Dielectrics chapt. 2-2 Prof. Kee-Joe Lim kjlim@chungbuk.ac.kr, 261-2424 School of Electrical and Computer Engineering Chungbuk National University http://imt.cbucc.net 2006/3/1
The internal field in solids and liquids The internal field, E i is defined as the field acting at the location of a given atom Applied field, E E i =E (gases) E i is not equal to E (solids and liquids) E i = E + E Example 1. a string of atom model Example 2. Lorentz internal fields 2
V r µ = θ Q Internal fields in a string of atoms model p( r, θ ) r 2 r 1 r 1 ( 1 ) E θ E r 1 Qδ cosθ = µ cosθ 2 2 4πε 0 r2 r1 4πε0 r 4πε 0 r δ r + cos 2 1 θ, E = gradv E r E θ = = 0 δ r 2 r cos θ ( r ff δ ) 2 V V V ar + aθ + a r r θ r sinθ φ ( φ 1 2µ cosθ = 3 4πε r 1 4πε 0 µ sinθ 3 r 1 ) E E i i 1 2µ E rb 1 = p(a,0) 3 4πε 0 a 1 2µ p( a, E rb 2 = 3 4πε 0 a 1 4µ Er( B1+ B2) = 3 4πε 0 a 1 2µ E rc 1 = p( 2a 3 4πε0 (2a) 1 2µ E rc 2 = 2 3 4πε 0 (2a) 1 4µ Er( C1+ C 2) = 3 4πε (2a) µ = E + ( ) πε n= ind 3 0a E = 1 1.2α / πε a e 0 1 3 1 n 3 0 1.2µ = E + πε E = 1 β ind 3 0a 180),0) p( a,180) 1.2α E = E + πε γp E i = E + ε 0 e i 3 0a 3
Lorentz internal field 4
o P n P n = P n = P cosθ P E 2 =0 분자가중성이고, 영구쌍극자가없고, 기체와같이그배열이완전히불규칙하거나입방정계와같이높은대칭성을갖는경우 ds상의전하가원점 O에만드는전계의P 방향성분 2 P cos θds de1 = ds = 2πr sinθrdθ 2 4πε r E 1 = P 2 π 0 2 cos θ sinθdθ = P 3ε ε 0 0 0 2 cos θd(cosθ ) = 3 cos θ 3 0 π 1 E i = E + 3ε 0 γ = 1 3 P 5
6 2.7 static dielectric constant of solids (i) Elemental dielectrics e o i e P P P P P = + + = ] [ 0 P E N E N P e i e ε λ α α + = = ) / ( 1 0 ε α γ α e e N E N P = 0 0 / 1 ) ( ε γα α ε ε e e r N = ) 3 / ( 0 ε α P E N P e + = ) 3 1) ( ( 1) ( 0 0 0 ε ε ε α ε ε E E N E r e r + = 0 3 2 1 ε α ε ε e r r N = + 0 0 3 2 1 ε α ρ ε ε e r r m N M P = + ρ NM N = 0 분자분극 (Clausius-Mosotti s eq.) ) 3 1 ( = γ * 단원자기체와원소상고체의비유전율차이
(ii) Ionic dielectrics without permanent dipoles P = P + P + P = P + ε 0 ( ε rs e i o 1) E = P + e P i e P i ε 0 ( ε 2 ε re = n 1)E = re P e 1 n = = v / c µ ε = ε r r r ( ε ε ) p rs ( ε ε ) re rs re i vs. 1 V dv dp (iii) Solids containing permanent dipole moments -Nitrobenzene (C 6 H 5 NO 2 ) -HCl 7
2.8 some properties of ferroelectric materials dielectrics; 결정점군기준 32 piezoelectricity; 대칭중심이없는결정군 21(20) pyroelectricity; 10 ferroelectricity; 자발분극, 반전 특성 polarization depends on history polarization is not unique function of the field strength P-E hysteresis Spontaneous polarization the specimen consists of a number of domains which are themselves spontaneously polarized with the direction of the polarization varying from one domain to another Ferroelectric Curie temperature θ f T θ f 상유전성 강유전성 8
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In ferroelectric region, i.e. below θ f, the dielectric constant is a function of the field strength and is no longer a constant. differential relative dielectric constant ε 0 ( ε r 1) = dp / de (defined along virgin curve at the origin) Above the Curie temperature Curie-Weiss law ; ε = C /( T θ ) Classification of ferroelectric materials θ : characteristic temperature, a few degrees smaller than θ Rochelle salt (NaKC 4 H 4 O 6. 4H 2 O; 주석산나트륨칼륨 ); -18~23 o C dihydrogen phosphates and arsenates of alkali metals, KDP(KH 2 PO 4 ) ; 123 o K ABO 3 or oxygen octahedron group, BaTiO 3 황산 guanidine aluminum(gash) ; 200 o C, 황산 glycine(tgs); 47 o C f 24
Barium titanate(batio 3 ) 25
Barium titanate(batio 3 ) 26
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MLCC (multi-layer ceramic capacitor) LTCC (low temperature co-fired ceramics) 35
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2.9 Spontaneous polarization Possibility of spontaneous polarization p Nα Ei = Nα[ E + ( γ / ε 0) p] p = E = p Nα = E 1 ( Nαγ / ε 0) p Nα = = E ( Nαγ / ε ) 1 1 0 0 0? A A β Aβ = Nαγ / ε 0 =1 High polarizability Barium titanate(batio 3 ) 경우 37
Why does spontaneous polarization usually occur only below a certain temperature? p = Nα ( Nαγ / ε ) 1 0 α,γ E Nα / ε 0 ε r 1 = ( T θ f ) 1 ( Nαγ / ε ) Let s are temperature independent and N is a function of temperature 1 N dn dt 1 = λ = V dv dt 온도증가, 체적증가, N 감소 어떤온도 T1에서온도에서 Nαγ 매우큰값이된다. Nαγ / ε 0 / ε 0 =1 0 가 1보다약간적다고할때, 재료를냉각하면 N의증가로특정이되어자발분극이생기게된다. 이특정온도근처에서유전율은 These qualitative arguments show that Curie temperature may arise in a material of high dielectric constants simply as a result of the contraction of the material upon cooling 38
How does the dielectric constant near T = θ f, but in the region T θ f, vary with temperature? N = ε 0 ε r 1 α ( ε 1) γ + 1 r ln N = lnε 0 lnα + ln( ε 1) ln[( ε 1) γ + 1] r r 1 N dn dt = λ = dε r dt 1 ( ε 1)[( ε 1) γ + 1] r r dε r dt 1 γε 2 r ε r ε = r dε ε r 2 r = λγ T θ f dt ε r λγ = 1/ T θ f ( T f > θ ) Curie-Weiss law의유도 -BaTiO3의 Curie상수잘일치됨 θ = θ - 으로유도되었으나, 실험적으로는인경우가많음 f θ < θ f 39
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Piezoelectric equation d15 In case of Poled polycrystalline ceramics d 31 52
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[ 보충자료 ] d 형식 E S = s T + de T D = dt + ε E e 형식 E T = c S ee S D = es + ε E S E = g 형식 s D T + gd T = gt + β D E T h 형식 S = hs + β D D = c S hd s E ; compliance@ E = 0 ε T ; 유전율@ T = 0 ; 압전변형정수 d ij E e = d / s S T ε = ε 2 d / s E e; 압전응력정수 g; 전압출력계수 h; 전압응력계수 D D D 1 2 3 d ij d = d d 11 21 31 d d d 12 22 32 d d d 13 23 33 d d d 14 24 34 d d d 15 25 35 d d d 16 26 36 T T T T T T 1 2 3 4 5 6 ; i( 결과), j( 원인) [ ] [ E ][ ] [ ] t S = s T + d [ E] 54
C cl F S T / C = ε / ε = 1 k 2 k = 2 d T ε ε E = 2 e T ε c E = T ε g E s 2 = s ε h D c 2 55
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[ 보충자료 ]; 압전정수측정법, 산출 πf s = π f k33 tan 2 f p 2 Cl ε T 33 = A 1 2 2 = 4ρf p l D s 33 p f p f s d 33 s = E 33 k s = 1 k 33 D 33 2 33 ( ε T s E ) 1/ 2 33 33 T g33 = d33 / ε 33 fr, fa; resonant, antiresonant freq. at Xe=0 fs; freq. at X1=0, fp; freq. at maximum Re fm, fn; freq. for min. and max. Z 2 2 2 2 C f 1 p fs fa f k = = C + C f f 1)Piezoelectric ceramic rod(area;a, length;l) 2) thin disk of diameter d 1 Q m 0 1 2 p 2 k p f p f = f J, J,ν 2 0 1 1 k p fs 2 2 2 2 1 π d fs ( 1 ν ) ρ = E 2 s η d 11 31 = k 31 1 ( ε T s E ) 1/ 2 33 11 s g 31 2 a 2 r 31 T 33 f 2 n f f 2 n 2 1 ν k31 = 2 d = ε 2 2 f f = 2πf s Zm 0 4 2 m 0 f p s ( C + C) π f Z ( C + C) p 2 m 2 k p 63
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상세내용 ; 세라믹유전체공학 ( 이경희역 ) p.231 참조 80
상세내용 ; 세라믹유전체공학 ( 이경희역 ) p.232 참조 81
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상세내용 ; 세라믹유전체공학 ( 이경희역 ) p.237 참조 84
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Micro-piezoelectric pump (Star microelectronics 사, 일본 ) Items Pump System Max Flow Rate Max Pump Pressure Drive Voltage Dimensions (W D H) Inlet / Outlet Weight : : : : : : : : Specifications Piezo-ceramic Diaphragm Pump 1,500 μl/min (Typ.) 60 KPa (Typ.) 100-300 Vp-p (sine wave or trapezoidal wave) 23 23 4.7 mm (Except for mount, inlet/outlet and power cable) O.D.: 1.2 mm, I.D.: 0.6 mm, Length: 2.5 mm Approx. 3 g (Except for power cable) 105
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압전세라믹응용제품 ( 전기적에너지 기계적에너지 ) 기능초음파발생음파발생액튜에이터 부저, 알람스피커전화기, Ringer 응용예 초음파세척기플라스틱용접기초음파가공기霧化器, 간이형세척기 Side mirror 의물기제거기 초음파모터잉크제트프린터헤드 Parts Feeder 압전 Fan 압전펌프, 서보밸브 AFM Cantilever( 외팔보 ) VTR 벨트 볼트체결란쥬반진동자 (BLT) MHz 矩形板진동자볼트체결란쥬반진동자볼트체결란쥬반진동자圓板진동자 Bimorph 진동자 Bimorph 진동자 Bimorph 진동자 형태 원반, Ring 원통 ( 圓筒 ), Bimorph 진동자 Bimorph 진동자 Bimorph 진동자 Bimorph 변위 ( 變位 ) 소자박막 ( 薄膜 ) Bimorph 변위소자 Bimorph 변위소자 116
압전세라믹응용제품 ( 기계적에너지 전기적에너지 ) 기능고압발생음파, 초음파수신센서 응용예 가스점화소자가스라이터 수중청음기마이크로폰 가속도계, 진동계유량계壓電자이로스코프압력계, AE 센터 圓柱환봉 형태 원통 Bimorph 薄板 Bimorph 117
압전세라믹응용제품 ( 전기적 기계적 전기적에너지 ) 기능전기신호처리거리측정電壓변환 세라믹필터 SAW 필터, 공진자세라믹공진자메카니칼필터 어군탐지소자수중 Sonar Back Sonar 초음파탐상 Probe 의료용초음파진단용 Probe 壓電트렌스퍼머 응용예 두께진동, 에너지차단표면탄성파두께진동, 간헐진동진동자 원반, Ring Bimorph 원반구형판, array 형 구형판, 적층 적용 118
산업명 제품명 실제제품 산업명 제품명 실제제품 레조네이터 Ignitor 필터 (KHz) 가정용전자기기 Buzzer, Sounder 통신기기 필터 (MHz) Transformer (Inverter) SMD- TYPE 필터 의료기기 초음파진단장치용탐촉자 센서기기 Ultrasonic Sensor Ultrasonic Probe 119
Ultrasonic Position Sensor Hydrophone Shock Sensor 기타 Ultrasonic Motor Gyroscope Ultrasonic Linear Motor Actuator Actuator Mirror Tilter 120
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