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

Abstract

AbstractThe effective resistivity (ρeff) 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 ρeff 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 ρeff 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 ρeff 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.