# import external modules import numpy as np import matplotlib.pyplot as plt plt.rcParams['font.size'] = 18 import scipy.signal as signal import os # import Comphy modules from ComphyV3.CoreV3.MOS_1D import MOS_1D from ComphyV3.CoreV3.Physics import BandGapModel_Tdep1 from ComphyV3.CoreV3.Physics import CarrierModel_Electrons_1 from ComphyV3.CoreV3.Physics import CarrierModel_Holes_1 from ComphyV3.CoreV3.Channel import Channel from ComphyV3.CoreV3.InsulatingLayer import InsulatingLayer from ComphyV3.CoreV3.Metal import Metal from ComphyV3.CoreV3.TrapBand import TrapBand_2S_NMP from ComphyV3.CoreV3.TrapBand import GeneratedInterfaceTraps from ComphyV3.CoreV3.GridSampler import GaussianGridSampler from ComphyV3.CoreV3.GridSampler import InterfaceGridSampler from ComphyV3.Utils.Plotter import plot_band_diagram, plot_potential_profile, plot_electric_field, plot_surface_potential # create new output directory output_dir = './Results/' os.makedirs(output_dir, exist_ok=True) ######################################################################################################################## # Basic Usage Part1: Create your own device ######################################################################################################################## Temperature = 300.0 my_device = MOS_1D( Tinit=Temperature, # initial temperature in K ) ###################################################################### # Step 2: Add semiconductor channel: bandgap_model = BandGapModel_Tdep1( Eg0=1.206, # band gap parameter in eV Eg1=-2.73E-4, # band gap parameter in eV/K ) e_model = CarrierModel_Electrons_1( Ncv0=2.541E25, # effective density of states of conduction band Mc=6, # equivalent minima of conduction band mt0=0.1905, # transversal effective mass ml=0.9163, # longitudinal effective mass bgmodel=bandgap_model, # bandgap model ) h_model = CarrierModel_Holes_1( Ncv0=2.54E25, # effective density of states of valence band mEff_a=0.4435870, # effective mass parameter mEff_b=0.3609528e-2, # effective mass parameter in K⁻¹ mEff_c=0.1173515e-3, # effective mass parameter in K⁻² mEff_d=0.1263218e-5, # effective mass parameter in K⁻³ mEff_e=0.3025581e-8, # effective mass parameter in K⁻⁴ mEff_f=0.4683382e-2, # effective mass parameter in K⁻¹ mEff_g=0.2286895e-3, # effective mass parameter in K⁻² mEff_h=0.7469271e-6, # effective mass parameter in K⁻⁶ mEff_i=0.1727481e-8, # effective mass parameter in K⁻⁸ ) Si = Channel( Nd=1.4E23, # donor concentration in m⁻³ Na=1.0E16, # acceptor concentration mass in m⁻³ name='Si', # material name Eg=bandgap_model, # band gap model of channel m_neff=e_model, # electron effective mass (or carrier model) m_peff=h_model, # hole effective mass (or carrier model) Xsi=4.05, # electron affinity in eV kval=11.68, # relative permittivity ccs_e=2.0E-23, # capture cross section for electrons in m⁻² ccs_h=2.0E-23, # capture cross section for holes in m⁻² ) my_device.channel = Si ###################################################################### # Step 3: Add oxide layers: SiO2 = InsulatingLayer( thickness=1.0E-9, # thickness of layer in m kval=3.9, # relative permittivity Eg=9.0, # band gap in eV (or bandgap model) Xsi=0.82, # electron affinity in eV material_name='SiO2', # name of layer-material mt=0.35, # relative tunneling mass ) my_device.insulating_layers.append(SiO2) HfO2 = InsulatingLayer( thickness=2.0E-9, # thickness of layer in m kval=20.0, # relative permittivity Eg=5.8, # band gap in eV (or bandgap model) Xsi=1.972, # electron affinity in eV material_name='HfO2', # name of layer-material mt=0.17, # relative tunneling mass ) my_device.insulating_layers.append(HfO2) ###################################################################### # Step 4: Add gate: WF = 4.05 + 0.56 + 0.1 gate = Metal( workfunction=WF, # work function in eV name='metal', # name of gate-material ccs=2.0E-23, # capture cross section for electrons in m⁻² ) my_device.gate = gate ###################################################################### # Step 5: Print basic device properties: # print basic device properties print("Vfb0 = {:.3f} V".format(my_device.get_Vfb0(T=Temperature))) print("Vth0 = {:.3f} V".format(my_device.get_Vth0(T=Temperature))) print("EOT = {:.3f} nm".format(my_device.EOT * 1.0E9)) print("Nd = {:.3e} cm⁻³".format(my_device.channel.Nd * 1.0E-6)) print("Na = {:.3e} cm⁻³".format(my_device.channel.Nd * 1.0E-6)) print("Ef = {:.3f} eV".format(my_device.channel.get_Fermilevel(T=Temperature))) for i, layer in enumerate(my_device.insulating_layers): print("layer {}:".format(i), layer) ###################################################################### # Step 5: Plot flatband diagram: # initialize devices my_device.initialize(Vg=0.521, T=Temperature) # plot band diagram plot_band_diagram(my_device, file=output_dir + "flat_band_diagram.png") ######################################################################################################################## # Basic Usage Part2: Adding charge traps to your device ######################################################################################################################## ###################################################################### # Step 1: Modeling the recoverable BTI component grid_sampler = GaussianGridSampler( dx=1.0E-10, # grid spacing for sampling xt in m dEt=0.05, # grid spacing for sampling of Et in eV dEr=0.1, # grid spacing for sampling of S in eV non_coverage=1.0E-4, # sets boundary of gaussian grid ) SiO2_shallow_trap_band = TrapBand_2S_NMP( x_start=0.0, # lower bound of spatial defect distribution in m x_end=SiO2.thickness, # upper bound of spatial defect distribution in m Et=-3.48, # mean energy level in eV Et_sigma=0.15, # standard dev. of energy level in eV Er=3.82, # mean relaxation energy in eV Er_sigma=1.36, # standard dev. of relaxation energy in eV R=0.407, # curvature ratio Nt=1.5e25, # defect concentration in m⁻³ trap_type='acceptor', # trap type sampler=grid_sampler, # a appropriate grid sampler device=my_device, # the device to which you want to add the traps ) my_device.trap_bands['SiO2_shallow_trap_band'] = SiO2_shallow_trap_band SiO2_deep_trap_band = TrapBand_2S_NMP( x_start=0.0, # lower bound of spatial defect distribution in m x_end=SiO2.thickness, # upper bound of spatial defect distribution in m Et=-5.65, # mean energy level in eV Et_sigma=0.20515, # standard dev. of energy level in eV Er=9.3438, # mean relaxation energy in eV Er_sigma=2.5526, # standard dev. of relaxation energy in eV R=1.809, # curvature ratio Nt=4.449E26, # defect concentration in m⁻³ trap_type='donor', # trap type sampler=grid_sampler, # a appropriate grid sampler device=my_device, # the device to which you want to add the traps ) my_device.trap_bands['SiO2_deep_trap_band'] = SiO2_deep_trap_band HfO2_shallow_trap_band = TrapBand_2S_NMP( x_start=1.0E-9, # lower bound of spatial defect distribution in m x_end=3.0E-9, # upper bound of spatial defect distribution in m Et=-3.18, # mean energy level in eV Et_sigma=0.25455, # standard dev. of energy level in eV Er=0.8684, # mean relaxation energy in eV Er_sigma=0.4045, # standard dev. of relaxation energy in eV R=0.0018121, # curvature ratio Nt=9.0534E25, # defect concentration in m⁻³ trap_type='acceptor', # trap type sampler=grid_sampler, # a appropriate grid sampler device=my_device, # the device to which you want to add the traps ) my_device.trap_bands['HfO2_shallow_trap_band'] = HfO2_shallow_trap_band HfO2_deep_trap_band = TrapBand_2S_NMP( x_start=1.0E-9, # lower bound of spatial defect distribution in m x_end=3.0E-9, # upper bound of spatial defect distribution in m Et=-5.232, # mean energy level in eV Et_sigma=0.23203, # standard dev. of energy level in eV Er=9.2285, # mean relaxation energy in eV Er_sigma=1.4948, # standard dev. of relaxation energy in eV R=1.5287, # curvature ratio Nt=4.1597E26, # defect concentration in m⁻³ trap_type='donor', # trap type sampler=grid_sampler, # a appropriate grid sampler device=my_device, # the device to which you want to add the traps ) my_device.trap_bands['HfO2_deep_trap_band'] = HfO2_deep_trap_band ###################################################################### # Step 2: Modeling the quasi-permanent BTI component interface_grid_sampler = InterfaceGridSampler( d_eps1=0.1, # grid spacing for sampling eps_1 in eV d_eps2=0.001, # grid spacing for sampling eps_2 in eV ) interface_traps = GeneratedInterfaceTraps( eps1=2.5297, # mean activation energy barrier in eV eps1_sigma=0.92612, # standard dev. of activation energy barriers in eV eps2=1.649, # mean passivation energy barrier in eV eps2_sigma=0.060114, # standard dev. of passivation energy barriers in eV k0=1.2336E13, # transition rate for zero barrier in s⁻¹ gamma=1.7052e-10, # field dependence of activation barrier in eV m V⁻¹ Nt=1.9096E17, # curvature ratio trap_type='donor', # trap type sampler=interface_grid_sampler, # interface grid sampler device=my_device, # the device to which you want to add the traps ) ###################################################################### # Step 3: Initializing the device my_device.initialize( Vg=-0.5, # initial gate voltage in V T=300.0, # initial temperature in K record_band_occus=False, # indicates whether or not to save all occupancies of all bands at all timesteps debug=True, threshold=1.0E-65 ) plot_band_diagram(my_device, file=output_dir + "band_diagram_equilibrium.png", draw_samples=None) ######################################################################################################################## # Basic Usage Part3: Performing a simple BTI simulation ######################################################################################################################## ###################################################################### # Step 1: Print basic device properties print("Vfb0 = {:.3f} V".format(my_device.get_Vfb0(T=Temperature))) print("Vth0 = {:.3f} V".format(my_device.get_Vth0(T=Temperature))) print("Vfb = {:.3f} V".format(my_device.Vfb)) print("Vth = {:.3f} V".format(my_device.Vth)) ###################################################################### # Step 2: Plot semiconductor potential plot_surface_potential(my_device, file=output_dir + "surface_potential.png",) ###################################################################### # Step 3: Calculate potential profile and electric field across the stack plot_potential_profile(my_device, file=output_dir + "potential_profile.png") plot_electric_field(my_device, file=output_dir + "electric_field.png") ###################################################################### # Step 4: Define stress pattern # define time steps time_per_step = 1 number_steps = 250 time = np.linspace(0.0, time_per_step * number_steps, number_steps) # define constant temperature profile temperature = np.full_like(time, 300.0) # define gate voltage profile min = -2.0 max = -0.5 frequency = 1.0 / 40.0 Vg = min + (max - min)*(signal.square(2 * np.pi * frequency * time)/2.0 + 0.5) # plot gate voltage profile figure = plt.figure(figsize=(8.0, 6.0)) plt.plot(time, Vg) plt.plot(time, Vg, 'o') plt.title("stress waveform") plt.xlabel("time [s]") plt.ylabel("gate voltage [V]") plt.tight_layout() plt.grid() plt.savefig(output_dir + "stress_waveform.png") plt.show() ###################################################################### # Step 5: Calculate shift of threshold voltage # apply stress pattern to device # let's initialize the device with the initial voltage and temperature my_device.initialize(Vg=Vg[0], T=temperature[0]) # Now, let's retrieve the threshold voltage of the unstressed device as reference Vth_ref = my_device.Vth # Now, we create a list to collect the threshold voltage shifts threshold_voltage_shifts = [0.0] # Now, we loop over the scenario we have set out. # We skip the first point as that is our initialization point. for idx in range(1, len(time)): # here we actually apply the voltage for a given timestep my_device.apply_gate_voltage( Vg=Vg[idx], T=temperature[idx], dt=time[idx] - time[idx-1], ) # now let's retrieve the threshold voltage after application of stress new_Vth = my_device.Vth # finally, we store the threshold voltage w.r.t to the reference point threshold_voltage_shifts.append(new_Vth - Vth_ref) # Now that we have the data, let's plot it figure = plt.figure(figsize=(8.0, 6.0)) plt.plot(time, np.abs(threshold_voltage_shifts)) plt.title("BTI sequence") plt.xlabel("time [s]") plt.ylabel("threshold voltage shift [V]") plt.tight_layout() plt.grid() plt.savefig(output_dir + "bti_sequence.png") plt.show()