RF Dielectric Properties of SiC
Ceramic Absorbers for the ARESCavity

Yasunao TAKEUCHI
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Notation• Permittivity
ε = ε′ - j ε″εr = ε/ε0 = εr′ - j εr″2?

• Single crystal of SiC ⇒ Semiconductor.
• SiC ceramics (polycrystal structure) have larger
dielectric constant and loss tangent than the
single crystal SiC.

• Where do these different dielectric
properties come from?
3!
Dielectric properties are explained by thestructure of the grain and grain boundary.
Grain : low resistivity, p-type semiconductor
Depletion layer near grain boundary : highresistivity* These dielectric properties of SiCceramics were predicted by Dr. Maeda etal. (Hitachi co.) in 1985 .
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ARES Cavity
Two SiC bullets per Waveguide

HWG
Input CouplerPort

HOM damper (wave guide type)

CFPumping PortHOM damper (grooved beam pipe type)
GBP

CCD
SC

Tuner Port

CC

AC
Tuner Port

Mode Shifting
Groove

HWG
GBP

ka Ua

Us ks

Two SiC bullets per Waveguide

Eight SiC tiles per Groove

CFHCCSS5

Two types of SiC ceramics

SiC-A

SiC-B

Bullet shape SiC ceramics(wave guide type HOM damper)

SiC tile(grooved beam pipe typeHOM damper)

Both SiC ceramics are α-type and sintered at normal pressure.
Boron is used as an additive on densification.

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ε′ is important parameter as well as ε″Diameter : 40 mm
ε′r : 22Frequency : 0.7 GHz
fc : ~0.9 GHz

Diameter : 40 mm
ε′r : 22Frequency : 1.5 GHz
fc : ~0.9 GHz

Dielectric rod in a parallel plate line.
Frequency < fc : HE11 mode propagates outside the rod mainly.
Frequency > fc : HE11 mode is propagates inside the rod.
Critical frequency (= fc) is a function of ε′ and diameter of the rod.
*Y.Takeuchi et al. “The SiC Absorber for the KEKB ARES Cavity”, EPAC 96.7

Measurement of permittivity• ε′, ε″• Measured withHP85070B Dielectric Probe
Kit+HP8510C NetworkAnalyzer• Frequency range
0.2~10 GHz. 0.1GHz step.
• Samples
All sintered lots.
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Typical Permittivities of the SiC
Ceramics
SiC-A

Dielectric relaxation ?

SiC-B

Dielectric relaxation.
This curve behavior is like aDebye-type relaxation.

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Debye Model
Input : Step function
Output : P0(t)=P0(1-e-t/τ)Debye equation

ε r0 − ε r∞
εr (ω ) = ε r∞ +1+ jωτ

(1)where εr0=εr′(ω=0), εr∞=εr′(ω=∞)τ : relaxation time.

Debye model is characterized by thethree parameters, εr0, εr∞ and τ.
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Cole-Cole Diagram• Horizontal axis : εr′• Vertical axis : εr″Locus ( Debye model)⇒ half circle

11Cole-Cole Diagram of SiC-A andSiC-B• SiC-B⇒ Debye type
Dielectric
Relaxation

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Three Parameters of Debye Model(SiC-B)

εr0 = 85.7
εr∞ = 13.6
τ = 2.55 x10-10 (sec)

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Schematic Model of SiC Ceramicswith BeO Addition
Grain boundary
Grain : P-Type Semiconductor(ρ<10 Ω·cm)
Carrier Depletion Layer(High Electric Insulation)
Resistivity of SiC Ceramics (BeOaddition) is higher than 1013 Ω·cm.

K.Maeda, et al., “Grain-boundary Effect in Highly Resistive SiC Ceramics with High Thermal Conductivity”, pp. 260-268 in Advances in Ceramics,
ol. 7, Additives and Interfaces in Electronic Ceramics, ed. M.F.Yan and A.H.Heuer, American Ceramics Society, Columbus, OH., 1984.
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Two-layer Model and EquivalentCircuit
ElectrodeCg

Rg

Grains
Depletion
LayersRdK. Maeda et al. (Hitachi co.)predicted dielectric properties ofSiC ceramics using this equivalentcircuit in 1985.

CdK.Maeda, et al., “Dielectric Behavior of SiC Ceramics with BeO Addition”, Extended Abstract of Electronics Div. 21-E-85, Annual Meeting, Am.
eram. Soc., 1985.
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Probably, SiC-B has a Similar Grain
Structure
Grain : P-type Semiconductor(Boron is doped ⇒ ρ«10 Ω·cm )ρ(Boron doped) < ρ(BeO doped) *Resistivity of SiC-B is about 2x105Ω·cm.

ρ(Al doped) < ρ(B doped) < ρ(BeO doped) *Y.Takeda et al. “Effects of Additives on Thermal Conductivity and Electrical Resistivity of SiC Ceramics”, Yogyo Kyokai-shi 95, [9],1987.
eramic Society of Japan.

18Effective Permittivity (SiC-B) Calculated
from Equivalent Circuit
Electrode

Effective permittivity
Cg

Rg

Grains
Depletion
LayersRdε r0 − εr∞εr '= ε r∞ +1+ ω 2τ 2εr"=(ε r0 − εr∞ )ωτCd

21+ ω τ2

σ+ε0ω

(2-1)
(2-2)

where σ is coductivity,
τ = RgRd(Cg+Cd)/(Rg+Rd)
Rg«Rd, Cg«Cd⇒ τ ≅ RgCdσ< 0.05 above 0.2GHz. ⇒ negligibly small
ε0ω(2-1) and (2-2) ⇒ Debye equations.

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The ε″ behavior at lower frequencies ispredicted by the model.
Permittivity (SiC-B) vs Frequency
Measured data

Permittivity (SiC-B) vs Frequency
Calculated from Equation (2-1) and (2-2).
Debye parameters( εr0, εr∞ and τ ) form themeasurement data are used.

The ε″ behavior at lower frequency ( < 0.2GHz ) should be confirmed.

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Conclusions• Dielectric properties of SiC-B are explained by the structure ofthe grain and grain boundary.
• We can probably control the dielectric constant of SiC ceramics
by using additives.
• We will use these results for the next future plan “SuperKEKB”.

Thank you.
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