Nonreciprocity of Gigahertz Surface Acoustic Wave Based on Mode Conversion in an Inclined Phononic Crystal Heterojunction

In this report, a rectifying surface acoustic wave (SAW) device is proposed and simulated based on a simple inclined phononic crystal (PnC) heterojunction, consisting of monolithic pillars on $\mathrm{Si}$ substrate. The designed nonreciprocal operation principle is initially based on the frequency alignment of the surface-coupled guiding bands in the first half of the $\mathrm{Pn}\mathrm{C}$ with the local-surface-resonance (LSR) band gap in the second half of the $\mathrm{Pn}\mathrm{C}$, along two different equivalent incident directions. Benefiting from flexible LSR band-gap engineering, we tune the band-gap central frequency by optimizing the structural dimensions of the pillars in a small chip area, which is not achievable in conventional Bragg band gaps without varying the lattice constant. The other physical principle that dominantly affects the broken reciprocity in our proposed structure is the induced SAW shear-to-sagittal mode conversion at a limited frequency range in the trapezoidal $\mathrm{Pn}\mathrm{C}$ half, which depends on the incident direction with respect to the inclined cut line of the $\mathrm{Pn}\mathrm{C}$. Moreover, we optimize the spacing gap between the PnCs to modulate the elastic coupling strength between the half $\mathrm{Pn}\mathrm{Cs}$, and prove a significant SAW nonreciprocity of 34 dB at a frequency of 6.9 GHz, in addition to an acceptable rectified transmission of about −10.68 dB, by the proposed $\mathrm{Pn}\mathrm{C}$-based operation principles. The presented design benefits from a simple $\mathrm{Si}$-based structure and a CMOS-compatible fabrication process, without the need for any external excitation, and it is a promising miniature and efficient SAW rectifying candidate for wireless-communication applications.

Figure 1

(a) Unit cell of the $\mathrm{Pn}\mathrm{C}$ used for calculating the related band structure. (b) Supercell of the $\mathrm{Pn}\mathrm{C},$ with 10 rows of pillars along the wave-propagation direction, used for calculating the transmission spectrum.

Figure 2

Calculated band structure for the unit cell with (a) r_L = 40 nm and a_L = 100 nm and (b) r_R = 85 nm and a_R = 200 nm. Inset in (b) shows the first irreducible Brillouin zone of the square lattice. Dashed bands in both band structures show surface bands of the bare substrate. (c) Profiles of total displacements (u) for points A, B, C, and D in (b). Displacement components along x (u_x), y (u_y), and z (u_z) directions for (d) point B and (e) point C.

Figure 3

Calculated reduced band structures along Γ-X and Γ-M directions, in addition to sagittal and shear transmission spectra for perfect $\mathrm{Pn}\mathrm{Cs}$ with (a),(c) r_L = 40 nm and a_L = 100 nm, and (b),(d) r_R = 85 nm and a_R = 200 nm.

Figure 4

Profile of stored elastic energy in supercells with (a),(c) r_L/a_L = 40/100 (nm/nm) at 6 GHz and (b),(d) r_R/a_R = 85/200 (nm/nm) at 7.5 GHz. (a),(b) 3D views; (c),(d) top views of the elastic energy distribution for shear and sagittal sources, respectively.

Figure 5

Proposed nonreciprocal device consists of two $\mathrm{Pn}\mathrm{Cs}$: right $\mathrm{Pn}\mathrm{C}$ with r_R = 85 nm and a_R = 200 nm and left $\mathrm{Pn}\mathrm{C}$ with r_L = 40 nm and a_L = 100 nm. Two $\mathrm{Pn}\mathrm{Cs}$ are cut at 45° and joined with an interspacing gap of d. Forward excitation is along +x and the backward one is along the −x direction.

Figure 6

(a) Scheme of the individual right $\mathrm{Pn}\mathrm{C}$. (b) Calculated band structure for the right $\mathrm{Pn}\mathrm{C}$. (c) Isofrequency plot around the second surface-coupled band; (d) magnified band structure around the second surface-coupled band of the $\mathrm{Pn}\mathrm{C}$.

Figure 7

(a) Normalized transmission spectra for forward (+x) and backward (−x) shear inputs. (b) Components of the backward transmission in (a) separated into shear (u_y²) and sagittal (u_x² + u_z²) components.

Figure 8

Total displacement distribution at 6.8 GHz for the right $\mathrm{Pn}\mathrm{C}$ for (a) forward (left, 3D; right, top view) and (b) backward (left, 3D; right, top view) transmissions. (c) Profile of total displacement in the x-z cross section.

Figure 9

Total displacement profiles of the right $\mathrm{Pn}\mathrm{C}$ in the x-z plane for forward and backward incident directions at a frequency of (a),(b) 5 GHz, (c),(d) 6.8 GHz, and (e),(f) 11 GHz.

Figure 10

(a) Individual left $\mathrm{Pn}\mathrm{C}$ and (b) related band structure. (c),(d) Isofrequency plots around the second and third bands of the left $\mathrm{Pn}\mathrm{C}$, and (e) corresponding magnified band structure.

Figure 11

Normalized transmissions in the left $\mathrm{Pn}\mathrm{C}$ for (a) forward and backward shear-polarized input and (b) forward (backward) shear- (sagittal-) polarized input.

Figure 12

Total displacement profiles of individual left $\mathrm{Pn}\mathrm{C}$ in the x-z plane for forward and backward incident directions at a frequency of (a),(b) 5.6 GHz, (c),(d) 6.8 GHz, and (e),(f) 11 GHz.

Figure 13

Simulation results of the proposed device. (a) Spectrum of calculated N_F versus varying N_ext for d = 0. (b) Forward and backward transmission spectra with N_ext= 5 and d = 0. (c) Variation of calculated N_F versus d value. (d) Forward and backward transmission values versus d.

Figure 14

Forward displacement, top-view scheme, and backward displacement for (a)–(c) d = 2a_L at 6.9 GHz, (d)–(f) d = 6a_L at 6.8 GHz, and (g)–(i) d = 20a_L at 6.8 GHz.

Figure 15

Forward and backward transmission spectra in the designed nonreciprocal device with structural parameters listed in Table 1.