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flex_rf.tidy3d.HammerstadSurfaceRoughness

Type: class Base(s): AbstractSurfaceRoughness

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

The power loss compared to smooth surface is described by:

1+(RF1)2πarctan(1.4Rq2δ2)1 + (RF-1) \frac{2}{\pi}\arctan(1.4\frac{R_q^2}{\delta^2})

where δ\delta is skin depth, RqR_q the RMS peak-to-vally height, and RF roughness factor.

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.

rq [PositiveFloat]

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.

roughness_correction_factor(frequency: ArrayFloat1D, skin_depths: ArrayFloat1D)

Complex-valued roughness correction factor applied to surface impedance.