tidy3d.SemiconductorMedium

tidy3d.SemiconductorMedium#

class SemiconductorMedium[source]#

Bases: AbstractChargeMedium

This class is used to define semiconductors.

Parameters:

  • attrs (dict = {}) – Dictionary storing arbitrary metadata for a Tidy3D object. This dictionary can be freely used by the user for storing data without affecting the operation of Tidy3D as it is not used internally. Note that, unlike regular Tidy3D fields, attrs are mutable. For example, the following is allowed for setting an attr obj.attrs['foo'] = bar. Also note that Tidy3D will raise a TypeError if attrs contain objects that can not be serialized. One can check if attrs are serializable by calling obj.json().

  • name (Optional[str] = None) – Optional unique name for medium.

  • frequency_range (Optional[Tuple[float, float]] = None) – [units = (Hz, Hz)]. Optional range of validity for the medium.

  • allow_gain (bool = False) – Allow the medium to be active. Caution: simulations with a gain medium are unstable, and are likely to diverge.Simulations where allow_gain is set to True will still be charged even if diverged. Monitor data up to the divergence point will still be returned and can be useful in some cases.

  • nonlinear_spec (Union[NonlinearSpec, NonlinearSusceptibility] = None) – Nonlinear spec applied on top of the base medium properties.

  • modulation_spec (Optional[ModulationSpec] = None) – Modulation spec applied on top of the base medium properties.

  • viz_spec (Optional[VisualizationSpec] = None) – Plotting specification for visualizing medium.

  • heat_spec (Union[FluidSpec, SolidSpec, SolidMedium, FluidMedium, NoneType] = None) – DEPRECATED: Use MultiPhysicsMedium. Specification of the medium heat properties. They are used for solving the heat equation via the HeatSimulation interface. Such simulations can beused for investigating the influence of heat propagation on the properties of optical systems. Once the temperature distribution in the system is found using HeatSimulation object, Simulation.perturbed_mediums_copy() can be used to convert mediums with perturbation models defined into spatially dependent custom mediums. Otherwise, the heat_spec does not directly affect the running of an optical Simulation.

  • permittivity (ConstrainedFloatValue = 1.0) – [units = None (relative permittivity)]. Relative permittivity.

  • N_c (Union[ConstantEffectiveDOS, IsotropicEffectiveDOS, MultiValleyEffectiveDOS, DualValleyEffectiveDOS, PositiveFloat]) – [units = 1/cm^3]. \(N_c\) Effective density of states in the conduction band.

  • N_v (Union[ConstantEffectiveDOS, IsotropicEffectiveDOS, MultiValleyEffectiveDOS, DualValleyEffectiveDOS, PositiveFloat]) – [units = 1/cm^3]. \(N_v\) Effective density of states in the valence band.

  • E_g (Union[ConstantEnergyBandGap, VarshniEnergyBandGap, PositiveFloat]) – [units = eV]. \(E_g\) Band-gap energy

  • mobility_n (Union[CaugheyThomasMobility, ConstantMobilityModel]) – Mobility model for electrons

  • mobility_p (Union[CaugheyThomasMobility, ConstantMobilityModel]) – Mobility model for holes

  • R (Tuple[Union[AugerRecombination, DistributedGeneration, RadiativeRecombination, ShockleyReedHallRecombination], ...] = []) – Array containing the R models to be applied to the material.

  • delta_E_g (Optional[SlotboomBandGapNarrowing] = None) – [units = eV]. \(\Delta E_g\) Bandgap narrowing model.

  • N_a (Union[NonNegativeFloat, SpatialDataArray, tuple[Union[tidy3d.components.tcad.doping.ConstantDoping, tidy3d.components.tcad.doping.GaussianDoping, tidy3d.components.tcad.doping.CustomDoping], ...]] = ()) – [units = 1/cm^3]. Concentration of acceptor impurities, which create mobile holes, resulting in p-type material. Can be specified as a single float for uniform doping, a SpatialDataArray for a custom profile, or a tuple of geometric shapes to define specific doped regions.

  • N_d (Union[NonNegativeFloat, SpatialDataArray, tuple[Union[tidy3d.components.tcad.doping.ConstantDoping, tidy3d.components.tcad.doping.GaussianDoping, tidy3d.components.tcad.doping.CustomDoping], ...]] = ()) – [units = 1/cm^3]. Concentration of donor impurities, which create mobile electrons, resulting in n-type material. Can be specified as a single float for uniform doping, a SpatialDataArray for a custom profile, or a tuple of geometric shapes to define specific doped regions.

Notes

Semiconductors are associated with Charge simulations. During these simulations the Drift-Diffusion (DD) equations will be solved in semiconductors. In what follows, a description of the assumptions taken and its limitations is put forward.

The iso-thermal DD equations are summarized here

\[\begin{equation} - \nabla \cdot \left( \varepsilon_0 \varepsilon_r \nabla \psi \right) = q \left( p - n + N_d^+ - N_a^- \right) \end{equation}\]
\[\begin{equation} q \frac{\partial n}{\partial t} = \nabla \cdot \mathbf{J_n} - qR \end{equation}\]
\[\begin{equation} q \frac{\partial p}{\partial t} = -\nabla \cdot \mathbf{J_p} - qR \end{equation}\]

As well as iso-thermal, the system is considered to be at \(T=300\). This restriction will be removed in future releases.

The above system requires the definition of the flux functions (free carrier current density), \(\mathbf{J_n}\) and \(\mathbf{J_p}\). We consider the usual form

\[\begin{equation} \mathbf{J_n} = q \mu_n \mathbf{F_{n}} + q D_n \nabla n \end{equation}\]
\[\begin{equation} \mathbf{J_p} = q \mu_p \mathbf{F_{p}} - q D_p \nabla p \end{equation}\]

where we simplify the effective field defined in [1] to

\[\begin{equation} \mathbf{F_{n,p}} = \nabla \psi \end{equation}\]

i.e., we are not considering the effect of band-gap narrowing and degeneracy on the effective electric field \(\mathbf{F_{n,p}}\). This is a good approximation for non-degenerate semiconductors.

Let’s explore how material properties are defined as class parameters or other classes.

Symbol

Parameter Name

Description

\(N_a\)

N_a

Ionized acceptors density

\(N_d\)

N_d

Ionized donors density

\(N_c\)

N_c

Effective density of states in the conduction band.

\(N_v\)

N_v

Effective density of states in valence band.

\(R\)

R

Generation-Recombination term.

\(E_g\)

E_g

Bandgap Energy.

\(\Delta E_g\)

delta_E_g

Bandgap Narrowing.

\(\sigma\)

conductivity

Electrical conductivity.

\(\varepsilon_r\)

permittivity

Relative permittivity.

\(q\)

tidy3d.constants.Q_e

Fundamental electron charge.

Example

>>> import tidy3d as td
>>> default_Si = td.SemiconductorMedium(
...     N_c=td.ConstantEffectiveDOS(N=2.86e19),
...     N_v=td.ConstantEffectiveDOS(N=3.1e19),
...     E_g=td.ConstantEnergyBandGap(eg=1.11),
...     mobility_n=td.CaugheyThomasMobility(
...         mu_min=52.2,
...         mu=1471.0,
...         ref_N=9.68e16,
...         exp_N=0.68,
...         exp_1=-0.57,
...         exp_2=-2.33,
...         exp_3=2.4,
...         exp_4=-0.146,
...     ),
...     mobility_p=td.CaugheyThomasMobility(
...         mu_min=44.9,
...         mu=470.5,
...         ref_N=2.23e17,
...         exp_N=0.719,
...         exp_1=-0.57,
...         exp_2=-2.33,
...         exp_3=2.4,
...         exp_4=-0.146,
...     ),
...     R=([
...         td.ShockleyReedHallRecombination(
...             tau_n=3.3e-6,
...             tau_p=4e-6
...         ),
...         td.RadiativeRecombination(
...             r_const=1.6e-14
...         ),
...         td.AugerRecombination(
...             c_n=2.8e-31,
...             c_p=9.9e-32
...         ),
...     ]),
...     delta_E_g=td.SlotboomBandGapNarrowing(
...         v1=6.92 * 1e-3,
...         n2=1.3e17,
...         c2=0.5,
...         min_N=1e15,
...     ),
...     N_a=[td.ConstantDoping(concentration=1e15)],
...     N_d=[td.ConstantDoping(concentration=1e15)]
... )

Warning

Current limitations of the formulation include:

  • Boltzmann statistics are supported

  • Iso-thermal equations with \(T=300K\)

  • Steady state only

  • Dopants are considered to be fully ionized

Note

  • Both \(N_a\) and \(N_d\) can be either a positive number or an xarray.DataArray.

  • Default values for parameters and models are those appropriate for Silicon.

  • The current implementation is a good approximation for non-degenerate semiconductors.

Attributes

attrs

Methods

check_eg_uses_model(val, values)

Issue deprecation warning if float is provided

check_na_uses_model(val, values)

Issue deprecation warning if float is provided

check_nc_uses_model(val, values)

Issue deprecation warning if float is provided

check_nd_uses_model(val, values)

Issue deprecation warning if float is provided

check_nv_uses_model(val, values)

Issue deprecation warning if float is provided

Inherited Common Usage

N_c#
N_v#
E_g#
mobility_n#
mobility_p#
R#
delta_E_g#
N_a#
N_d#
classmethod check_nc_uses_model(val, values)[source]#

Issue deprecation warning if float is provided

classmethod check_nv_uses_model(val, values)[source]#

Issue deprecation warning if float is provided

classmethod check_eg_uses_model(val, values)[source]#

Issue deprecation warning if float is provided

classmethod check_nd_uses_model(val, values)[source]#

Issue deprecation warning if float is provided

classmethod check_na_uses_model(val, values)[source]#

Issue deprecation warning if float is provided

__hash__()#

Hash method.