Dynamic Frequency Scaling Aware Opportunistic Through-Silicon-Via Inductor Utilization in Resonant Clocking

LC resonant clock is a viable option for low power on-chip clock distributions. A major limiting factor to its implementation is the large area overhead due to the use of conventional spiral inductors. On the other hand, idle through-silicon-vias (TSVs) in 3-D integrated circuits (3-D ICs) can form vertical inductors with minimal footprint and have little noise coupling with horizontal traces, particularly suitable for the application of LC resonant clock. However, due to the strict constraints on the location of idle TSVs, the use of the TSV inductor is constrained by its location, inductance, and quality factor. The problem is further complicated by dynamic frequency scaling (DFS), where the resonant tanks need to accommodate multiple clock frequencies. Moreover, these TSV inductors can be in any orientation with any distance apart, thereby causing complicated coupling effects. In this paper, we first present a novel scheme to opportunistically use idle TSVs to form inductors in LC resonant clock of 3-D ICs for maximum power reduction in clock-distribution network (CDN) at a fixed frequency, and then extend it to DFS schemes. Experimental results on a few industrial designs for the resonant CDNs operated at a fixed frequency of 3 GHz show that the power consumption is reduced by up to 47.9% compared with the conventional CDNs without resonant clocking. In addition, for the resonant CDNs with DFS scheme, the power consumption reduced by up to 42.3%, 39.0%, 38.3%, 34.3%, and 28.6% at 3, 2.5, 2, 1.5, and 1 GHz frequency, respectively, compared with the CDNs without resonant clocking. When compared with CDNs with conventional spiral inductors, our scheme with TSV inductors can reduce the inductor footprint by up to $6.30 \times$ with the same power consumption.