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Integrated Inductors with Magnetic Materials for On-Chip ... - Hot Chips

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Complex Permeability Model<br />

δ =<br />

2ρ<br />

ωµ iµ o<br />

δ = skin depth<br />

ρ = resistivity of magnetic film<br />

ω = frequency<br />

µ i = relative dc permeability<br />

d = film thickness<br />

µ =<br />

µ<br />

i<br />

( 1<br />

2δ ( 1+<br />

j)<br />

d<br />

tanh<br />

+ j)<br />

d 2δ<br />

High resistivity materials<br />

are needed to reduce<br />

the eddy currents and<br />

increase the skin depth.<br />

CoZrTa ρ = 100 µΩ-cm

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