ELECTROTHERMAL EFFECTS IN HIGH DENSITY THROUGH SILICON VIA (TSV) ARRAYS

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.