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:

  • 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

A

B

E_0

sigma

A#
B#
E_0#
sigma#