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 (sic(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 (sic(Z(c)));. Finally, it is shown that this extraction method enables the correct extraction of substrate parameters up to 220 GHz.