Effective resistivity extraction of low-loss silicon substrates at millimeter-wave frequencies

Abstract

The effective resistivity (ρ eff ) is a figure of merit commonly used to assess the radio-frequency performance of a substrate from the measurements of coplanar waveguide lines. For highly resistive substrates, such as the trap-rich (TR) substrate, the extracted ρ eff decreases by several orders of magnitude at millimeter-wave frequencies. The explanation for this decay is twofold. First, the imaginary part of the characteristic impedance ${\rm \lpar \Im }\lpar Z_c\rpar \rpar$ is not well extracted, which leads to an incorrect separation of the total losses among the metal and substrate losses. Second, the original expression of ρ eff does not include dielectric losses, which might become non-negligible at millimeter-wave frequencies. 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 ${\rm \Im }\lpar {Z_c} \rpar$ . Furthermore, it is shown that this extraction method enables the correct extraction of substrate parameters up to 220 GHz of TR and high-resistivity silicon substrates. Finally, the origin of the large extracted value of dielectric loss is discussed in the potential presence of surface roughness and surface wave radiation. Both phenomena are discounted thanks to measurements of an additional reflective structure and a standard impedance substrate.

High-Temperature Characterization of Multiple Silicon-Based Substrate for RF-IC Applications

“…Those fluctuations come from the fact that these substrates are quasilossless, and the lineic conductance parameters extracted from the CPW line measurements are then very low, and prone to calibration and probing errors as well as measurement noise. It is then a challenge to extract accurate ρ eff data above 10 kΩ • cm [18]. Std silicon substrate exhibits a ρ eff of 10 Ω • cm from 5 GHz and up to 40 GHz.…”