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

The effective resistivity (ρ
_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 ρ
_eff
decreases by several orders of magnitude at millimeter-wave frequencies. The explanation for this decay is twofold. First, the original expression of ρ
_eff
does not include dielectric losses. Second, the imaginary part of the characteristic impedance (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 ρ
_eff
and the dielectric losses simultaneously and by introducing a novel method to correct J(Z
_c
). Finally, it is shown that this extraction method enables the correct extraction of substrate parameters up to 220 GHz.