464 lines
15 KiB
Python
464 lines
15 KiB
Python
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# Copyright 2013 DEVSIM LLC
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#
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# SPDX-License-Identifier: Apache-2.0
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from .simple_dd import CreateBernoulli, CreateElectronCurrent, CreateHoleCurrent
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from .model_create import (
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CreateSolution,
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CreateNodeModel,
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CreateNodeModelDerivative,
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CreateContactNodeModel,
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CreateContactNodeModelDerivative,
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CreateEdgeModel,
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CreateEdgeModelDerivatives,
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CreateContinuousInterfaceModel,
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InEdgeModelList,
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InNodeModelList,
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)
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from devsim import (
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contact_equation,
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equation,
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get_contact_current,
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get_parameter,
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interface_equation,
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set_parameter,
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)
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contactcharge_edge = "contactcharge_edge"
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ece_name = "ElectronContinuityEquation"
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hce_name = "HoleContinuityEquation"
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celec_model = "(1e-10 + 0.5*abs(NetDoping+(NetDoping^2 + 4 * n_i^2)^(0.5)))"
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chole_model = "(1e-10 + 0.5*abs(-NetDoping+(NetDoping^2 + 4 * n_i^2)^(0.5)))"
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q = 1.6e-19 # coul
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k = 1.3806503e-23 # J/K
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eps_0 = 8.85e-14 # F/cm^2
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# T = 300 # K
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eps_si = 11.1
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eps_ox = 3.9
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# TODO: make this temperature dependent
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n_i = 1.0e10 # #/cm^3
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# constant in our approximation
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mu_n = 400
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mu_p = 200
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def GetContactBiasName(contact):
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return "{0}_bias".format(contact)
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def GetContactNodeModelName(contact):
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return "{0}nodemodel".format(contact)
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def PrintCurrents(device, contact):
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"""
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print out contact currents
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"""
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# TODO add charge
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_contact_bias_name = GetContactBiasName(contact)
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electron_current = get_contact_current(
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device=device, contact=contact, equation=ece_name
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)
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hole_current = get_contact_current(
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device=device, contact=contact, equation=hce_name
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)
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total_current = electron_current + hole_current
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voltage = get_parameter(device=device, name=GetContactBiasName(contact))
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print(
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"{0}\t{1}\t{2}\t{3}\t{4}".format(
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contact, voltage, electron_current, hole_current, total_current
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)
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)
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# in the future, worry about workfunction
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def CreateOxideContact(device, region, contact):
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_conteq = "Permittivity*ElectricField"
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contact_bias_name = GetContactBiasName(contact)
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contact_model_name = GetContactNodeModelName(contact)
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eq = "Potential - {0}".format(contact_bias_name)
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CreateContactNodeModel(device, contact, contact_model_name, eq)
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CreateContactNodeModelDerivative(
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device, contact, contact_model_name, eq, "Potential"
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)
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# TODO: make everyone use dfield
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if not InEdgeModelList(device, region, contactcharge_edge):
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CreateEdgeModel(
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device, region, contactcharge_edge, "Permittivity*ElectricField"
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)
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CreateEdgeModelDerivatives(
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device,
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region,
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contactcharge_edge,
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"Permittivity*ElectricField",
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"Potential",
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)
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contact_equation(
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device=device,
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contact=contact,
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name="PotentialEquation",
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node_model=contact_model_name,
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edge_charge_model=contactcharge_edge,
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)
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#####
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##### Constants
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#####
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def SetOxideParameters(device, region, T):
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"""
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Sets physical parameters
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"""
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set_parameter(
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device=device, region=region, name="Permittivity", value=eps_ox * eps_0
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)
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set_parameter(device=device, region=region, name="ElectronCharge", value=q)
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def SetSiliconParameters(device, region, T):
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"""
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Sets physical parameters assuming constants
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"""
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#### TODO: make T a free parameter and T dependent parameters as models
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set_parameter(
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device=device, region=region, name="Permittivity", value=eps_si * eps_0
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)
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set_parameter(device=device, region=region, name="ElectronCharge", value=q)
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set_parameter(device=device, region=region, name="n_i", value=n_i)
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set_parameter(device=device, region=region, name="T", value=T)
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set_parameter(device=device, region=region, name="kT", value=k * T)
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set_parameter(device=device, region=region, name="V_t", value=k * T / q)
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set_parameter(device=device, region=region, name="mu_n", value=mu_n)
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set_parameter(device=device, region=region, name="mu_p", value=mu_p)
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# default SRH parameters
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set_parameter(device=device, region=region, name="n1", value=n_i)
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set_parameter(device=device, region=region, name="p1", value=n_i)
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set_parameter(device=device, region=region, name="taun", value=1e-5)
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set_parameter(device=device, region=region, name="taup", value=1e-5)
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def CreateSiliconPotentialOnly(device, region):
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"""
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Creates the physical models for a Silicon region
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"""
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if not InNodeModelList(device, region, "Potential"):
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print("Creating Node Solution Potential")
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CreateSolution(device, region, "Potential")
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elec_i = "n_i*exp(Potential/V_t)"
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hole_i = "n_i^2/IntrinsicElectrons"
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charge_i = "kahan3(IntrinsicHoles, -IntrinsicElectrons, NetDoping)"
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pcharge_i = "-ElectronCharge * IntrinsicCharge"
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# require NetDoping
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for i in (
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("IntrinsicElectrons", elec_i),
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("IntrinsicHoles", hole_i),
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("IntrinsicCharge", charge_i),
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("PotentialIntrinsicCharge", pcharge_i),
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):
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n = i[0]
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e = i[1]
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CreateNodeModel(device, region, n, e)
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CreateNodeModelDerivative(device, region, n, e, "Potential")
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### TODO: Edge Average Model
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for i in (
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("ElectricField", "(Potential@n0-Potential@n1)*EdgeInverseLength"),
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("PotentialEdgeFlux", "Permittivity * ElectricField"),
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):
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n = i[0]
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e = i[1]
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CreateEdgeModel(device, region, n, e)
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CreateEdgeModelDerivatives(device, region, n, e, "Potential")
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equation(
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device=device,
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region=region,
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name="PotentialEquation",
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variable_name="Potential",
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node_model="PotentialIntrinsicCharge",
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edge_model="PotentialEdgeFlux",
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variable_update="log_damp",
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)
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def CreateSiliconPotentialOnlyContact(device, region, contact, is_circuit=False):
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"""
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Creates the potential equation at the contact
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if is_circuit is true, than use node given by GetContactBiasName
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"""
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# Means of determining contact charge
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# Same for all contacts
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#### TODO: This is the same as D-Field
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if not InEdgeModelList(device, region, "contactcharge_edge"):
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CreateEdgeModel(
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device, region, "contactcharge_edge", "Permittivity*ElectricField"
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)
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CreateEdgeModelDerivatives(
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device,
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region,
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"contactcharge_edge",
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"Permittivity*ElectricField",
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"Potential",
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)
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# set_parameter(device=device, region=region, name=GetContactBiasName(contact), value=0.0)
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contact_model = "Potential -{0} + ifelse(NetDoping > 0, \
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-V_t*log({1}/n_i), \
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V_t*log({2}/n_i))".format(GetContactBiasName(contact), celec_model, chole_model)
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contact_model_name = GetContactNodeModelName(contact)
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CreateContactNodeModel(device, contact, contact_model_name, contact_model)
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# Simplify it too complicated
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CreateContactNodeModel(
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device, contact, "{0}:{1}".format(contact_model_name, "Potential"), "1"
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)
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if is_circuit:
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CreateContactNodeModel(
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device,
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contact,
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"{0}:{1}".format(contact_model_name, GetContactBiasName(contact)),
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"-1",
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)
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if is_circuit:
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contact_equation(
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device=device,
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contact=contact,
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name="PotentialEquation",
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node_model=contact_model_name,
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edge_model="",
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node_charge_model="",
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edge_charge_model="contactcharge_edge",
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node_current_model="",
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edge_current_model="",
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circuit_node=GetContactBiasName(contact),
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)
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else:
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contact_equation(
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device=device,
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contact=contact,
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name="PotentialEquation",
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node_model=contact_model_name,
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edge_model="",
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node_charge_model="",
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edge_charge_model="contactcharge_edge",
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node_current_model="",
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edge_current_model="",
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)
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def CreateSRH(device, region):
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USRH = "(Electrons*Holes - n_i^2)/(taup*(Electrons + n1) + taun*(Holes + p1))"
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Gn = "-ElectronCharge * USRH"
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Gp = "+ElectronCharge * USRH"
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CreateNodeModel(device, region, "USRH", USRH)
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CreateNodeModel(device, region, "ElectronGeneration", Gn)
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CreateNodeModel(device, region, "HoleGeneration", Gp)
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for i in ("Electrons", "Holes"):
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CreateNodeModelDerivative(device, region, "USRH", USRH, i)
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CreateNodeModelDerivative(device, region, "ElectronGeneration", Gn, i)
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CreateNodeModelDerivative(device, region, "HoleGeneration", Gp, i)
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def CreateECE(device, region, mu_n):
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CreateElectronCurrent(device, region, mu_n)
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NCharge = "-ElectronCharge * Electrons"
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CreateNodeModel(device, region, "NCharge", NCharge)
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CreateNodeModelDerivative(device, region, "NCharge", NCharge, "Electrons")
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equation(
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device=device,
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region=region,
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name="ElectronContinuityEquation",
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variable_name="Electrons",
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time_node_model="NCharge",
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edge_model="ElectronCurrent",
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variable_update="positive",
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node_model="ElectronGeneration",
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)
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def CreateHCE(device, region, mu_p):
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CreateHoleCurrent(device, region, mu_p)
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PCharge = "ElectronCharge * Holes"
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CreateNodeModel(device, region, "PCharge", PCharge)
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CreateNodeModelDerivative(device, region, "PCharge", PCharge, "Holes")
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equation(
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device=device,
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region=region,
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name="HoleContinuityEquation",
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variable_name="Holes",
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time_node_model="PCharge",
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edge_model="HoleCurrent",
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variable_update="positive",
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node_model="HoleGeneration",
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)
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def CreatePE(device, region):
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pne = "-ElectronCharge*kahan3(Holes, -Electrons, NetDoping)"
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CreateNodeModel(device, region, "PotentialNodeCharge", pne)
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CreateNodeModelDerivative(device, region, "PotentialNodeCharge", pne, "Electrons")
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CreateNodeModelDerivative(device, region, "PotentialNodeCharge", pne, "Holes")
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equation(
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device=device,
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region=region,
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name="PotentialEquation",
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variable_name="Potential",
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node_model="PotentialNodeCharge",
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edge_model="PotentialEdgeFlux",
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time_node_model="",
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variable_update="log_damp",
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)
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def CreateSiliconDriftDiffusion(device, region, mu_n="mu_n", mu_p="mu_p"):
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CreatePE(device, region)
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CreateBernoulli(device, region)
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CreateSRH(device, region)
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CreateECE(device, region, mu_n)
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CreateHCE(device, region, mu_p)
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def CreateSiliconDriftDiffusionAtContact(device, region, contact, is_circuit=False):
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"""
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Restrict electrons and holes to their equilibrium values
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Integrates current into circuit
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"""
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contact_electrons_model = (
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"Electrons - ifelse(NetDoping > 0, {0}, n_i^2/{1})".format(
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celec_model, chole_model
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)
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)
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contact_holes_model = "Holes - ifelse(NetDoping < 0, +{1}, +n_i^2/{0})".format(
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celec_model, chole_model
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)
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contact_electrons_name = "{0}nodeelectrons".format(contact)
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contact_holes_name = "{0}nodeholes".format(contact)
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CreateContactNodeModel(
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device, contact, contact_electrons_name, contact_electrons_model
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)
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# TODO: The simplification of the ifelse statement is time consuming
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# CreateContactNodeModelDerivative(device, contact, contact_electrons_name, contact_electrons_model, "Electrons")
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CreateContactNodeModel(
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device, contact, "{0}:{1}".format(contact_electrons_name, "Electrons"), "1"
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)
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CreateContactNodeModel(device, contact, contact_holes_name, contact_holes_model)
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CreateContactNodeModel(
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device, contact, "{0}:{1}".format(contact_holes_name, "Holes"), "1"
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)
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# TODO: keyword args
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if is_circuit:
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contact_equation(
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device=device,
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contact=contact,
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name="ElectronContinuityEquation",
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node_model=contact_electrons_name,
|
||
|
|
edge_current_model="ElectronCurrent",
|
||
|
|
circuit_node=GetContactBiasName(contact),
|
||
|
|
)
|
||
|
|
|
||
|
|
contact_equation(
|
||
|
|
device=device,
|
||
|
|
contact=contact,
|
||
|
|
name="HoleContinuityEquation",
|
||
|
|
node_model=contact_holes_name,
|
||
|
|
edge_current_model="HoleCurrent",
|
||
|
|
circuit_node=GetContactBiasName(contact),
|
||
|
|
)
|
||
|
|
|
||
|
|
else:
|
||
|
|
contact_equation(
|
||
|
|
device=device,
|
||
|
|
contact=contact,
|
||
|
|
name="ElectronContinuityEquation",
|
||
|
|
node_model=contact_electrons_name,
|
||
|
|
edge_current_model="ElectronCurrent",
|
||
|
|
)
|
||
|
|
|
||
|
|
contact_equation(
|
||
|
|
device=device,
|
||
|
|
contact=contact,
|
||
|
|
name="HoleContinuityEquation",
|
||
|
|
node_model=contact_holes_name,
|
||
|
|
edge_current_model="HoleCurrent",
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
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, "ElectricField", efield)
|
||
|
|
CreateEdgeModelDerivatives(device, region, "ElectricField", efield, "Potential")
|
||
|
|
dfield = "Permittivity*ElectricField"
|
||
|
|
CreateEdgeModel(device, region, "PotentialEdgeFlux", dfield)
|
||
|
|
CreateEdgeModelDerivatives(device, region, "PotentialEdgeFlux", dfield, "Potential")
|
||
|
|
equation(
|
||
|
|
device=device,
|
||
|
|
region=region,
|
||
|
|
name="PotentialEquation",
|
||
|
|
variable_name="Potential",
|
||
|
|
edge_model="PotentialEdgeFlux",
|
||
|
|
variable_update=update_type,
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
def CreateSiliconOxideInterface(device, interface):
|
||
|
|
"""
|
||
|
|
continuous potential at interface
|
||
|
|
"""
|
||
|
|
model_name = CreateContinuousInterfaceModel(device, interface, "Potential")
|
||
|
|
interface_equation(
|
||
|
|
device=device,
|
||
|
|
interface=interface,
|
||
|
|
name="PotentialEquation",
|
||
|
|
interface_model=model_name,
|
||
|
|
type="continuous",
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
#
|
||
|
|
##TODO: similar model for silicon/silicon interface
|
||
|
|
## should use quasi-fermi potential
|
||
|
|
def CreateSiliconSiliconInterface(device, interface):
|
||
|
|
"""
|
||
|
|
Enforces potential, electron, and hole continuity across the interface
|
||
|
|
"""
|
||
|
|
CreateSiliconOxideInterface(device, interface)
|
||
|
|
ename = CreateContinuousInterfaceModel(device, interface, "Electrons")
|
||
|
|
interface_equation(
|
||
|
|
device=device,
|
||
|
|
interface=interface,
|
||
|
|
name="ElectronContinuityEquation",
|
||
|
|
interface_model=ename,
|
||
|
|
type="continuous",
|
||
|
|
)
|
||
|
|
hname = CreateContinuousInterfaceModel(device, interface, "Holes")
|
||
|
|
interface_equation(
|
||
|
|
device=device,
|
||
|
|
interface=interface,
|
||
|
|
name="HoleContinuityEquation",
|
||
|
|
interface_model=hname,
|
||
|
|
type="continuous",
|
||
|
|
)
|