A novel synthesis of Rent's rule and effective-media theory predicts FEOL and BEOL reliability of self-heated ICs

Precise specification of local temperature, T(x, y, z), in ICs with self-heated surround-gate transistors (SG-FET) is essential to predict transistor and interconnect reliability, especially for Arrhenius-activated degradation modes, such as NBTI, HCI, electromigration, etc. One may calculate T(x, y, z) by 3D Finite element modeling (FEM), but the complex back end of line (BEOL) structure, with 8~10 layers of multiple-connected percolating interconnects, makes this approach impractical for pre-Silicon design/optimization or fast turn-around reliability modeling. In this context, a physics-based, predictive effective media theory (EMT) for BEOL will transform the reliability modeling of self-heated SG-FET technologies. Therefore, in this paper, we (i) develop a physics based electro-thermal compact model for ICs (including the BEOL), based on an innovative synthesis of Rent's rule, EMT for ellipsoidal inclusion, and thermal image charge theory; (ii) validate the model by comparing against 3D FEM results and experimental data from the industry, and (iii) predict BEOL reliability (i.e., electromigration at the specific metal level) and front end of line (FEOL) reliability (i.e., NBTI, HCI) based on the temperature profile. Since the model anticipates changes in T(x, y, z) with interconnect layout and geometry (e.g., wire length and number distribution, metal volumetric fraction, thermal resistance, etc.), our physics-based model suggests exciting opportunities for reliability-aware optimization of self-heated IC.