03 Sound
A crystal that rings
A crystal that turns a voltage into a ripple and a ripple into a voltage; most SAW filters in phones ride on it or on its sibling LiTaO3.
| Key value, congruent LN | value | status |
|---|---|---|
| d22, d33, d15 (pC/N) | 20.3, 8.69, 66.4 | derived |
| k15, kt (thickness shear, extensional) | 0.600, 0.247 | derived |
| ε11T, ε33T (ε0) | 83.3, 28.5 | P |
| Z longitudinal, measured (m/s) | 7328.20 | P |
| Z longitudinal, stiffened / e = 0 (m/s) | 7328.6 / 7102.1 | derived |
| 128° Y-X Rayleigh v, k² | 3978.4 m/s, 5.41% | derived |
| Y-Z Rayleigh v, k² | 3486.4 m/s, 4.23% | derived |
| 64° / 41° Y-X leaky v, k² | 4691.4, 10.37% / 4749.3, 15.71% | derived |
| SAW wavelength at 1 GHz, 128° Y-X (µm) | 3.978 | derived |
| microwave-to-optical, TFLN, 300 K, blue pump | 5.5% | reported |
| microwave-to-optical, LN on Si, < 10 mK, continuous | 4.9% | reported |
| nanobender tuning, small signal | ≈ 5 nm/V | reported |
SAW coupling k² vs rotated Y-X cut, Kushibiki et al. 1999 constants derived
24% |
|ooooooo oo
| ooooo ooooo
17% | ooo ooo
| oooo
| oooo
11% | ooo
| oooo
| oooooo
4% | oooooooo************
|*** *******o ***********
0% | *******************************
+------------------------------------------------------------
0 45 90 135 180 deg
* Rayleigh o leaky SAW (YXl) theta, X propagation 8 finger pairs and the launched ripple at the same pitch
================================= | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ================================= ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ 128° Y-X, 1 GHz: λ = 3.98 µm (one period = 4 characters)
Drawn to scale: 1 GHz on 128° Y-X, λ = 3.98 µm derived
Sections
| No. | Section | L1 phenomenon | L2 model | L3 computation | Figures |
|---|---|---|---|---|---|
| 3.1 | Piezoelectricity | charge from pressure; 20 pm per volt along Y | four IEEE 176 forms; 3m tensors; coupling factors | convention of 2s; sign frame; clamped vs free | longitudinal response surface; constitutive forms and the convention of 2s |
| 3.2 | Elastic constants and bulk waves | 3.5 to 7.4 km/s; stiffening along Z | cE sets; Christoffel with e and εS | eigen-solver; group velocity; fitted-data caveat | slowness surfaces with piezoelectric stiffening |
| 3.3 | Surface and guided waves | a ripple 4 µm long at 1 GHz | partial waves; k2 = 2Δv/v; standard cuts | root selection; threshold windows; constant-set spread | SAW fields vs depth |
| 3.4 | Cuts and coupling | cut angle sets speed and coupling | (YXl) θ sweep; Rayleigh vs leaky | threshold-pinned roots; set dependence | rotated Y-X cut sweep |
| 3.5 | IDTs and SAW filters | a comb that launches and filters | f0 = v/p; bandwidth 2/N; LN vs LT; POI, XBAR | models not included: loading, reflection, diffraction | IDT synchronous frequency and array factor |
| 3.6 | Acousto-optics | light diffracted and shifted by sound | p tensor sets; figures of merit; Bragg angle | p14/p41 sign pairing; 633 nm data only | Bragg cell; photoelastic tensor and the sign pairing |
| 3.7 | GHz phononics and piezo-optomechanics | microwave → phonon → photon | transduction model; heralding; nanobenders | efficiency bookkeeping; material limits | microwave photon chain; heralded photon addition; nanobender scaling |
Cross-links
Chapter 01 (crystal): point group 3m, the +Z sense, congruent composition (SAW-grade CLN). Chapter 02 (light): clamped vs free electro-optic coefficients, rT − rS = p d, the index ellipsoid (2.2). Chapter 04 (quirks): pyroelectric charging of SAW wafers. Chapter 05 (making): thin-film transfer, LN on sapphire, POI by Smart Cut. Chapters 06 and 08 (devices, industry): RF filter market, Murata XBAR, Soitec POI. Chapter 07 (history): White and Voltmer 1965; Shibayama et al. 1976; Spencer, Lenzo and Nassau 1965.