Electrothermal effects in various through silicon via (TSV) arrays are investigated in this paper. An equivalent lumped-element circuit model of a TSV pair is derived. The temperature-dependent TSV capacitance, silicon substrate capacitance and conductance are examined for low-, medium-, and high-resistivity silicon substrates, respectively. The partial-element equivalent-circuit (PEEC) method is employed for calculating per-unit-length (p.u.l.) resistance, inductance, insertion loss and characteristic impedances of copper and polycrystalline silicon (poly-Si) TSV arrays, and their frequency- and temperature-dependent characteristics are treated rigorously. The modified time-domain finite-element method (TD-FEM), in the presence of a set of periodic differential-mode voltage pulses, is also employed for studying transient electrothermal responses of 4- and 5-TSV arrays made of different materials, with their maximum temperatures and thermal crosstalk characterized thoroughly.
"Electrothermal Effects in High Density through
Silicon via (Tsv) Arrays," Progress In Electromagnetics Research,
Vol. 115, 223-242, 2011. doi:10.2528/PIER11030503
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