Derivation and Analysis of a Hemispherical Physical Model and the Correction Factors for the Sidewall Roughness of Through-Glass Vias

The sidewall roughness of through-glass vias (TGVs) at high frequencies significantly impacts the integrity and reliability of signal transmissions via the inductance and resistance-correction factors resulting from the combined effect of the skin depth and sidewall roughness. Here, to further investigate the generation and mechanism of the correction factors, a hemispherical physical model of the sidewall roughness of actual TGVs is proposed, and the
${RL}$
model comprising the skin depth and sidewall roughness is derived; the measured results were compared with the causal hemispherical model and the multilevel causal Huray model, and it was verified that the proposed hemispherical model can calculate the
${RL}$
parasitic parameters of TGV with high accuracy. Concurrently, the proposed hemispherical model confirms that the correction factor for internal inductance is larger than that for resistance; it can explore the main source of sidewall-roughness-induced parasitic effects. Moreover, the model offers a solution for reducing the sidewall-roughness-induced parasitic effects.