Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan) RF DIELECTRIC PROPERTIES OF SiC CERAMICS AT LOW TEMPERATURESÜe`Ï#, A), ¸­m B)
Yasunao Takeuchi #, A), Masaru SawamuraB)
A)High Energy Accelerator Research Organization (KEK)
B)
Japan Atomic Energy Agency (JAEA)

Abstract
Two products of SiC Ceramics, which were adopted as HOM absorbing materials for the KEKB ARES cavity, havetypical dielectric relaxation properties. These properties can be explained by polycrystalline structure model withelectrically conductive (extrinsic semiconductor) grains and non-conductive grain boundaries. We have measured thedielectric responses of the SiC ceramics to the RF frequency from room temperature to 40K to verify this model. The
results of the experiment have shown that the dielectric relaxation time in the SiC ceramics increases with decreasing
temperature. These behaviors of the dielectric properties can be explained by the polycrystalline structure model. In thispaper, the RF dielectric properties of the SiC ceramics at low temperatures are discussed based on the model.

1.

3Ćãªße 2HJ.Á-j© ïÿÆ n-ð#*ÎÍ.KE>-»j SiC
5NBK è[+ ïÿf¤Å ¾+ ã¯ïÿf¤Å 2HJ.Á^ * Ôî+[2] [3]j÷x Ąv¹j÷ÚºÝ òĄÐÚþ{·\É+*ĄµGO=ąHOMĆ¼çx&D/4M¹
9EOMO=Ý!½ D/4M¹Ă ïElectrodeÿ£-hÉÿ¹urZ SiC 7IE:4
6 \É+*] "KEKB j÷x
ARES Úº!2 ×ă |Ãã~ SiC 7I
Cg
E:46
HOM urZ\É+*Rg++1Ć¹Þ~ HOM ¼çxÉÓ SiC 7IGrainsE:46èwtĈHexoloy®ąV SiC-A ÌĆDepletion2Ć¿WAOF@/B~ HOM ¼çxÉ SiC 8/KLayersèwtĈCERASIC®-BąV SiC-B ÌĆ*Rd ' ³x !l[v¹¥urCdZ úgéâïÿÆ a-  êSs´* PåpãªÂnÇâąSiCĆ!1?K3O
3H:Bà 3eV oZÑ(+ )
¶ïÿÆ! 6.510 Ö*, ãªFigure 1: Two-layer model of the hot pressed SiC
ÃãZ* SiC 7IE:46!Qö urZ
ceramics with BeO addition, and its equivalent circuit.
É]%ë(+*' D/4M¹éâ¶ïÿÆąεr = ε'r – jε"rĆ ¶ôÍ¥û P¦KEKÜe(!KEKB-ARES Úº ¿æ¥û- %}* ' pãª WAOF@/B~ HOM ¼çx¡É+|Ã
SiC  ïÿÆ ñ ù!SiC 7IE:46 ã~ SiC 7IE:46ąSiC-BĆ D/4M¹
ãªÃãZ ²ø (È+*ä ( Ăd~Í Debye ~ïÿf¤Å-%
+*-ë qz-µ ' f® [4][5]1Ć
SiC 7IE:46ü!1980 Xą°Ć  7IE:46!Ããk¬C0âąBĆ§Ûè[ iÊ(' BeO »jC:<BL6»j+* (ãªßeąßàć
SiC 7IE:46 ²øñíÒÙ mĆ! p ~ SáÄoZ* U+*
+*1Ć
SiC 7IE:46!¶ôÍ 2ĆSiC 7IE:46.47B8cSáÄ oZ (*ãªßeą10-1 Ωm YĀ! Àì ù (BeO < B < AlRĆßËõb 2HJ.ÚT (*ā2HJ.Á j* Ñ(+* [6]ûf (²+*²ø-  Ôî  7IE:46 ãªße a!
+ [1] 2ĆïÿÆ ñ-¨( *$ iö BeO »jw aą10-1 Ωm YRĆ')
Figure 1 Õ²øG;KÝ_yó ¢±+  «+*3Ć ý 7IE:4
6 ZØÆ!à 2103 Ωm 4Ć#ytake@post.kek.jp____________________________________________- 597 -

Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)ėĬy¿éµı0.2~10GHzĲã4 âª&_Ä%kċÇħá¥3#ēĤ43ãĉÏ" 2SiC-B #ÓġVJZ%¡´3#
č143 3Ĳ1%KEK &ÿv1'SiC-B&ċÇħ&âªéµ&ēÎ1ĉÈĄv&=W
Y7äª%0!ċÇħ6|²"3#č
!SiC-B &ĐġÕĪ" Al è6~=WY7äª&ð$3ĕÁ6n¸!İÝėĬy¿éµ6ã &ĉÏd¶Ġ2Al &Éëε −ε(1-1)
ε 'r = ε r∞ + r0 2 r∞2
ı=WY7äª%¡´3Ĳ&~%k!ċÇ1+ ω τħá¥3ĉÏ6± &ċÝÀ&|²ÂÜ'Ã%KEKB & HOM áďí SiC EXSH(ε − ε )ωτ σ?C&Đġ%´í4!3ε"r = r0 r∞+(1-2)
1+ ω 2τ 2ε 0ω^ÂJAEA &ÛÌ1%0!ARES ýß&£ÝĂ HOM áďí%ĕn4 SiC EXSH?
mü»ºëĆ 2103 m "'ı1-2ĲĀeĭ' CıĐĴHexoloy®SiC-A1 #ïĲ&ĕÁl
0.2GHz g_&ÝÀ" 0.05 g`#$2æĒ"3 âĮ"ã4Ô&0$ĉÏ±14 [10]
 & ĉ Ï  ı 1-1 Ĳ  ı 1-2 Ĳ b « '  ı 1-3 Ĳ & 1Ĳε'r '¨â"'ÝÀİ$3%°!¤Debye &«"Ď4SiC F9Z¼ Debye ė $! 2) 80K "'lÝÀ%!- ε'rĬy¿éµ6ĘÅ"3á¥ε"r  0 %Ğ İÝ m#
!'oí"$
ε r 0 − ε r∞&lâĮ"& SiC-A1 &İÝėĬéµ&ã
ε r = ε r∞ +(1-3)
ĉÏ%!'ì+"&SiC-BSiC-A &y1+ jωτÎĉÏ6í!Ô&0%ēĤ"3 1ĲSiC-A1&ĉÈĄv&=WY7äªâª&l`%k!
"ċÇħ τ 'τ = RgRd(Cg+Cd)/(Rg+Rd)á¥ċÇħ~ıċÝÀl`Ĳ3"Č43 CgRg 'ĉÈĄv&ĥ)»
2Ĳ&%02İÝĮıp( 0.2~10GHzĲº6ĎCdRd '=WY7ýc¦1$3Ąî"& ε'r ' εr∞%Ğ 10 }¯&t#$3 +ģy&ĥ0)»º6Ď σ ' Rg # Rd 6ô{İÝĮ"& ε"r '0 %Ğ %¾Ċ#&ĬØj£ª%¡´3 &VJ
&0$č 1øĢ'SiC EXSH?CZ"'Rg<<RdCg<<Cd " 31ċÇħ'&lâĮ"&İÝėĬéµ6ę*3#'τ ≈ RgCd #$2 Rg # Cd "Ú+3ÇÀ"Ď4ĉÈÓġ%Ě3 SiC EXSH?C&ėĬë&ñ
3 Rg 'Ąv&=WY7äª#ùª"Ú+3ìU<LDT&ÑĔ%­þ#čSiC-A1ı_ğεr0εr∞'44ω0ω∞"& ε'r &Òĩt&ĕÁ#^&-&ĲSiC-ASiC-B & 2 ûį&Đ
6ĎRg<<RdCg<<Cd &Íi"'εr0 Cd& 3 s&ĕÁ6300~40K &ħ" 20K Ö%ãεrCg #$3
 &0$ċİÝėĬéµ6ę*3
SiC EXSH?C&İÝėĬy¿éµ&âªq%'â"&ċÝÀĆ 0.1~0.6GHz #×ĝµā%Ĩ!KEK &ÿv1%021Ĳ 3Ĳ&
òİ SiC-B &0$ĕÁ6í3#ċÝÀ
0$õđ±14!3[4][5][8][9] 1ĲSiC-B &ėĬfĞ&ãÆ#$3 "é%SiC-B &y¿éµ6Ć 300~350K &ă& 6 å"ããĉÏ%Þó!ēÎãJ]F6 Debye &«%O8HI8\@3#%02âª"& Debye & 3 s&NXU]Fıεr0 2.
εrτĲ6Ù, &ĉÏċÇħ τ &âª%023#öĖ4 1 2.1 ĕÁ%&éµ'Figure 1 &ÓġVJZ%!
lâĮ&ėĬë&ã'Nicolson-Ross Ü6íĉÈĄvıp £m#d¶43Ĳ&=WY7ä [11] ĕÁ'APC-7 Ĝ¬ê" 2¢í&ªaćèĮ% 3#h3#=WY7ä B\PZRZG%½u43 Nicolson-Ross Ü%0ª&âªéµ%0!ĘÅ"3#÷4
3ã¹Ü'B\PZĦg/4 "020ã+aćè&;MZ>][QZ ΔE 'Ć 0.36eV # öªÊ®43 [12] ^&Ħ&ĕÁ"©đü-147?EPF'Áv%aćè#! ÝÀãă&ã'ī" 3 Ħ'ċ3 Alı7ZSL:TĲ.çĉË#!o ÝÀ%Ğ 1GHz }¯&ã6¶~§ąª6
í43 BıR:ĈĲ%¡´3-&#d¶4 č·!Ć 7.5mm # SiC-A1 &ĜĕÁ'
2ĲARES ýß&£ÝĂ HOM áď%oí4! JAEA &ÛÌ1&ã [10]"oí4-&#3 SiC EXSH?CıSiC-AĲ%!'ċ &" 3 SiC-A &ĜĕÁ'50mm50mm &ÝÀ frı=1/(2πτ) ĲĆ 1~10MHz úª&ċ wÐ1SiC-B &ĜĕÁ'48mm48mmėĬy¿éµ#d¶43ĉÏ±14!320mm &F9Z¬ê1z2x-&" 3SiC-B #0%Ć 300~350K &ă"İÝ
0$č #èµt6-#%& SiC EXSH?
C}ğ& BeO à~RHKP[C SiC EXSH?
C"ñđ4 l»ºĉÈĄv#İ»ºĉÈĄî&é³6¼#h3#ėĬy¿éµ Figure1 &ārěı5/3Maxwell-Wagner &ĳ¦A
\J\BVJZ[7]Ĳ%0!ı1-1Ĳı1-2Ĳ«&0%Ď43- 598 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)z{¢Ý· 300KÞ¹-¯85070B 67
SiC-B  SiC-A Z¢£zg <H£z] 85071E 67<H£z])& 2 ±Ü ÉÙ¨ÝRÒÏ®¨- !"o(¦-¯+RZ¢£zq%Þ-£z#APC-7 oÌ§È- Â½£z]¼suc¦-Á+ Ë]+#
f*gSiC-B 9/LSTÚWÍÉ 5GHz XS ε"rFigure4¯(85071E
67<HÏ®
Ù¨-ÉÙ¨£zDMQCÝHP85070BÞ-©¨£z]0.1~10GHz
µtμ'r ≈ 1μ"r ≈ 0
 0.2~10.0GHzÝ0.1GHz Õ×Þr¡µt£z-!"¤+Z¢£zÂ½£z £z μr = 1 -YzDMQC-ÆÈÁÚ)j} S11 -£z ¦0.8GHz XT 4GHz XS ])w,ÉÙ¨-´b+ +SiC-A  +Î+Z¢£zÂ½-© 280K XT
' SiC-B ooÌ§Èd*bg £z¹'o^p $),+ ,)¹
_³ÚÉÙ¨-£zSiC-A  SiC- |Z¢Â½-[©h¸B  APC-7 oÌ§È-{¢§ÖÙ 85071E 67<H Ê ~¾),y ©Ô«°Ã APC-7 4ODLEL:ßHP8510C +SiC-ASiC-B  85071E £z¹) ,A ; > N Q 2 P . @ K / 5 ß Agilent Technologies )  SiC 8 K G ; 2 7  Ï ® ¨    'r ≈ 185071E £z67<H-©ÉÙ¨Ï®¨- Ý0.1~10GHzÞ+&85070B 67<HÉ
Nicolson-Ross£zÝ0.1~18.0GHz0.1GHz Ù¨£z]-© +eZ¢Â½
Õ×Þ £z67<HZ¢£z67< £z]280K XT£z]-q&0.2GHz XH  ÄØ APC-7 3A29³Ú T4GHz XSÊ x   V,-v¥Ú+¬£zm¿ ) £z67<H¶ºÊ-¯+¾),+
2.2 {¢£zÝSiC-BSiC-AÞ£zÊ~2.3 Z¢£zGM `a-©Z¢£zÂ½È-8;>¢) 40K #¢µt- 20K Õ×£zÝ0.05~20.05GHz25MHz Õ×ÞÈi
4ODLEL:­²Uk&),+,)Â½ JAEA )£z[10][©,'oR'+[©+ NicolsonRoss £z APC-7 oÌ§4ODL
EL:8;>,Èj}\ÏÑ\£z+ (ÉÙ¨Ï®¨-´b+ +n£z¢4ODLE
L:»,+ APC-7 3A29³Ú-v¥Ú+A;>NQ2P.@K/5 ¦ÓÅ+ Û-q&£zÛÐ* Figure 2: Permittivities of SiC-B measured with 85070B
+
and 85071E at room temperature.
• nFQ>©1;>-lW +• n¢ S BKIQ9-A;>NQ2P.@
K/5£z+
• 0QDO6JQ>MQ?7LQ1;>£z-ÛªÀ• £z S BKIQ9-©n¢A;>
NQ2P.@K/5=Q9-Ç´+• È-8;>n¢ S BKIQ9-&+• A;>NQ2P.@K/5=Q9-v
È S BKIQ9-+•  S BKIQ9-©ÈÉÙ¨PÏ®¨-Ç´+

3.

3.1{¢£zÝSiC-BÞ

Figure 2~3 {¢Ý· 300KÞ£z SiC-BÉÙ¨r¡¦Z¢£zÂ½-©£Figure 3: Permittivities of SiC-B measured with / without
low temperature unit at room temperature.

- 599 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)Á¤²lqa  )¡-,
300~220K 0.2~­ 3GHz«p w¯{Ì1-3ÍDebye/¢ fitting /¶Debye
3 [ <C@H7Ìεr0εr∞τÍ/
' ¯ VKT εr0\116.7Ì300KÍ55.6Ì220KÍ|,²lÆ τ
εr0
|(Ç.*0.48nsec
Ì300KÍ1.17nsecÌ220KÍusb,εr∞!%+td#$Iw, a    - * ¯  !  KEK©]*
300~350K wSiC 6C?845Ìj¸m, Pnwm!fG8: £,Í¯ [4][5] ËU +¯¬] 2BD0  É ¡-,´ *-,Figure 4: Permeability of SiC-B measured with / without
low temperature unit at room temperature.
3.2Vw·³/¢wÌSiC-BÍ

Figure 5~6 V·³w SiC-B »Èk/§²lqa¥
0.2~4GHz«p 9H7/¢ VK
T²lk V,) ¹Å,Figure 7  Cole-Cole plot (0.2~4GHz) /§
300~140K i ¿½!e^Â± IÄO + VK(¿½ e^~K¨c,140~280K¿½!"je^Âj±J, 300K¿½!|-,-* ¯ *yQJ¦º-, SiC-B »È²l Figure 6: Temperature dependence of the relaxation curveqa ²lk 300K140K
ÆV of SiC-B (180~60K).
,¹Å, ,}300K
w & _` ÃÀ- uMx-' wS  300K¿½ | - fo,hµ ,120~40K¿½(j ¹Å¼,¯,

Figure 7: Cole-Cole plots of SiC-B (300~140K).

Figure 5: Temperature dependence of the relaxation curveof SiC-B (300~220K).
Figure 7Cole-Cole plot¯/g´Figure 1A9EªYn¾´z,τ ≈RgCdεr0  Cd )+ Rg  τ/εr0 ÇZ ,Rg!¯¬] 2BD0¨cW,   RgN2BD0Xv300~220K«pL®Êr,Rw,
Rg ! exp(ΔE/2kT)W,ΔE !04
6=7 1;E3HF>Ek ! Boltzmann wT!°{,Figure8 §) - 600 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

τ/εr0 !Z t!È.  fitting .³  Îx!®jh fr  1~10MHz §y»©'#$!È L²) fitting ) ΔE . ), +Ïy!UM S®jhU
&+ 0.23eV *­«]!/48=9     +  ¼ Å   +    -   SiC-A r + BÎ?IJÏAlÎ/G@<0AÏ SiC-A1
'SiC-B fC;GÍh¾! / 4 8 = 9 H > G Î B : 0.3~0.723eV  Al : Ê¿+z,+
0.19~0.49eVÏ[13] Á Z|),y!UMS
εr0 !u"­«]!3DF/y!u 4.
S­« !3DF/ªOw!cpb
ARES ª HOM ¶lÊgdVW
+ (+° ),+,)!­"U , +2 ¨Ì! SiC 8E@:46!¹k!
Ën'SiC-B !¾Ê!Íh_ Íh¾Ê.300~40K !yr Figure 1 ¥, +U­«] !­ \m¢ Debye m¾Ê_.¥Í­« !q­Â¿+. 1 ¨Ì!¹kÎSiC-BÏ  "y!UM
i+
Sεr0 !u®jÇ τ !oa¤½,

Figure 8: εr0, εr∞ and τ/εr0 vs. temperature (SiC-B). The
values of τ/εr0 are largely affected by the carrierconcentrations in the grains.

!À"SiC 8E@:46!¾Ê¡B2<7A.µU­«]Í­« !
q­Â!C;G­«]!3DF/yy!UM[ u+¿+
' L¨Ì! SiC 8E@:46ÎSiC-ASiC-A1Ï
!¾Ê'!C;G¿e± +,)!­"UËn
'U­«]Í­« !¾Ê¡C;G,)! 2 ¨Ì! SiC 8E@:46 Ãe± +.¥ +%,)!­)100K
RM!UËn"0.2~10GHz !h!¾Ê"­«]!3DF/yu+ (*®jhuε'r  εr∞Î=¬ 10 §yÏε"r0 +P,+sÉ!
rZ'f!­|),{,)!
SiC 8E@:46"UËnÎ
100K RMÏ"ÊgdV!W Ã !}º +

Figure 9: Temperature dependence of the relaxation curveof SiC-A (300~220K).
3.3

Ur·¯.

rÎSiC-ASiC-A1Ï

Figure 9
SiC-A !UËn!¾Ê!h.¥SiC-A1 !r­"SiC-A !­ÌT!­,)!­)SiC-A
SiC-A1 !¾Ê'®jm_. [1] K. Maeda, et al., “Grain-boundary Effect in Highly
Resistive SiC Ceramics with High Thermal Conductivity”,
pp. 260-268 in Advances in Ceramics, Vol. 7, Additives
and Interfaces in Electronic Ceramics, ed. M. F. Yan and A.
H. Heuer, American Ceramics Society, Columbus, OH.,
1984.
[2] K. Maeda, et al., “Dielectric Behavior of SiC Ceramics withBeO Addition”, Extended Abstract of Electronics Div. 21E-85, Annual Meeting, Am. Ceram. Soc., 1985.
[3] `Ä¸¦X
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