import pydantic.v1 as pd
from tidy3d.components.base import Tidy3dBaseModel
from tidy3d.components.types import Union
from tidy3d.constants import PERCMCUBE, SECOND
class FossumCarrierLifetime(Tidy3dBaseModel):
"""
Parameters for the Fossum carrier lifetime model
Notes
-----
This model expresses the carrier lifetime as a function of the temperature and doping concentration.
.. math::
\\tau = \\frac{\\tau_{300} \\left( T/300 \\right)^\\alpha_T}{A + B (N/N_0) + C (N/N_0)^\\alpha}
Example
-------
>>> import tidy3d as td
>>> default_Si = td.FossumCarrierLifetime(
... tau_300=3.3e-6,
... alpha_T=-0.5,
... N0=7.1e15,
... A=1,
... B=0,
... C=1,
... alpha=1
... )
References
----------
Fossum, J. G., and D. S. Lee. "A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon." Solid-State Electronics 25.8 (1982): 741-747.
"""
tau_300: pd.PositiveFloat = pd.Field(
..., title="Tau at 300K", description="Carrier lifetime at 300K", units=SECOND
)
alpha_T: float = pd.Field(
..., title="Exponent for thermal dependence", description="Exponent for thermal dependence"
)
N0: pd.PositiveFloat = pd.Field(
..., title="Reference concentration", description="Reference concentration", units=PERCMCUBE
)
A: float = pd.Field(..., title="Constant A", description="Constant A")
B: float = pd.Field(..., title="Constant B", description="Constant B")
C: float = pd.Field(..., title="Constant C", description="Constant C")
alpha: float = pd.Field(..., title="Exponent constant", description="Exponent constant")
CarrierLifetimeType = Union[FossumCarrierLifetime]
[docs]
class AugerRecombination(Tidy3dBaseModel):
"""
Parameters for the Auger recombination model.
Notes
-----
The Auger recombination rate ``R_A`` is primarily defined by the electrons and holes Auger recombination
coefficients, :math:`C_n` and :math:`C_p`, respectively.
.. math::
R_A = \\left( C_n n + C_p p \\right) \\left( np - n_0 p_0 \\right)
Example
-------
>>> import tidy3d as td
>>> default_Si = td.AugerRecombination(
... c_n=2.8e-31,
... c_p=9.9e-32,
... )
"""
c_n: pd.PositiveFloat = pd.Field(
..., title="Constant for electrons", description="Constant for electrons in cm^6/s"
)
c_p: pd.PositiveFloat = pd.Field(
..., title="Constant for holes", description="Constant for holes in cm^6/s"
)
[docs]
class RadiativeRecombination(Tidy3dBaseModel):
"""
Defines the parameters for the radiative recombination model.
Notes
-----
This is a direct recombination model primarily defined by a radiative recombination coefficient :math:`R_{\\text{rad}}`.
.. math::
R_{\\text{rad}} = C \\left( np - n_0 p_0 \\right)
Example
-------
>>> import tidy3d as td
>>> default_Si = td.RadiativeRecombination(
... r_const=1.6e-14
... )
"""
r_const: float = pd.Field(
...,
title="Radiation constant in cm^3/s",
description="Radiation constant in cm^3/s",
)
[docs]
class ShockleyReedHallRecombination(Tidy3dBaseModel):
"""Defines the parameters for the Shockley-Reed-Hall (SRH) recombination model.
Notes
-----
The recombination rate parameter from this model is defined from [1]_ as follows:
.. math::
R_{SRH} = \\frac{n p - n_0 p_0}{\\tau_p \\left(n + \\sqrt{n_0 p_0}\\right) + \\tau_n \\left(p + \\sqrt{n_0 p_0}\\right)}.
Note that the electron and holes densities are defined within the :class:`SemiconductorMedium`. The electron
lifetime :math:`\\tau_n` and hole lifetimes :math:`\\tau_p` need to be defined.
.. [1] Schenk. A model for the field and temperature dependence of shockley-read-hall
lifetimes in silicon. Solid-State Electronics, 35:1585–1596, 1992.
Example
-------
>>> import tidy3d as td
>>> default_Si = td.ShockleyReedHallRecombination(
... tau_n=3.3e-6,
... tau_p=4e-6,
... )
Note
----
Important considerations when using this model:
- Currently, lifetimes are considered constant (not dependent on temperature or doping).
- This model represents mid-gap traps Shockley-Reed-Hall recombination.
"""
tau_n: Union[pd.PositiveFloat, CarrierLifetimeType] = pd.Field(
..., title="Electron lifetime", description="Electron lifetime", union=SECOND
)
tau_p: Union[pd.PositiveFloat, CarrierLifetimeType] = pd.Field(
..., title="Hole lifetime", description="Hole lifetime", units=SECOND
)
