Hammerstad Surface Roughness

HammerstadSurfaceRoughness is a modified Hammerstad model for surface roughness correction in a LossyMetalMedium.

This object corresponds to tidy3d.rf.HammerstadSurfaceRoughness (opens new window).

Roughness

rq: RMS peak-to-valley height of the surface roughness.

• Type: float number
• Unit: um
• Constraint: greater than 0
• Required field

Roughness Factor

roughness_factor: Expected maximum increase in conductor loss due to the roughness effect.

• Type: float number
• Constraint: greater than 1
• Default: 2

Roughness Correction

The power loss compared to a smooth surface is modeled as:

$1 + (RF - 1)\frac{2}{\pi}\arctan\left(1.4\frac{R_q^2}{\delta^2}\right)$

where $\delta$ is skin depth, $R_q$ is the RMS peak-to-valley height, and $RF$ is the roughness factor.

NOTE

The model is commonly used for RF conductors when the Hammerstad roughness approximation is appropriate for the surface finish and frequency range.