Frequency- and Temperature-Dependent Modeling of Coaxial Through-Silicon Vias for 3-D ICs

Abstract

Temperature-dependent investigations of circular and square coaxial through-silicon vias (C-TSVs) are carried out in this paper, which can provide an effective solution to suppressing various couplings, such as intra- and intersubstrate, and crosstalk among multi-TSVs. An equivalent lumped-element circuit model is proposed for both C-TSVs, and their parasitic capacitance values, per-unit-height distributed parameters, characteristic impedance values, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters are characterized and compared numerically for different frequencies and temperatures. Furthermore, self-heating effects in both C-TSVs are investigated with a set of closed-form equations derived for determining their thermal resistances. Their average power handling capabilities are addressed, which are verified using the static finite-element method.