コード例 #1
0
 def set_semiconductor(self, Semicond=None):
     # measurement_type = self.Project.add_measurement_type('Metal work function', measurement_type_description='Metal work function measurement')
     try:
         semiconductor_label = self.Project.get_project_info('Semiconductor')
     except:
         semiconductor_label = None
     if Semicond is None:
         if semiconductor_label is None:
             raise Exception('Semiconductor is needed for Schottky diode')
         else:
             self.Semiconductor = Semiconductor(semiconductor_label, lookup=True)
     else:
         if Semicond.reference['name'] != semiconductor_label:
             self.Project.add_project_info_if_changed('Semiconductor', Semicond.reference['name'])
         self.Semiconductor = Semicond
コード例 #2
0
from Schottky.Notation import q, Eg
from Schottky.Metal import Metal
from Schottky.Semiconductor import Semiconductor, Trap, Dopant, Dislocation, BondingInterface
from Schottky.Diode import SchottkyDiode, Poisson, Kinetics, Visual
from Schottky.Helpers import Psi_approx

colors = [
    'b', 'g', 'y', 'k', 'm', 'c', 'b', 'g', 'y', 'k', 'm', 'c', 'b', 'g', 'y',
    'k', 'm', 'c', 'b', 'g', 'y', 'k', 'm', 'c'
]

Electrode = Metal('Au', q * 5.1)

P = Dopant('Phosphorus', 1.0e21, [[+1, 0.045 * q, 1], [0, 0.045 * q, 1]])

Si = Semiconductor('Si', lookup=True)
Si.add_dopant(P)

a = 5.43e-10
b = a * np.sqrt(2) / 2

S_e1 = Trap('Shallow electron trap',
            charge_states=[[0, 0.1 * q, 1], [-1, 0.1 * q, 1]],
            energy_distribution_function='Single Level',
            energy_spread=0.01 * q)
D_e1 = Trap('Deep electron trap',
            charge_states=[[0, 0.3 * q, 1], [-1, 0.3 * q, 1]],
            energy_distribution_function='Single Level',
            energy_spread=0.1 * q)

# S_h1 = Trap('Shallow hole trap', charge_states=[[1, Eg - 0.1 * q, 1], [0, Eg - 0.1 * q, 1]],
コード例 #3
0
    "k",
    "m",
    "c",
    "b",
    "g",
    "y",
    "k",
    "m",
    "c",
]

Electrode = Metal("Au", q * 5.1)

P = Dopant("Phosphorus", 1.0e21, [[+1, 0.045 * q, 1], [0, 0.045 * q, 1]])

Si = Semiconductor("Si", lookup=True)
Si.add_dopant(P)

a = 5.43e-10
b = a * np.sqrt(2) / 2

S_e1 = Trap(
    "Shallow electron trap",
    charge_states=[[0, 0.1 * q, 1], [-1, 0.1 * q, 1]],
    energy_distribution_function="Single Level",
    energy_spread=0.01 * q,
)
D_e1 = Trap(
    "Deep electron trap",
    charge_states=[[0, 0.3 * q, 1], [-1, 0.3 * q, 1]],
    energy_distribution_function="Single Level",
コード例 #4
0
class SchottkyDiode(object):
    '''
    Schottky Diode class
    '''

    def __init__(self, Project, label, Metal=None, Semiconductor=None, Area=None, Rs=None, T=None, Va=None,
                 DeadLayer=None, L=None):
        '''
        Constructor
        '''
        self.Project = Project
        self.Project.log_record('Project database opened', 'Information')
        self.tool_id = self.Project.add_tool('1D_SchottkySym', '1D Schottky Diode Simulator')
        self.measurements_types = self.register_measurement_types()

        self.label = self.Project.add_project_info_if_changed('Project name', label)

        self.set_electrode(Metal)
        self.set_semiconductor(Semiconductor)
        self.set_contact_area(Area)
        self.set_Rs(Rs)
        self.set_DeadLayer(DeadLayer)
        self.FieldInversionPoint = 0.0
        self.FieldInversionPsi = 0.0
        self.set_L(L)

        self.rho_z_Psi_memo = {}
        self.Psi_memo = {}

        self.set_T(T)
        self.set_Va(Va)

    def __str__(self, *args, **kwargs):
        record = 'Schottky diode: %s' % (self.label)
        return record

    def set_electrode(self, Metal=None):
        measurement_type = self.Project.add_measurement_type('Metal work function',
                                                             measurement_type_description='Metal work function measurement')
        try:
            metal_label = self.Project.get_project_info('Schottky electrode')
            measurement_id = self.Project.add_measurement(measurement_type, 'Electrode work function',
                                                          'Work function of metal electrode',
                                                          measurement_datetime=None, create_new=False)
            WF_arr, _, _, _ = self.Project.get_data_points(measurement_id, 'Metal electrode work function')
            if len(WF_arr) > 0:
                WF = WF_arr[-1]
        except:
            metal_label = None
            WF = 0
        if Metal is None:
            if metal_label is None:
                raise Exception('Metal electriode is needed for Schottky diode')
            else:
                self.Metal = MetalElectrode(metal_label, WF)
        else:
            if Metal.label != metal_label:
                self.Project.add_project_info_if_changed('Schottky electrode', Metal.label)
                _, WF = self.Project.add_monitored_datapoint(measurement_type, 'Electrode work function',
                                                             'Work function of metal electrode',
                                                             self.tool_id, 'Metal electrode work function', 'Metal WF',
                                                             'J', None, to_numeric(Metal.WF))
            self.Metal = Metal

    def set_semiconductor(self, Semicond=None):
        # measurement_type = self.Project.add_measurement_type('Metal work function', measurement_type_description='Metal work function measurement')
        try:
            semiconductor_label = self.Project.get_project_info('Semiconductor')
        except:
            semiconductor_label = None
        if Semicond is None:
            if semiconductor_label is None:
                raise Exception('Semiconductor is needed for Schottky diode')
            else:
                self.Semiconductor = Semiconductor(semiconductor_label, lookup=True)
        else:
            if Semicond.reference['name'] != semiconductor_label:
                self.Project.add_project_info_if_changed('Semiconductor', Semicond.reference['name'])
            self.Semiconductor = Semicond

    def register_measurement_types(self):
        measurements_dict = {
            'Length measurement': self.Project.add_measurement_type('Length measurement',
                                                                    measurement_type_description='Length measurement'),
            'Area measurement': self.Project.add_measurement_type('Area measurement',
                                                                  measurement_type_description='Area measurement'),
            'Resistance measurement': self.Project.add_measurement_type('Resistance measurement',
                                                                        measurement_type_description='Resistance measurement'),
            'Temperature measurement': self.Project.add_measurement_type('Temperature measurement',
                                                                         measurement_type_description='Temperature measurement'),
            'Built-in voltage measurement': self.Project.add_measurement_type('Built-in voltage measurement',
                                                                              measurement_type_description='Built-in voltage measurement'),
            'Bias voltage': self.Project.add_measurement_type('Bias voltage monitor',
                                                              measurement_type_description='Applied bias voltage measurement'),
            'Potential and Electric Field measurement': self.Project.add_measurement_type(
                'Potential and Electric Field',
                measurement_type_description='Potential and Electric Field in the diode measurement'),
            'Traps kinetics measurement': self.Project.add_measurement_type(
                'Transient experiment',
                measurement_type_description='Time-resolved measurement of traps kinetic'),
        }
        return measurements_dict

    def set_contact_area(self, Area):
        point_name_long = 'Area'
        point_name_short = 'A'
        point_unit_name = 'm^-2'
        default_d = 1.5e-3
        default = np.pi * (default_d ** 2) / 4.0
        _, self.Area = self.Project.add_monitored_datapoint(self.measurements_types['Area measurement'], 'Contact area',
                                                            'Contact area measurement',
                                                            self.tool_id, point_name_long, point_name_short,
                                                            point_unit_name, default, Area)

    def set_contact_diameter(self, d=1.5e-3):
        if not isinstance(d, (float, int)):
            Area = None
        else:
            Area = np.pi * (d ** 2) / 4.0
        self.set_contact_area(Area)

    def set_L(self, L=10e-6):
        point_name_long = 'Schottky diode semiconductor thickness'
        point_name_short = 'L'
        point_unit_name = 'm'
        _, self.L = self.Project.add_monitored_datapoint(self.measurements_types['Length measurement'],
                                                         'Diode thickness', 'Thickness of semiconductor',
                                                         self.tool_id, point_name_long, point_name_short,
                                                         point_unit_name, 10e-6, L)

    def set_Rs(self, Rs=10):
        point_name_long = 'Serial Resistance'
        point_name_short = 'Rs'
        point_unit_name = 'Ohm'
        _, self.Rs = self.Project.add_monitored_datapoint(self.measurements_types['Resistance measurement'],
                                                          'Serial Resistance', 'Serial resistance of diode base',
                                                          self.tool_id, point_name_long, point_name_short,
                                                          point_unit_name, 10, Rs)

    def set_DeadLayer(self, DeadLayer=0.0):
        point_name_long = 'Dead Layer thickness'
        point_name_short = 'DL'
        point_unit_name = 'm'
        _, self.DeadLayer = self.Project.add_monitored_datapoint(self.measurements_types['Length measurement'],
                                                                 'Dead Layer', 'Dead Layer thickness',
                                                                 self.tool_id, point_name_long, point_name_short,
                                                                 point_unit_name, 0, DeadLayer)

    def set_T(self, T=300):
        point_name_long = 'Temperature'
        point_name_short = 'T'
        point_unit_name = 'K'
        self.T_measurement_id, self.T = self.Project.add_monitored_datapoint(
            self.measurements_types['Temperature measurement'], 'Temperature', 'Diode temperature',
            self.tool_id, point_name_long, point_name_short, point_unit_name, 300, T)
        try:
            self.Project.log_record('Temperature: %2.2f K' % (T), 'Information')
        except:
            pass

    def set_Va(self, V=0):
        point_name_long = 'Bias'
        point_name_short = 'Va'
        point_unit_name = 'V'
        self.Va_measurement_id, self.Va = self.Project.add_monitored_datapoint(self.measurements_types['Bias voltage'],
                                                                               'Va', 'Diode bias voltage monitor',
                                                                               self.tool_id, point_name_long,
                                                                               point_name_short, point_unit_name, 0, V)
        try:
            self.Project.log_record('Va: %2.2f V' % (V), 'Information')
        except:
            pass

    def V_bi(self, eV=False):
        measurement_id = self.Project.add_measurement(self.measurements_types['Built-in voltage measurement'], 'Vbi',
                                                      'Built-in voltage',
                                                      measurement_datetime=None, create_new=False)
        point_name_long = 'Vbi'
        Vbi_array, _, measurement_date_array, unit_name_array = self.Project.get_data_points(measurement_id,
                                                                                             point_name_long)
        for i in range(len(Vbi_array)):
            T, _ = self.Project.get_data_point_at_datetime(self.T_measurement_id, 'Temperature',
                                                           measurement_date_array[i], interpolation_type='step')
            if T == self.T:
                Vbi = Vbi_array[i]
                if eV:
                    if unit_name_array[i] == 'J':
                        Vbi /= to_numeric(q)
                else:
                    if unit_name_array[i] == 'V':
                        Vbi *= to_numeric(q)
                return np.float(Vbi)
        point_name_short = 'Vbi'
        point_unit_name = 'V' if eV else 'J'
        point_order = self.Project.get_next_data_point_order(measurement_id, point_name_long)
        if eV:
            Vbi = to_numeric(self.Metal.WF / q) - self.Semiconductor.WF(self.T, z=1e3, eV=eV)
        else:
            Vbi = to_numeric(self.Metal.WF) - self.Semiconductor.WF(self.T, z=1e3, eV=eV)
        self.Project.add_datapoint(point_order, measurement_id, self.tool_id,
                                   point_name_long, point_name_short, point_unit_name,
                                   Vbi, datetime.datetime.now())
        return np.float(Vbi)

    def EfEc(self, Psi=Psi_zero, z=0, eV=False):
        coeff = 1 if eV else to_numeric(q)
        Psi_nodes = Psi(z)
        xi = np.float(self.Semiconductor.Ech_pot(T=self.T, z=1e3, eV=eV, debug=False))
        return -coeff * Psi_nodes + xi

    def dopants_set_eq_F(self, z, Psi, debug=False):
        '''
        Sets dopants filling level to equilibrium
        '''
        for dopant in self.Semiconductor.dopants:
            Ef = self.EfEc(Psi, z, eV=False)
            if isinstance(z, (mp.mpf, float, int)):
                F = dopant.equilibrium_f(self.T, self.Semiconductor, Ef, electron_volts=False, debug=debug)
                dF = dopant.d_equilibrium_f_d_fermi_energy(self.T, self.Semiconductor, Ef, electron_volts=False, debug=debug)
            elif isinstance(z, (np.ndarray, list, tuple)):
                F = dopant.equilibrium_f(self.T, self.Semiconductor, Ef, electron_volts=False, debug=debug)
                dF = dopant.d_equilibrium_f_d_fermi_energy(self.T, self.Semiconductor, Ef, electron_volts=False, debug=debug)
                # F = np.array([dopant.equilibrium_f(self.T, self.Semiconductor, Ef_z, eV=False, debug=debug) for Ef_z in Ef])
                # dF = np.array([dopant.d_equilibrium_f_d_fermi_energy(self.T, self.Semiconductor, Ef_z, eV=False, debug=debug) for Ef_z in Ef])
            else:
                raise ValueError('Wrong type of Z: ' + str(type(z)))
            dopant.set_F_interp(z, F)
            dopant.set_dF_interp(z, dF)

    def disl_eq_F(self, Ef, disl_traps, eV=True, debug=False):
        F = []
        dF = []
        for i, trap in enumerate(disl_traps):
            F.append(trap[0].equilibrium_f(self.T, self.Semiconductor, Ef, eV, debug))
            dF.append(trap[0].d_equilibrium_f_d_fermi_energy(self.T, self.Semiconductor, Ef, eV, debug))
            if debug: print 'F = %2.2g' % F[i]
            if debug: print 'dF = %2.2g' % dF[i]
        return np.array(F), np.array(dF)

    def BI_set_eq_F(self, BI, Psi, eV=False, debug=False):
        Ef = self.EfEc(Psi, BI.depth, eV)
        BI.dsl_tilt_f, BI.dsl_tilt_df = self.disl_eq_F(Ef, BI.dsl_tilt.traps, eV, debug)
        BI.dsl_twist_f, BI.dsl_twist_df = self.disl_eq_F(Ef, BI.dsl_twist.traps, eV, debug)
        BI.set_traps_f(BI.dsl_tilt_f, BI.dsl_twist_f)
        BI.set_traps_df(BI.dsl_tilt_df, BI.dsl_twist_df)

    def build_rho_z_Psi(self, Psi=Psi_zero, carriers_charge=False):
        if not (Psi, self.T, carriers_charge) in self.rho_z_Psi_memo:
            def rho_z_Psi(z, Psi):
                rho = 0
                if carriers_charge:
                    if Psi != Psi_zero:
                        n, p = self.n_carriers_theory(Psi, z)
                        if self.Semiconductor.dop_type == 'n':
                            p = 0
                        elif self.Semiconductor.dop_type == 'p':
                            n = 0
                        rho += p - n
                for dopant in self.Semiconductor.dopants:
                    Nd = dopant.concentration(z)
                    rho += Nd * (
                        (dopant.charge_states[1][0] - dopant.charge_states[0][0]) * dopant.F(z) +
                        dopant.charge_states[0][
                            0])
                for BI in self.Semiconductor.bonding_interfaces:
                    rho += smooth_dd(z - BI.depth, BI.smooth_dirac_epsilon) * BI.density_of_charge
                return to_numeric(q) * rho

            self.rho_z_Psi_memo[(Psi, self.T, carriers_charge)] = rho_z_Psi
        return self.rho_z_Psi_memo[(Psi, self.T, carriers_charge)]

    def get_phi_bn(self, Psi=Psi_zero, Va=0, SchottkyEffect=False):
        chg_sign = 1 if self.Semiconductor.dop_type == 'n' else -1
        F = to_numeric(q / (16 * np.pi * epsilon0 * self.Semiconductor.reference['epsilon']))
        if not SchottkyEffect:
            F = 0

        def f(z):
            if F != 0:
                if not isinstance(z, np.ndarray):
                    return chg_sign * (Psi(z) + chg_sign * F / z)
                else:
                    return chg_sign * np.array([Psi(zz) + chg_sign * F / zz for zz in z])
            else:
                if not isinstance(z, np.ndarray):
                    return chg_sign * Psi(z)
                else:
                    #return chg_sign * np.array([Psi(zz) for zz in z])
                    return chg_sign * Psi(z)
        z_0 = np.linspace(1e-10, np.float(self.L), num=50)
        extrema_z = np.zeros_like(z_0)
        warnings.filterwarnings("ignore", category=RuntimeWarning)
        for i in range(z_0.size):
            extrema_z[i] = fmin(f, z_0[i], disp=False)
            # print extrema_z[i]*1e6
        warnings.resetwarnings()
        extrema = f(extrema_z)
        # _, (ax1, ax2, ax3) = plt.subplots(3)
        # ax1.plot(z_0*1e6, f(z_0))
        # ax2.plot(z_0*1e6, extrema_z*1e6)
        # ax3.plot(extrema_z*1e6, extrema)
        # plt.show()

        z_max = extrema_z[np.argmin(extrema)]
        if z_max < 0:
            z_max = 1e-15
        xi = self.Semiconductor.Ech_pot(T=self.T, z=1e3, eV=True, debug=False)
        Eg = self.Semiconductor.band_gap(self.T, symbolic=False, electron_volts=True)
        if self.Semiconductor.dop_type == 'n':
            phi_bn = abs(-f(z_max) + xi + Va)
            delta_phi = abs(self.Ec(Psi, Va, z_max, eV=True) - phi_bn)
            phi_b = phi_bn - xi
        else:
            phi_bn = abs(f(z_max) + xi - Va - Eg)
            delta_phi = abs(self.Ev(Psi, Va, z_max, eV=True) - phi_bn)
            phi_b = phi_bn - Eg + xi
        # print 'Z_max =', z_max*1e6, 'um'
        return np.float(z_max), np.float(phi_bn), np.float(delta_phi), np.float(phi_b)

    def ThermionicEmissionCurrent(self, Va, phi_bn, debug=False):
        kT = to_numeric(k * self.T)
        q_n = to_numeric(q)
        A = self.Area
        Rs = self.Rs
        if self.Semiconductor.dop_type == 'n':
            Ar = self.Semiconductor.reference['A_R_coeff_n'] * constants['A_R']
        else:
            Ar = self.Semiconductor.reference['A_R_coeff_p'] * constants['A_R']
        Js = Ar * (self.T ** 2) * mp.exp(-q_n * phi_bn / kT)
        if debug: print 'Js, Is =', Js, A * Js
        J = -Js + kT / (q_n * A * Rs) * mp.lambertw((q_n * A * Rs * Js / kT) * mp.exp(q_n * (Va + A * Js * Rs) / kT))
        if debug: print 'J, I =', J, A * J
        Vd = Va - A * J * Rs
        return np.float(Vd), np.float(J)

    def Ec(self, Psi=Psi_zero, Va=0, z=0, eV=False):
        coeff = 1.0 if eV else to_numeric(q)
        Psi_nodes = Psi(z)
        xi = np.float(self.Semiconductor.Ech_pot(T=self.T, z=1e3, eV=eV, debug=False))
        type_sign = -1 if self.Semiconductor.dop_type == 'p' else 1
        Ec = -coeff * Psi_nodes + xi + coeff * type_sign * Va
        return Ec

    def Ev(self, Psi=Psi_zero, Va=0, z=0, eV=False):
        Eg = self.Semiconductor.band_gap(self.T, symbolic=False, electron_volts=eV)
        Ec = self.Ec(Psi, Va, z, eV=eV)
        Ev = Ec - Eg
        return Ev

    def n_carriers_theory(self, Psi=Psi_zero, z=0):
        '''
        Charge carrier concentration in the main band
        '''
        k_n = to_numeric(k)
        Ef = self.EfEc(Psi, z, eV=False)
        Eg = self.Semiconductor.band_gap(self.T, symbolic=False, electron_volts=False)
        F_n = np.exp(-Ef / (k_n * self.T))
        F_p = np.exp((Ef - Eg) / (k_n * self.T))
        n = np.float(self.Semiconductor.Nc(self.T, symbolic=False)) * F_n
        p = np.float(self.Semiconductor.Nv(self.T, symbolic=False)) * F_p
        if isinstance(z, np.ndarray):
            idx = np.where(z < self.DeadLayer)[0]
            # print idx
            if idx.size > 0:
                n[idx] = 0.0
                p[idx] = 0.0
            idx = np.where(z < self.FieldInversionPoint)[0]
            if idx.size > 0:
                n[idx] = 0.0
                p[idx] = 0.0
        elif z < self.DeadLayer or z < self.FieldInversionPoint:
            n = 0
            p = 0
        return n, p

    def dn_carriers_dEf_theory(self, Psi=Psi_zero, z=0):
        k_n = to_numeric(k)
        Ef = self.EfEc(Psi, z, eV=False)
        Eg = self.Semiconductor.band_gap(self.T, symbolic=False, electron_volts=False)
        F_n = np.exp(-Ef / (k_n * self.T))
        F_p = np.exp((Ef - Eg) / (k_n * self.T))
        dn = np.float(self.Semiconductor.Nc(self.T, symbolic=False)) / (k_n * self.T) * F_n
        dp = np.float(-self.Semiconductor.Nv(self.T, symbolic=False)) / to_numeric(k * self.T) * F_p
        if isinstance(z, np.ndarray):
            idx = np.where(z < self.DeadLayer)[0]
            if idx.size > 0:
                dn[idx] = 0.0
                dp[idx] = 0.0
            idx = np.where(z < self.FieldInversionPoint)[0]
            if idx.size > 0:
                dn[idx] = 0.0
                dp[idx] = 0.0
        elif z < self.DeadLayer or z < self.FieldInversionPoint:
            dn = 0
            dp = 0
        return dn, dp
コード例 #5
0
import numpy as np

from Schottky.Notation import q
from Schottky.Metal import Metal
from Schottky.Semiconductor import Semiconductor, Trap, Dopant, Dislocation, BondingInterface
from Potential.Potential_3D import ConstantFieldPotential, SuperposedPotential, ChargedCylinderPotential, \
    DislocationDeformationPotential

data_dir = join(dirname(__file__), '03-data')
prefix = '03_Au_nSi_BW'

electrode = Metal('Au', q * 5.1)

dopant = Dopant('Phosphorus', 1.0e21, [[+1, 0.045 * q, 1], [0, 0.045 * q, 1]])

silicon = Semiconductor('Si', lookup=True)
silicon.add_dopant(dopant)

lattice_parameter = 5.43e-10
burgers_vector = lattice_parameter * np.sqrt(2) / 2

dp = DislocationDeformationPotential('Deformation', 5, 4e-10)
cc = ChargedCylinderPotential('Charged Dislocation', charge_sign=-1, linear_charge_density=1e7 * 0,
                              radius=1e-9, epsilon=11.8)
ef = ConstantFieldPotential('External Field', (0.0, 0.0, 0.0))
sp = SuperposedPotential('Superposed', [dp, cc, ef])

shallow_electron_trap = Trap('Shallow electron trap', charge_states=[[0, 0.15 * q, 1], [-1, 0.15 * q, 1]],
                             energy_distribution_function='Single Level', energy_spread=0.01 * q, trap_potential=sp)
deep_electron_trap = Trap('Deep electron trap', charge_states=[[0, 0.3 * q, 1], [-1, 0.3 * q, 1]],
                          energy_distribution_function='Single Level', energy_spread=0.1 * q, trap_potential=sp)