Abstract:
The electrical behavior of on-chip interconnects has become a dominant factor
in silicon-based high speed, RF, and mixed-signal integrated circuits. In particular,
the frequency-dependent loss mechanisms in heavily-doped silicon substrates can
have a large influence on the transmission characteristics of on-chip interconnects.
To optimize the performance of the integrated circuit, efficient interconnect models
should be available in the design environment. Interconnect models in the form
of closed-form expressions or ideal element equivalent circuits are often desirable
for fast simulation and circuit optimization. This thesis work is concentrated on
the analysis and the methodology for developing closed-form expressions for the
frequency-dependent line parameters R(ω), L(ω), G(ω), and C(ω) for coplanar-type
on-chip interconnects on silicon substrates. In addition, the closed-form expressions
for the frequency-dependent series impedance parameters are extended to general
interconnect on-chip structures on multilayer substrates.
The complete solutions of the frequency-dependent line parameters are formulated
in terms of corresponding static (lossless) configurations for which closed-form
solutions are readily available. The closed-form expressions for the frequency-dependent series impedance parameters, R(ω) and L(ω), are obtained from a generalized complex image approach together with a surface impedance formulation including the effects of the frequency-dependent horizontal currents (eddy currents)
in the multilayer lossy silicon substrates. Results for single and coupled microstrips
on multilayer silicon substrates are shown over a broadband frequency range of 20
GHz and compared with full-wave electromagnetic solutions. For single and coupled
coplanar on-chip interconnects, the results are compared with quasi-analytical
solutions and validated with available measurement data. The frequency-dependent
shunt admittance parameters, G(ω) and C(ω), are derived in terms of low- and
high-frequency asymptotic solutions of the equivalent circuit model combined with
the complex image method. Comparisons and validation with measurements are
also presented.
