An Embedded Multi-Layer Spiral Square Inductor for Integrated Power Delivery - Physical Design and Analytical Models

Planar inductors are widely utilized in traditional, PCB-level switching mode power supplies. To mitigate prohibitive power loss in modern high-performance integrated systems, power converters should be embedded closer to points-of-load (POLs). The large footprint and limited inductance density of planar inductors, is a primary concern in these modern power delivery architectures. To mitigate the insufficient inductor current density, vertically stacked on/in-interposer inductors have recently proposed. To facilitate vertically stacked inductors in practical systems, device architecture and respective analytical models are required. In this paper, a fully embedded multi-layer spiral square inductor is proposed to maximize inductance density through coupling. The inductor is designed and simulated with COMSOL Multiphysics, yielding the inductance density of up to 440 nH/mm2 (as compared to 127 nH/mm2 with state-of-the-art). Comprehensive design space exploration of inductor performance is, however, impractical with COMSOL due to high computational complexity of the underlying Finite Element Method (FEM). To facilitate an efficient exploration of tradeoffs with the proposed architecture, analytical physics-aware models are proposed. The model is validated based on COMSOL Multiphysics with up to ten layers, exhibiting over 95.8% accuracy with more than two layers.