Characterization of dielectric and magnetic properties of materials Irena Zivkovic

Outline • Motivation • Basics of material losses mechanisms • Permittivity and permeability – physical models • Material characterization

• Conclusion

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Motivation for our work • Our interest – absorbing materials from Emerson&Cuming company, we use these absorbers in several projects for calibration targets design • Emerson&Cuming is big supplier of absorbing materials worldwide • Motivation:company provided limited knowledge about ε and µ up to 18GHz • We need parameter knowledge of absorbers up to 150GHz frequency

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IAP projects with E&C absorbing materials • •

ALMA – Atacama Large Millimeter/submillimeter Array Goal S11< -55dB

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IAP Projects with E&C absorbing materials • Sentinel 3 satellite - microwave radiometer ground calibration target • 23.8GHz and 36.5GHz

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IAP projects with E&C absorbing materials • LMCL – Low Mass Calibration Load hybrid design

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Other applications of absorbing materials

     

Invisible airplanes (military applications) Calibration targets Electromagnetic shielding Antennas Anechoic chambers etc…

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Material parameters ε and µ -

Dielectric permittivity

ε

- Magnetic permeability

[] F m

μ

[] H m

ε= ε0 ε r

μ= μ r μ 0

D= ε E

B= μH

D – dielectric displacement field E – electric field B – magnetic flux density H – magnetic field ε, μ relative complex permittivity and permeability

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Complex permittivity and permeability • Complex permittivity

ε = ε '+ jε ''

• Dielectric loss tangent

ε '' tan δ e = ' ε

• Complex permeability

μ= μ'+ jμ''

• Magnetic loss tangent

μ '' tan δ m = ' μ

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Kramers – Kronig relation • Real and imaginary parts of ε and µ are not independent

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Propagation loss in materials •

Inside of material:

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wavelength shorter velocity slower magnitude attenuated

γ is a propagation constant α is attenuation constant β is phase constant

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Dielectric loss • Electric field : - tries to align electric dipoles that exist - induces electric dipoles and then align them •

The total effect of electromagnetic field on material is polarization: - Interface polarization - Electronic polarization - Ionic polarization - Orientational polarization

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Dielectric loss – electronic polarization

• Weak for spherical atoms • Non spherical atoms (Si, Ge, etc.) ε comes exclusively from electronic polarization (Si ε=12) • Atoms in crystals and solids usually not spherical

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Dielectric loss – ionic polarization

• NaCl, natural dipoles but net polarization is zero • Try to adjust dipole moments with external field

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Dielectric loss – orientational polarization

• Liquids and gases – molecules can freely rotate • Example - water

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Dielectric losses – frequency dependence

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Magnetic loss • Magnetic moment – whenever current flows in closed circle • Magnetic domain wall displacement and rotation and eddy currents

• Increasing of external field change behavior in materials until it reach saturation (need external field in opposite direction to return them - hysteresis) • Low frequencies – domain wall movement and eddy currents (if it is conductive magnetic material) 17

Debye model

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Relaxation behavior: dielectric materials, magnetic composite materials

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Lorenzian model

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Resonance behavior: magnetic domain wall displacement 19

ε and µ of composite materials • •

Composite materials – epoxy (matrix) + magnetic particles (inclusion) Maxwell-Garnett formula for effective permittivity of composite materials

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Emerson and Cuming materials notation • CRXXX (CR110,CR112,etc.) or CRSXXX (silicon based, CRS110, CRS112, etc.) • Composite materials, epoxy (matrix) + magnetic particles (inclusions) (magnetically loaded) • Materials that we use are CR110, CR114 and CRS117

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Measurements and parameter extractions • Scattering parameters S11 and S21

b1 S11= a1

b2 S21= a1

• Some measurement techniques for S11 and S21: - open ended coaxial probe method - transmission – reflection type waveguide method - free space method

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Open ended coaxial probe method • Advantages: broadband and noninvasive, good for liquids and semi-solids • Shortcomings: semi infinite samples, non magnetic materials, flat, no air gaps

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Transmission – reflection type waveguide method • Advantages: calculate both ε and µ, broadband, anisotropic materials can be measured • Shortcomings: big error if air gaps exist between sample and the wall of waveguide, homogeneous samples, smooth flat faces

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Free space technique • Advantages: non destructive technique, suitable for high temperatures, for both dielectric and magnetic materials • Shortcomings: sample size (low frequency – big sample), homogeneous and flat plane-parallel samples

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Instruments at IAP • Network analyzer HP 8510 (frequencies up to 50GHz) • Submillimeter Vector Network Analyzer from Abmm (frequencies up to 0.8THz, amplitude and phase measurements) • Corrugated horn antennas and waveguides

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Free space measurements • Abmm Network Analyzer • Free space measurements with corrugated horn antennas • Measured frequency range is from 22 to 145GHz • For frequencies from 100 to 145GHz optical setup is used

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Parameter extraction - Nicolson Ross Weir technique

• Needs two indipendent measurements : S11 and S21 of one material sample • Advantages: accurate result for noise free data • Shortcomings: sensitive to noisy data, phase ambiguity - many possible solutions

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Our approach – numerical least square fitting method • Models that represents ε and µ • Model for S21 calculation from free space measurements (input parameters are frequency, thickness of the sample, ε and µ) • Non-linear least square fitting routine (simulated data fitted with measurements) • Not possible to calculate ε and µ only from transmission measurements • Starting points: - low frequency ε calculated from measured capacitance of the sample - high frequency µ=1 29

Free space measurements and fitted results CR110 red, CR114 blue and CRS117 green

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Free space measurements and fitted results – phase CR110 red, CR114 blue and CRS117 green

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Real part of permittivity for all samples from fitted data CR110 red, CR114 blue and CRS117 green

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Imaginary part of permittivity of all samples from fitted data

CR110 red, CR114 blue and CRS117 green

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Real part of permeability for all samples from fitted data CR110 red, CR114 blue and CRS117 green

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Imaginary part of permeability for all samples from fitted data CR110 red, CR114 blue and CRS117 green

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Fitted model for permittivity of CR110, CR114 and CRS117 •

CR110

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CR114

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CRS117

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Fitted model for permeability of CR110, CR114 and CRS117 •

CR110

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CR114

•

CRS117

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Comparison between modeled and measured S11 data CR110 red, CR114 blue and CRS117 green

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Simulated S11 and S21 for all materials from developed models CR110 red, CR114 blue and CRS117 green

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Conclusion • We characterized absorbing materials up to frequency of 150GHz • Model parameters for ε and µ are obtained from fitted results • Future work – make magnetically loaded absorbing materials and tune their properties from theoretical prediction of ε and µ • Make absorbing materials with only dielectric characteristics (composites with SiC for example)

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