Magnetic Core TSV-Inductor Design and Optimization for On-chip DC-DC Converter

The conventional on-chip spiral inductor consumes a significant top-metal routing area, thereby preventing its popularity in many on-chip applications. Recently through-silicon-via– (TSV) based inductor (also known as a TSV-inductor) with a magnetic core has been proved to be a viable option for the on-chip DC-DC converter. The operating conditions of these inductors play a major role in maximizing the performance and efficiency of the DC-DC converter. However, there is a critical need to study the design and optimization details of magnetic core TSV-inductors with the unique three-dimensional structure embedding magnetic core. This article aims to provide a clear understanding of the modeling details of a magnetic core TSV-inductor and a design and optimization methodology to assist efficient inductor design. Moreover, a machine learning–assisted model combining physical details and artificial neural network is also proposed to extract the equivalent circuit to further facilitate DC-DC converter design. Experimental results show that the optimized TSV-inductor with the magnetic core and air-gap can achieve inductance density improvement of up to 7.7 \( \times \) and quality factor improvements of up to 1.6 \( \times \) for the same footprint compared with the TSV-inductor without a magnetic core. For on-chip DC-DC converter applications, the converter efficiency can be improved by up to 15.9% and 6.8% compared with the conventional spiral and TSV-inductor without magnetic core, respectively.