Orientation of Piezoelectric Crystals and Acoustic Wave Propagation

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1 Orientation of Piezoelectric Crystals and Acoustic Wave Propagation Guigen Zhang Department of Bioengineering Department of Electrical and Computer Engineering Institute for Biological Interfaces of Engineering Clemson University 2012 Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston

2 Overview Surface Acoustic Wave (SAW) devices Wireless filters, resonators, sensors, etc. Confinement of acoustic energy near the surface of a piezoelectric substrate SAW sensors Wireless remote operations High temperature operations Hazardous environment operations High frequency, high precision and sensitivity

3 Overview SAW generation and signal measurement One-port or two-port SAW devices Interdigitated transducer (IDT): transmitting IDT and receiving IDT a b

4 Constitutive and Wave Equations T cs e E D es E T, S, E and D are vectors of stress, strain, electric field and displacement; c, e and ε are matrices of the elastic modulus (stiffness), piezoelectric stress constant and dielectric permittivity of the substrate material. [ e] [ c u] u 0 [ e u] [ ] s ρ is density, u and ü are particle displacement and acceleration, and is electric potential. s Wave field near the surface: Surface stresses: Surface electric displacements: u exp( z / V )exp[ i( t x / V )] T cs e E csu e D esu s s

5 Anisotropy and Crystal Rotation Piezoelectric materials are anisotropic Different orientation (or cut) of a piezoelectric substrate leads to different material properties, hence different wave characteristics Euler angles c c11 c12 c13 c14 c15 c16 c22 c23 c24 c25 c 26 c33 c34 c35 c 36 c44 c45 c46 c55 c 56 symm c66 e e e e e e e e e e e e e e e e e e e A crystal cut is defined by a set of Euler angles (,,) defines the rotation about Z, about X and about Z XYZ crystal axes symm 33 Z X Y

6 Rotation and Transformation Transformation of material property matrices The material matrices: [c] is 66, [e] is 36 and [] is 33 How to perform matrix transformation for 66, 36 and 33 matrices with only a 33 rotation matrix?

7 Crystal Rotation: The Hard Way

8 Crystal Matrix Rotation Calculator Available at: zephrasoft.com c' M CM e' aem ' aa T T T M a a a a a a a a a a xx xy xz yx yy yz zx zy zz axx axy axz 2axyaxz 2axzaxx 2axxa xy ayx ayy ayz 2ayyayz 2ayzayx 2ayxayy azx azy azz 2azyazz 2azzazx 2azxa zy ayxazx ayyazy ayzazz ayyazz ayzazy ayxazz ayzazx ayyazx ayxazy azxaxx azyaxy azzaxz axyazz axzazy axzazx axxazz axxazy axya zx a xxayx axyayy axzayz axyayz axzayy axza yx axxa yz axxa yy axya yx

9 Material Properties in Crystal Axes c c Trigonal 32 and 3m crystals 32 crystal: Langasite (La 3 Ga 3 SiO 14 ) c11 c12 c13 c c22 c23 c c c c44 c 14 ( c11 c12 ) / 2 e11 e11 0 e e e e m crystal: Lithium Niobate (LiNbO 3 ) c11 c12 c13 c c22 c23 c c c c44 c 14 ( c11 c12 ) / e e e e22 e22 0 e e31 e31 e Langasite: (,, ) = (0, 0, 0) C Nm -2 C Nm -2 C Nm -2 C Nm -2 C Nm -2 C Nm -2 e Cm -2 e Cm -2 e Cm -2 ε ε ρ 5739 Kg m -3 Lithium Niobate: (,, ) = (0, 0, 0) C Nm -2 C Nm -2 C Nm -2 C Nm -2 C Nm -2 C Nm -2 e Cm -2 e Cm -2 e Cm -2 e Cm -2 ε ε ρ 4600 Kg m -3

10 IL 20 log10v output / V input Modeling Consideration Two-port delay-line SAW sensor Reciprocal and symmetric design: S11=S22, S12=S21 Insertion loss (IL): 20log S12 SAW travel velocity V s = f 0, is wavelength (=20 m) and f 0 is resonant frequency IL 20log 10 F F V V output input F FourierTransform V S f 0 V output V input

11 Electric-Excited Acoustic Waves Applied potential within 1 ns Induced acoustic displacement and waves

12 Insertion Loss (db) Insertion Loss (db) Reveiver Potential (V) SAW Signal and Insertion Loss 2.0E E-03 LGS ZY LGS XY 1.0E E E+00 LGS YX LGS ZX LGS YZ LGS XZ -5.0E E E E Time (ns) IL 20log 10 Langasite: La 3 Ga 3 SiO 14 F V F V output input LGS ZY LGS XY LGS YX LGS ZX LGS YZ LGS XZ Frequency (MHz) Frequency (MHz) VS f0 20( m) ( MHz) ( m / s)

13 Reveiver Potential (V) Insertion Loss (db) Good and Bad Crystal Cuts 2.0E E E-03 (90,0,0) (0,90,90) (90,0,0) (0,90,90) Langasite: La 3 Ga 3 SiO 14 t = 80 ns 5.0E E E E E (0,90,90) -2.0E Time (ns) Frequency (MHz) (90,0,0) (90,0,0) (0,90,90)

14 Insertion Loss (db) Crystal Cuts and SAW Behavior (-10,130,25) (-10,130,45) (-10,150,25) (-10,150,45) (10,130,25) (10,130,45) (10,150,25) (10,150,45) (0,19,40) Langasite: La 3 Ga 3 SiO Frequency (MHz) VS f0 20( m) ( MHz) ( m / s)

15 Insertion Loss (db) Crystal Cuts and SAW Behavior (0,137,27.6) (0,137,62.5) (0,137,117.5) (0,137,152.5) (0,167,45) (0,167,135) (0,12.8,0) (0,12.8,90) Langasite: La 3 Ga 3 SiO Frequency (MHz) VS f0 20( m) ( MHz) ( m / s)

16 Insertion Loss (db) Crystal Cuts and SAW Behavior (0,80,0) (0,170,90) (0,14,90) (0,171,32) (0,171,143) (0,14.5,45) (0,14.5,134) (0,80,0) (0,170,0) Langasite: La 3 Ga 3 SiO Frequency (MHz) VS f0 20( m) ( MHz) ( m / s)

17 Insertion Loss (db) Crystal Cuts and SAW Behavior 0 5 (0,-26,0) (0,38,0) Lithium Niobate: LiNbO (0,-26,90) (0,80,90) Frequency (MHz) VS f0 20( m) ( MHz) ( m / s)

18 Summary Crystal cut angles and wave propagation direction affect SAW velocity and insertion loss significantly Selection of an appropriate crystal cut is crucial to deriving desired performances for SAW devices Computer simulation provides a quick and cost-effective way to identify optimal crystal cuts for the development of high-performance SAW devices Acknowledgement Institute for Biological Interface of Engineering Clemson Palmetto Cluster Super Computing Facility zephrasoft.com for the use of the Crystal Matrix Rotation Calculator Thank You!