tidy3d.SelberherrImpactIonization

tidy3d.SelberherrImpactIonization#

class SelberherrImpactIonization[source]#

Bases: Tidy3dBaseModel

This class defines the parameters for the Selberherr impact ionization model. Two formulations are available that depend on the driving field, as described in [1] (\(\| E \|\)) and [2] (\(E \cdot J_{\nu} / \| E \|\) for \(\nu = n,p\)).

Parameters:

  • alpha_n_inf (PositiveFloat) – [units = 1/cm]. Electron ionization coefficient at infinite field.

  • alpha_p_inf (PositiveFloat) – [units = 1/cm]. Hole ionization coefficient at infinite field.

  • E_n_crit (PositiveFloat) – [units = V/cm]. Critical electric field for electrons.

  • E_p_crit (PositiveFloat) – [units = V/cm]. Critical electric field for holes.

  • beta_n (PositiveFloat) – Exponent for electrons.

  • beta_p (PositiveFloat) – Exponent for holes.

  • formulation (Literal['Selberherr', 'PQ'] = PQ) – Formulation used for impact ionization. Options are ‘Selberherr’ or ‘PQ’ for Selberherr and Palankovski and Quay formulations, respectively.

Notes

The impact ionization rate \alpha_{\nu} (for \(\nu = p\) (holes) and \(\nu = n\) (electrons)) is defined by:

\[\alpha_{\nu} = \alpha_{\nu}^\infty \cdot \exp \left( - \left( \frac{E_{\nu}^{\text{crit}} \cdot |\mathbf{J}_{\nu}|}{E \cdot \mathbf{J}_{\nu}} \right)^{\beta_{\nu}} \right)\]

where \(\alpha_{\nu}^\infty\), \(E_{\nu}^{\text{crit}}\), and \(\beta_{\nu}\) are material-dependent parameters.

Example

>>> import tidy3d as td
>>> default_Si = td.SelberherrImpactIonization(
...   alpha_n_inf=7.03e5,
...   alpha_p_inf=1.582e6,
...   E_n_crit=1.23e6,
...   E_p_crit=2.03e6,
...   beta_n=1,
...   beta_p=1,
...   formulation='PQ'
... )

References

Attributes

alpha_n_inf

alpha_p_inf

E_n_crit

E_p_crit

beta_n

beta_p

formulation

alpha_n_inf#
alpha_p_inf#
E_n_crit#
E_p_crit#
beta_n#
beta_p#
formulation#