Acoustic waves in elastic solids

Surface acoustic wave resonators on thin film piezoelectric substrates in the quantum regime

“…SAW resonators can be understood as the elastic-wave analogon of an electromagnetic Fabry-Perot cavity, where a standing SAW is confined between two highly reflective mirrors (see figure 1(a)). The mirrors are realized in the form of distributed Bragg reflectors formed by a large number of periodically arranged parallel or curved lines, which modulate the surface mass loading and/or the piezo-electric boundary conditions [33]. Here, the pitch p and the line width a define the reflective acoustic properties which are characterized as a so-called stop-band of the mirror with center frequency f 0 and bandwidth ∆f [34].…”

“…At f 0 these partially reflected waves interfere constructively enabling the reflective behavior of the mirror with a total reflection coefficient Γ ≈ tanh(N g r). Γ approaches unity for N g r ≫ 1 within the stop-band bandwidth ∆f = 2f 0 r/π [33]. Two of these mirrors separated by the distance L form an SAW cavity.…”

“…Two of these mirrors separated by the distance L form an SAW cavity. The resonator supports multiple standing SAW modes within ∆f separated in frequency by the so-called free spectral range (FSR) ∆f FSR = v p /2L eff , where v p is the phase velocity of the mode and L eff is the effective mirror separation which differs from L due to the distributed reflection inherent to Bragg mirrors [33,34].…”

“…To compare the properties of SAW resonators fabricated on standard bulk LNO crystals with devices based on multi-layer substrates, we use three different sample types A, B and C (see figure 1(c)): (A) a 128 • -rotated Y-X-cut bulk LNO crystal-the standard material for SAW resonators and filters [2,33], (B) a thin film LNOI stack composed of a 500 nm thin 128 • -rotated Y-cut LNO thin film on a 2 µm thick SiO x buffer layer on a 350 µm thick Si(100) substrate, and (C) a 300 nm thin Y-X cut LNO thin film on a 500 µm thick Si(111) substrate.…”

“…Thus, their integration with acoustics requires SAW devices operating at these frequencies as well as an efficient transduction of electromagnetic into elastic excitations and vice versa [35]. Our SAW resonators are designed for a center frequency of f 0 ≈ 5 GHz and we chose standard, single-electrode interdigitated transducers (IDTs) for the transduction [33]. The transducer consists of alternating signal and ground aluminum electrodes (see figures 1(a) and (b)) with a pitch of p = 0.4 µm and a metallization ratio of η = 0.5 (i.e.…”