Anisotropy-induced polarization mixture of surface acoustic waves in $\mathrm{Ga}\mathrm{N}∕c$-sapphire heterostructures

The characteristics of surface acoustic waves (SAWs) in GaN layers grown on $c$-plane sapphire are investigated. Besides Rayleigh mode, Sezawa and Love modes, which are confined in the nitride layers, arise because of the slow sound propagation in GaN compared with the substrate. In addition, pseudo-SAWs leaking into the bulk are observed. The trigonal crystal symmetry of sapphire not only leads to an anisotropic propagation of the SAWs in the heterostructures, despite the isotropic elastic properties in the $c$-plane GaN, but also mixes their polarization even for the propagation along high-crystal-symmetry directions. Love modes, which are normally piezoelectrically inactive, can be excited by interdigital transducers through this polarization mixture. The nonzero value of the elastic coefficient $c_{14}$ of sapphire is indicated to be the origin of the coupling of sagittal and shear horizontal displacements.

Figure 1

(Color online) (a) Transmission and (b) reflection characteristics of two SAW filters on a $1.2\text{−}\mu \mathrm{m}$-thick GaN film along the $\left[11\overline{2}0\right]$ and $\left[1\overline{1}00\right]$ directions of sapphire. The configuration of the two orthogonal delay lines is illustrated in the inset of (a). The resonances are associated with the Rayleigh $\left(\mathrm{R}\right)$ and the first Love mode $\left({\mathrm{L}}_1\right)$. The inset of (b) shows a micrograph of the interdigital transducer having a period of $8\mu \mathrm{m}$.

Figure 2

(Color online) Transmission spectra of two SAW delay lines on a $1.7\text{−}\mu \mathrm{m}$-thick GaN film along the $\left[11\overline{2}0\right]$ and $\left[1\overline{1}00\right]$ directions of sapphire. The peaks associated with the Rayleigh mode, the first Love mode, and the first pseudobulk mode are labeled $\mathrm{R}$, ${\mathrm{L}}_1$, and ${\mathrm{PB}}_1$, respectively. The SAW wavelength is $8\mu \mathrm{m}$.

Figure 3

Surface and pseudosurface modes and their dispersion in the GaN/sapphire structures. The propagation is along the directions (a) $\left[1\overline{1}00\right]$ and (b) $\left[11\overline{2}0\right]$ of sapphire. The solid lines show the dispersion calculated using the transfer matrix approach. The experimental data are shown by the circles. The gray scale indicates the magnitude of the shear vertical component of the acoustic waves for the values of the velocity and $kH$ calculated using the Green’s function formalism. The brighter the scale is, the larger the magnitude. Rayleigh, Sezawa, Love, and pseudobulk modes are denoted $\mathrm{R}$, ${\mathrm{S}}_{\mathrm{i}}$, ${\mathrm{L}}_{\mathrm{i}}$, and ${\mathrm{PB}}_{\mathrm{i}}$, respectively. The dotted lines indicate the longitudinal $\left(v_L\right)$ and fast $\left(v_{FT}\right)$ and slow $\left(v_{ST}\right)$ transverse bulk velocities of the substrate and the overlayer.

Figure 4

(Color online) Angular dependence of the velocity of the Rayleigh $\left(\mathrm{R}\right)$ and first Love $\left({\mathrm{L}}_1\right)$ modes for $kH=0.94$. The symbols show the experimental data, whereas the numerical results are shown by the lines. The propagation angle is defined from $\left[1\overline{1}00\right]$ toward $\left[11\overline{2}0\right]$. The angle of 30° is equivalent to $\left[11\overline{2}0\right]$ due to the sixfold symmetry in the $c$-plane sapphire.

Figure 5

Normalized particle displacements, $u_i$, and potential, $\varphi$, when $kH=0.94$. The modes are Rayleigh $\left(\mathrm{R}\right)$, (a) and (b), first Love $\left({\mathrm{L}}_1\right)$, (c) and (d), and first pseudobulk $\left({\mathrm{PB}}_1\right)$, (e) and (f). The propagation is along the $\left[11\overline{2}0\right]$ direction for the upper panels and the $\left[1\overline{1}00\right]$ direction for the lower panels. The displacements $u_1$, $u_2$, and $u_3$ are the longitudinal, shear horizontal, and shear vertical components, respectively.

Figure 6

Normalized particle displacements, $u_i$, and potential, $\varphi$, of the first Sezawa $\left({\mathrm{S}}_1\right)$ mode when $kH=6$. The propagation direction is (a) $\left[11\overline{2}0\right]$ and (b) $\left[1\overline{1}00\right]$ of the sapphire substrate. The displacements $u_1$, $u_2$, and $u_3$ are the longitudinal, shear horizontal, and shear vertical components, respectively.