3.5 IDTs and SAW filters

An interdigital transducer (IDT) is a pair of interleaved metal combs on the crystal. A voltage across the combs strains the surface under every finger gap; the ripples add up only at the frequency whose wavelength equals the comb period, so the comb is both a launcher and a filter. Two combs facing each other make a delay line; resonators and ladders of them make many of the radio filters in phones, which carried more than 50 acoustic filters (SAW and BAW) per mid- and high-tier 4G phone in 2018, with more than 70 expected with 5G (vendor contribution in trade press, 2018 V).

Doubling N halves the bandwidth: the ripples from many gaps add in phase only at f₀. Detune the test tone by f₀/N and watch them cancel.

=================================================================================
 |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |  
 |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |  
   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
=================================================================================
/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_/‾\_  λ = p
20 pairs

Invention. White and Voltmer launched surface elastic waves with an interdigital transducer in 1965 (White & Voltmer 1965 S); the device had aluminum electrodes on a quartz bar, not LN (same-title Berkeley memorandum P). Elastic wave propagation in LN was reported the same year (Spencer et al. 1965 S).

p is the electrode period (one finger pair). On 128° Y-X (v_free = 3978.4 m/s derived): p = 4 µm gives f₀ = 994.6 MHz; a 2 GHz filter needs p = 1.989 µm, i.e. 0.50 µm fingers at metallization ratio 0.5 derived. In the delta-function model (Smith et al. 1969 equivalent-circuit lineage) an N-pair uniform IDT has a radiation conductance with a sinc² shape, so the fractional bandwidth between first nulls is 2/N. The shape is the textbook result; the absolute prefactor in terms of k², the capacitance per pair and the aperture is not shown.

Measured TFLN example. An IDT on suspended TFLN with 1.9 mS peak conductance and 3.36 MHz bandwidth, matched to 50 Ω at 1.85 GHz (Jiang et al. 2020, arXiv v1 reported).

LN vs LT in phones

POI substrates. Soitec Connect POI, a thin LT or LN layer by Smart Cut on buried oxide on silicon: LT6-MHB, LT6-LB, LN6 at 150 mm; LT8-MHB, LT8-LB at 200 mm; for 5G, GNSS, Wi-Fi coexistence (Soitec product page P). In 2020 Soitec announced volume POI supply (300 nm to 1 µm LT on oxide on high-resistivity Si) for Qualcomm RF filters (trade press S).

XBAR on thin LN. First report 2019 (Plessky et al. 2019 reported); Murata completed its acquisition of Resonant Inc., the developer of XBAR, on 2022-03-28 (Murata release P).

The equivalent-circuit and coupling-of-modes models (Smith et al. 1969 S; Hashimoto 2000 S) are the standard design tools. The figure uses only the normalized array factor and f₀ = v/p; absolute admittance needs the prefactor, not computed here.

Second-order effects not modelled: electrode mass loading and reflection (velocity shift with metal thickness), bulk-wave radiation, diffraction for small apertures, and triple-transit echoes. The array-factor form above has a grating lobe at 2f₀; a finger-resolved form is needed beyond about 1.5 f₀ (the plot stays within 0.8 to 1.2 f₀).

Velocities in the figure are the partial-wave results for the free or the metallized surface (selectable in both views); a real IDT region is partly metallized (ratio η), so the true synchronous frequency lies between the two values.