Accurate Electrical Modeling of Through Silicon Via with Minority Carrier Redistribution Effect

Accurate electrical models for Through Silicon Via (TSV) are critical for 3D integration system design, in which TSV capacitance plays an important role. Minority carrier redistribution (MCR) effect, the spatial position rearrangement of minority carrier in inversion layer, is considered in TSV modeling in this paper. The importance of taking MCR into account is illustrated by comparing the TSV capacitance calculated by capacitance models with and without MCR for a square-shape TSV. Parametric study of errors result from neglecting MCR is performed on several physical and material parameters. A more accurate electrical model for square-shape TSV based on 3D transmission line matrix method (3D-TLM) is proposed, and transient analysis using this model is performed to reveal the effect of MCR on the noise coupling.