pchang718
485 lines
19 KiB
Python
485 lines
19 KiB
Python
# Copyright 2013 Devsim LLC
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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from devsim import *
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from .model_create import *
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def SetUniversalParameters(device, region):
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universal = {
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'q' : 1.6e-19, #, 'coul'),
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'k' : 1.3806503e-23, #, 'J/K'),
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'Permittivity_0' : 8.85e-14 #, 'F/cm^2')
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}
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for k, v in universal.items():
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set_parameter(device=device, region=region, name=k, value=v)
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def SetSiliconParameters(device, region):
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'''
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Sets Silicon device parameters on the specified region.
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'''
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SetUniversalParameters(device, region)
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##D. B. M. Klaassen, J. W. Slotboom, and H. C. de Graaff, "Unified apparent bandgap narrowing in n- and p-type Silicon," Solid-State Electronics, vol. 35, no. 2, pp. 125-29, 1992.
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par = {
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'Permittivity' : 11.1*get_parameter(device=device, region=region, name='Permittivity_0'),
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'NC300' : 2.8e19, # '1/cm^3'
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'NV300' : 3.1e19, # '1/cm^3'
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'EG300' : 1.12, # 'eV'
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'EGALPH' : 2.73e-4, # 'eV/K'
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'EGBETA' : 0 , # 'K'
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'Affinity' : 4.05 , # 'K'
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# Canali model
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'BETAN0' : 2.57e-2, # '1'
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'BETANE' : 0.66, # '1'
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'BETAP0' : 0.46, # '1'
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'BETAPE' : 0.17, # '1'
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'VSATN0' : 1.43e9,
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'VSATNE' : -0.87,
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'VSATP0' : 1.62e8,
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'VSATPE' : -0.52,
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# Arora model
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'MUMN' : 88,
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'MUMEN' : -0.57,
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'MU0N' : 7.4e8,
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'MU0EN' : -2.33,
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'NREFN' : 1.26e17,
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'NREFNE' : 2.4,
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'ALPHA0N' : 0.88,
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'ALPHAEN' : -0.146,
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'MUMP' : 54.3,
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'MUMEP' : -0.57,
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'MU0P' : 1.36e8,
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'MU0EP' : -2.23,
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'NREFP' : 2.35e17,
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'NREFPE' : 2.4,
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'ALPHA0P' : 0.88,
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'ALPHAEP' : -0.146,
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# SRH
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"taun" : 1e-5,
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"taup" : 1e-5,
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"n1" : 1e10,
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"p1" : 1e10,
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# TEMP
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"T" : 300
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}
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for k, v in par.items():
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set_parameter(device=device, region=region, name=k, value=v)
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def CreateQuasiFermiLevels(device, region, electron_model, hole_model, variables):
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'''
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Creates the models for the quasi-Fermi levels. Assuming Boltzmann statistics.
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'''
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eq = (
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('EFN', 'EC + V_t * log(%s/NC)' % electron_model, ('Potential', 'Electrons')),
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('EFP', 'EV - V_t * log(%s/NV)' % hole_model, ('Potential', 'Holes')),
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)
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for (model, equation, variable_list) in eq:
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#print "MODEL: " + model + " equation " + equation
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CreateNodeModel(device, region, model, equation)
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vset = set(variable_list)
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for v in variables:
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if v in vset:
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CreateNodeModelDerivative(device, region, model, equation, v)
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def CreateDensityOfStates(device, region, variables):
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'''
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Set up models for density of states.
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Neglects Bandgap narrowing.
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'''
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eq = (
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('NC', 'NC300 * (T/300)^1.5', ('T',)),
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('NV', 'NV300 * (T/300)^1.5', ('T',)),
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('NTOT', 'Donors + Acceptors', ()),
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# Band Gap Narrowing
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('DEG', '0', ()),
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#('DEG', 'V0.BGN * (log(NTOT/N0.BGN) + ((log(NTOT/N0.BGN)^2 + CON.BGN)^(0.5)))', ()),
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('EG', 'EG300 + EGALPH*((300^2)/(300+EGBETA) - (T^2)/(T+EGBETA)) - DEG', ('T')),
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('NIE', '((NC * NV)^0.5) * exp(-EG/(2*V_t))*exp(DEG)', ('T')),
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('EC', '-Potential - Affinity - DEG/2', ('Potential',)),
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('EV', 'EC - EG + DEG/2', ('Potential', 'T')),
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('EI', '0.5 * (EC + EV + V_t*log(NC/NV))', ('Potential', 'T')),
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)
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for (model, equation, variable_list) in eq:
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#print "MODEL: " + model + " equation " + equation
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CreateNodeModel(device, region, model, equation)
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vset = set(variable_list)
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for v in variables:
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if v in vset:
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CreateNodeModelDerivative(device, region, model, equation, v)
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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 CreateVT(device, region, variables):
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'''
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Calculates the thermal voltage, based on the temperature.
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V_t : node model
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V_t_edge : edge model from arithmetic mean
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'''
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CreateNodeModel(device, region, 'V_t', "k*T/q")
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CreateArithmeticMean(device, region, 'V_t', 'V_t_edge')
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if 'T' in variables:
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CreateArithmeticMeanDerivative(device, region, 'V_t', 'V_t_edge', 'T')
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def CreateEField(device, region):
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'''
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Creates the EField and DField.
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'''
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edge_average_model(device=device, region=region, node_model="Potential",
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edge_model="EField", average_type="negative_gradient")
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edge_average_model(device=device, region=region, node_model="Potential",
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edge_model="EField", average_type="negative_gradient", derivative="Potential")
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def CreateDField(device, region):
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CreateEdgeModel(device, region, "DField", "Permittivity * EField")
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CreateEdgeModel(device, region, "DField:Potential@n0", "Permittivity * EField:Potential@n0")
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CreateEdgeModel(device, region, "DField:Potential@n1", "Permittivity * EField:Potential@n1")
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def CreateSiliconPotentialOnly(device, region):
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'''
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Creates the physical models for a Silicon region for equilibrium simulation.
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'''
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variables = ("Potential",)
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CreateVT(device, region, variables)
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CreateDensityOfStates(device, region, variables)
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SetSiliconParameters(device, region)
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# require NetDoping
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for i in (
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("IntrinsicElectrons", "NIE*exp(Potential/V_t)"),
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("IntrinsicHoles", "NIE^2/IntrinsicElectrons"),
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("IntrinsicCharge", "kahan3(IntrinsicHoles, -IntrinsicElectrons, NetDoping)"),
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("PotentialIntrinsicCharge", "-q * IntrinsicCharge")
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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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CreateQuasiFermiLevels(device, region, 'IntrinsicElectrons', 'IntrinsicHoles', variables)
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CreateEField(device, region)
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CreateDField(device, region)
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equation(device=device, region=region, name="PotentialEquation", variable_name="Potential",
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node_model="PotentialIntrinsicCharge", edge_model="DField", variable_update="log_damp")
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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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if not InNodeModelList(device, region, "contactcharge_node"):
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CreateNodeModel(device, region, "contactcharge_node", "q*IntrinsicCharge")
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celec_model = "(1e-10 + 0.5*abs(NetDoping+(NetDoping^2 + 4 * NIE^2)^(0.5)))"
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chole_model = "(1e-10 + 0.5*abs(-NetDoping+(NetDoping^2 + 4 * NIE^2)^(0.5)))"
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contact_model = "Potential -{0} + ifelse(NetDoping > 0, \
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-V_t*log({1}/NIE), \
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V_t*log({2}/NIE))".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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CreateContactNodeModel(device, contact, "{0}:{1}".format(contact_model_name,"Potential"), "1")
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if is_circuit:
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CreateContactNodeModel(device, contact, "{0}:{1}".format(contact_model_name,GetContactBiasName(contact)), "-1")
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if is_circuit:
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contact_equation(device=device, contact=contact, name="PotentialEquation",
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node_model=contact_model_name, edge_model="",
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node_charge_model="contactcharge_node", edge_charge_model="DField",
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node_current_model="", edge_current_model="", circuit_node=GetContactBiasName(contact))
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else:
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contact_equation(device=device, contact=contact, name="PotentialEquation",
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node_model=contact_model_name, edge_model="",
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node_charge_model="contactcharge_node", edge_charge_model="DField",
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node_current_model="", edge_current_model="")
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def CreateSRH(device, region, variables):
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'''
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Shockley Read hall recombination model in terms of generation.
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'''
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USRH="(Electrons*Holes - NIE^2)/(taup*(Electrons + n1) + taun*(Holes + p1))"
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Gn = "-q * USRH"
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Gp = "+q * 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", "T"):
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if i in variables:
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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, Jn):
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'''
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Electron Continuity Equation using specified equation for Jn
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'''
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NCharge = "q * 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(device=device, region=region, name="ElectronContinuityEquation", variable_name="Electrons",
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time_node_model = "NCharge",
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edge_model=Jn, variable_update="log_damp", node_model="ElectronGeneration")
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def CreateHCE(device, region, Jp):
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'''
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Hole Continuity Equation using specified equation for Jp
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'''
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PCharge = "-q * 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(device=device, region=region, name="HoleContinuityEquation", variable_name="Holes",
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time_node_model = "PCharge",
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edge_model=Jp, variable_update="log_damp", node_model="HoleGeneration")
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def CreatePE(device, region):
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'''
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Create Poisson Equation assuming the Electrons and Holes as solution variables
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'''
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pne = "-q*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(device=device, region=region, name="PotentialEquation", variable_name="Potential",
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node_model="PotentialNodeCharge", edge_model="DField",
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time_node_model="", variable_update="log_damp")
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def CreateSiliconDriftDiffusion(device, region, mu_n="mu_n", mu_p="mu_p", Jn='Jn', Jp='Jp'):
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'''
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Instantiate all equations for drift diffusion simulation
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'''
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CreateDensityOfStates(device, region, ("Potential",))
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CreateQuasiFermiLevels(device, region, "Electrons", "Holes", ("Electrons", "Holes", "Potential"))
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CreatePE(device, region)
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CreateSRH(device, region, ("Electrons", "Holes", "Potential"))
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CreateECE(device, region, Jn)
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CreateHCE(device, region, Jp)
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def CreateSiliconDriftDiffusionContact(device, region, contact, Jn, Jp, 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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CreateSiliconPotentialOnlyContact(device, region, contact, is_circuit)
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celec_model = "(1e-10 + 0.5*abs(NetDoping+(NetDoping^2 + 4 * NIE^2)^(0.5)))"
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chole_model = "(1e-10 + 0.5*abs(-NetDoping+(NetDoping^2 + 4 * NIE^2)^(0.5)))"
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contact_electrons_model = "Electrons - ifelse(NetDoping > 0, {0}, NIE^2/{1})".format(celec_model, chole_model)
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contact_holes_model = "Holes - ifelse(NetDoping < 0, +{1}, +NIE^2/{0})".format(celec_model, chole_model)
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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(device, contact, contact_electrons_name, contact_electrons_model)
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CreateContactNodeModel(device, contact, "{0}:{1}".format(contact_electrons_name, "Electrons"), "1")
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CreateContactNodeModel(device, contact, contact_holes_name, contact_holes_model)
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CreateContactNodeModel(device, contact, "{0}:{1}".format(contact_holes_name, "Holes"), "1")
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if is_circuit:
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contact_equation(device=device, contact=contact, name="ElectronContinuityEquation",
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node_model=contact_electrons_name,
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edge_current_model=Jn, circuit_node=GetContactBiasName(contact))
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contact_equation(device=device, contact=contact, name="HoleContinuityEquation",
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node_model=contact_holes_name,
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edge_current_model=Jp, circuit_node=GetContactBiasName(contact))
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else:
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contact_equation(device=device, contact=contact, name="ElectronContinuityEquation",
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node_model=contact_electrons_name,
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edge_current_model=Jn)
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contact_equation(device=device, contact=contact, name="HoleContinuityEquation",
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node_model=contact_holes_name,
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edge_current_model=Jp)
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def CreateBernoulliString (Potential="Potential", scaling_variable="V_t", sign=-1):
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'''
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Creates the Bernoulli function for Scharfetter Gummel
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sign -1 for potential
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sign +1 for energy
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scaling variable should be V_t
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Potential should be scaled by V_t in V
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Ec, Ev should scaled by V_t in eV
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returns the Bernoulli expression and its argument
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Caller should understand that B(-x) = B(x) + x
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'''
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tdict = {
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"Potential" : Potential,
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"V_t" : scaling_variable
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}
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#### test for requisite models here
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if sign == -1:
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vdiff="(%(Potential)s@n0 - %(Potential)s@n1)/%(V_t)s" % tdict
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elif sign == 1:
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vdiff="(%(Potential)s@n1 - %(Potential)s@n0)/%(V_t)s" % tdict
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else:
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raise NameError("Invalid Sign %s" % sign)
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Bern01 = "B(%s)" % vdiff
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return (Bern01, vdiff)
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def CreateElectronCurrent(device, region, mu_n, Potential="Potential", sign=-1, ElectronCurrent="ElectronCurrent", V_t="V_t_edge"):
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'''
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Electron current
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mu_n = mobility name
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Potential is the driving potential
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'''
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EnsureEdgeFromNodeModelExists(device, region, "Potential")
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EnsureEdgeFromNodeModelExists(device, region, "Electrons")
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EnsureEdgeFromNodeModelExists(device, region, "Holes")
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if Potential == "Potential":
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(Bern01, vdiff) = CreateBernoulliString(scaling_variable=V_t, Potential=Potential, sign=sign)
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else:
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raise NameError("Implement proper call")
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tdict = {
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'Bern01' : Bern01,
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'vdiff' : vdiff,
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'mu_n' : mu_n,
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'V_t' : V_t
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}
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Jn = "q*%(mu_n)s*EdgeInverseLength*%(V_t)s*kahan3(Electrons@n1*%(Bern01)s, Electrons@n1*%(vdiff)s, -Electrons@n0*%(Bern01)s)" % tdict
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CreateEdgeModel(device, region, ElectronCurrent, Jn)
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for i in ("Electrons", "Potential", "Holes"):
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CreateEdgeModelDerivatives(device, region, ElectronCurrent, Jn, i)
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def CreateHoleCurrent(device, region, mu_p, Potential="Potential", sign=-1, HoleCurrent="HoleCurrent", V_t="V_t_edge"):
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'''
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Hole current
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'''
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EnsureEdgeFromNodeModelExists(device, region, "Potential")
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EnsureEdgeFromNodeModelExists(device, region, "Electrons")
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EnsureEdgeFromNodeModelExists(device, region, "Holes")
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# Make sure the bernoulli functions exist
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if Potential == "Potential":
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(Bern01, vdiff) = CreateBernoulliString(scaling_variable=V_t, Potential=Potential, sign=sign)
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else:
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raise NameError("Implement proper call for " + Potential)
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tdict = {
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'Bern01' : Bern01,
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'vdiff' : vdiff,
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'mu_p' : mu_p,
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'V_t' : V_t
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}
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Jp ="-q*%(mu_p)s*EdgeInverseLength*%(V_t)s*kahan3(Holes@n1*%(Bern01)s, -Holes@n0*%(Bern01)s, -Holes@n0*%(vdiff)s)" % tdict
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CreateEdgeModel(device, region, HoleCurrent, Jp)
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for i in ("Holes", "Potential", "Electrons"):
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CreateEdgeModelDerivatives(device, region, HoleCurrent, Jp, i)
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def CreateAroraMobilityLF(device, region):
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'''
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Creates node mobility models and then averages them on edge
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Uses model from Muller and Kamins
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Add T derivative dependence later
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'''
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models = (
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('Tn', 'T/300'),
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('mu_arora_n_node',
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'MUMN * pow(Tn, MUMEN) + (MU0N * pow(T, MU0EN))/(1 + pow((NTOT/(NREFN*pow(Tn, NREFNE))), ALPHA0N*pow(Tn, ALPHAEN)))'),
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('mu_arora_p_node',
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'MUMP * pow(Tn, MUMEP) + (MU0P * pow(T, MU0EP))/(1 + pow((NTOT/(NREFP*pow(Tn, NREFPE))), ALPHA0P*pow(Tn, ALPHAEP)))')
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)
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for k, v in models:
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CreateNodeModel(device, region, k, v)
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CreateArithmeticMean(device, region, 'mu_arora_n_node', 'mu_arora_n_lf')
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CreateArithmeticMean(device, region, 'mu_arora_p_node', 'mu_arora_p_lf')
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CreateElectronCurrent(device, region, mu_n = 'mu_arora_n_lf', Potential="Potential", sign=-1, ElectronCurrent="Jn_arora_lf", V_t="V_t_edge")
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CreateHoleCurrent(device, region, mu_p = 'mu_arora_p_lf', Potential="Potential", sign=-1, HoleCurrent="Jp_arora_lf", V_t="V_t_edge")
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return {
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'mu_n' : 'mu_arora_n_lf',
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'mu_p' : 'mu_arora_p_lf',
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'Jn' : 'Jn_arora_lf',
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'Jp' : 'Jp_arora_lf',
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}
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|
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def CreateHFMobility(device, region, mu_n, mu_p, Jn, Jp):
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'''
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Add T derivatives when debugged
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use parameters to set model flags
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|
Caughey Thomas
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'''
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|
|
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tdict = {
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'Jn' : Jn,
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'mu_n' : mu_n,
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'Jp' : Jp,
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|
'mu_p' : mu_p
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}
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|
tlist = (
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|
("vsat_n", "VSATN0 * pow(T, VSATNE)" % tdict, ('T')),
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("beta_n", "BETAN0 * pow(T, BETANE)" % tdict, ('T')),
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|
("Epar_n",
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|
"ifelse((%(Jn)s * EField) > 0, abs(EField), 1e-15)" % tdict, ('Potential')),
|
|
("mu_n", "%(mu_n)s * pow(1 + pow((%(mu_n)s*Epar_n/vsat_n), beta_n), -1/beta_n)"
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|
% tdict, ('Electrons', 'Holes', 'Potential', 'T')),
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|
("vsat_p", "VSATP0 * pow(T, VSATPE)" % tdict, ('T')),
|
|
("beta_p", "BETAP0 * pow(T, BETAPE)" % tdict, ('T')),
|
|
("Epar_p",
|
|
"ifelse((%(Jp)s * EField) > 0, abs(EField), 1e-15)" % tdict, ('Potential')),
|
|
("mu_p", "%(mu_p)s * pow(1 + pow(%(mu_p)s*Epar_p/vsat_p, beta_p), -1/beta_p)"
|
|
% tdict, ('Electrons', 'Holes', 'Potential', 'T')),
|
|
)
|
|
|
|
variable_list = ('Electrons', 'Holes', 'Potential')
|
|
for (model, equation, variables) in tlist:
|
|
CreateEdgeModel(device, region, model, equation)
|
|
for v in variable_list:
|
|
if v in variables:
|
|
CreateEdgeModelDerivatives(device, region, model, equation, v)
|
|
|
|
# This create derivatives automatically
|
|
CreateElectronCurrent(device, region, mu_n='mu_n', Potential="Potential", sign=-1, ElectronCurrent="Jn", V_t="V_t_edge")
|
|
CreateHoleCurrent( device, region, mu_p='mu_p', Potential="Potential", sign=-1, HoleCurrent="Jp", V_t="V_t_edge")
|
|
return {
|
|
'mu_n' : 'mu_n',
|
|
'mu_p' : 'mu_p',
|
|
'Jn' : 'Jn',
|
|
'Jp' : 'Jp',
|
|
}
|
|
|
|
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