def test_tlmextraction(self):
# path = '/home/connor/Documents/Stanford_Projects/Extractions/src/SampleData/FETExampleData/nano_patterning.csv'
# idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/TLMExampleData'
idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/SemiPy/SampleData/TLMExampleDataShort'
# idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/TLMExampleDataShort'
# idvd_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt'
# idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt'
widths = Value(4.0, ureg.micrometer)
# lengths = Value.array_like(np.array([0.5, 1.0, 2.0, 2.5, 3.0, 3.5]), unit=ureg.micrometer)
lengths = Value.array_like(np.array([1.0, 0.5, 2.0]),
unit=ureg.micrometer)
tox = Value(90, ureg.nanometer)
result = TLMExtractor(widths=widths,
lengths=lengths,
tox=tox,
epiox=3.9,
device_polarity='n',
idvg_path=idvg_path,
vd_values=[1.0, 2.0])
result.save_tlm_plots()
a = 5
def test_ambiFET(self):
idvd_path = get_abs_semipy_path(
'SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt')
idvg_path = get_abs_semipy_path(
'SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt')
gate_oxide = SiO2(thickness=Value(30, ureg.nanometer))
channel = MoS2(layer_number=1)
substrate = Silicon()
fet = ambiTFT(gate_oxide=gate_oxide,
channel=channel,
width=Value(1, ureg.micrometer),
substrate=substrate,
length=Value(1, ureg.micrometer))
result = FETExtractor(FET=fet,
idvg_path=idvg_path,
idvd_path=idvd_path)
print("~~~~~~TFT Extracted Values~~~~~~")
print("~~~~~~n-type~~~~~~")
print(result.FET.NBranch.Vt_avg)
print(result.FET.NBranch.Vt_fwd)
print(result.FET.NBranch.Vt_bwd)
print(result.FET.NBranch.min_ss)
print("~~~~~~p-type~~~~~~")
print(result.FET.PBranch.Vt_avg)
print(result.FET.PBranch.Vt_fwd)
print(result.FET.PBranch.Vt_bwd)
print(result.FET.PBranch.min_ss)
class Al2O3(MetalOxide):
bandgap = matprop.Bulk.Electrical.BandGap(
value=Value(7.5, unit=ureg.electron_volt))
relative_permittivity = matprop.Bulk.Electrical.RelativePermittivity(
value=Value(8.5, ureg.dimensionless))
def test_value(self):
a = np.array([1, 2, 3, 4])
b = Value.array_like(array=a, unit=ureg.amp)
print(b[0])
a = np.array([[1, 2, 3, 4], [1, 2, 3, 4]])
b = Value.array_like(array=a, unit=ureg.amp)
print(b[0][0])
f = Field(field='voltage', name='nothing')
print(f)
a = Value(value=3.0,
unit=ureg.amp,
name='input_voltage',
tf_shape=(None, 1))
c = 1 / a
array = np.array([a, a, a], dtype=object)
b = Value(value=2.0, unit=ureg.volt * ureg.volt, name='input_current')
d = ureg.amp * array
r = array * b
f = b * array
boo = r == f
tmep = 1.0 * ureg.volt
f = 2.0 * ureg.microvolt
temp = tmep + f
temp = tmep.to_reduced_units()
d = a * 2.0
f = 2.0 * a
c = 1.0
r = 1.0 * ureg.volt
t = ureg.volt * 1.0
d = a == b
r = a.tensor
d = 5
def test_igzo(self):
# This test models an a-IGZO device with 20nm IGZO, 100nm SiO2 on Si substrate.
# Documentation notes:
# 1. Add material and copy material properties
# 2. Set model in unittest
# 3. Files
# TODO: Change filepaths to point correctly
idvd_path = get_abs_semipy_path(
'SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt')
idvg_path = get_abs_semipy_path(
'SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt')
gate_oxide = SiO2(thickness=Value(100, ureg.nanometer))
channel = aIGZO(thickness=Value(20, ureg.nanometer))
substrate = Silicon()
fet = pTFT(gate_oxide=gate_oxide,
channel=channel,
width=Value(180, ureg.micrometer),
substrate=substrate,
length=Value(30, ureg.micrometer))
result = FETExtractor(FET=fet,
idvg_path=idvg_path,
idvd_path=idvd_path)
print(result.FET.max_gm)
print(result.FET.max_mobility)
print(result.FET.Vt_avg)
print(result.FET.min_ss)
def compute_diffusion_current(self, ambient_temp, vgs, vd):
# Capacitance Values
c_Q = self.compute_quantum_cap(ambient_temp, vgs)
# self.c_Q = Value(0, ureg.meter ** -2 * ureg.coulomb / ureg.volt)
c_i = self.cox_t
# c_it = electron_charge_C * Value(1e16, ureg.meter ** -2 / ureg.volt)
c_it = Value(0, ureg.meter**-2 * ureg.coulomb / ureg.volt)
cap_r = 1 + (c_Q + c_it) / c_i
#Mobility
mobility_temp = Value(295, ureg.kelvin)
T = ambient_temp
mobility = self.compute_mobility_temperature(
self.FET.max_mobility, mobility_temp,
T).adjust_unit(ureg.meter**2 / ureg.second / ureg.volt)
#Compute Diffusion Current
# i_diff = (mobility * (self.c_Q + self.c_it) * (self.FET.width / self.FET.length) * (self.vth ** 2) * (1-math.exp(-vd/self.vth)) * math.exp((vgs-self.FET.Vt_avg)/(self.vth * self.cap_r))).adjust_unit(ureg.ampere)
I_diff_term_1 = math.log(
math.exp((vgs - self.FET.Vt_avg) / (self.vth * cap_r)) + 1)
I_diff_term_2 = math.log(
math.exp((vgs - self.FET.Vt_avg - vd) / (self.vth * cap_r)) + 1)
i_diff = (self.vth * electron_charge_C * mobility *
(self.FET.width * self.NDOS / self.FET.length) *
(I_diff_term_1 - I_diff_term_2)).base_units()
print("Diffusion Current is {0} at Vg = {1}".format(i_diff, vgs))
return i_diff
def __check_properties(length, width):
# make sure given properties are values
if not isinstance(length, Value):
warnings.warn(
'Given length is not a value. Assuming units are micrometers.')
length = Value(value=length, unit=ureg.micrometer)
else:
assert length.unit.dimensionality == ureg.meter.dimensionality, 'Your length is not given in meters, but {0}.'.format(
length.unit.dimensionality)
if not isinstance(width, Value):
warnings.warn(
'Given width is not a value. Assuming units are micrometers.')
width = Value(value=width, unit=ureg.micrometer)
else:
assert width.unit.dimensionality == ureg.meter.dimensionality, 'Your length is not given in meters, but {0}.'.format(
width.unit.dimensionality)
# if not isinstance(tox, Value):
# warnings.warn('Given Tox is not a value. Assuming units are nanometers.')
# tox = Value(value=tox, unit=ureg.nanometer)
# else:
# assert tox.unit.dimensionality == ureg.meter.dimensionality, 'Your length is not given in meters, but {0}.'.format(tox.unit.dimensionality)
#
# if not isinstance(epiox, Value):
# epiox = Value(value=epiox)
# now return all the properties
return length, width
def test_2DFETExtraction_and_stanford2dsmodel(self):
idvd_path = get_abs_semipy_path(
'SampleData/FETExampleData/MoS2AlOx/MoS2_15AlOxALD_Id_Vd.csv')
idvg_path = get_abs_semipy_path(
'SampleData/FETExampleData/MoS2AlOx/MoS2_15AlOxALD_Id_Vg.txt')
gate_oxide = SiO2(thickness=Value(30.0, ureg.nanometer))
channel = MoS2(layer_number=1)
substrate = Silicon()
fet = nTFT(channel=channel,
gate_oxide=gate_oxide,
length=Value(400, ureg.nanometer),
width=Value(2.2, ureg.micrometer),
substrate=substrate)
result = FETExtractor(FET=fet,
idvg_path=idvg_path,
idvd_path=idvd_path)
fet = result.FET
fet.Rc.set(Value(480.0, ureg.ohm * ureg.micrometer),
input_values={'n': Value(1e13, ureg.centimeter**-2)})
fet.mobility_temperature_exponent.set(Value(0.85, ureg.dimensionless))
fet.max_mobility.set(Value(
35, ureg.centimeter**2 / (ureg.volt * ureg.second)),
input_values={
'Vd': Value(1, ureg.volt),
'Vg': Value(1, ureg.volt)
})
S2DModel = Stanford2DSModel(FET=fet)
Vds = ModelInput(0.0, 5.0, num=40, unit=ureg.volt)
Vgs = ModelInput(0.0, 30.0, num=4, unit=ureg.volt)
ambient_temperature = Value(300, ureg.kelvin)
id = S2DModel.model_output(Vds,
Vgs,
heating=True,
vsat=True,
diffusion=False,
drift=True,
ambient_temperature=ambient_temperature)
plot = IdVdPlot('IdVd')
plot.add_idvd_dataset(result.idvd, marker='o')
for key in id.keys():
if 'Id' in key:
plot.add_data(Vds.range, id[key], linewidth=4.0)
plot.show_plot()
def compute_metal_thermal_resistance(self):
#using 1 for now to account for the contact resistance
km = Value(1, ureg.watt / (ureg.meter * ureg.kelvin))
tm = Value(50, ureg.nanometer)
Lhm = (tm * self.FET.gate_oxide.thickness * km /
self.FET.gate_oxide.thermal_conductivity)**.5
return Lhm / (km * tm * (self.FET.width.base_units() + 2 * Lhm))
class aIGZO(MetalOxide):
bandgap = matprop.Bulk.Electrical.BandGap(
value=Value(3.2, unit=ureg.electron_volt))
relative_permittivity = matprop.Bulk.Electrical.RelativePermittivity(
value=Value(3.9, ureg.dimensionless))
thermal_conductivity = matprop.Bulk.Thermal.ThermalConductivity(
value=Value(1.4, ureg.watt / (ureg.kelvin * ureg.meter)),
input_values={'temperature': Value(300, ureg.kelvin)})
class MoS2SiO2(BaseInterface):
"""
The MoS2 SiO2 interface.
"""
material1 = MoS2
material2 = SiO2
thermal_boundary_conductance = matprop.Interfaces.Thermal.ThermalBoundaryConductance(
value=Value(15e6, ureg.watt / (ureg.kelvin * ureg.meter**2)),
cited=True,
input_values={'temperature': Value(300, ureg.kelvin)},
citation=MoS2SiO2AlNThermalBoundaryResistance())
def vg_to_n(self, vg):
# adding extra values to make the units be centimeter ** -2
try:
# replace any Vg < Vt_avg with Vt_avg
vg[vg < self.Vt_avg.value] = self.Vt_avg.value
n = Value(value=1.0, unit=ureg.coulomb) * self.gate_oxide.capacitance * (vg - self.Vt_avg.value)\
/ (electron_charge_C * Value(value=1.0, unit=ureg.volt * ureg.farad))
except Exception as e:
assert self.Vt_avg.value is not None, \
'You must calculate the average Vt by running FET.compute_properties() before computing the carrier density'
raise e
return n
def test_fetextraction(self):
# path = '/home/connor/Documents/Stanford_Projects/Extractions/src/SampleData/FETExampleData/nano_patterning.csv'
idvd_path = '/home/connor/Documents/Stanford_Projects/Extractions/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt'
idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt'
#
# idvd_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt'
# idvg_path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt'
gate_oxide = SiO2(thickness=Value(30, ureg.nanometer))
channel = MoS2(layer_number=1)
result = FETExtractor(width=1,
length=1,
gate_oxide=gate_oxide,
channel=channel,
device_polarity='n',
idvg_path=idvg_path,
idvd_path=idvd_path)
result.FET.publish_csv('.')
result.save_plots()
print(result.FET.max_gm)
print(result.FET.min_ss)
a = 5
class WS2(TwoDMaterial, Semiconductor):
"""
The material MoS2. Single layer thickness is 0.615 nm taken from <citation>.
"""
layer_thickness = matprop.Bulk.Basic.Thickness(value=Value(0.615, ureg.nanometer))
def __init__(self, *args, **kwargs):
super(WS2, self).__init__(*args, **kwargs)
def min_ss(self, _in):
if isinstance(_in, np.ndarray):
# remove any zeros
_in = _in.flatten()
zero_val = Value(0.0, _in[0].unit)
zero_i = [i for i in range(len(_in)) if _in[i] == zero_val]
_in = np.delete(_in, zero_i)
_in = self.min_slope_value(_in)
_in = _in.adjust_unit(ureg.meter * ureg.millivolt / ureg.amp)
self._min_ss = _in
def test_idvgdataset(self):
path = get_abs_semipy_path(
'SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt')
dataset = IdVgDataSet(data_path=path)
result = dataset.get_column(column_name='vg_fwd',
master_independent_value_range=[0, 10.0])
self.assertEqual(
result[0][0], Value(0.0, ureg.volt),
'Error in the IdVgDataSet object get column function when requesting master'
' independent value range. Lowest Vg value should be 0.0 volt but is {0}'
.format(result[0][0]))
self.assertEqual(
result[0][-1], Value(9.5, ureg.volt),
'Error in the IdVgDataSet object get column function when requesting master'
' independent value range. Highest Vg value should be 9.5 volt but is {0}'
.format(result[0][-1]))
result, vd = dataset.get_column(column_name='id',
return_set_values=True)
self.assertEqual(
result[0][-1], Value(1.921e-6, ureg.amp),
'Error in the IdVgDataSet object get column function. Highest Id value should '
'be 1.921e-6 amps but is {0}'.format(result[0][-1]))
self.assertEqual(
vd[-1], Value(2.0, ureg.volt),
'Error in the IdVgDataSet object get column function. Highest Vd value should '
'be 2.0 volts but is {0}'.format(result[0][-1]))
result = dataset.get_column_set(column_name='id',
secondary_value=Value(1.0, ureg.volt))
self.assertEqual(
len(result.shape), 1,
'Error in the IdVgDataSet object get column set function. Result should only have '
'1 dimension but it has {0}'.format(len(result.shape)))
class MoS2(TwoDMaterial, Semiconductor):
"""
The material MoS2. Single layer thickness is 0.615 nm taken from <citation>.
"""
relative_permittivity = matprop.Bulk.Electrical.RelativePermittivity(value=Value(4.2, ureg.dimensionless))
thermal_conductivity = matprop.Bulk.Thermal.ThermalConductivity(value=Value(90, ureg.watt/(ureg.kelvin*ureg.meter)),
input_values={'temperature': Value(300, ureg.kelvin)},
citation=MonolayerMoS2ThermalConductivityYan)
saturation_velocity = matprop.Bulk.Electrical.SaturationVelocity(value=Value(3.2e6, ureg.centimeter/ureg.seconds),
input_values={'temperature': Value(300, ureg.kelvin)})
layer_thickness = matprop.Bulk.Basic.Thickness(value=Value(0.615, ureg.nanometer),
citation=MonolayerMoS2ThicknessDickinson)
#ADDED
bandgap = matprop.Bulk.Electrical.BandGap(value=Value(2.2, ureg.electron_volt))
def __init__(self, *args, **kwargs):
super(MoS2, self).__init__(*args, **kwargs)
def test_metavalue(self):
class MetaValueTest(MetaValue):
def __init__(self, value):
self.value = value
# test math operations
a = Value(1, ureg.amp)
a_meta = MetaValueTest(Value(1, ureg.amp))
a_n = 1
b = Value(2, ureg.amp)
b_meta = MetaValueTest(b)
c = Value(3, ureg.amp)
c_meta = MetaValueTest(c)
d = Value(4, ureg.volt)
d_meta = MetaValueTest(d)
e = Value(2, ureg.ohm)
e_meta = MetaValueTest(e)
# test the add function
self.assertEqual(c, b + a_meta, 'Error in MetaValue.__add__()')
self.assertEqual(c, a_meta + b_meta, 'Error in MetaValue.__add__()')
# test the subtract function
self.assertEqual(c - b, a_meta, 'Error in MetaValue.__sub__()')
self.assertEqual(c - b_meta, a_meta, 'Error in MetaValue.__sub__()')
# test the multiply function
self.assertEqual(d, b * e_meta, 'Error in MetaValue.__mul__()')
self.assertEqual(a, a * a_n, 'Error in MetaValue.__mul__()')
# test the divide function
self.assertEqual(d / e_meta, b, 'Error in MetaValue.__truediv__()')
self.assertEqual(d_meta / e_meta, b,
'Error in MetaValue.__truediv__()')
self.assertEqual(a, a / a_n, 'Error in MetaValue.__truediv__()')
class Silicon(Semiconductor):
"""
The semiconductor material Silicon
"""
# relative_permittivity = matprop.Bulk.Electrical.RelativePermittivity(value=Value(4.2, ureg.dimensionless))
thermal_conductivity = matprop.Bulk.Thermal.ThermalConductivity(value=Value(140, ureg.watt/(ureg.kelvin*ureg.meter)),
input_values={'temperature': Value(300, ureg.kelvin)})
# saturation_velocity = matprop.Bulk.Electrical.SaturationVelocity(value=Value(3.4e6, ureg.centimeter/ureg.seconds),
# input_values={'temperature': Value(300, ureg.kelvin)})
def __init__(self, *args, **kwargs):
super(Semiconductor, self).__init__(*args, **kwargs)
def test_tlmextraction(self):
# Change these filepaths to match TLM data
idvd_path = get_abs_semipy_path(
'SampleData/TLMExampleData/WSe2_Sample_4_Id_Vd.txt') # unused
idvg_path = get_abs_semipy_path('SampleData/TLMExampleData')
widths = Value(4.0, ureg.micrometer)
lengths = Value.array_like(np.array([0.5, 1.0, 2.0, 2.5, 3.0, 3.5]),
unit=ureg.micrometer)
#lengths = Value.array_like(np.array([1.0, 2.0, 0.5]), unit=ureg.micrometer)
#lengths = Value.array_like(np.array([2.0, 0.5, 1.0]), unit=ureg.micrometer)
gate_oxide = SiO2(thickness=Value(30, ureg.nanometer))
channel = MoS2(layer_number=1)
result = TLMExtractor(widths=widths,
lengths=lengths,
gate_oxide=gate_oxide,
channel=channel,
FET_class=nTFT,
idvg_path=idvg_path,
vd_values=[1.0, 2.0],
substrate=Silicon())
result.save_tlm_plots()
def test_transistor(self):
# path = '/home/connor/Documents/Stanford_Projects/Extractions/src/SampleData/FETExampleData/nano_patterning.csv'
# path = '/home/connor/Documents/Stanford_Projects/Extractions/src/SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt'
# path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/src/SampleData/FETExampleData/WSe2_Sample_4_Id_Vd.txt'
path = '/home/connor/Documents/Stanford_Projects/Extractions/fetextraction/SemiPy/SampleData/FETExampleData/WSe2_Sample_4_Id_Vg.txt'
dataset = IdVgDataSet(data_path=path)
result = dataset.get_column(column_name='vg_fwd', master_independent_value_range=[0, 18.0])
result, vd = dataset.get_column(column_name='id', return_set_values=True)
result = dataset.get_column_set(column_name='id', secondary_value=Value(1.0, ureg.volt))
a = 5
def set(self, value, input_values=None):
"""
Set the property and input values for this Device Property.
Args:
value (physics.Value): The Value to be set for this property
input_values (dict): A dictionary of the input values, using the convention {'input_name': input_value}
Returns:
None
"""
# save the prop value
assert_value(value)
assert value.unit.dimensionality == self.prop_dimensionality.dimensionality, 'Your dimensionality is incorrect for {0}. Yours is {1}, but it should be' \
' {2}'.format(self.prop_name, value.unit.dimensionality, self.prop_dimensionality.dimensionality)
self.value = value
# now if the standard units were given, then adjust the value units
if self.prop_standard_units is not None:
self.value = self.value.adjust_unit(self.prop_standard_units)
# now round the value to 2 decimal places
self.value = Value(value=round(self.value.value * 100) / 100,
unit=self.value.unit)
# save the input values, making sure that they match the given names
for i, input_name in enumerate(self.input_value_names):
input_value = input_values.get(input_name, None)
assert input_value is not None, 'You are missing the required {0} input for this property'.format(
input_name)
assert_value(input_value)
assert input_value.unit.dimensionality == self.input_dimensionalities[i].dimensionality,\
'Your dimensionality is incorrect for input {0}. Yours is {1}, but it should be' \
' {2}'.format(input_name, input_value.unit.dimensionality, self.input_dimensionalities[i].dimensionality)
self.input_values[input_name] = input_value
# now go through the optional input values if there a given input values
if input_values is not None:
for i, optional_name in enumerate(self.optional_input_value_names):
input_value = input_values.get(optional_name, None)
if input_value is not None:
assert_value(input_value)
assert input_value.unit.dimensionality == self.input_dimensionalities[i].dimensionality, \
'Your dimensionality is incorrect for input {0}. Yours is {1}, but it should be' \
' {2}'.format(optional_name, input_value.unit.dimensionality, self.input_dimensionalities[i].dimensionality)
self.input_values[optional_name] = input_value
def __init__(self,
min_value,
max_value,
unit,
num=None,
step=None,
*args,
**kwargs):
assert num is not None or step is not None, 'You must give a step or num value'
if num is not None:
self.range = np.linspace(min_value, max_value, num)
elif step is not None:
self.range = np.arange(min_value, max_value, step)
self.range = Value.array_like(self.range, unit=unit)
class TLMExtractor(Extractor):
"""
An extractor object for Transfer Length Method (TLM) measurements.
Args:
length (list): The list of the physical FET length. Should be Values with correct units for floats in micrometers
width (Value, float, or list): Physical width of the FET. Should be a Value with correct units or float in micrometers.
tox (Value or float): Physical thickness of the FET oxide. Should be a Value with correct units or float in nanometers.
epiox (Value or float): Dielectric constant of the oxide. Should be a Value or float (unitless).
device_polarity (str): The polarity of the device, either 'n' or 'p' for electron or hole, respectively.
idvg_path (str): Path to the folder with all the IdVg data.
Attributes:
tlm_datasets: A dict of SemiPy.Datasets.IVDataset.TLMDataSet indexed by Vd values
FETs: A list of all the SemiPy.Devices.FET.Transistor.FETs analyzed from the IdVg data
Example:
Example of how to extract TLM data from IdVg data
>>> from physics.value import Value, ureg
# path points to a folder with all the IdVg data
>>> widths = Value(4.0, ureg.micrometer)
>>> lengths = Value.array_like(np.array([1.0, 0.5, 2.0]), unit=ureg.micrometer)
>>> tox = Value(90, ureg.nanometer)
>>> tlm = TLMExtractor(widths=widths, lengths=lengths, tox=tox, epiox=3.9, device_polarity='n', idvg_path=path, vd_values=[1.0, 2.0])
# save all the plots of the TLM
>>> tlm.save_tlm_plots()
"""
maximum_n_varience = Value(8e11, ureg.centimeter**-2)
def __init__(self,
lengths,
widths,
channel,
gate_oxide,
FET_class,
vd_values=None,
idvg_path=None,
*args,
**kwargs):
super(TLMExtractor, self).__init__()
# now create FETExtractors for every set of IdVg data
self.FETs = []
self.data_dict = {'n': [], 'r': [], 'l': []}
self.n_max = []
self.vd_values = vd_values
for root, dirs, idvg_data in os.walk(idvg_path):
# make sure there are lengths for each data file
assert len(lengths) == len(idvg_data), 'There are too many or too few channel' \
' lengths given for the data. ({0})'.format(idvg_data)
for i, idvg in enumerate(idvg_data):
path = os.path.join(root, idvg)
fet = FET_class(gate_oxide=gate_oxide,
channel=channel,
width=widths,
length=lengths[i],
*args,
**kwargs)
self.FETs.append(
FETExtractor(fet, idvg_path=path, vd_values=vd_values))
# self.FETs.append(FETExtractor(width=widths, length=lengths[i], epiox=epiox, tox=tox,
# device_polarity=device_polarity, idvg_path=path,
# vd_values=vd_values))
new_fet_vd_values = self.FETs[
-1].idvg.get_secondary_indep_values()
if self.vd_values is None:
self.vd_values = new_fet_vd_values
assert new_fet_vd_values == self.vd_values,\
'The IdVg data at {0} for this TLM does not have consistent Vd values.' \
' Make sure that all the Vd values are the same for every dataset'.format(idvg_path)
# grab the n and resistances and create the l column
self.data_dict['n'].append(self.FETs[-1].idvg.get_column('n'))
self.n_max.append(np.max(self.data_dict['n'][-1], axis=-1))
self.data_dict['r'].append(
self.FETs[-1].idvg.get_column('resistance'))
self.data_dict['l'].append(
np.ones_like(self.data_dict['n'][-1]) *
self.FETs[-1].FET.length)
# create_scatter_plot(self.FETs[-1].idvg.get_column('n')[0], self.FETs[-1].idvg.get_column('id')[-1], scale='lin', show=True, autoscale=True)
# now lets start processing the data, first creating a TLMDataSet for each Vd value
self.tlm_datasets = {}
# convert to np arrays for easy indexing
self.data_dict = {
key: np.array(data)
for key, data in self.data_dict.items()
}
# make sure there is actually data in the data_dict
assert len(
self.data_dict['n']
) != 0, 'There is no data in the file path you gave. Make sure the path is correct.'
for i, vd in enumerate(self.vd_values):
new_dataset = TLMDataSet(data_path=pd.DataFrame.from_dict({
key + '_' + str(j): self.data_dict[key][j, i, :]
for j in range(len(lengths)) for key in ('n', 'r', 'l')
}))
self.tlm_datasets[vd] = new_dataset
def save_tlm_plots(self):
"""
Saves TLM plots for this TLM instance at all Vd values. This includes R vs. Length, Rc vs. n, Rsheet vs. n
"""
for i, vd in enumerate(self.vd_values):
new_dataset = self.tlm_datasets[vd]
# now we can start computing TLM properties
n_full = new_dataset.get_column('n')
# get the column with the lowest max min
min_max_n_col = np.argmin(np.max(n_full, axis=1))
# get the min_max n value
min_max_n = np.min(np.max(n_full, axis=1))
# now get the min n value from the column with the min_max_n. This is important to ensure we get a rectangular n array
max_min_n = np.partition(
n_full[min_max_n_col][np.where(
n_full[min_max_n_col, :] >= 1.0)[0]], 2)[2]
# value = 989429999999.9993 = 9.89e+11
# expr: np.where((n_full[1]>max_min_n) & (n_full[1]<min_max_n))
# looks like for n_full[1] range is 29-122 with gap 68-83 for total of 78 values
# n_full[0]: 37-114, missing 75-76 for total 76 values
# n_full[2]: 31-120, missing 68-83 for total 76 values
n = new_dataset.get_column('n',
master_independent_value_range=[
max_min_n, min_max_n.magnitude
])
# check to make sure the n values are close enough. If the Vg step is not fine enough and the device Vts are hihgly varied, the n values may not be close enough
# to extract TLM data at a specific n
max_n_varience = np.max(n[:, 1]) - np.min(n[:, 1])
assert max_n_varience < self.maximum_n_varience, 'Varience in carrier density between the devices is {0}, which is greater than {1}. As such,' \
'accurate TLM extraction is not possible. This could be the result of too small a gate' \
'voltage step and high varience between device threshold voltages. You can try to remove ' \
'device data with high varience, or lower the maximum_n_varience value in the' \
'TLMExtractor object.'.format(max_n_varience, self.maximum_n_varience)
n_r = np.round(np.array(n, dtype=float) * 1e-12)
r = new_dataset.get_column('r',
master_independent_value_range=[
max_min_n, min_max_n.magnitude
])
l = new_dataset.get_column('l',
master_independent_value_range=[
max_min_n, min_max_n.magnitude
])
n_units = '10<sup>12</sup> cm<sup>-2</sup>'
r_units = '\u03A9\u2022\u03BCm' # ;×μm'
l_units = '\u03BCm'
# create_scatter_plot(l[:, 0], r[:, 0], scale='lin', show=True, autoscale=True)
r_sheet, r_sheet_error, rc, rc_error = self.linear_regression(l, r)
# now add r_sheet and rc to the dataset
# new_dataset.add_column()
max_l = float(max(l[:, 0]))
r_plot = BasicPlot(x_label='length {0}'.format(l_units),
y_label='total resistance {0}'.format(r_units),
marker_size=8.0,
x_min=0.0,
x_max=max_l * 1.2)
for i in range(0, len(n[0]), round(len(n[0]) / 5)):
r_plot.add_data(x_data=l[:, i],
y_data=r[:, i],
mode='markers',
name='n = {0} {1}'.format(n_r[0][i], n_units),
text='n')
r_plot.add_line(x_data=[0.0, max_l],
y_data=[float(rc[i]),
float(r[-1, i])],
name=None)
r_plot.save_plot(name='r_at_vd_{0}'.format(vd))
rc_plot = BasicPlot(
x_label='carrier density {0}'.format(n_units),
y_label='contact resistance {0}'.format(r_units),
marker_size=8.0)
rc_plot.add_data(x_data=n[0] * 1e-12,
y_data=rc,
error_y={
'type': 'data',
'array': np.array(rc_error, dtype=float),
'visible': True
},
mode='markers',
name='n',
text='n')
rc_plot.save_plot(name='rc_at_vd_{0}'.format(vd))
rsheet_plot = BasicPlot(
x_label='carrier density {0}'.format(n_units),
y_label='sheet resistance',
marker_size=8.0)
rsheet_plot.add_data(x_data=n[0] * 1e-12,
y_data=r_sheet,
error_y={
'type': 'data',
'array': np.array(r_sheet_error,
dtype=float),
'visible': True
},
mode='markers',
name='n',
text='n')
rsheet_plot.save_plot(name='rsheet_at_vd_{0}'.format(vd))
"""
import unittest
from SemiPy.Extractors.TLM.TLMExtractor import TLMExtractor
from SemiPy.Devices.Devices.FET.ThinFilmFET import nTFT
from SemiPy.Devices.Materials.Oxides.MetalOxides import SiO2
from SemiPy.Devices.Materials.Semiconductors.BulkSemiconductors import Silicon
from SemiPy.Devices.Materials.TwoDMaterials.TMD import MoS2
from SemiPy.helper.paths import get_abs_semipy_path
from physics.value import Value, ureg
import numpy as np
idvd_path = get_abs_semipy_path(
'SampleData/TLMExampleData/WSe2_Sample_4_Id_Vd.txt') # unused
idvg_path = get_abs_semipy_path('SampleData/TLMExampleData')
widths = Value(4.0, ureg.micrometer)
lengths = Value.array_like(np.array([0.5, 1.0, 2.0, 2.5, 3.0, 3.5]),
unit=ureg.micrometer)
gate_oxide = SiO2(thickness=Value(30, ureg.nanometer))
channel = MoS2(layer_number=1)
result = TLMExtractor(widths=widths,
lengths=lengths,
gate_oxide=gate_oxide,
channel=channel,
FET_class=nTFT,
idvg_path=idvg_path,
vd_values=[1.0, 2.0],
substrate=Silicon())
result.save_tlm_plots()
# just give fundamental constants
from physics.value import ureg, Value
free_space_permittivity_F_div_m = Value(value=8.85e-12,
unit=ureg.farad / ureg.meter)
free_space_permittivity_F_div_cm = Value(value=8.85e-14,
unit=ureg.farad / ureg.centimeter)
electron_charge_C = Value(value=1.602176634e-19, unit=ureg.coulomb)
def model_output(self,
Vds,
Vgs,
heating=True,
vsat=True,
diffusion=True,
drift=True,
ambient_temperature=None,
iterations=2,
linestyle='-',
IdVd=True):
mobility_temp = Value(295, ureg.kelvin)
if ambient_temperature is None:
ambient_temperature = Value(295, ureg.kelvin)
# colors = ['C0', 'C2', 'C3']
assert isinstance(Vds, ModelInput)
assert isinstance(Vgs, ModelInput)
# first calculate an initial Id value assuming room temperature (at low Vds this is a good assumption)
# make sure the starting field is less than 0.25 V / um
# if Vds.range[0] == 0.0:
# Vds.range[0] = Vds.range[1]
# make sure the Vgs is above threshold
# assert Vgs.range[0] > self.FET.Vt_avg, 'The Vgs values should be above the average threshold voltage {0},' \
# ' your min is {1}'.format(self.FET.Vt_avg, Vgs.range[0])
# assert Vds.range[0] / self.FET.length <= Value(0.25, ureg.volt / ureg.micrometer),\
# 'Your starting field should be less than 0.25 V /um, yours is {0}'.format(Vds.range[0] / self.FET.length)
# create a holder for the data
if IdVd:
dataset = IdVdDataSet
master_independent = Vds
secondary_independent = Vgs
else:
dataset = IdVgDataSet
master_independent = Vgs
secondary_independent = Vds
id_data = {}
for i_vg in range(len(secondary_independent.range)):
id_data['id({0})'.format(i_vg)] = []
id_data['T({0})'.format(i_vg)] = []
id_data['vsat({0})'.format(i_vg)] = []
id_data['vgs({0})'.format(i_vg)] = []
id_data['n({0})'.format(i_vg)] = []
id_data['vds({0})'.format(i_vg)] = []
# now loop through the Vgs values
for i_vgs, vgs in enumerate(Vgs):
# first calculate an initial Id
prev_Id = Value(0.0, ureg.amp)
# prev_Id = self.compute_drift_current(Vds.range[0], self.FET.max_mobility, Vgs.range[0], prev_Id)
effective_mobility = self.FET.max_mobility
# now loop through each Vds value
for i_vds, vds in enumerate(Vds):
if IdVd:
i_master = i_vgs
else:
i_master = i_vds
# for i in range(iterations):
# vds = self.compute_vds_rc(vds, prev_Id)
power = self.compute_power(vds, vgs, effective_mobility,
prev_Id)
# If self heating is turned off, then just use the ambient tempeature
if not heating:
temperature = ambient_temperature
else:
temperature = self.compute_temperature(
power, ambient_temperature)
# compute the new mobility at this temperature
effective_mobility = self.compute_mobility_temperature(
self.FET.max_mobility, mobility_temp, temperature)
# now compute the mobility at this field
if vsat:
effective_mobility, vsat = self.compute_mobility_velocity_saturation(
effective_mobility, vds, temperature)
id_data['vsat({0})'.format(i_master)].append(vsat)
# now calculate the new current
new_Id = Value(0.0, ureg.amp)
if drift and vgs > self.FET.Vt_avg:
new_Id += self.compute_drift_current(
vds, effective_mobility, vgs, prev_Id).base_units()
if diffusion:
new_Id += self.compute_diffusion_current(
temperature, vgs, vds)
# idvd_data['Vg = {0}'.format(vgs)].append([])
id_data['id({0})'.format(i_master)].append(new_Id /
self.FET.width)
prev_Id = new_Id
id_data['T({0})'.format(i_master)].append(temperature)
id_data['n({0})'.format(i_master)].append(
self.FET.vg_to_n(vgs))
id_data['vgs({0})'.format(i_master)].append(vgs)
id_data['vds({0})'.format(i_master)].append(vds)
return dataset(data_path=id_data)
class Stanford2DSModel(BaseModel):
"""
Compact model for modeling traps, parasitic capacitances, velocity saturation, self-heating, and field effects of 2D FETs. The
reference paper is <citation>, which gives full physical details on the model.
"""
# Rtbr = Value(1e-7, ureg.meters**2*ureg.kelvin/(ureg.watt))
# ksub = Value(150, ureg.watt/(ureg.kelvin*ureg.meter))
eta = 5
hwop = Value(35e-3, ureg.eV)
k = Value(
scipy.constants.physical_constants["Boltzmann constant in eV/K"][0],
ureg.eV / ureg.kelvin)
k_J = Value(scipy.constants.physical_constants["Boltzmann constant"][0],
ureg.J / ureg.kelvin)
hcross = Value(
scipy.constants.physical_constants["reduced Planck constant"][0],
ureg.J * ureg.seconds)
# Constants for Quantum Capacitance Calculation that need to be defined
WFTG = Value(4.3, ureg.volt) # Top Gate Work Function [V]
WFBG = Value(4.3, ureg.volt) # Bottom Gate Work Function [V]
VFBT = Value(0.305, ureg.volt) # Top Gate Cutoff voltage[V]
VFBB = Value(0.305, ureg.volt) # Bottom Gate Cutoff voltage[V]
# WFTG = 4.3
# WFBG = 4.3
# VFBT = 0.305
# VFBB =0.305
def __init__(self, FET, *args, **kwargs):
super(Stanford2DSModel, self).__init__(*args, **kwargs)
assert isinstance(
FET, TFT
), 'The Stanford 2DS Model only works with Thin Film transistors. Yours is {0}'.format(
type(FET))
self.FET = FET
# get the gate_oxide-channel interface
self.gate_oxide_channel_interface = import_interface(
self.FET.gate_oxide, self.FET.channel)
self.Rtbr = 1 / self.gate_oxide_channel_interface.thermal_boundary_conductance
self.thermal_conductance = self.compute_device_thermal_conductance()
self.thermal_healing_length = self.compute_thermal_healing_length()
self.vO = self.compute_v0()
def compute_metal_thermal_resistance(self):
#using 1 for now to account for the contact resistance
km = Value(1, ureg.watt / (ureg.meter * ureg.kelvin))
tm = Value(50, ureg.nanometer)
Lhm = (tm * self.FET.gate_oxide.thickness * km /
self.FET.gate_oxide.thermal_conductivity)**.5
return Lhm / (km * tm * (self.FET.width.base_units() + 2 * Lhm))
def compute_thermal_healing_length(self):
lh = (self.FET.channel.thermal_conductivity *
self.FET.channel.thickness *
(self.FET.width / self.thermal_conductance + self.Rtbr))**0.5
lh_compact = lh.compact_units()
return lh.compact_units()
# return Value(100, ureg.nanometers)
def compute_power(self, Vds, Vgs, mobility, Id):
Vds = self.compute_vds_rc(Vds, Vgs, mobility)
return Id * Vds
def compute_device_thermal_conductance(self):
weff = self.FET.width + 2 * self.FET.gate_oxide.thickness
# computing the inverse of the thermal conductance
inv_g_1 = self.Rtbr / self.FET.width.base_units()
inv_g_2 = ((pi * self.FET.gate_oxide.thermal_conductivity) /
log(6 * (self.FET.gate_oxide.thickness.base_units() /
self.FET.width.base_units() + 1)) +
self.FET.gate_oxide.thermal_conductivity *
self.FET.width.base_units() /
self.FET.gate_oxide.thickness.base_units())**-1
inv_g_3 = (1 / (self.FET.substrate.thermal_conductivity * 2) *
(self.FET.length / weff)**0.5)
g = (inv_g_1 + inv_g_2 + inv_g_3)**(-1)
return g
def compute_vds_rc(self, Vds, Vgs, mobility):
if self.FET.Rc is not None:
# Vds = Vds - 2 * previous_Id * self.FET.Rc / self.FET.width
rch = self.compute_channel_resistance(self.FET.vg_to_n(Vgs),
mobility)
Vds = Vds * rch / (rch + 2 * self.FET.Rc)
return Vds
def compute_channel_resistance(self, n, mobility):
rsh = compute_sheet_resistance(n, mobility)
rch = rsh * self.FET.length
return rch
def compute_drift_current(self, Vds, mobility, Vgs, previous_Id):
# Vds = self.compute_vds_rc(Vds, previous_Id)
n = self.FET.vg_to_n(Vgs)
rch = self.compute_channel_resistance(n, mobility)
Vds = Vds * rch / (rch + 2 * self.FET.Rc)
return electron_charge_C * n * mobility * (
Vds / self.FET.length) * self.FET.width
def compute_mobility_temperature(self, ambient_mobility,
ambient_temperature, temperature):
return ambient_mobility * (temperature / ambient_temperature)**(
self.FET.mobility_temperature_exponent * -1)
def compute_v0(self):
Nop = self.compute_nop(Value(295, ureg.kelvin))
# Nop = 1 / (math.exp(self.hwop / (self.k * Value(295, ureg.kelvin))))
return self.FET.channel.saturation_velocity * (Nop + 1)
def compute_nop(self, temp):
return 1 / (math.exp(self.hwop / (self.k * temp)) - 1)
def compute_saturation_velocity(self, Temp):
Nop = self.compute_nop(Temp)
return self.vO / (Nop + 1)
def compute_mobility_velocity_saturation(self, effective_mobility, Vds,
Temp):
#return effective_mobility
field = Vds / self.FET.length.adjust_unit(ureg.centimeter)
vsat = self.compute_saturation_velocity(Temp)
#return effective_mobility / (1 + (effective_mobility * field / self.FET.channel.saturation_velocity)**self.eta)**(1/self.eta)
return effective_mobility / (1 + (effective_mobility * field / vsat)**
self.eta)**(1 / self.eta), vsat
def compute_temperature(self,
power,
ambient_temperature,
metal_thermal_resistance=None):
if metal_thermal_resistance is None:
#metal_thermal_resistance = Value(0.0, unit=ureg.kelvin / ureg.watt)
metal_thermal_resistance = self.compute_metal_thermal_resistance()
x = tanh(self.FET.length.base_units() /
(2 * self.thermal_healing_length.base_units()))
t_part = self.thermal_conductance * self.thermal_healing_length.base_units(
) * metal_thermal_resistance * x
t_1 = (1 + t_part - 2 * x * self.thermal_healing_length.base_units() /
self.FET.length.base_units()) / (1 + t_part)
average_temperature = ambient_temperature + power * (
1 /
(self.thermal_conductance * self.FET.length.base_units())) * t_1
return average_temperature
def compute_quantum_cap(self, ambient_temperature, Vgs):
T = ambient_temperature
# Material Parameters
self.g = 2 # Spin Degenracy
self.gv1 = 1 # Degenracy of first valley
self.gv2 = 1 # Degeneracy of second valley
self.me1_eff = Value(0.45 * scipy.constants.electron_mass,
ureg.kilograms) # Effective mass of first valley
self.me2_eff = Value(0.45 * scipy.constants.electron_mass,
ureg.kilograms) # Effective mass of second valley
self.vth = self.k_J * T / electron_charge_C
self.delEC = 3 * self.vth # Energy difference from the first valley(Set high to ignore this valley in charge calculations)
self.epsilon_channel = self.FET.channel.relative_permittivity * free_space_permittivity_F_div_cm
self.d = self.FET.channel.thickness.base_units() # channel thickness
self.epsilon_ox = self.FET.gate_oxide.relative_permittivity * free_space_permittivity_F_div_cm
self.EOT = self.FET.gate_oxide.thickness
# self.epsilon_ox_b =
# self.EOTB =
self.cox_t = (self.epsilon_ox / self.EOT).adjust_unit(
ureg.coulombs / (ureg.volts * ureg.meter**2))
self.cox_b = (self.epsilon_ox / Value(1e10, ureg.meter)).adjust_unit(
ureg.coulombs / (ureg.volts * ureg.meter**2))
# Calculate electrostatic screening lengths
self.lambdaT = (self.epsilon_channel * self.d / self.cox_t)**(1 / 2)
self.lambdaB = (self.epsilon_channel * self.d / self.cox_b)**(1 / 2)
self.A = (self.lambdaT**(-2) + self.lambdaB**(-2))**(1 / 2)
# Calculate Effective density of states for each valley
self.NDOS1 = (self.gv1 * self.me1_eff * self.k_J *
T) / (pi * self.hcross**2)
self.NDOS2 = (self.gv2 * self.me2_eff * self.k_J *
T) / (pi * self.hcross**2)
self.NDOS = self.NDOS2
self.alpha = self.NDOS1 / self.NDOS
self.beta = self.NDOS2 / self.NDOS
self.Nimp = Value(3.5e11, ureg.meters**-2)
VDS = Value(0.0, ureg.volts)
VS = Value(0.0, ureg.volts)
VD = VS + VDS
VG = [Vgs, Vgs + .01]
xg_length = len(VG)
array_size = 10000
self.phi = np.zeros(array_size)
self.f = np.zeros(array_size)
self.fd = np.zeros(array_size)
self.phis = np.zeros(array_size)
self.n2d = np.zeros(len(VG))
Es = np.zeros(len(VG))
Eox = np.zeros(len(VG))
self.Cg = np.zeros(len(VG))
self.Cq = np.zeros(len(VG))
for j in range(xg_length):
# VBG = Value(VG[j], ureg.volts)
VBG = VG[j]
# VBG = VBG
B = ((VBG - self.VFBT) / (self.lambdaT**2)) + ((VBG - self.VFBB) /
(self.lambdaB**2))
i = 1
self.phi[i] = VBG
self.p = Value(self.phi[i], ureg.volts)
self.f[i] = (1 + math.exp(
(self.p - VS) / self.vth))**self.alpha * (1 + math.exp(
(self.p - VS) / self.vth) * math.exp(
-self.delEC / self.vth))**self.beta - math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B -
(self.A**2) * self.p) + (self.Nimp / self.NDOS))
self.fd[i] = (1 + math.exp(
(self.p - VS) / self.vth))**self.alpha * (1 + math.exp(
(self.p - VS) / self.vth
) * math.exp(-self.delEC / self.vth))**self.beta * (
((self.beta * math.exp((self.p - VS) / self.vth) *
math.exp(-self.delEC / self.vth)) /
(self.vth *
(1 + math.exp((self.p - VS) / self.vth) *
math.exp(-self.delEC / self.vth)))) +
((self.alpha * math.exp(
(self.p - VS) / self.vth)) / (self.vth * (1 + math.exp(
(self.p - VS) / self.vth))))) + (
(self.A**2) *
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS))) * math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B - (self.A**2) * self.p) +
(self.Nimp / self.NDOS))
iter = 0
while abs(self.f[i]) > 1e-06: # termination condition
iter = iter + 1
self.phi[i + 1] = (self.phi[i] - (self.f[i]) / (self.fd[i]))
p_1 = Value(self.phi[i + 1], ureg.volts)
self.f[i + 1] = (1 + math.exp(
(p_1 - VS) / self.vth))**self.alpha * (1 + math.exp(
(p_1 - VS) / self.vth) * math.exp(
-self.delEC / self.vth))**self.beta - math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B -
(self.A**2) * p_1) + (self.Nimp / self.NDOS))
self.fd[i + 1] = (1 + math.exp(
(p_1 - VS) / self.vth))**self.alpha * (1 + math.exp(
(p_1 - VS) / self.vth
) * math.exp(-self.delEC / self.vth))**self.beta * (
((self.beta * math.exp((p_1 - VS) / self.vth) *
math.exp(-self.delEC / self.vth)) /
(self.vth *
(1 + math.exp((p_1 - VS) / self.vth) *
math.exp(-self.delEC / self.vth)))) +
((self.alpha * math.exp((p_1 - VS) / self.vth)) /
(self.vth * (1 + math.exp(
(p_1 - VS) / self.vth))))) + (
(self.A**2) *
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS))) * math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B - (self.A**2) * p_1) +
(self.Nimp / self.NDOS))
i = i + 1
self.phis[j] = self.phi[i]
self.ph = Value(self.phis[j], ureg.volts)
# Charge density in the 2D layer(m ^ -2)
self.n2d[j] = (self.epsilon_channel * self.d / electron_charge_C
) * (B - (self.A**2) * self.ph) + self.Nimp
# Electic field at the surface (V/m)
Es[j] = electron_charge_C * self.n2d[j] / self.epsilon_channel
# Electric field in the oxide
Eox[j] = (self.epsilon_ox / self.epsilon_channel) * (
(VG[j] - self.VFBT - self.phis[j]) / self.EOT)
self.n2d = np.trim_zeros(self.n2d, 'b')
self.phis = np.trim_zeros(self.phis, 'b')
# Capacitance Calculation
Cg = Value(
np.diff(electron_charge_C * self.n2d * 1e-4) / np.diff(VG)[0],
ureg.coulomb / ureg.meter**2 / ureg.volt)
CQ = Value(
np.diff(electron_charge_C * self.n2d * 1e-4) /
np.diff(self.phis)[0], ureg.coulomb / ureg.meter**2 / ureg.volt)
#print("Vgs is ", VG)
print("CQ is ", CQ.adjust_unit(ureg.microfarad / (ureg.centimeter**2)))
return CQ
def compute_diffusion_current(self, ambient_temp, vgs, vd):
# Capacitance Values
c_Q = self.compute_quantum_cap(ambient_temp, vgs)
# self.c_Q = Value(0, ureg.meter ** -2 * ureg.coulomb / ureg.volt)
c_i = self.cox_t
# c_it = electron_charge_C * Value(1e16, ureg.meter ** -2 / ureg.volt)
c_it = Value(0, ureg.meter**-2 * ureg.coulomb / ureg.volt)
cap_r = 1 + (c_Q + c_it) / c_i
#Mobility
mobility_temp = Value(295, ureg.kelvin)
T = ambient_temp
mobility = self.compute_mobility_temperature(
self.FET.max_mobility, mobility_temp,
T).adjust_unit(ureg.meter**2 / ureg.second / ureg.volt)
#Compute Diffusion Current
# i_diff = (mobility * (self.c_Q + self.c_it) * (self.FET.width / self.FET.length) * (self.vth ** 2) * (1-math.exp(-vd/self.vth)) * math.exp((vgs-self.FET.Vt_avg)/(self.vth * self.cap_r))).adjust_unit(ureg.ampere)
I_diff_term_1 = math.log(
math.exp((vgs - self.FET.Vt_avg) / (self.vth * cap_r)) + 1)
I_diff_term_2 = math.log(
math.exp((vgs - self.FET.Vt_avg - vd) / (self.vth * cap_r)) + 1)
i_diff = (self.vth * electron_charge_C * mobility *
(self.FET.width * self.NDOS / self.FET.length) *
(I_diff_term_1 - I_diff_term_2)).base_units()
print("Diffusion Current is {0} at Vg = {1}".format(i_diff, vgs))
return i_diff
def plot_diffusion_current(self, ambient_temp, vgs_array, vd_array):
idiff_vgs_dict = {"vgs": vgs_array}
length = len(vgs_array)
for d in vd_array:
i_diff = []
cq = []
for i in range(length):
i_diff.append(
self.compute_diffusion_current(ambient_temp, vgs_array[i],
d))
cq.append(self.Cq)
idiff_vgs_dict["vds = " + str(d)] = np.array(i_diff)
idiff_vgs_dict["cq = " + str(d)] = np.array(cq)
plt.plot(vgs_array, idiff_vgs_dict["vds = " + str(vd_array[0])])
plt.yscale('log')
plt.show()
# plt.plot(vgs_array, idiff_vgs_dict["cq = " + str(vd_array[1])])
# plt.yscale('log')
# plt.show()
def model_output(self,
Vds,
Vgs,
heating=True,
vsat=True,
diffusion=True,
drift=True,
ambient_temperature=None,
iterations=2,
linestyle='-',
IdVd=True):
mobility_temp = Value(295, ureg.kelvin)
if ambient_temperature is None:
ambient_temperature = Value(295, ureg.kelvin)
# colors = ['C0', 'C2', 'C3']
assert isinstance(Vds, ModelInput)
assert isinstance(Vgs, ModelInput)
# first calculate an initial Id value assuming room temperature (at low Vds this is a good assumption)
# make sure the starting field is less than 0.25 V / um
# if Vds.range[0] == 0.0:
# Vds.range[0] = Vds.range[1]
# make sure the Vgs is above threshold
# assert Vgs.range[0] > self.FET.Vt_avg, 'The Vgs values should be above the average threshold voltage {0},' \
# ' your min is {1}'.format(self.FET.Vt_avg, Vgs.range[0])
# assert Vds.range[0] / self.FET.length <= Value(0.25, ureg.volt / ureg.micrometer),\
# 'Your starting field should be less than 0.25 V /um, yours is {0}'.format(Vds.range[0] / self.FET.length)
# create a holder for the data
if IdVd:
dataset = IdVdDataSet
master_independent = Vds
secondary_independent = Vgs
else:
dataset = IdVgDataSet
master_independent = Vgs
secondary_independent = Vds
id_data = {}
for i_vg in range(len(secondary_independent.range)):
id_data['id({0})'.format(i_vg)] = []
id_data['T({0})'.format(i_vg)] = []
id_data['vsat({0})'.format(i_vg)] = []
id_data['vgs({0})'.format(i_vg)] = []
id_data['n({0})'.format(i_vg)] = []
id_data['vds({0})'.format(i_vg)] = []
# now loop through the Vgs values
for i_vgs, vgs in enumerate(Vgs):
# first calculate an initial Id
prev_Id = Value(0.0, ureg.amp)
# prev_Id = self.compute_drift_current(Vds.range[0], self.FET.max_mobility, Vgs.range[0], prev_Id)
effective_mobility = self.FET.max_mobility
# now loop through each Vds value
for i_vds, vds in enumerate(Vds):
if IdVd:
i_master = i_vgs
else:
i_master = i_vds
# for i in range(iterations):
# vds = self.compute_vds_rc(vds, prev_Id)
power = self.compute_power(vds, vgs, effective_mobility,
prev_Id)
# If self heating is turned off, then just use the ambient tempeature
if not heating:
temperature = ambient_temperature
else:
temperature = self.compute_temperature(
power, ambient_temperature)
# compute the new mobility at this temperature
effective_mobility = self.compute_mobility_temperature(
self.FET.max_mobility, mobility_temp, temperature)
# now compute the mobility at this field
if vsat:
effective_mobility, vsat = self.compute_mobility_velocity_saturation(
effective_mobility, vds, temperature)
id_data['vsat({0})'.format(i_master)].append(vsat)
# now calculate the new current
new_Id = Value(0.0, ureg.amp)
if drift and vgs > self.FET.Vt_avg:
new_Id += self.compute_drift_current(
vds, effective_mobility, vgs, prev_Id).base_units()
if diffusion:
new_Id += self.compute_diffusion_current(
temperature, vgs, vds)
# idvd_data['Vg = {0}'.format(vgs)].append([])
id_data['id({0})'.format(i_master)].append(new_Id /
self.FET.width)
prev_Id = new_Id
id_data['T({0})'.format(i_master)].append(temperature)
id_data['n({0})'.format(i_master)].append(
self.FET.vg_to_n(vgs))
id_data['vgs({0})'.format(i_master)].append(vgs)
id_data['vds({0})'.format(i_master)].append(vds)
return dataset(data_path=id_data)
def test_stanford2dsmodel(self):
gate_oxide = SiO2(thickness=Value(30.0, ureg.nanometer))
channel = MoS2(layer_number=1, thickness=Value(0.6, ureg.nanometer))
# set the channel vsat to 7e6 cm/s
channel.saturation_velocity.set(
Value(3e6, ureg.centimeter / ureg.seconds),
input_values={'temperature': Value(300, ureg.kelvin)})
substrate = Silicon()
fet = TFT(channel=channel,
gate_oxide=gate_oxide,
length=Value(400, ureg.nanometer),
width=Value(2000, ureg.nanometer),
substrate=substrate)
fet.Vt_avg.set(Value(-10.0, ureg.volt))
fet.Rc.set(Value(2000.0, ureg.ohm * ureg.micrometer),
input_values={'n': Value(1e13, ureg.centimeter**-2)})
fet.max_mobility.set(Value(
30, ureg.centimeter**2 / (ureg.volt * ureg.second)),
input_values={
'Vd': Value(1, ureg.volt),
'Vg': Value(1, ureg.volt)
})
fet.mobility_temperature_exponent.set(Value(1.15, ureg.dimensionless))
S2DModel = Stanford2DSModel(FET=fet)
Vds = ModelInput(0.0, 10.0, num=5, unit=ureg.volt)
Vgs = ModelInput(-12.0, 30.0, num=40, unit=ureg.volt)
ambient_temperature = Value(300, ureg.kelvin)
# plot = IdVdPlot('IdVg')
# fig = plt.figure(dpi=160)
# ax = fig.gca()
# I_units = '\u03BCA/\u03BCm'
# colors = ['C0', 'C2', 'C3', 'C4', 'C5', 'C6']
# linestyle = '-'
# plt.rc('xtick', labelsize=12) # fontsize of the tick labels
# plt.rc('ytick', labelsize=12)
# ax.axes.get_xaxis().set_ticks([])
# ax.axes.get_yaxis().set_ticks([])
# now compute the model output with self-heating
idvd_data = S2DModel.model_output(
Vds,
Vgs,
heating=True,
vsat=True,
diffusion=False,
drift=True,
ambient_temperature=ambient_temperature,
IdVd=False)
idvd_plot = IdVgPlot(name='IdVd', dpi=160)
idvd_plot.add_idvg_dataset(idvd_data)
idvd_plot.show_plot()
def compute_quantum_cap(self, ambient_temperature, Vgs):
T = ambient_temperature
# Material Parameters
self.g = 2 # Spin Degenracy
self.gv1 = 1 # Degenracy of first valley
self.gv2 = 1 # Degeneracy of second valley
self.me1_eff = Value(0.45 * scipy.constants.electron_mass,
ureg.kilograms) # Effective mass of first valley
self.me2_eff = Value(0.45 * scipy.constants.electron_mass,
ureg.kilograms) # Effective mass of second valley
self.vth = self.k_J * T / electron_charge_C
self.delEC = 3 * self.vth # Energy difference from the first valley(Set high to ignore this valley in charge calculations)
self.epsilon_channel = self.FET.channel.relative_permittivity * free_space_permittivity_F_div_cm
self.d = self.FET.channel.thickness.base_units() # channel thickness
self.epsilon_ox = self.FET.gate_oxide.relative_permittivity * free_space_permittivity_F_div_cm
self.EOT = self.FET.gate_oxide.thickness
# self.epsilon_ox_b =
# self.EOTB =
self.cox_t = (self.epsilon_ox / self.EOT).adjust_unit(
ureg.coulombs / (ureg.volts * ureg.meter**2))
self.cox_b = (self.epsilon_ox / Value(1e10, ureg.meter)).adjust_unit(
ureg.coulombs / (ureg.volts * ureg.meter**2))
# Calculate electrostatic screening lengths
self.lambdaT = (self.epsilon_channel * self.d / self.cox_t)**(1 / 2)
self.lambdaB = (self.epsilon_channel * self.d / self.cox_b)**(1 / 2)
self.A = (self.lambdaT**(-2) + self.lambdaB**(-2))**(1 / 2)
# Calculate Effective density of states for each valley
self.NDOS1 = (self.gv1 * self.me1_eff * self.k_J *
T) / (pi * self.hcross**2)
self.NDOS2 = (self.gv2 * self.me2_eff * self.k_J *
T) / (pi * self.hcross**2)
self.NDOS = self.NDOS2
self.alpha = self.NDOS1 / self.NDOS
self.beta = self.NDOS2 / self.NDOS
self.Nimp = Value(3.5e11, ureg.meters**-2)
VDS = Value(0.0, ureg.volts)
VS = Value(0.0, ureg.volts)
VD = VS + VDS
VG = [Vgs, Vgs + .01]
xg_length = len(VG)
array_size = 10000
self.phi = np.zeros(array_size)
self.f = np.zeros(array_size)
self.fd = np.zeros(array_size)
self.phis = np.zeros(array_size)
self.n2d = np.zeros(len(VG))
Es = np.zeros(len(VG))
Eox = np.zeros(len(VG))
self.Cg = np.zeros(len(VG))
self.Cq = np.zeros(len(VG))
for j in range(xg_length):
# VBG = Value(VG[j], ureg.volts)
VBG = VG[j]
# VBG = VBG
B = ((VBG - self.VFBT) / (self.lambdaT**2)) + ((VBG - self.VFBB) /
(self.lambdaB**2))
i = 1
self.phi[i] = VBG
self.p = Value(self.phi[i], ureg.volts)
self.f[i] = (1 + math.exp(
(self.p - VS) / self.vth))**self.alpha * (1 + math.exp(
(self.p - VS) / self.vth) * math.exp(
-self.delEC / self.vth))**self.beta - math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B -
(self.A**2) * self.p) + (self.Nimp / self.NDOS))
self.fd[i] = (1 + math.exp(
(self.p - VS) / self.vth))**self.alpha * (1 + math.exp(
(self.p - VS) / self.vth
) * math.exp(-self.delEC / self.vth))**self.beta * (
((self.beta * math.exp((self.p - VS) / self.vth) *
math.exp(-self.delEC / self.vth)) /
(self.vth *
(1 + math.exp((self.p - VS) / self.vth) *
math.exp(-self.delEC / self.vth)))) +
((self.alpha * math.exp(
(self.p - VS) / self.vth)) / (self.vth * (1 + math.exp(
(self.p - VS) / self.vth))))) + (
(self.A**2) *
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS))) * math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B - (self.A**2) * self.p) +
(self.Nimp / self.NDOS))
iter = 0
while abs(self.f[i]) > 1e-06: # termination condition
iter = iter + 1
self.phi[i + 1] = (self.phi[i] - (self.f[i]) / (self.fd[i]))
p_1 = Value(self.phi[i + 1], ureg.volts)
self.f[i + 1] = (1 + math.exp(
(p_1 - VS) / self.vth))**self.alpha * (1 + math.exp(
(p_1 - VS) / self.vth) * math.exp(
-self.delEC / self.vth))**self.beta - math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B -
(self.A**2) * p_1) + (self.Nimp / self.NDOS))
self.fd[i + 1] = (1 + math.exp(
(p_1 - VS) / self.vth))**self.alpha * (1 + math.exp(
(p_1 - VS) / self.vth
) * math.exp(-self.delEC / self.vth))**self.beta * (
((self.beta * math.exp((p_1 - VS) / self.vth) *
math.exp(-self.delEC / self.vth)) /
(self.vth *
(1 + math.exp((p_1 - VS) / self.vth) *
math.exp(-self.delEC / self.vth)))) +
((self.alpha * math.exp((p_1 - VS) / self.vth)) /
(self.vth * (1 + math.exp(
(p_1 - VS) / self.vth))))) + (
(self.A**2) *
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS))) * math.exp(
(self.epsilon_channel * self.d /
(electron_charge_C * self.NDOS)) *
(B - (self.A**2) * p_1) +
(self.Nimp / self.NDOS))
i = i + 1
self.phis[j] = self.phi[i]
self.ph = Value(self.phis[j], ureg.volts)
# Charge density in the 2D layer(m ^ -2)
self.n2d[j] = (self.epsilon_channel * self.d / electron_charge_C
) * (B - (self.A**2) * self.ph) + self.Nimp
# Electic field at the surface (V/m)
Es[j] = electron_charge_C * self.n2d[j] / self.epsilon_channel
# Electric field in the oxide
Eox[j] = (self.epsilon_ox / self.epsilon_channel) * (
(VG[j] - self.VFBT - self.phis[j]) / self.EOT)
self.n2d = np.trim_zeros(self.n2d, 'b')
self.phis = np.trim_zeros(self.phis, 'b')
# Capacitance Calculation
Cg = Value(
np.diff(electron_charge_C * self.n2d * 1e-4) / np.diff(VG)[0],
ureg.coulomb / ureg.meter**2 / ureg.volt)
CQ = Value(
np.diff(electron_charge_C * self.n2d * 1e-4) /
np.diff(self.phis)[0], ureg.coulomb / ureg.meter**2 / ureg.volt)
#print("Vgs is ", VG)
print("CQ is ", CQ.adjust_unit(ureg.microfarad / (ureg.centimeter**2)))
return CQ