Effective Resistivity Extraction of Low-Loss Silicon Substrate at Millimeter-Wave Frequencies

The effective resistivity $(\rho_{eff})$ is a Figure of merit commonly used to compare the RF performance of a substrate from the measurements of CPW lines. For highly resistive substrates, such as the trap-rich substrate, the extracted $\rho_{eff}$ decreases by several orders of magnitude at millimeter-wave frequencies. The explanation for this decay is twofold. First, the original expression of $\rho_{eff}$ does not include dielectric losses. Second, the imaginary part of the characteristic impedance $(\mathfrak{J}(Z_{c}))$ is not well extracted, which leads to an incorrect separation of the total losses among the metal and substrate losses. This paper solves both issues by presenting a new procedure to extract $\rho_{eff}$ and the dielectric losses simultaneously and by introducing a novel method to correct $\mathfrak{J}(Z_{c})$. Finally, it is shown that this extraction method enables the correct extraction of substrate parameters up to 220 GHz.