tidy3d.rf.HammerstadSurfaceRoughness

tidy3d.rf.HammerstadSurfaceRoughness#

class HammerstadSurfaceRoughness[source]#

Bases: AbstractSurfaceRoughness

Modified Hammerstad surface roughness model. It’s a popular model that works well under 5 GHz for surface roughness below 2 micrometer RMS.

Parameters:

  • rq (PositiveFloat) – [units = um]. RMS peak-to-valley height (Rq) of the surface roughness.

  • roughness_factor (float = 2.0) – Expected maximal increase in conductor losses due to roughness effect. Value 2 gives the classic Hammerstad equation.

Note

The power loss compared to smooth surface is described by:

\[1 + (RF-1) \frac{2}{\pi}\arctan(1.4\frac{R_q^2}{\delta^2})\]

where \(\delta\) is skin depth, \(R_q\) the RMS peak-to-vally height, and RF roughness factor.

Note

This model is based on:

Y. Shlepnev, C. Nwachukwu, “Roughness characterization for interconnect analysis”, 2011 IEEE International Symposium on Electromagnetic Compatibility, (DOI: 10.1109/ISEMC.2011.6038367), 2011.

V. Dmitriev-Zdorov, B. Simonovich, I. Kochikov, “A Causal Conductor Roughness Model and its Effect on Transmission Line Characteristics”, Signal Integrity Journal, 2018.

Attributes

rq

roughness_factor

Methods

roughness_correction_factor(frequency, ...)

Complex-valued roughness correction factor applied to surface impedance.
rq#
roughness_factor#
roughness_correction_factor(frequency, skin_depths)[source]#

Complex-valued roughness correction factor applied to surface impedance.

Notes

The roughness correction factor should be causal. It is multiplied to the surface impedance of the lossy metal to account for the effects of surface roughness.

Parameters:

  • frequency (ArrayFloat1D) – Frequency to evaluate roughness correction factor at (Hz).

  • skin_depths (ArrayFloat1D) – Skin depths of the lossy metal that is frequency-dependent.

Returns:

The causal roughness correction factor evaluated at frequency.

Return type:

ArrayComplex1D