def SetupInitialResistorSystem(device, region, net_doping=1e16):
'''
resistor physics
'''
devsim.set_parameter(device=device, region=region, name='net_doping', value=net_doping)
devsim.node_solution(device=device, region=region, name='Potential')
devsim.edge_from_node_model(device=device, region=region, node_model='Potential')
# node models
for name, equation in (
("NetDoping", "net_doping"),
("IntrinsicElectrons", "NetDoping"),
("IntrinsicCharge", "-IntrinsicElectrons + NetDoping"),
("IntrinsicCharge:Potential", "-IntrinsicElectrons:Potential"),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
# edge models
for name, equation in (
("ElectricField", "(Potential@n0 - Potential@n1)*EdgeInverseLength"),
("ElectricField:Potential@n0", "EdgeInverseLength"),
("ElectricField:Potential@n1", "-EdgeInverseLength"),
("PotentialEdgeFlux", "Permittivity*ElectricField"),
("PotentialEdgeFlux:Potential@n0", "diff(Permittivity*ElectricField, Potential@n0)"),
("PotentialEdgeFlux:Potential@n1", "-PotentialEdgeFlux:Potential@n0"),
):
devsim.edge_model(device=device, region=region, name=name, equation=equation)
####
#### PotentialEquation
####
devsim.equation(device=device, region=region, name="PotentialEquation", variable_name="Potential", edge_model="PotentialEdgeFlux", variable_update="log_damp")
def createSiliconPotentialOnly(device, region):
ie = devsim.node_model(device=device,
region=region,
name="IntrinsicElectrons",
equation="n_i*exp(Potential/V_t)")
res = devsim.node_model(device=device,
region=region,
name="IntrinsicElectrons:Potential",
equation="diff(%s, Potential)" % ie)
for name, equation in (
("IntrinsicHoles", "n_i^2/IntrinsicElectrons"),
("IntrinsicHoles:Potential",
"diff(n_i^2/IntrinsicElectrons, Potential)"),
("IntrinsicCharge", "IntrinsicHoles-IntrinsicElectrons + NetDoping"),
("IntrinsicCharge:Potential",
"diff(IntrinsicHoles-IntrinsicElectrons, Potential)"),
("PotentialIntrinsicNodeCharge", "-ElectronCharge*IntrinsicCharge"),
("PotentialIntrinsicNodeCharge:Potential",
"diff(-ElectronCharge*IntrinsicCharge, Potential)"),
):
devsim.node_model(device=device,
region=region,
name=name,
equation=equation)
for name, equation in (
("ElectricField", "(Potential@n0-Potential@n1)*EdgeInverseLength"),
("ElectricField:Potential@n0", "EdgeInverseLength"),
("ElectricField:Potential@n1", "-ElectricField:Potential@n0"),
("PotentialEdgeFlux", "Permittivity*ElectricField"),
("PotentialEdgeFlux:Potential@n0",
"diff(Permittivity*ElectricField,Potential@n0)"),
("PotentialEdgeFlux:Potential@n1", "-PotentialEdgeFlux:Potential@n0"),
):
devsim.edge_model(device=device,
region=region,
name=name,
equation=equation)
devsim.equation(device=device,
region=region,
name="PotentialEquation",
variable_name="Potential",
node_model="PotentialIntrinsicNodeCharge",
edge_model="PotentialEdgeFlux",
variable_update="log_damp")
def SetupCarrierResistorContact(device,
contact,
use_circuit_bias=False,
circuit_node=""):
'''
Electron continuity equation at contact
'''
if circuit_node:
bias_name = circuit_node
else:
bias_name = contact + "bias"
region = devsim.get_region_list(device=device, contact=contact)[0]
if 'celec' not in devsim.get_node_model_list(device=device, region=region):
devsim.node_model(
device=device,
region=region,
name="celec",
equation=
"0.5*(NetDoping+(NetDoping^2 + 4 * IntrinsicDensity^2)^(0.5))")
for name, equation in (
("%snodeelectrons" % contact, "Electrons - celec"),
("%snodeelectrons:Electrons" % contact, "1."),
):
devsim.contact_node_model(device=device,
contact=contact,
name=name,
equation=equation)
if use_circuit_bias:
devsim.contact_equation(device=device,
contact=contact,
name="ElectronContinuityEquation",
variable_name="Electrons",
node_model="%snodeelectrons" % contact,
edge_current_model="ElectronCurrent",
circuit_node=bias_name)
else:
devsim.contact_equation(device=device,
contact=contact,
name="ElectronContinuityEquation",
variable_name="Electrons",
node_model="%snodeelectrons" % contact,
edge_current_model="ElectronCurrent")
def setup_dg_volume(device, region, normalized=False):
#
# Lambda Equations
#
#em = (
# ("Le_eqn", "Le/b_n"),
# ("Le_eqn:Le", "1/b_n"),
# ("Lh_eqn", "Lh/b_p"),
# ("Lh_eqn:Lh", "1/b_p"),
#)
em = (
# ("Le_eqn", "Le - AtOx*1e2"),
("Le_eqn", "Le - AtOx*b_nox*SurfaceArea/(NodeVolume*x_np)"),
("Le_eqn:Le", "1"),
# ("Lh_eqn", "Lh"),
("Lh_eqn", "Lh - AtOx*b_pox*SurfaceArea/(NodeVolume*x_pp)"),
("Lh_eqn:Lh", "1"),
)
for e in em:
ds.node_model(device=device, region=region, name=e[0], equation=e[1])
def CreateNodeModel(device, region, model, expression):
'''
Creates a node model
'''
result = ds.node_model(device=device,
region=region,
name=model,
equation=expression)
if debug:
print(("NODEMODEL {d} {r} {m} \"{re}\"".format(d=device,
r=region,
m=model,
re=result)))
def createPotentialOnly(device, region):
for name, equation in (
("IntrinsicElectrons", "n_i*exp(Potential/V_t)"),
("IntrinsicElectrons:Potential", "diff(n_i*exp(Potential/V_t), Potential)"),
("IntrinsicHoles", "n_i^2/IntrinsicElectrons"),
("IntrinsicHoles:Potential", "diff(n_i^2/IntrinsicElectrons, Potential)"),
("IntrinsicCharge", "IntrinsicHoles-IntrinsicElectrons + NetDoping"),
("IntrinsicCharge:Potential", "diff(IntrinsicHoles-IntrinsicElectrons, Potential)"),
("PotentialIntrinsicNodeCharge", "-ElectronCharge*IntrinsicCharge"),
("PotentialIntrinsicNodeCharge:Potential", "diff(-ElectronCharge*IntrinsicCharge, Potential)"),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
for name, equation in (
("EField", "(Potential@n0-Potential@n1)*EdgeInverseLength"),
("EField:Potential@n0", "EdgeInverseLength"),
("EField:Potential@n1", "-EField:Potential@n0"),
):
devsim.edge_model(device=device, region=region, name=name, equation=equation)
devsim.element_from_edge_model(edge_model="EField", device=device, region=region)
devsim.element_from_edge_model(edge_model="EField", derivative="Potential", device=device, region=region)
foo="dot2d(EField_x, EField_y, unitx, unity)"
for name, equation in (
("ElectricField", foo),
("ElectricField:Potential@en0", "diff(%s, Potential@en0)" % foo),
("ElectricField:Potential@en1", "diff(%s, Potential@en1)" % foo),
("ElectricField:Potential@en2", "diff(%s, Potential@en2)" % foo),
("PotentialEdgeFlux", "Permittivity*ElectricField"),
("PotentialEdgeFlux:Potential@en0", "diff(Permittivity*ElectricField,Potential@en0)"),
("PotentialEdgeFlux:Potential@en1", "diff(Permittivity*ElectricField,Potential@en1)"),
("PotentialEdgeFlux:Potential@en2", "diff(Permittivity*ElectricField,Potential@en2)"),
):
devsim.element_model(device=device, region=region, name=name, equation=equation)
devsim.equation(device=device, region=region, name="PotentialEquation", variable_name="Potential",
node_model="PotentialIntrinsicNodeCharge", element_model="PotentialEdgeFlux", variable_update="log_damp")
devsim.edge_from_node_model(device=device, region=region, node_model="Potential") devsim.edge_model(device=device, region=region, name="ElectricField", equation="(Potential@n0 - Potential@n1)*EdgeInverseLength") devsim.edge_model(device=device, region=region, name="ElectricField:Potential@n0", equation="EdgeInverseLength") devsim.edge_model(device=device, region=region, name="ElectricField:Potential@n1", equation="-EdgeInverseLength") devsim.set_parameter(device=device, region=region, name="topbias", value=1.0e-0) devsim.set_parameter(device=device, region=region, name="botbias", value=0.0) devsim.edge_model(device=device, region=region, name="PotentialEdgeFlux", equation="Permittivity*ElectricField") devsim.edge_model(device=device, region=region, name="PotentialEdgeFlux:Potential@n0", equation="diff(Permittivity*ElectricField, Potential@n0)") devsim.edge_model(device=device, region=region, name="PotentialEdgeFlux:Potential@n1", equation="-PotentialEdgeFlux:Potential@n0") devsim.equation(device=device, region=region, name="PotentialEquation", variable_name="Potential", edge_model="PotentialEdgeFlux", variable_update="default") devsim.node_model(device=device, region=region, name="topnode_model" , equation="Potential - topbias") devsim.node_model(device=device, region=region, name="topnode_model:Potential", equation="1") devsim.node_model(device=device, region=region, name="botnode_model" , equation="Potential - botbias") devsim.node_model(device=device, region=region, name="botnode_model:Potential", equation="1") devsim.contact_equation(device=device, contact="top", name="PotentialEquation", variable_name="Potential", node_model="topnode_model", edge_charge_model="PotentialEdgeFlux") devsim.contact_equation(device=device, contact="bot", name="PotentialEquation", variable_name="Potential", node_model="botnode_model", edge_charge_model="PotentialEdgeFlux") devsim.solve(type="dc", absolute_error=1.0, relative_error=1e-10, maximum_iterations=30) print(devsim.get_contact_charge(device=device, contact="top", equation="PotentialEquation")) print(devsim.get_contact_charge(device=device, contact="bot", equation="PotentialEquation")) devsim.write_devices(file="trimesh3.msh", type="devsim_data")
def createDriftDiffusion(device, region):
for name, equation in (
("PotentialNodeCharge" , "-ElectronCharge*(Holes -Electrons + NetDoping)"),
("PotentialNodeCharge:Electrons", "+ElectronCharge"),
("PotentialNodeCharge:Holes" , "-ElectronCharge"),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
devsim.equation(device=device, region=region, name="PotentialEquation", variable_name="Potential", node_model="PotentialNodeCharge",
element_model="PotentialEdgeFlux", variable_update="log_damp")
for name, equation in (
("vdiff" , "(Potential@n0 - Potential@n1)/V_t"),
("vdiff:Potential@n0" , "V_t^(-1)"),
("vdiff:Potential@n1" , "-V_t^(-1)"),
("Bern01" , "B(vdiff)"),
("Bern01:Potential@n0", "dBdx(vdiff)*vdiff:Potential@n0"),
("Bern01:Potential@n1", "dBdx(vdiff)*vdiff:Potential@n1"),
("Bern10" , "Bern01 + vdiff"),
("Bern10:Potential@n0", "Bern01:Potential@n0 + vdiff:Potential@n0"),
("Bern10:Potential@n1", "Bern01:Potential@n1 + vdiff:Potential@n1"),
):
devsim.edge_model(device=device, region=region, name=name, equation=equation)
Jn ="ElectronCharge*mu_n*EdgeInverseLength*V_t*(Electrons@n1*Bern10 - Electrons@n0*Bern01)"
dJndn0 ="simplify(diff( %s, Electrons@n0))" % Jn
dJndn1 ="simplify(diff( %s, Electrons@n1))" % Jn
dJndpot0="simplify(diff( %s, Potential@n0))" % Jn
dJndpot1="simplify(diff( %s, Potential@n1))" % Jn
for name, equation in (
("ElectronCurrent" , Jn),
("ElectronCurrent:Electrons@n0", dJndn0),
("ElectronCurrent:Electrons@n1", dJndn1),
("ElectronCurrent:Potential@n0", dJndpot0),
("ElectronCurrent:Potential@n1", dJndpot1),
):
devsim.edge_model(device=device, region=region, name=name, equation=equation)
Jp ="-ElectronCharge*mu_p*EdgeInverseLength*V_t*(Holes@n1*Bern01 - Holes@n0*Bern10)"
dJpdp0 ="simplify(diff(%s, Holes@n0))" % Jp
dJpdp1 ="simplify(diff(%s, Holes@n1))" % Jp
dJpdpot0="simplify(diff(%s, Potential@n0))" % Jp
dJpdpot1="simplify(diff(%s, Potential@n1))" % Jp
for name, equation in (
("HoleCurrent" , Jp),
("HoleCurrent:Holes@n0" , dJpdp0),
("HoleCurrent:Holes@n1" , dJpdp1),
("HoleCurrent:Potential@n0", dJpdpot0),
("HoleCurrent:Potential@n1", dJpdpot1),
):
devsim.edge_model(device=device, region=region, name=name, equation=equation)
NCharge="-ElectronCharge * Electrons"
dNChargedn="-ElectronCharge"
for name, equation in (
("NCharge", NCharge),
("NCharge:Electrons", dNChargedn),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
PCharge="-ElectronCharge * Holes"
dPChargedp="-ElectronCharge"
for name, equation in (
("PCharge", PCharge),
("PCharge:Holes", dPChargedp),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
ni=devsim.get_parameter(device=device, region=region, name="n_i")
for name, value in (
("n1", ni),
("p1", ni),
("taun", 1e-5),
("taup", 1e-5),
):
devsim.set_parameter(device=device, region=region, name=name, value=value)
USRH="-ElectronCharge*(Electrons*Holes - n_i^2)/(taup*(Electrons + n1) + taun*(Holes + p1))"
dUSRHdn="simplify(diff($USRH, Electrons))"
dUSRHdp="simplify(diff($USRH, Holes))"
for name, equation in (
("USRH", USRH),
("USRH:Electrons", dUSRHdn),
("USRH:Holes", dUSRHdp),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
devsim.equation(device=device, region=region, name="ElectronContinuityEquation", variable_name="Electrons",
edge_model="ElectronCurrent", variable_update="positive",
time_node_model="NCharge", node_model="USRH")
devsim.equation(device=device, region=region, name="HoleContinuityEquation", variable_name="Holes",
edge_model="HoleCurrent", variable_update="positive",
time_node_model="PCharge", node_model="USRH")
def set_dg_parameters(device, region):
##From Cogenda default Si physics:
#TODO: parameter units
ds.set_parameter(device=device,
region=region,
name="h",
value=6.62606876e-34) # J*s
ds.set_parameter(device=device,
region=region,
name="hbar",
value=1.054571596e-34) # J*s
ds.set_parameter(device=device, region=region, name="Gamman", value=1)
ds.set_parameter(device=device, region=region, name="Gammap", value=1)
ds.set_parameter(device=device, region=region, name="Gammanox", value=1)
ds.set_parameter(device=device, region=region, name="Gammapox", value=1)
ds.set_parameter(device=device,
region=region,
name="mass_electron",
value=9.10938188e-31) # kg
ds.node_model(device=device,
region=region,
name="meff_elec",
equation="1.0903*mass_electron")
ds.node_model(device=device,
region=region,
name="meff_hole",
equation="1.1525*mass_electron")
ds.node_model(device=device,
region=region,
name="b_n",
equation="(1e4*Gamman*hbar^2)/(q*6*meff_elec)") # eV*cm^2
ds.node_model(device=device,
region=region,
name="b_p",
equation="(1e4*Gammap*hbar^2)/(q*6*meff_hole)") # eV*cm^2
# Oxide
#
#ds.node_model(device=device, region=region, name="b_nox", equation="1e-100") # eV*cm^2
ds.node_model(
device=device,
region=region,
name="b_nox",
equation="1e4*Gammanox*hbar^2/(6*q*0.14*mass_electron)") # eV*cm^2
ds.node_model(
device=device,
region=region,
name="b_pox",
equation="1e4*Gammapox*hbar^2/(6*q*1.0*mass_electron)") # eV*cm^2
#ds.node_model(device=device, region=region, name="b_nox", equation="10*hbar^2/(6*q*0.14*mass_electron)") # eV*cm^2
#ds.node_model(device=device, region=region, name="b_pox", equation="10*hbar^2/(6*q*0.14*mass_electron)") # eV*cm^2
#ds.node_model(device=device, region=region, name="b_nox", equation="(1e4*Gammanox*hbar^2)/(q*6*meff_elec)") # eV*cm^2
#ds.node_model(device=device, region=region, name="b_pox", equation="(1e4*Gammapox*hbar^2)/(q*6*meff_hole)") # eV*cm^2
ds.node_model(device=device,
region=region,
name="x_np",
equation="1e2*hbar/(2*0.4*mass_electron*q*3.15)^0.5") # cm
ds.node_model(device=device,
region=region,
name="x_pp",
equation="1e2*hbar/(2*0.4*mass_electron*q*4.50)^0.5") # cm
#const PetscScalar b_nox = hbar*hbar/(6*e*0.14*me);
#const PetscScalar b_pox = hbar*hbar/(6*e*1.0*me);
#const PetscScalar bn = mt->band->Gamman()*hbar*hbar/(6*e*mt->band->EffecElecMass(T));
#const PetscScalar bp = mt->band->Gammap()*hbar*hbar/(6*e*mt->band->EffecHoleMass(T));
# const PetscScalar x_np = hbar/sqrt(2*0.4*me*3.15*eV);
# const PetscScalar x_pp = hbar/sqrt(2*0.4*me*4.50*eV);
# eV = 1.602176462e-19*J;
# e = 1.602176462e-19*C;
# ELECMASS = 1.0903*me;
# HOLEMASS = 1.1525*me;
#
# Edge Integration
#
em = (
("b_n", "b_ne", "arithmetic", ()),
("b_p", "b_pe", "arithmetic", ()),
)
for e in em:
ds.edge_average_model(device=device,
region=region,
node_model=e[0],
edge_model=e[1],
average_type=e[2])
for d in e[3]:
ds.edge_average_model(device=device,
region=region,
node_model=e[0],
edge_model=e[1],
average_type=e[2],
derivative=d)
device="MyDevice" region="MyRegion" # basic linear circuit solved by itself devsim.circuit_element(name="V1", n1=1, n2=0, value=1.0) devsim.circuit_element(name="R1", n1=1, n2="cnode1", value=5.0) devsim.circuit_element(name="R2", n1="cnode1", n2=0, value=5.0) devsim.solve(type="dc", absolute_error=1.0, relative_error=1e-14, maximum_iterations=3) devsim.circuit_alter(name="V1", value=2.0) devsim.solve(type="dc", absolute_error=1.0, relative_error=1e-14, maximum_iterations=30) test_common.CreateSimpleMesh(device, region) devsim.node_model(device=device, region=region, name="erf", equation="erf(x);") devsim.print_node_values(device=device, region=region, name="erf") devsim.node_model(device=device, region=region, name="d_erf_dx", equation="diff(erf(x),x);") devsim.print_node_values(device=device, region=region, name="d_erf_dx") devsim.node_model(device=device, region=region, name="erfc", equation="erfc(x);") devsim.print_node_values(device=device, region=region, name="erfc") devsim.node_model(device=device, region=region, name="d_erfc_dx", equation="diff(erfc(x),x);") devsim.print_node_values(device=device, region=region, name="d_erfc_dx") devsim.node_model(device=device, region=region, name="d_abs_dx", equation="diff(abs(x),x);") devsim.print_node_values(device=device, region=region, name="d_abs_dx") devsim.set_parameter(name="param", value=-1.0) devsim.node_model(device=device, region=region, name="deptest", equation="param;") devsim.print_node_values(device=device, region=region, name="deptest") devsim.set_parameter(name="param", value=1.0)
def createSiliconDriftDiffusion(device, region):
for name, equation in (
("PotentialNodeCharge",
"-ElectronCharge*(Holes -Electrons + NetDoping)"),
("PotentialNodeCharge:Electrons", "+ElectronCharge"),
("PotentialNodeCharge:Holes", "-ElectronCharge"),
):
devsim.node_model(device=device,
region=region,
name=name,
equation=equation)
devsim.equation(device=device,
region=region,
name="PotentialEquation",
variable_name="Potential",
node_model="PotentialNodeCharge",
edge_model="PotentialEdgeFlux",
variable_update="log_damp")
createBernoulli(device, region)
createElectronCurrent(device, region)
createHoleCurrent(device, region)
NCharge = "-ElectronCharge * Electrons"
dNChargedn = "-ElectronCharge"
devsim.node_model(device=device,
region=region,
name="NCharge",
equation=NCharge)
devsim.node_model(device=device,
region=region,
name="NCharge:Electrons",
equation=dNChargedn)
PCharge = "-ElectronCharge * Holes"
dPChargedp = "-ElectronCharge"
devsim.node_model(device=device,
region=region,
name="PCharge",
equation=PCharge)
devsim.node_model(device=device,
region=region,
name="PCharge:Holes",
equation=dPChargedp)
ni = devsim.get_parameter(device=device, region=region, name="n_i")
devsim.set_parameter(device=device, region=region, name="n1", value=ni)
devsim.set_parameter(device=device, region=region, name="p1", value=ni)
devsim.set_parameter(device=device, region=region, name="taun", value=1e-5)
devsim.set_parameter(device=device, region=region, name="taup", value=1e-5)
USRH = "-ElectronCharge*(Electrons*Holes - n_i^2)/(taup*(Electrons + n1) + taun*(Holes + p1))"
dUSRHdn = "simplify(diff(%s, Electrons))" % USRH
dUSRHdp = "simplify(diff(%s, Holes))" % USRH
devsim.node_model(device=device, region=region, name="USRH", equation=USRH)
devsim.node_model(device=device,
region=region,
name="USRH:Electrons",
equation=dUSRHdn)
devsim.node_model(device=device,
region=region,
name="USRH:Holes",
equation=dUSRHdp)
devsim.equation(device=device,
region=region,
name="ElectronContinuityEquation",
variable_name="Electrons",
edge_model="ElectronCurrent",
variable_update="positive",
time_node_model="NCharge",
node_model="USRH")
devsim.equation(device=device,
region=region,
name="HoleContinuityEquation",
variable_name="Holes",
edge_model="HoleCurrent",
variable_update="positive",
time_node_model="PCharge",
node_model="USRH")
devsim.add_2d_interface(mesh="mos", name="gate_oxide", region0="gate", region1="oxide")
devsim.add_2d_interface(mesh="mos", name="bulk_oxide", region0="bulk", region1="oxide")
devsim.finalize_mesh(mesh="mos")
devsim.create_device(mesh="mos", device=device)
format_dict= {
'gate_doping' : gate_doping,
'source_doping' : source_doping,
'drain_doping' : drain_doping,
'body_doping' : body_doping,
'bulk_doping' : bulk_doping,
'x_gate_left' : x_gate_left,
'x_gate_right' : x_gate_right,
'x_diffusion_decay' : x_diffusion_decay,
'y_diffusion' : y_diffusion,
'y_diffusion_decay' : y_diffusion_decay,
'y_bulk_bottom' : y_bulk_bottom,
}
devsim.node_model(name="NetDoping" , device=device, region="gate", equation="%(gate_doping)s" % format_dict)
devsim.node_model(name="DrainDoping" , device=device, region="bulk", equation="0.25*%(drain_doping)s*erfc((x-%(x_gate_left)s)/%(x_diffusion_decay)s)*erfc((y-%(y_diffusion)s)/%(y_diffusion_decay)s)" % format_dict)
devsim.node_model(name="SourceDoping", device=device, region="bulk", equation="0.25*%(source_doping)s*erfc(-(x-%(x_gate_right)s)/%(x_diffusion_decay)s)*erfc((y-%(y_diffusion)s)/%(y_diffusion_decay)s)" % format_dict)
devsim.node_model(name="BodyDoping", device=device, region="bulk", equation="0.5*%(body_doping)s*erfc(-(y-%(y_bulk_bottom)s)/%(y_diffusion_decay)s)" % format_dict)
devsim.node_model(name="NetDoping" , device=device, region="bulk", equation="DrainDoping + SourceDoping + %(bulk_doping)s + BodyDoping" % format_dict)
devsim.write_devices( file="mos_2d", type="vtk")
devsim.write_devices( file="mos_2d.flps", type="floops")
def SetupCarrierResistorSystem(device, region):
'''
This adds electron continuity
'''
devsim.node_solution(device=device, region=region, name='Electrons')
devsim.edge_from_node_model(device=device,
region=region,
node_model='Electrons')
devsim.set_node_values(device=device,
region=region,
name='Electrons',
init_from='IntrinsicElectrons')
####
#### PotentialNodeCharge
####
for name, equation in (
("PotentialNodeCharge", "-ElectronCharge*(-Electrons + NetDoping)"),
("PotentialNodeCharge:Electrons", "+ElectronCharge"),
):
devsim.node_model(device=device,
region=region,
name=name,
equation=equation)
####
#### PotentialEquation modified for carriers present
####
devsim.equation(device=device,
region=region,
name='PotentialEquation',
variable_name='Potential',
node_model='PotentialNodeCharge',
edge_model="PotentialEdgeFlux",
variable_update="default")
####
#### vdiff, Bern01, Bern10
####
for name, equation in (
("vdiff", "(Potential@n0 - Potential@n1)/ThermalVoltage"),
("vdiff:Potential@n0", "ThermalVoltage^(-1)"),
("vdiff:Potential@n1", "-ThermalVoltage^(-1)"),
("Bern01", "B(vdiff)"),
("Bern01:Potential@n0", "dBdx(vdiff)*vdiff:Potential@n0"),
("Bern01:Potential@n1", "dBdx(vdiff)*vdiff:Potential@n1"),
("Bern10", "Bern01 + vdiff"),
("Bern10:Potential@n0", "Bern01:Potential@n0 + vdiff:Potential@n0"),
("Bern10:Potential@n1", "Bern01:Potential@n1 + vdiff:Potential@n1"),
):
devsim.edge_model(device=device,
region=region,
name=name,
equation=equation)
####
#### Electron Current
####
current_equation = "ElectronCharge*mu_n*EdgeInverseLength*ThermalVoltage*(Electrons@n1*Bern10 - Electrons@n0*Bern01)"
for name, equation in (
("ElectronCurrent", current_equation),
("ElectronCurrent:Electrons@n0",
"simplify(diff(%s, Electrons@n0))" % current_equation),
("ElectronCurrent:Electrons@n1",
"simplify(diff(%s, Electrons@n1))" % current_equation),
("ElectronCurrent:Potential@n0",
"simplify(diff(%s, Potential@n0))" % current_equation),
("ElectronCurrent:Potential@n1",
"simplify(diff(%s, Potential@n1))" % current_equation),
):
devsim.edge_model(device=device,
region=region,
name=name,
equation=equation)
####
#### Time derivative term
####
for name, equation in (
("NCharge", "-ElectronCharge * Electrons"),
("NCharge:Electrons", "-ElectronCharge"),
):
devsim.node_model(device=device,
region=region,
name=name,
equation=equation)
####
#### Electron Continuity Equation
####
devsim.equation(device=device,
region=region,
name="ElectronContinuityEquation",
variable_name="Electrons",
edge_model="ElectronCurrent",
time_node_model="NCharge",
variable_update="positive")
quantum_data[index] = qdict
#print max(get_node_model_values(device=device, region=region_si, name='n_classical'))
#print max(get_node_model_values(device=device, region=region_si, name='n_quantum'))
if carrier_var == 'Electrons':
ds.edge_model(device=device,
region=region_si,
name="surface_term",
equation="del_log_n1*EdgeCouple")
ds.edge_model(device=device,
region=region_si,
name="edge_volume_term",
equation="del_log_n2*EdgeNodeVolume")
ds.node_model(device=device,
region=region_si,
name="volume_term",
equation="Le_eqn*NodeVolume")
elif carrier_var == 'Holes':
ds.edge_model(device=device,
region=region_si,
name="surface_term",
equation="del_log_p1*EdgeCouple")
ds.edge_model(device=device,
region=region_si,
name="edge_volume_term",
equation="del_log_p2*EdgeNodeVolume")
ds.node_model(device=device,
region=region_si,
name="volume_term",
equation="Lh_eqn*NodeVolume")
else:
devsim.add_2d_region( mesh="dog", material="gas", region="gas2", yl=1.0, yh=1.001)
devsim.add_2d_region( mesh="dog", material="Oxide", region="r0", xl=xmin, xh=xmax, yl=ymid1, yh=ymin)
devsim.add_2d_region( mesh="dog", material="Silicon", region="r1", xl=xmin, xh=xmax, yl=ymid2, yh=ymid1)
devsim.add_2d_region( mesh="dog", material="Silicon", region="r2", xl=xmin, xh=xmax, yl=ymid2, yh=ymax)
#warn when leftover triangles are not encapsulated by region
# not specifying bounding box means all intersecting nodes
#bounding box is optional
devsim.add_2d_interface( mesh="dog", name="i0", region0="r0", region1="r1")
devsim.add_2d_interface( mesh="dog", name="i1", region0="r1", region1="r2", xl=0, xh=1, yl=ymid2, yh=ymid2, bloat=1.0e-10)
devsim.add_2d_contact( mesh="dog", name="top", region="r0", yl=ymin, yh=ymin, bloat=1.0e-10, material="metal")
devsim.add_2d_contact( mesh="dog", name="bot", region="r2", yl=ymax, yh=ymax, bloat=1.0e-10, material="metal")
#contact can only apply interface
devsim.finalize_mesh( mesh="dog")
devsim.create_device(mesh="dog", device=device)
devsim.node_model(device=device, name="NetDoping", region="gas1", equation="1e18")
devsim.node_model(device=device, name="NetDoping", region="r0", equation="1e18")
devsim.node_model(device=device, name="NetDoping", region="r1", equation="-1e15")
devsim.node_model(device=device, name="NetDoping", region="r2", equation="-1e15")
devsim.node_model(device=device, name="NetDoping", region="gas2", equation="-1e15")
devsim.interface_normal_model(device=device, region="r0", interface="i0")
devsim.interface_normal_model(device=device, region="r1", interface="i0")
devsim.interface_normal_model(device=device, region="r1", interface="i1")
devsim.interface_normal_model(device=device, region="r2", interface="i1")
devsim.set_parameter(name="raxis_zero", value=0.0)
devsim.set_parameter(name="raxis_variable", value="x")
for region in ("r0", "r1", "r2"):
devsim.cylindrical_node_volume( device=device, region=region)
### Create the bulk equation
###
devsim.equation(device=device, region=region, name="PotentialEquation", variable_name="Potential",
edge_model="DField", variable_update="default")
# the topbias is a circuit node, and we want to prevent it from being overridden by a parameter
devsim.set_parameter(device=device, region=region, name="botbias", value=0.0)
for name, equation in (
("topnode_model", "Potential - topbias"),
("topnode_model:Potential", "1"),
("topnode_model:topbias", "-1"),
("botnode_model", "Potential - botbias"),
("botnode_model:Potential", "1"),
):
devsim.node_model(device=device, region=region, name=name, equation=equation)
# attached to circuit node
devsim.contact_equation(device=device, contact="top", name="PotentialEquation", variable_name="Potential",
node_model="topnode_model", edge_charge_model="DField", circuit_node="topbias")
# attached to ground
devsim.contact_equation(device=device, contact="bot", name="PotentialEquation", variable_name="Potential",
node_model="botnode_model", edge_charge_model="DField")
#
# Voltage source
#
devsim.circuit_element(name="V1", n1=1, n2=0, value=1.0, acreal=1.0)
devsim.circuit_element(name="R1", n1="topbias", n2=1, value=1e3)
#
# See the License for the specific language governing permissions and
# limitations under the License.
#Purpose: Fermi integral and inverse
import devsim
import test_common
device = "MyDevice"
region = "MyRegion"
test_common.CreateSimpleMesh(device, region)
devsim.set_parameter(name="Nc", value=1e22)
devsim.node_model(device=device,
region=region,
name="Electrons",
equation="2e15*(1 - x) + 1e10;")
devsim.node_model(device=device,
region=region,
name="r",
equation="Electrons/Nc;")
devsim.node_model(device=device,
region=region,
name="Eta",
equation="InvFermi(r);")
devsim.node_model(device=device,
region=region,
name="r2",
equation="Fermi(Eta);")
devsim.node_model(device=device,
