tidy3d.HurkxDirectBandToBandTunneling

tidy3d.HurkxDirectBandToBandTunneling#

class HurkxDirectBandToBandTunneling[source]#

Bases: Tidy3dBaseModel

This class defines a direct band-to-band tunneling recombination model based on the Hurkx model as described in [1].

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().

  • A (PositiveFloat = 400000000000000.0) – [units = 1/(cm^3 s)]. Parameter \(A\) in the direct BTBT Hurkx model.

  • B (float = 1900000.0) – [units = V/cm]. Parameter \(B\) in the direct BTBT Hurkx model.

  • E_0 (PositiveFloat = 1) – [units = V/cm]. Reference electric field \(E_0\) in the direct BTBT Hurkx model.

  • sigma (float = 2.5) – Exponent \(\sigma\) in the direct BTBT Hurkx model. For direct semiconductors \(\sigma\) is typically 2.0, while for indirect semiconductors \(\sigma\) is typically 2.5.

Notes

The direct band-to-band tunneling recombination rate \(R^{\text{BTBT}}\) is primarily defined by the material’s bandgap energy \(E_g\) and the electric field \(F\).

Default values are provided for silicon.

\[R^{\text{BTBT}} = A \cdot \frac{n \cdot p - n_i^2}{(n + n_i) \cdot (p + n_i)} \cdot \left( \frac{|\mathbf{E}|}{E_0} \right)^{\sigma} \cdot \exp \left(-\frac{B}{|\mathbf{E}|} \cdot \left( \frac{E_g}{E_{g, 300}} \right)^{3/2} \right)\]

where \(A\), \(B\), \(E_0\), and \(\sigma\) are material-dependent parameters.

Example

>>> import tidy3d as td
>>> default_Si = td.HurkxDirectBandToBandTunneling(
...   A=1e19,
...   B=1.9e6,
...   E_0=1,
...   sigma=2.5
... )

References

Attributes

attrs

Methods

Inherited Common Usage

A#
B#
E_0#
sigma#
__hash__()#

Hash method.