Modeling of Short-Millimeter-Wave CMOS Transmission Line with Lossy Dielectrics with Specific Absorption Spectrum

On-chip transmission lines are widely used in ultrahigh-frequency integrated circuits. One of the issues in modeling such transmission lines is that no reference impedance can be established on a chip. Conventionally, the parallel admittance Y-p has been adopted as a reference parameter for on-chip transmission lines instead of a reference characteristic impedance of 50 Omega. In the case of CMOS processes, however, Y-p can have complicated characteristics in the short-millimeter-wave band owing to the frequency characteristics of the electric permittivity of low-k materials, which cannot be expressed using a simple circuit. To solve this problem, we propose the use of the series impedance Z(s) as a reference parameter for transmission-line modeling since it basically can be determined from the geometrical dimensions and the frequency-stable permeability and resistivity. The parameters of transmission lines obtained by the proposed method were compared with those obtained by conventional methods using a 40 nm CMOS process. By using the equivalent circuit model of Y-p along with PLC resonators, it is shown that the peaks of the frequency characteristics of Y-p can be used to explain the absorption spectrum of the dielectric. This suggests that the proposed method is suitable for CMOS short-millimeter-wave transmission lines.