def DriftDiffusionInitialSolution(device, region, circuit_contacts=None):
####
#### drift diffusion solution variables
###
CreateSolution(device, region, "Electrons")
CreateSolution(device, region, "Holes")
####
#### create initial guess from dc only solution
####
ds.set_node_values(device=device,
region=region,
name="Electrons",
init_from="IntrinsicElectrons")
ds.set_node_values(device=device,
region=region,
name="Holes",
init_from="IntrinsicHoles")
###
### Set up equations
###
CreateSiliconDriftDiffusion(device, region)
for i in ds.get_contact_list(device=device):
if circuit_contacts and i in circuit_contacts:
CreateSiliconDriftDiffusionAtContact(device, region, i, True)
else:
CreateSiliconDriftDiffusionAtContact(device, region, i)
def setup_poisson(device, region, variable_update='log_damp', **kwargs):
"""
Sets up poisson equation solution
Requires:
setup physical constants and setup poisson parameters
:param kwargs:
:return:
"""
logger.debug("Setting up Poisson Equation")
# These are variables that are to be solved during the simulation
# for sol_variable in [hole_density, electron_density, potential, qfn, qfp]:
for sol_variable in [potential, electron_density, hole_density]:
create_solution(device, region, sol_variable)
total_charge_eq = f'kahan3({hole_density},-{electron_density},{p_doping})' #f'{hole_density}-{electron_density}+{p_doping}-{n_doping}' #f'-{q}*kahan4({hole_density}, -{electron_density}, {p_doping}, -{n_doping})'
int_chg_eq = '1e11'# f'({Nc}*{Nv})^(1/2)*exp(-{bandgap}/(2*k*T))'
# Order matters!
for name, eq in zip([intrinsic_charge, total_charge, ],
[int_chg_eq, total_charge_eq,]):
create_node_and_derivatives(device, region, name, eq, [potential, electron_density, hole_density])
ds.edge_from_node_model(device=device, region=region,node_model=electron_density)
ds.edge_from_node_model(device=device, region=region, node_model=hole_density)
e_field_eq = f"({potential}@n0-{potential}@n1)*EdgeInverseLength"
d_field_eq = f'{e_field}*{permittivity}*{eps_0}'
for name, eq in zip([e_field, d_field],[e_field_eq, d_field_eq]):
create_edge_and_derivatives(device, region, name, eq, [potential])
# Lastly, setup the equation to solve for 'potential'
# TODO check initial values
ds.set_node_values(device=device, region=region, name=electron_density, init_from=intrinsic_charge)
ds.set_node_values(device=device, region=region, name=hole_density, init_from=intrinsic_charge)
ds.equation(device=device, region=region, name='PoissonEq', variable_name=potential,
node_model=total_charge, edge_model=d_field, variable_update=variable_update)
def drift_diffusion_initial_solution(self):
# TODO: move it to somewhere else
# drift diffusion solution variables
self.create_solution_variable("Electrons")
self.create_solution_variable("Holes")
for region in self.mesh.regions:
# Create initial guess from DC only solution
set_node_values(device=self.name,
region=region.name,
name="Electrons",
init_from="IntrinsicElectrons")
set_node_values(device=self.name,
region=region.name,
name="Holes",
init_from="IntrinsicHoles")
# Set up equations
CreateSiliconDriftDiffusion(self.name, region.name)
for c in self.mesh.contacts:
CreateSiliconDriftDiffusionAtContact(self.name, region.name, c)
def set_dd_parameters(device,
region,
permittivity=11.1,
n_i=1E10,
T=300,
mu_n=400,
mu_p=200,
taun=1E-5,
taup=1E-5):
names = [
'permittivity', 'q', 'n_i', 'T', 'k', 'kT', 'V_t', 'mobility_n',
'mobility_p', 'n1', 'p1', 'taun', 'taup'
]
values = [
permittivity * eps_0, q, n_i, T, k, k * T, k * T / q, mu_n, mu_p, n_i,
n_i, taun, taup
]
for name, value in zip(names, values):
ds.set_parameter(device=device, region=region, name=name, value=value)
# Setup the solutions for the potential, electron and hole densities
pot = 'potential'
electron_density = 'electron_density'
hole_density = 'hole_density'
for var in [pot, electron_density, hole_density]:
create_solution(device=device, region=region, name=var)
# Now for some poisson's equation
# Create some nodemodels
n_ie = 'n_ie', f"n_i*exp(q*{pot}/k*T)" # Intrinsic electron density
n_ih = 'n_ih', f'n_i^2/{n_ie[0]}' # Intrinsic hole density
net_n_i = 'net_n_i', f'kahan4(-{n_ie[0]}, {n_ih[0]}, p_doping, -n_doping)' # Net intrinsic charge
net_n_i_charge = 'net_n_i_charge', f'q*{net_n_i[0]}' #PotentialIntrinsicCharge
for name, eq in [n_ie, n_ih, net_n_i, net_n_i_charge]:
ds.node_model(device=device, region=region, name=name, equation=eq)
create_derivatives(device, region, name, eq, pot)
E_field = 'E_field', f'({pot}@n0-{pot}@n1)*EdgeInverseLength'
D_field = 'D_field', 'E_field * permittivity' #PotentialEdgeFlux ?? wtf
# Initialize the electron and hole densities
for carrier, init in zip([electron_density, hole_density], [n_ie, n_ih]):
ds.set_node_values(device=device,
region=region,
name=carrier,
init_from=init[0])
# setup edge nodes
for edge_name, eq in [E_field, D_field]:
ds.edge_model(device=device,
region=region,
name=edge_name,
equation=eq)
create_derivatives(device, region, edge_name, eq, pot)
# Create PE
poisson_RHS = 'PoissonRHS', f'({hole_density} - {electron_density} + p_doping - n_doping)' #*q/(permittivity)'
# AKA pne
ds.node_model(device=device,
region=region,
name=poisson_RHS[0],
equation=poisson_RHS[1])
create_derivatives(device, region, poisson_RHS[0], poisson_RHS[1],
hole_density, electron_density)
ds.equation(device=device,
region=region,
name="PoissonEquation",
variable_name=pot,
node_model=poisson_RHS[0],
edge_model=D_field[0])
# Use stupid bernouli formalism
# Check if exists?
ds.edge_from_node_model(device=device, region=region, node_model=pot)
beta_vdiff = 'beta_vdiff', f'({pot}@n0 - {pot}@n1)*q/kT'
ds.edge_model(device=device,
region=region,
name=beta_vdiff[0],
equation=beta_vdiff[1])
bernouli = 'bern', f'B({beta_vdiff[0]})'
ds.edge_model(device=device,
region=region,
name=bernouli[0],
equation=bernouli[1])
# Create continuity equations
E_qf_n = (
'quasi_fermi_n',
f'q*({pot}-electron_affinity) + k*T*log({electron_density}/N_cond)')
E_qf_p = (
'quasi_fermi_p',
f'q*({pot}-electron_affinity) - k*T*log({hole_density}/N_val) - band_gap'
)
J_e = 'e_current', f'q*mobility_n*{electron_density}*EdgeInverseLength*({E_qf_n[0]}@n0-{E_qf_n[0]}@n1)'
J_h = 'h_current', f'q*mobility_p*{hole_density}*EdgeInverseLength*({E_qf_p[0]}@n0-{E_qf_p[0]}@n1)'
for J in [E_qf_n, E_qf_p, J_e, J_h]:
ds.edge_model(device=device, region=region, name=J[0], equation=J[1])
ds.node_model(device=device, region=region, name=J[0], equation=J[1])
for node_model in [pot, electron_density, hole_density]:
# Check if exists?!
ds.edge_from_node_model(device=device,
region=region,
node_model=node_model)
create_derivatives(device, region, J[0], J[1], node_model)
for node_model in [n_ie, n_ih, net_n_i, net_n_i_charge]:
ds.print_node_values(device=device, region=region, name=node_model[0])
for edge_model in [E_qf_n, E_qf_p, J_e, J_h]:
ds.print_edge_values(device=device, region=region, name=edge_model[0])