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Abstract-In nanometer technologies, shallow trench isolation (STI) induces thermal residual stress in active silicon due to post-manufacturing thermal mismatch. The amount of STI around an active region depends on the layout of the design, and the biaxial stress due to STI results in placement-dependent variations in the the transistor mobilities and threshold voltages of the active devices. An analytical model based on inclusion theory in micromechanics is employed to accurately estimate the stresses and the strains induced in the active region by the surrounding STI in the layout. The induced changes in mobility and threshold voltage changes are computed at the transistor level, and then propagated to the gate and circuit levels to predict circuit-level delay and leakage power for a given placement.

In 3-D ICs, through silicon via (TSV)-induced thermal residual stress impacts several transistor electrical parameters-low-field mobility, saturation velocity, and threshold voltage. These thermal-stress related shifts are coupled with other temperature effects on transistor parameters that are seen even in the absence of TSVs. In this paper, analytical models are developed to holistically represent the effect of thermallyinduced variations on circuit timing. A biaxial stress model is built, based on a superposition of 2-D axisymmetric and Boussinesq-type elasticity models. The computed stresses and strains are then employed to evaluate transistor mobility, saturation velocity, and threshold voltage. The electrical variations are translated into gate-level delay and leakage power calculations, which are then elevated to circuit-level analysis to thoroughly evaluate the variations in circuit performanceinduced by TSV stress. Index Terms-3-D IC, finite element method (FEM), static timing analysis, through silicon via (TSV).

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