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 7.7x and quality factor improvements of up to 1.6x for the same footprint compared with the TSVinductor 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.