A physics-aware methodology for equivalent circuit model extraction of TSV-inductors

TSV-inductor has become a viable on-chip inductor option to ensure low-power, low-cost, and high-integration. Thus, it is imperative to accurately and efficiently model the electrical behavior of a TSV-inductor. Unlike the conventional 3D electro-magnetic wave model that suffers from its incapability of efficient time-domain SPICE simulation, in this paper, a systematic equivalent circuit model extraction methodology is presented to accurate the model of on-chip TSV-inductors in 3D IC. The circuit topology is based on a π -circuit with additional branches accounting for substrate coupling, signal crosstalk, skin and proximity effects. The parasitics are then extracted from the measured network parameters using an improved vector fitting method. Experimental results show that the proposed methodology is able to achieve a TSV-inductor equivalent circuit with very high accuracy with up to 10−4 deviation in S parameter comparison and 0.024% relative error in quality comparison.