Physics-based modeling of cobalt-doped nickel-zinc on-chip ferrite inductors

Abstract

The miniaturization of integrated voltage regulators (IVRs) for multi-core processors is fundamentally bottlenecked by the high-frequency magnetic losses of conventional inductor cores. This study presents a rigorous computational framework to optimize Cobalt-doped Nickel-Zinc ferrite (Ni_(1-x) Zn_0.4 Co_x Fe_2 O_4) for 10 MHz on-chip power delivery. Utilizing Landau-Lifshitz-Gilbert (LLG) relaxation dynamics and Maxwell-Wagner interfacial polarization, the complex electromagnetic dispersion was modeled and quantitatively validated against recent empirical literature. Furthermore, high-temperature power loss density was bounded using the trust region reflective (TRF) numerical curve fitting algorithm to validate an anisotropy-compensated "thermal valley" at 80 °C. A multi-objective sensitivity analysis identified a high-efficiency Cobalt "sweet spot" at a concentration of x=0.04. This specific formulation optimally stiffens domain walls, safely shifting the resonance frequency to 40 MHz and maximizing the quality factor (Q) at the 10 MHz operational target. When applied to a simulated 3.5 V to 1.0 V DC-DC buck converter, the optimized x=0.04 core demonstrated its adequacy for on-chip applications by maintaining >90% power efficiency under a rigorous 2.0 A load. These predictive results mathematically prove that precision Cobalt doping is a highly viable strategy for suppressing parasitic losses in next-generation 3D-IC power delivery networks.