Add effective DOS and energy band gap model

tests/test_components/test_heat_charge.py

@@ -11,6 +11,8 @@
 from tidy3d.components.tcad.types import (
     AugerRecombination,
     CaugheyThomasMobility,
+    ConstantEffectiveDOS,
+    ConstantEnergyBandGap,
     SlotboomBandGapNarrowing,
 )
 from tidy3d.exceptions import DataError
@@ -39,9 +41,9 @@ class CHARGE_SIMULATION:
             permittivity=11.7,
             N_d=0,
             N_a=0,
-            N_c=2.86e19,
-            N_v=3.1e19,
-            E_g=1.11,
+            N_c=ConstantEffectiveDOS(N=2.86e19),
+            N_v=ConstantEffectiveDOS(N=3.1e19),
+            E_g=ConstantEnergyBandGap(eg=1.11),
             mobility_n=CaugheyThomasMobility(
                 mu_min=52.2,
                 mu=1471.0,

tidy3d/__init__.py

@@ -68,12 +68,19 @@
     AugerRecombination,
     CaugheyThomasMobility,
     ConstantMobilityModel,
+    ConstantEffectiveDOS,
+    ConstantEnergyBandGap,
+    QuadraticEnergyBandGap,
+    VarshniEnergyBandGap,
     ConvectionBC,
     CurrentBC,
+    DualValleyEffectiveDOS,
     HeatFluxBC,
     HeatFromElectricSource,
     HeatSource,
     InsulatingBC,
+    IsotropicEffectiveDOS,
+    MultiValleyEffectiveDOS,
     RadiativeRecombination,
     ShockleyReedHallRecombination,
     SlotboomBandGapNarrowing,
@@ -451,6 +458,10 @@ def set_logging_level(level: str) -> None:
     "CoaxialLumpedResistor",
     "ConstantDoping",
     "ConstantMobilityModel",
+    "ConstantEffectiveDOS",
+    "IsotropicEffectiveDOS",
+    "MultiValleyEffectiveDOS",
+    "DualValleyEffectiveDOS",
     "ContinuousWave",
     "ContinuousWaveTimeModulation",
     "ContourPathAveraging",
@@ -716,4 +727,7 @@ def set_logging_level(level: str) -> None:
     "set_logging_console",
     "set_logging_file",
     "wavelengths",
+    "ConstantEnergyBandGap",
+    "QuadraticEnergyBandGap",
+    "VarshniEnergyBandGap",
 ]

tidy3d/components/material/tcad/charge.py

@@ -9,6 +9,8 @@
 from tidy3d.components.tcad.doping import DopingBoxType
 from tidy3d.components.tcad.types import (
     BandGapNarrowingModelType,
+    EffectiveDOSModelType,
+    EnergyBandGapModelType,
     MobilityModelType,
     RecombinationModelType,
 )
@@ -254,21 +256,21 @@ class SemiconductorMedium(AbstractChargeMedium):
 
     """
 
-    N_c: pd.PositiveFloat = pd.Field(
+    N_c: EffectiveDOSModelType = pd.Field(
         ...,
         title="Effective density of electron states",
         description=r"$N_c$ Effective density of states in the conduction band.",
         units="cm^(-3)",
     )
 
-    N_v: pd.PositiveFloat = pd.Field(
+    N_v: EffectiveDOSModelType = pd.Field(
         ...,
         title="Effective density of hole states",
         description=r"$N_v$ Effective density of states in the valence band.",
         units="cm^(-3)",
     )
 
-    E_g: pd.PositiveFloat = pd.Field(
+    E_g: EnergyBandGapModelType = pd.Field(
         ...,
         title="Band-gap energy",
         description="Band-gap energy",

tidy3d/components/tcad/bandgap_energy.py

@@ -0,0 +1,111 @@
+from __future__ import annotations
+
+import pydantic.v1 as pd
+
+from tidy3d.components.base import Tidy3dBaseModel
+from tidy3d.constants import ELECTRON_VOLT
+
+
+class ConstantEnergyBandGap(Tidy3dBaseModel):
+    """Constant Energy band gap"""
+
+    eg: pd.PositiveFloat = pd.Field(
+        title="Band Gap",
+        description="Energy band gap",
+        units=ELECTRON_VOLT,
+    )
+
+
+class QuadraticEnergyBandGap(Tidy3dBaseModel):
+    """
+    Models the temperature dependence of the energy band gap (Eg) using a
+    quadratic approximation.
+
+    Notes
+    -----
+    The model uses the following formula:
+
+        .. math::
+
+            E_g(T) = E_g(300) + \\alpha T + \\beta T^2
+
+    Example
+    -------
+    >>> model = QuadraticEnergyBandGap(
+    ...     eg_300=1.12,
+    ...     alpha=-4.73e-4,
+    ...     beta=-2.0e-7,
+    ... )
+    """
+
+    eg_300: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Band Gap at 300 K",
+        description="Energy band gap at a reference temperature of 300 K.",
+        units=ELECTRON_VOLT,
+    )
+
+    alpha: float = pd.Field(
+        ...,
+        title="Linear Temperature Coefficient (alpha)",
+        description="Linear coefficient for the temperature dependence of the band gap.",
+        units="eV/K",
+    )
+
+    beta: float = pd.Field(
+        ...,
+        title="Quadratic Temperature Coefficient (beta)",
+        description="Quadratic coefficient for the temperature dependence of the band gap.",
+        units="eV/K²",
+    )
+
+
+class VarshniEnergyBandGap(Tidy3dBaseModel):
+    """
+    Models the temperature dependence of the energy band gap (Eg)
+    using the Varshni formula.
+
+    Notes
+    -----
+    The model implements the following formula:
+
+        .. math::
+
+            E_g(T) = E_g(0) - \\frac{\\alpha T^2}{T + \\beta}$
+
+    Example
+    -------
+    >>> # Parameters for Silicon (Si)
+    >>> si_model = VarshniBandGap(
+    ...     eg_0=1.17,
+    ...     alpha=4.73e-4,
+    ...     beta=636.0,
+    ... )
+
+    References
+    -------
+
+        Varshni, Y. P. (1967). Temperature dependence of the energy gap in semiconductors. Physica, 34(1), 149-154.
+
+    """
+
+    eg_0: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Band Gap at 0 K",
+        description="Energy band gap at absolute zero (0 Kelvin).",
+        units=ELECTRON_VOLT,
+    )
+
+    alpha: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Varshni Alpha Coefficient",
+        description="Empirical Varshni coefficient (α).",
+        units="eV/K",
+    )
+
+    beta: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Varshni Beta Coefficient",
+        description="Empirical Varshni coefficient (β), related to the Debye temperature.",
+        units="K",
+    )

tidy3d/components/tcad/effective_DOS.py

@@ -0,0 +1,158 @@
+from abc import ABC, abstractmethod
+
+import numpy as np
+import pydantic.v1 as pd
+
+from tidy3d.components.base import Tidy3dBaseModel
+from tidy3d.constants import C_0, HBAR, K_B
+
+from ...exceptions import DataError
+
+# constants definition
+m_e_C_square = 0.51099895069e6  # (electron mass * C_0^2) in eV
+m_e_eV = m_e_C_square / C_0 / C_0  # equivalent electron mass in eV
+um_3_to_cm_3 = 1e12  # conversion factor from micron^(-3) to cm^(-3)
+
+DOS_aux_const = 2.0 * np.power((m_e_eV * K_B) / (2 * np.pi * HBAR * HBAR), 1.5) * um_3_to_cm_3
+
+
+class EffectiveDOS(Tidy3dBaseModel, ABC):
+    """Abstract class for the effective density of states"""
+
+    @abstractmethod
+    def calc_eff_dos(self, T: float):
+        """Abstract method to calculate the effective density of states."""
+        pass
+
+    @abstractmethod
+    def calc_eff_dos_derivative(self, T: float):
+        """Abstract method to calculate the temperature derivative of the effective density of states."""
+        pass
+
+    def get_effective_DOS(self, T: float):
+        if T <= 0:
+            raise DataError(
+                f"Incorrect temperature value ({T}) for the effectve density of states calculation."
+            )
+
+        return self.calc_eff_dos(T)
+
+    def get_effective_DOS_derivative(self, T: float):
+        if T <= 0:
+            raise DataError(
+                f"Incorrect temperature value ({T}) for the effectve density of states calculation."
+            )
+
+        return self.calc_eff_dos_derivative(T)
+
+
+class ConstantEffectiveDOS(EffectiveDOS):
+    """Constant effective density of states model."""
+
+    N: pd.PositiveFloat = pd.Field(
+        ..., title="Effective DOS", description="Effective density of states", units="cm^(-3)"
+    )
+
+    def calc_eff_dos(self, T: float):
+        return self.N
+
+    def calc_eff_dos_derivative(self, T: float):
+        return 0.0
+
+
+class IsotropicEffectiveDOS(EffectiveDOS):
+    """Effective density of states model that assumes single valley and isotropic effective mass.
+    The model assumes the standard equation for the 3D semiconductor with parabolic energy dispersion:
+
+    .. math::
+
+        \\begin{equation}
+             \\mathbf{N_eff} = 2 * (\\frac{m_eff * m_e * k_B T}{2 \\pi \\hbar^2})^(3/2)
+        \\end{equation}
+    """
+
+    m_eff: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Effective mass",
+        description="Effective mass of the carriers",
+        units="Electron mass",
+    )
+
+    def calc_eff_dos(self, T: float):
+        return np.power(self.m_eff * T, 1.5) * DOS_aux_const
+
+    def calc_eff_dos_derivative(self, T: float):
+        return self.calc_eff_dos(T) * 1.5 / T
+
+
+class MultiValleyEffectiveDOS(EffectiveDOS):
+    """Effective density of states model that assumes multiple equivalent valleys and anisotropic effective mass.
+    The model assumes the standard equation for the 3D semiconductor with parabolic energy dispersion:
+
+    .. math::
+
+        \\begin{equation}
+             \\mathbf{N_eff} = 2 * N_valley * (m_{eff_long} * m_{eff_trans} * m_{eff_trans})^(1/2) *(\\frac{m_e * k_B * T}{2 \\pi * \\hbar^2})^(3/2)
+        \\end{equation}
+    """
+
+    m_eff_long: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Longitudinal effective mass",
+        description="Effective mass of the carriers in the longitudinal direction",
+        units="Electron mass",
+    )
+
+    m_eff_trans: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Longitudinal effective mass",
+        description="Effective mass of the carriers in the transverse direction",
+        units="Electron mass",
+    )
+
+    N_valley: pd.PositiveFloat = pd.Field(
+        ..., title="Number of valleys", description="Number of effective valleys"
+    )
+
+    def calc_eff_dos(self, T: float):
+        return (
+            self.N_valley
+            * np.power(self.m_eff_long * self.m_eff_trans * self.m_eff_trans, 0.5)
+            * np.power(T, 1.5)
+            * DOS_aux_const
+        )
+
+    def calc_eff_dos_derivative(self, T: float):
+        return self.calc_eff_dos(T) * 1.5 / T
+
+
+class DualValleyEffectiveDOS(EffectiveDOS):
+    """Effective density of states model that assumes combibation of light holes and heavy holes with isotropic effective masses.
+    The model assumes the standard equation for the 3D semiconductor with parabolic energy dispersion:
+
+    .. math::
+
+        \\begin{equation}
+             \\mathbf{N_eff} = 2 * ( {\\frac{m_{eff_lh} * m_e * k_B * T}{2 \\pi \\hbar^2})^(3/2) + (\\frac{m_{eff_hh} * m_e * k_B * T}{2 \\pi \\hbar^2})^(3/2) )
+        \\end{equation}
+    """
+
+    m_eff_lh: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Light hole effective mass",
+        description="Effective mass of the light holes",
+        units="Electron mass",
+    )
+
+    m_eff_hh: pd.PositiveFloat = pd.Field(
+        ...,
+        title="Heavy hole effective mass",
+        description="Effective mass of the heavy holes",
+        units="Electron mass",
+    )
+
+    def calc_eff_dos(self, T: float):
+        return (np.power(self.m_eff_lh * T, 1.5) + np.power(self.m_eff_hh * T, 1.5)) * DOS_aux_const
+
+    def calc_eff_dos_derivative(self, T: float):
+        return self.calc_eff_dos(T) * 1.5 / T

tidy3d/components/tcad/types.py

@@ -5,6 +5,17 @@
 from tidy3d.components.tcad.bandgap import SlotboomBandGapNarrowing
 from tidy3d.components.tcad.boundary.charge import CurrentBC, InsulatingBC, VoltageBC
 from tidy3d.components.tcad.boundary.heat import ConvectionBC, HeatFluxBC, TemperatureBC
+from tidy3d.components.tcad.effective_DOS import (
+    ConstantEffectiveDOS,
+    DualValleyEffectiveDOS,
+    IsotropicEffectiveDOS,
+    MultiValleyEffectiveDOS,
+)
+from tidy3d.components.tcad.bandgap_energy import (
+    ConstantEnergyBandGap,
+    QuadraticEnergyBandGap,
+    VarshniEnergyBandGap,
+)
 from tidy3d.components.tcad.generation_recombination import (
     AugerRecombination,
     RadiativeRecombination,
@@ -23,6 +34,10 @@
 from tidy3d.components.tcad.source.heat import HeatSource, UniformHeatSource
 from tidy3d.components.types import Union
 
+EffectiveDOSModelType = Union[
+    ConstantEffectiveDOS, IsotropicEffectiveDOS, MultiValleyEffectiveDOS, DualValleyEffectiveDOS
+]
+EnergyBandGapModelType = Union[ConstantEnergyBandGap, QuadraticEnergyBandGap, VarshniEnergyBandGap]
 MobilityModelType = Union[CaugheyThomasMobility, ConstantMobilityModel]
 RecombinationModelType = Union[
     AugerRecombination, RadiativeRecombination, ShockleyReedHallRecombination