level_e,
10 * to_numeric(self.energy_spread),
to_numeric(self.energy_spread) / 1000)
energy_range_h = centered_linspace(conduction_band - trap_energy_level_h,
10 * to_numeric(self.energy_spread),
to_numeric(self.energy_spread) / 1000)
energy_distribution_function_e = sym.lambdify(energy, energy_distribution_e, 'numpy')
energy_distribution_function_h = sym.lambdify(energy, energy_distribution_h, 'numpy')
energy_range_grid_e, barrier_lowering_grid_e = np.meshgrid(energy_range_e, barrier_lowering_e)
energy_range_grid_h, barrier_lowering_grid_h = np.meshgrid(energy_range_h, barrier_lowering_h)
exp_term_e = np.exp(-(conduction_band - energy_range_grid_e + barrier_lowering_grid_e) / energy_scale)
exp_term_h = np.exp(-(energy_range_grid_h - barrier_lowering_grid_h - valence_band) / energy_scale)
emission_rate_e = energy_distribution_function_e(energy_range_e) * exp_term_e * fore_factor_n
emission_rate_h = energy_distribution_function_h(energy_range_h) * exp_term_h * fore_factor_p
emission_rate_e_max = np.max(emission_rate_e, axis=1)
emission_rate_h_max = np.max(emission_rate_h, axis=1)
emission_time_constant_e = 1 / emission_rate_e_max
emission_time_constant_h = 1 / emission_rate_h_max
if not use_mpmath:
if debug:
print 'Numeric integration (numpy.trapz)'
energy_range_grid_e, fermi_level_grid_e = np.meshgrid(energy_range_e, quasi_fermi_level)
energy_range_grid_h, fermi_level_grid_h = np.meshgrid(energy_range_h, quasi_fermi_level)
fermi_function_e = 1 / (1 + g_ratio_e * np.exp((energy_range_grid_e - fermi_level_grid_e) / energy_scale))
fermi_function_h = 1 - 1 / (1 + g_ratio_h * np.exp((energy_range_grid_h - fermi_level_grid_h) / energy_scale))
exp_term_e = np.exp(-(conduction_band - energy_range_grid_e + barrier_lowering_e) / energy_scale)
exp_term_h = np.exp(-(energy_range_grid_h - barrier_lowering_h - valence_band) / energy_scale)
emission_rate_e = energy_distribution_function_e(energy_range_grid_e) * exp_term_e
emission_rate_h = energy_distribution_function_h(energy_range_grid_h) * exp_term_h
integrand_array_e = emission_rate_e * fermi_function_e
integrand_array_h = emission_rate_h * fermi_function_h
emission_e = np.trapz(integrand_array_e, energy_range_grid_e, axis=1) * fore_factor_n
emission_h = np.trapz(integrand_array_h, energy_range_grid_h, axis=1) * fore_factor_p
else:
if debug:
print 'Numeric integration (mpmath.quad)'
exp_term_e = sym.exp(-(conduction_band - energy + barrier_lowering_e) / energy_scale)
exp_term_h = sym.exp(-(energy - barrier_lowering_h - valence_band) / energy_scale)
quasi_fermi_level_grid, = np.meshgrid(quasi_fermi_level)
emission_e = np.zeros_like(quasi_fermi_level_grid)
emission_h = np.zeros_like(quasi_fermi_level_grid)
for i, quasi_fermi_level_i in enumerate(quasi_fermi_level_grid):
fermi_function_e = fermi(energy, quasi_fermi_level_i, temperature, g_ratio_e)
fermi_function_e = fermi_function_e.subs(k, to_numeric(k))
fermi_function_h = fermi(quasi_fermi_level_i, energy, temperature, g_ratio_h)
fermi_function_h = fermi_function_h.subs(k, to_numeric(k))
integrand_e = sym.lambdify(energy, energy_distribution_e * fermi_function_e * exp_term_e)
integrand_h = sym.lambdify(energy, energy_distribution_h * fermi_function_h * exp_term_h)
emission_integral_e = mp.quad(integrand_e,
[to_numeric(trap_energy_level_e_positive - 10 * self.energy_spread),
to_numeric(trap_energy_level_e_positive - 0.5 * self.energy_spread),
to_numeric(trap_energy_level_e_positive + 0.5 * self.energy_spread),
to_numeric(trap_energy_level_e_positive + 10 * self.energy_spread)])
emission_integral_h = mp.quad(integrand_h,
[to_numeric(trap_energy_level_h_positive - 10 * self.energy_spread),
to_numeric(trap_energy_level_h_positive - 0.5 * self.energy_spread),
to_numeric(trap_energy_level_h_positive + 0.5 * self.energy_spread),
to_numeric(trap_energy_level_h_positive + 10 * self.energy_spread)])
emission_e[i] = np.float(emission_integral_e * fore_factor_n)
emission_h[i] = np.float(emission_integral_h * fore_factor_p)
if isinstance(emission_e, np.ndarray):
if emission_e.size == 1:
emission_e = emission_e[0]
emission_h = emission_h[0]
emission_time_constant_e = emission_time_constant_e[0]
emission_time_constant_h = emission_time_constant_h[0]
if debug: print 'emission_e =', emission_e
if debug: print 'emission_h =', emission_h
if debug: print 'emission_tau_e =', emission_time_constant_e
if debug: print 'emission_tau_h =', emission_time_constant_e
return emission_e, emission_h, emission_time_constant_e, emission_time_constant_h
def d_equilibrium_f_d_fermi_energy(self,
temperature,
semiconductor,
fermi_level_from_conduction_band,
electron_volts=False,
use_mpmath=False,
debug=False):
"""
Calculates trap equilibrium filling derivative for given Fermi level position
on small Fermi level change
:param temperature: Temperature, K
:param semiconductor: Semiconductor object
:param fermi_level_from_conduction_band: distance from Conduction band to Fermi level
:param electron_volts: if True assume all energy values to be in eV
:param use_mpmath: if True integration is done using mpmath.quad function instead of numpy.trapz (default)
:param debug: if True prints out some debug information
:return: equilibrium f between 0 and 1
"""
if electron_volts:
energy_coefficient = to_numeric(q)
energy_unit = 'eV'
else:
energy_coefficient = 1
energy_unit = 'J'
energy_scale = to_numeric(k * temperature) / energy_coefficient
conduction_band = 0
fermi_level = conduction_band - fermi_level_from_conduction_band
trap_energy_level = self.energy_level(temperature,
semiconductor,
charge_state_idx=0,
electron_volts=electron_volts)
if debug:
print 'Et = %2.2g ' % (
(conduction_band - trap_energy_level)) + energy_unit
print 'Ef =,', fermi_level, energy_unit
g_ratio = self.charge_states[0][2] / self.charge_states[1][2]
if self.energy_distribution_function in energy_distribution_functions[
'Single Level']:
fermi_level_grid, = np.meshgrid(fermi_level)
exp_arg = (np.float(conduction_band - trap_energy_level) -
fermi_level_grid) / energy_scale
exp_term = np.exp(exp_arg)
exp_term = np.array(map(mp.exp, exp_arg))
a = g_ratio / (energy_coefficient * energy_scale)
#print exp_term #/ (1 + g_ratio * exp_term)
b = exp_term / (1 + g_ratio * exp_term)**2
d_f = a * b
# d_f = g_ratio / (energy_coefficient * energy_scale) * exp_term / (1 + g_ratio * exp_term) ** 2
d_f[np.where(d_f == np.nan)] = 0
else:
energy = sym.symbols('E')
energy_distribution = self.energy_distribution.subs([
('Et', trap_energy_level * energy_coefficient),
('Ecb', conduction_band * energy_coefficient)
])
energy_distribution = energy_distribution.subs(q, to_numeric(q))
if not use_mpmath:
if debug:
print 'Numeric integration (numpy.trapz)'
energy_range = centered_linspace(
conduction_band - trap_energy_level,
10 * to_numeric(self.energy_spread) / energy_coefficient,
to_numeric(self.energy_spread) / energy_coefficient / 1000)
energy_range_grid, fermi_level_grid = np.meshgrid(
energy_range, fermi_level)
exp_term = np.exp(
(energy_range_grid - fermi_level_grid) / energy_scale)
fore_factor = g_ratio / (energy_coefficient * energy_scale)
d_fermi_function = fore_factor * exp_term / (
1 + g_ratio * exp_term)**2
d_fermi_function[np.where(d_fermi_function == np.nan)] = 0
energy_distribution_function = sym.lambdify(
energy, energy_distribution, 'numpy')
integrand_array = energy_distribution_function(
energy_range_grid * energy_coefficient) * d_fermi_function
d_f = np.trapz(integrand_array,
energy_range_grid * energy_coefficient,
axis=1)
else:
if debug:
print 'Numeric integration (mpmath.quad)'
fermi_level_grid, = np.meshgrid(fermi_level)
d_f = np.zeros_like(fermi_level_grid)
for i, fermi_level_i in enumerate(fermi_level_grid):
d_fermi_function = d_fermi_d_delta_fermi_energy(
energy, fermi_level_i * energy_coefficient,
temperature, g_ratio)
d_fermi_function = d_fermi_function.subs(k, to_numeric(k))
integrand = sym.lambdify(
energy, energy_distribution * d_fermi_function)
d_f[i] = mp.quad(integrand, [
to_numeric(energy_coefficient *
(conduction_band - trap_energy_level) -
10 * self.energy_spread),
to_numeric(energy_coefficient *
(conduction_band - trap_energy_level) -
0.5 * self.energy_spread),
to_numeric(energy_coefficient *
(conduction_band - trap_energy_level) +
0.5 * self.energy_spread),
to_numeric(energy_coefficient *
(conduction_band - trap_energy_level) +
10 * self.energy_spread)
])
if debug:
print 'dF =', d_f
if d_f.size == 1:
d_f = d_f[0]
return d_f
