Accurate Modeling of the Capacitance of Through-Silicon Via Considering Minority Carrier Effects

The 3-D integration of integrated circuits based on through-silicon via (TSV) is a promising technology to achieve high-performance, multifunctional, and heterogeneous microsystem. The voltage-dependent and frequency-dependent TSV capacitances have a predominant impact on system performance. Accordingly, accurate electrical modeling of TSV capacitance is critical for system design. This article proposes an accurate small-signal analysis method capable of modeling the low-frequency and high-frequency TSV capacitances. The contribution of both fixed carriers and mobile carriers are considered in the model. Moreover, the minority carrier effects are incorporated to model the high-frequency capacitance accurately. The proposed model shows a good correlation with measurement and device-level simulation. Analysis and experiment demonstrate neglecting the minority carrier effects lead to huge inaccuracy of TSV capacitance, which can be up to 30.1% in the strong inversion region. Therefore, it is important to consider the minority carrier effects in the modeling of high-frequency TSV capacitance. In addition, the proposed model consumes small computational cost benefit from efficient iterative procedures.