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 setup_dg_equation(device, region, e_name, v_name, e_m, e_v_m, n_m):
ds.equation(device=device,
region=region,
name=e_name,
variable_name=v_name,
edge_model=e_m,
edge_volume_model=e_v_m,
node_model=n_m,
variable_update="default")
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 CreateSiliconPotentialOnly(device, region):
'''
Creates the physical models for a Silicon region for equilibrium simulation.
'''
variables = ("Potential", )
CreateVT(device, region, variables)
CreateDensityOfStates(device, region, variables)
SetSiliconParameters(device, region)
# require NetDoping
for i in (
("IntrinsicElectrons",
"NIE*exp(ifelse(((Potential-Le)/V_t) < 80, ((Potential-Le)/V_t), 80))"
),
("IntrinsicHoles",
"NIE*exp(ifelse(((-Potential-Lh)/V_t) < 80, ((-Potential-Lh)/V_t), 80))"
), ("IntrinsicCharge",
"kahan3(IntrinsicHoles, -IntrinsicElectrons, NetDoping)"),
("PotentialIntrinsicCharge", "-q * IntrinsicCharge")):
n = i[0]
e = i[1]
CreateNodeModel(device, region, n, e)
CreateNodeModelDerivative(device, region, n, e, 'Potential')
CreateNodeModelDerivative(device, region, n, e, 'Le')
CreateNodeModelDerivative(device, region, n, e, 'Lh')
CreateQuasiFermiLevels(device, region, 'IntrinsicElectrons',
'IntrinsicHoles', variables)
CreateEField(device, region)
CreateDField(device, region)
ds.equation(device=device,
region=region,
name="PotentialEquation",
variable_name="Potential",
node_model="PotentialIntrinsicCharge",
edge_model="DField",
variable_update="log_damp")
def createOxidePotentialOnly(device, region):
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)
devsim.equation(device=device,
region=region,
name="PotentialEquation",
variable_name="Potential",
edge_model="PotentialEdgeFlux",
variable_update="log_damp")
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")
def CreateOxidePotentialOnly(device, region, update_type="default"):
'''
Create electric field model in oxide
Creates Potential solution variable if not available
'''
if not InNodeModelList(device, region, "Potential"):
print("Creating Node Solution Potential")
CreateSolution(device, region, "Potential")
efield = "(Potential@n0 - Potential@n1)*EdgeInverseLength"
# this needs to remove derivatives w.r.t. independents
CreateEdgeModel(device, region, "EField", efield)
CreateEdgeModelDerivatives(device, region, "EField", efield, "Potential")
dfield = "Permittivity*EField"
CreateEdgeModel(device, region, "PotentialEdgeFlux", dfield)
CreateEdgeModelDerivatives(device, region, "PotentialEdgeFlux", dfield,
"Potential")
ds.equation(device=device,
region=region,
name="PotentialEquation",
variable_name="Potential",
edge_model="PotentialEdgeFlux",
variable_update=update_type)
###
### Model the D Field
###
devsim.edge_model(device=device, region=region, name="DField",
equation="Permittivity*ElectricField")
devsim.edge_model(device=device, region=region, name="DField:Potential@n0",
equation="diff(Permittivity*ElectricField, Potential@n0)")
devsim.edge_model(device=device, region=region, name="DField:Potential@n1",
equation="-DField:Potential@n0")
###
### 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",
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 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")
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")
