**1. Introduction**

Known piezoelectric materials such as quartz, lithium niobate, lithium tantalate, langasite, etc. have been widely used as the substrates in a number of acoustoelectronic devices such as resonators, acoustic filters, delay lines, sensors, etc. Such devices can operate on one or several typesofacousticwaves,suchasconventionalbulk(BAW)acousticwaves,surface(SAW)acoustic waves (Rayleigh, Sezawa, Gulyaev-Bleustein, shear-horizontal (*SH*), and Love waves), normal plate waves of Lamb-type, and Stoneley acoustic waves on the interface between two differ‐ ent solids. In the twenty-first century, state-of-art technologies have a clear requirement for passive electronic and acoustoelectronic components operating at high and ultra-high (UHF) frequencies with low insertion losses. Previously, conventional structures and materials could not be applied at UHF due to their high acoustic attenuation. Possible solution is to use piezoelectric layered structures (PLS) based on appropriate single crystalline substrates with low UHF acoustic attenuation. Modern precise technologies of thin-film deposition provide fabrication of submicron piezoelectric layers with excellent parameters. Hexagonal alumi‐ numnitride(AlN)filmsareusedmoreoftenthanzincoxide(ZnO)filmsduetotheirbestdielectric properties and thermal stability. Applying PLS approach, one can extend a set of substrate materials to be used up to non-piezoelectric crystals with outstanding physical properties.

Well-known types of BAW resonators are the conventional piezoelectric resonators more often produced out of crystalline quartz, including the high-frequency resonator as inverse mesa structure, thin-film bulk acoustic resonators (FBAR) [1], and solidly mounted resonators (SMR) [1,2], but they have significantly lower both *Q* factor and operating frequencies compared to high overtone bulk acoustic resonator (HBAR). Such HBARs can be used at high frequencies up to 10 GHz because the elastic energy is mainly concentrated within the substrate material [3]. Usually HBARs are designed as PLS with a specified electrode structure deposed on a crystalline substrate with low UHF acoustic attenuation. In earlier investigated BAW resona‐ tors, single crystalline and fused quartz, silicon [4], sapphire [4,5], and yttrium aluminum garnet (YAG) substrates [6] were used. It was proved that diamond single crystal has a low acoustic attenuation at UHF and diamond-based HBARs are known operating at frequencies up to 20 GHz [3].

The choice of HBAR's substrate material is a problem of high importance since it is necessary to take into account an appropriate combination of physical and chemical properties, low acoustic attenuation at UHF, crystalline quality, possibility of precise treatment, etc. It is well known that physical properties of thin films such as the density and elastic constants can considerably differ from the ones measured on the bulk specimens. HBAR can be used as an instrument for determination of material properties of substrates and thin films at microwave frequencies with high accuracy. Additionally, HBAR application gives a unique possibility to measure frequency-sensitive properties, for example, the acoustic attenuation of substrate's material within a wide frequency range of 0.5–10 GHz.

Application of diamond as a substrate material in this chapter is caused by its unique physical and acoustical properties: it is the hardest crystal with highest BAW and SAW velocities (in [111] direction, the phase velocity of BAW longitudinal type *vl* = 18860 m/s [7]); it has high thermal conductivity up to 2200 W/cm⋅K [8]; high thermal and radiation stabilities [9]; low acoustical losses at UHF [10], and so on. As there are many types of diamond crystals, which vary in terms of boron or nitrogen doping concentration, here we will discuss only dielectric IIa-type synthetic diamond crystals with low impurities concentration: *N* < 2 ppm.

The main objectives of this chapter consist of the theoretical, experimental, and modeling study of acoustic wave propagation, especially Lamb modes, and its dispersive properties in diamond-based piezoelectric layered structures.
