Determining the Effective Permeability of a Laminated CoZrTaB (CZTB) Film Through Consideration of Demagnetization Effects and Eddy-Displacement Currents

Multilaminated thin-film inductors are a key to emerging technology that enables highly integrated, on-chip voltage regulators. The permeability of a magnetic core at high frequency is a key determiner of inductance density. In this article, a multilamination magnetic core made up of alternate CoZrTaB (CZTB) amorphous, uniaxially anisotropic magnetic films and AlN dielectric layers is investigated. The individual films are approximately 200 nm thick, appropriate for operation at over 100 MHz, but the laminated structure and overall thickness of several micrometers mean that analytical methods are impractical for computing demagnetization. Magnetostatic finite element analysis (FEAs) is used to model the magnetic core demagnetization, accounting for various length/width dimensions, magnetic film thicknesses, and dielectric thicknesses. At higher frequencies, the dielectric layers, which are included in the structure to suppress induced eddy currents, allow displacement currents to flowthrough the dielectric layers and lead to increased eddy currents circulating around the overall core structure, thus further increasing loss and reducing permeability. Eddy current FEA simulations, which include the displacement currents and an analytically derived equivalent circuit model (ECM), are used to model the real and imaginary (loss) components of permeability spectra. The work, therefore, determines the combined contributions of both demagnetization effects and eddy displacement currents to the reductions in real permeability and the increase in loss components for thicker multilaminated magnetic cores. Permeameter measurements on fabricated cores, having ten laminations, and with various AlN thicknesses (10, 20, 40, and 60 nm) gave excellent agreement with the predicted effective permeability through the approach of combining the FEA and ECM models, over the 10 MHz to 1 GHz frequency range. It was shown, that at 100 MHz, for multilaminated cores with thin or higher k dielectric layers, displacement-eddy currents are dominant, giving a power loss an order of magnitude higher than would be for magnetically induced eddy currents alone.