Piezoelectric phononic integrated circuits

Piezoelectric microresonators¹ underpin modern wireless communication by enabling compact, high-performance radio frequency filters² in mobile phones.³ Despite billions of these devices being in widespread everyday use across a wide range of materials, frequencies, and device geometries, every piezoelectric device in current commercial operation shares one common characteristic, they all manipulate quasi-plane waves of sound, i.e., the transverse extent of the acoustic fields in these devices is at least 10–50  $×$ the acoustic wavelength (⁠ $λa$⁠). While the ideas around using waveguides to confine acoustic fields to transverse dimensions $≈λa$ have been around since the early days of ultrasonics research,⁴ they have not had the expected impact on state-of-the-art (commercial) piezoelectric devices. However, over the past decade, there has been a convergence of developments in related areas, which makes it interesting to reconsider the prospect of manipulating gigahertz acoustic waves in low-loss chipscale platforms. In this article, we discuss the prospects for such piezoelectric phononic integrated circuits (PnICs), named in analogy with their photonic counterparts, for a wide range of applications in sensing, communications, and information processing. We also outline the key research challenges that need to be addressed for these devices to realize their potential and make the necessary transition from proof-of-principle device demonstrations to impacting future systems.

While the original motivation for developing guided wave acoustic devices was the prospect of shrinking the size of piezoelectric resonators with a view toward monolithic integration of resonators and active devices (amplifiers, switches) for future RF front-ends, this has proved challenging in practice. The main hurdle has been the excess insertion loss, discussed in Sec. IV, that arises due to the challenge of injecting and extracting gigahertz acoustic waves from wavelength-scale devices⁵ with near-unity efficiency. This excess loss, coupled with the stringent performance requirements imposed on RF filters in mobile phones has made it such that any potential size reductions are currently more than offset by the excess noise (and increased bit error rate) that would accompany a switch to guided wave devices. We would like to clarify here that in this article, we are focused on 2D transverse confinement with waveguide cross sections $≈λa2$⁠, cf. Fig. 1. 1D confinement has already been exploited in commercial devices, such as the surface acoustic wave (IHP-SAW)™ devices from Murata⁶ to demonstrate stronger electromechanical coupling (higher $keff2$⁠), higher quality factors, and lower temperature coefficient of frequency by choosing the guiding and cladding layers appropriately.⁷ 

In the past decade, there has been a convergence of developments from areas outside wireless communications that has re-ignited interest in the development of low-loss guided wave piezoelectric platforms. The primary one is the spectacular success of (silicon) integrated photonics in revolutionizing optical communications by showing the benefits of routing and manipulating light with strong transverse confinement in chipscale platforms,^8, Figs. 1(a) and 1(c). Key was the realization that one can do much more than simply replacing optical fibers with silicon waveguides. Routing light in a semiconductor platform provides new avenues for dynamic control (through free carrier mediated electro-optic interactions⁹) and enhanced nonlinear interactions (because of the increased local field strength, geometric control of waveguide dispersion, and phase matching over long path lengths in low-loss platforms¹⁰) and the prospect of exploiting the strong index contrast to design computationally optimized geometries to achieve inverse-designed electric field profiles.¹¹ These arguments, in principle, apply equally well to PnICs, Figs. 1(b) and 1(d).

A second thrust has come from efforts to build large-scale (⁠ $≈106$ qubits) quantum computers and the spectacular progress on the hardware front in developing superconducting qubit based devices,¹² which are arguably the leading platform in the current noisy intermediate scale quantum computing (NISQ) era. It has become increasingly clear that networking small quantum processors in a modular architecture with photonic links is necessary¹³ to achieve the scale required for useful quantum computing. This requires the development of quantum transducers that can convert quantum information back and forth between the microwave and optical frequency domains. Acoustic waves provide a natural route toward bridging the wavelength disparity between microwave (⁠ $λ≈$ cm) and optical (⁠ $λ≈$ μm) photons, and piezoelectric optomechanical devices are one of the leading candidates for realizing efficient quantum transducers.^14,15 Such “quantum acoustic” devices have spurred a lot of research in geometries that can effectively confine gigahertz acoustic waves in micrometer-scale cavities in order to enhance the interaction strength and minimize dissipation.

In parallel, advances in understanding and controlling mechanical dissipation at the nanoscale have led to the realization that acoustic dissipation in micrometer-scale geometries can be significantly lower than that in bulk geometries. It was long believed that surface roughness and surface dissipation would automatically imply that guided wave devices with strong acoustic confinement would have higher dissipation in comparison with their bulk counterparts. However, guided wave geometries provide additional degrees of freedom that one can exploit to reduce dissipation. The two main ones being film stress to exploit dissipation dilution¹⁶ and the use of periodic structures that can open up phononic bandgaps¹⁷ that allow a mechanical mode to be tightly confined with negligible leakage. This has led to the demonstration of gigahertz resonators with phonon lifetimes > 1 s [at millidegrees Kelvin temperatures, $Q>$ 50 × 10⁹ (Ref. 18)], and the isolation of these mechanical modes from the noisy thermal bath has been used to observe quantum back-action effects of light on mechanical motion at room temperature.¹⁹ 

These developments put together make it timely to consider the role that strong transverse confinement and waveguiding can play on future acoustic devices and what impact it might have on future systems. The main goal of this article is to outline the unique opportunities that PnIC platforms provide that one cannot traditionally access in bulk geometries and what material and devices advances are needed to fully realize these benefits. Before we proceed, we would first like to clarify our nomenclature and restrict the scope of the devices being considered. We refer to the gigahertz vibrations in solids as acoustic waves to stay consistent with the nomenclature of the RF filter community, although elastic waves might be more technically appropriate. Although there are many ways to confine and guide acoustic waves at the micrometer-scale,⁵ we restrict ourselves to traditional unsuspended “slow-on-fast” layer geometries and strip waveguides, such as shown in Fig. 1(d). While suspended geometries allow one to eliminate substrate leakage and work with widely available material systems such as silicon and gallium arsenide,²⁰ they place severe restrictions on device length due to the need for tethering, and more importantly limit the available coupling mechanisms, as discussed below. Finally, we focus our discussion on the electromechanical (piezoelectric) excitation of vibrations with microwave systems in mind. Therefore, related work on optomechanical excitation²¹ and, in particular, stimulated Brillouin scattering,²² falls outside the scope of this article.

While in principle any slow-on-fast layer on substrate combination can be used for building PnICs (cf. Fig. 2 for representative devices), the available choices are restricted once we account for other factors like substrate availability, future foundry compatibility, and potential application areas. Broadly, the materials can be divided into two categories: (a) taking strong (⁠ $keff2>0.05$⁠) piezoelectric insulators like lithium niobate,^23,24 lithium tantalate,²⁵ and scandium aluminum nitride²⁶ that constitute traditional piezoelectric devices¹ and using them as thin (sub-micrometer) waveguiding layers on fast substrates like sapphire and silicon carbide by wafer bonding, and (b) moderate (⁠ $keff2≈0.01$⁠) piezoelectric semiconductors like gallium nitride that can hetero-epitaxially be grown on fast substrates like sapphire²⁷ and silicon carbide^28,29 with low defect density.

The two platforms provide complementary performance tradeoffs. The higher $keff2$ in LN, LT, and ScAlN helps reduce insertion loss and transducer size and is critical for loss-sensitive applications like wireless communication and quantum transduction.¹⁵ On the contrary, they provide manufacturing challenges in terms of substrate availability and nano-patterning (dry etching). We would like to point out here that there has been enormous progress in understanding nanofabrication in these media over the past decade driven primarily by integrated photonics, and the fabrication recipes³⁰ can be directly applied to PnICs given the similarity in wavelength.

The interest in piezoelectric semiconductor platforms, despite their lower $keff2$⁠, arises primarily from the prospect of engineering acoustoelectric interactions between carriers and acoustic waves in confined geometries. Acoustoelectric interactions can be harnessed^31,32 for a variety of applications ranging from amplification, non-reciprocal signal processing, and dynamic control. Recent advances in both the materials³³ and device fabrication²⁹ fronts, coupled with a push toward monolithically integrated RF front-ends in mobile devices, has made it attractive to harness these interactions in guided wave platforms, as we discuss in detail below.

It goes without saying that advances in materials go hand-in-hand with advances in nanofabrication methods, especially in the context of adoption for chipscale guided wave platforms, but an exhaustive review of nanofabrication methods as applied to PnICs lies outside the scope of this article.

The main advantage that any guided wave platform provides is the enhancement of (local) field strength due to increased geometrical wave confinement, and the prospect of maintaining this increased field strength over long propagation distances in low-loss chipscale platforms. This leads to much stronger wave–matter interaction strengths than in bulk (plane wave) geometries and lies at the heart of cavity quantum electrodynamics³⁷ and nonlinear optics.¹⁰ Strong field confinement in wavelength scale cavities makes them more sensitive to perturbations opening the route toward sensing applications. Finally, geometrical waveguiding enables confined routing of acoustic waves in highly mechanically anisotropic materials like LN and LT. Unsuspsended device platforms provide the most natural route toward harnessing these advantages as the device geometries can avoid clamping and tethering losses [Fig. 2(a)] and the interaction can be maintained over centimeter-scale distances [Fig. 2(c)] With applications in mind, we can classify PnICs by the primary features they exploit in a guided wave geometry, using the building blocks shown in Fig. 2.

In a piezoelectric material, the acoustic and electric fields are related by the constitutive relations. Therefore, an increase in the local acoustic field strength results in a proportional enhancement in the electric field strengths as well, and one can think of the acoustic field as an intermediary for manipulating the electric field at deeply sub-wavelength scales. Applications such as microwave to optical quantum transducers,¹⁵ which are necessary for generating entanglement between distant superconducting qubits, require efficient quantum frequency conversion between the microwave and optical domains. The wavelength mismatch between the microwave and optical fields limits the overall interaction strength, and acoustic fields provide a natural way to circumvent this problem. State-of-the-art experiments^38–40 require the acoustic and optical fields to be strongly confined to wavelength scale optical cavities and architectures⁴¹ for efficiently injecting acoustic fields into these cavities. At high frequencies and especially with strong field confinement, the surface magnetic field in piezoelectric devices, which is usually ignored in the quasistatic approximation, becomes significant and can be used for efficient nanoscale spin detection⁴² and improving the spin detection sensitivity of electron spin resonance.

In piezoelectric semiconductors, the interaction between carriers and electric fields can be harnessed for acoustoelectric (AE) effects.³² Harnessing AE effects can allow one to exert exquisite dynamic control on the acoustic field, including inducing phase shifts and gain or attenuation. Given that AE interactions lead to either gain or loss depending on whether the acoustic field and the carrier co-/counter propagate, they can form the building blocks of compact, non-reciprocal microwave devices that avoid magnetic fields. Such non-reciprocal devices with high-performance and compact footprint are a key component of future simultaneous transmit and receive (STAR) and full-duplex wireless systems.⁴³ The main attraction of engineering AE interactions in guided wave geometries [cf. Fig. 3(c)], in a FinFET⁴⁴ like architecture with a 2D electron gas layer on top of the acoustic waveguide, is that provided the propagation loss is sufficiently low,²⁹ a (weak) interaction can be effectively integrated over long interaction lengths, measured approximately in centimeters. In addition, like all nonlinear interactions, field confinement can significantly enhance the gain for nonlinear mixing processes (three wave and four wave) that use carriers as an intermediary.³⁶ Putting all of these effects together in a chipscale platform: gain, non-reciprocal signal processing, and signal frequency translation through efficient wave mixing opens up the prospect of building a complex RF front-end on a single die and pushes the integration between active and passive microwave devices to its ultimate limits.

Confining fields to small mode volumes increases their sensitivity to perturbation. Using perturbation theory,⁴⁵ one can show that the change in frequency (of the cavity) $∝|a|2$⁠, where |a| represents the cavity (mode) displacement amplitude, with $|a|∝1/Vm$⁠, where $Vm$ is the cavity mode volume. While in principle any nanomechanical sensor for chemical, biological, or environmental (force) detection⁴⁶ can be redesigned in the PnIC platform to work with wavelength-scale cavities, it is not obvious that one gets a performance (sensitivity) improvement over traditional suspended devices and non-piezoelectric readout mechanisms in terms of signal-to-noise ratios.⁴⁷ There is one class of devices where PnIC platforms provided a distinct advantage. Building rotation sensors [cf. Fig. 3(a)] using the effect of Coriolis forces^34,48 in a PnIC platform provides a sensor platform with a unique performance niche that is well adapted to harsh environments (high temperature, shock, and large accelerations). Such devices²⁷ combine the footprint and integration of traditional MEMS based gyroscopes with the harsh environment performance of fiber-optic gyroscopes. By incorporating phononic bandgap structures⁴⁹ for localizing sound to wavelength-scale mode volumes, the performance metrics of these devices can potentially be significantly improved, although this needs to be demonstrated in practice.

The exquisite perturbation sensitivity of confined acoustic fields can also be used to design active PnICs, which provide mechanisms to dynamically control⁵⁰ propagating acoustic waves in chipscale platforms. Given that all the traditional mechanisms for exerting phase changes on acoustic fields, like temperature,⁵¹ stress,⁵⁰ electric field,⁵² and carriers,³³ are relatively weak effects, the only way to realize practical devices with adequate performance is to incorporate them in low-loss waveguide platforms where the weak effects can be effectively integrated over long path lengths $≈$ mm to get a $π$ phase shift.⁵² While this might sound restrictive, similar weak carrier based electro-optic phase modulators⁵³ lie at the heart of active silicon photonic integrated circuits.

The high surface to volume ratios in waveguide geometry, which expose the acoustic field to surface states, and the presence of surface roughness, which could lead to mode conversion, were long considered a detriment to developing high-performance PnICs compared to their bulk counterparts. However, as silicon photonics has shown,⁵⁴ modern nanofabrication methods have sufficiently advanced that sound propagation at the nanoscale can be exquisitely controlled with the result that integrated devices have quality factors that currently exceed their bulk counterparts at comparable frequencies.^16,18,29 There are two main reasons for this increase in performance in guided wave devices. Traditional piezoelectric microresonators, both bulk acoustic wave (BAW)² and surface acoustic wave⁵⁵ based, rely on metals [cf. electrodes in film bulk acoustic wave resonators (FBAR), grating reflectors in SAW devices] to confine the acoustic fields, which results in excess damping and scattering. PnICs can instead exploit whispering gallery modes in microring resonator geometries.^{23,27–29,56} In an unsuspended PnIC platform, one also avoids tether and clamping loss, and substrate scattering. The other advantage that PnIC platforms can exploit is using tensile stress for dissipation dilution and periodic patterning of phononic bandgap structures¹⁷ to confine acoustic fields with low loss at the wavelength scale. While many of these ideas have currently been demonstrated in suspended geometries,¹⁸ they can be extended to solidly mounted platforms.⁵⁷ 

A low-loss chip scale platform with high fQ metrics¹ opens up the route toward demonstrating compact microsecond spiral delay lines²⁹ with programmable signal delays, as needed for 5G multiple-input-multiple-output (MIMO) systems. The high-Q microring resonators [cf. Fig. 3(b)] can underpin low phase noise high frequency and high power oscillators.³⁵ An interesting future direction for these high integrated devices depends on their cryogenic performance. Provided the quality factor scales with temperature (⁠ $≈1/T4−6$⁠) as predicted from theory,⁵⁸ with the exponent determined by the limiting damping mechanism, the low temperature performance of these acoustic oscillators should exceed that of current cryogenically cooled sapphire oscillators,⁵⁹ in addition to the inherent footprint and integration advantages. These precision sapphire oscillators currently underpin a wide range of applications from secondary time standards to generating low noise microwave signals for resonant gravitational wave detection.

To realize the benefits outlined in Sec. III, a number of challenges currently facing PnICs need to be addressed.

As alluded to above in Sec. I, excess insertion loss is the main hurdle PnICs face. We define insertion loss here as the excess loss measured in a two port microwave transmission measurement (⁠ $S21$⁠) when the acoustic wave is focused into and out of a wavelength scale device. We here ignore the propagation loss, which we tackle separately below. There are two critical components to the IL: (a) designing efficient focusing transducers that are simultaneously impedance matched to $50 Ω$⁠, and can focus gigahertz frequency acoustic waves to micrometer dimensions, and (b) getting this focused acoustic field into and out of strip waveguide [cf. Figs. 2(a) and 4(a)] with near-unity efficiency.

To get a sense for the problem, a shape-optimized focusing IDT structure⁶⁰ in a suspended platform with a short waveguide shows a peak transmission (⁠ $S21$⁠) of −15 dB (0 dB represents no IL), with representative PnIC platforms being more typically in the −20 dB range.²⁸ As noted above, this IL needs to be ideally < 2 dB from a system's perspective. On the transducer front, the main challenge is to design efficient unidirectional⁶¹ focusing transducers that can avoid excess scattering⁶² at the metal electrodes. In principle, one could combine traditional (straight electrode) unidirectional transducers with adiabatic tapers⁶³ or add on-chip impedance matching structures to alleviate the matching constraints, but in both cases one trades off on-chip footprint for efficiency.

Focusing acoustic waves into and out of wavelength scale waveguides is trickier than the analogous optical problem because of the presence of surface/edge modes. Unlike in optics, the slower acoustic fields are almost always on the surface. To see this in practice, consider the receiving IDT scenario in which the acoustic field is leaking out of a waveguide. At the waveguide taper interface, only a fraction of the acoustic field is radiated into the central beam, which can be picked up by the receiving IDT. A significant fraction of the power is radiated into two acoustic sidelobes, which correspond to edge modes on the surface, cf. Fig. 4(a). Suppressing these edge modes by designing a phononic bandgap could potentially improve the transmission efficiency, although this needs to be verified in practice. One could potentially try and inverse design the whole transmission chain using modern optimization tools such as is now common in integrated photonics,¹¹ but the problem is more complicated in the acoustic case because the waveguide geometry is intrinsically multimoded and most of the current inverse design optimizations implicitly assume single mode waveguide operation, which is relatively easy to achieve in photonics.

A closely related problem is the challenge of critical coupling to wavelength scale microcavities.⁶⁴ Given that the acoustic field cannot couple through vacuum, one is limited to substrate coupling only for efficient energy transfer into phononic microring resonators.²⁹ This increases the effective coupling length [cf. Fig. 4(b)] significantly (for realistic waveguide resonator gaps) in comparison to the equivalent photonics problem for the same wavelength. While pulley-coupling architectures can be used to compensate for microring geometries, new coupling approaches need to be developed for efficient power transfer into and out of more strongly confined geometries like 1D/2D phononic crystals. End fire coupling⁶⁵ in these geometries is usually not efficient for exciting the mode of interest because of the prospect of unwanted mode conversion and scattering that accompanies the acoustic wave transmission through the mirror holes. This is related to the earlier argument about phononic waveguides being multimode and the bandgaps usually being defined only for certain symmetry conditions.^17,66

We would like to note here that while IL is the main problem PnICs face, the level of IL that can be tolerated depends on the application, and need to be carefully analyzed in the context of the sensitivity advantages that PnIC platforms provide. A critical thrust for future research is therefore to find (possibly niche) applications, such as rotation sensing in extreme environments as outlined above, where relatively high levels of IL (⁠ $≈$ 5–10 dB) can be tolerated.

While phononic microring resonators have already shown very low acoustic dissipation,²⁹ it is still unclear what the ultimate dissipation limits are on waveguide geometries. Most of the theoretical damping models (Akhiezer and Landau–Rumer) are derived assuming plane acoustic waves and are not directly applicable to strongly confined geometries.⁴⁷ Understanding the role of surface dissipation and measuring cryogenic performance of these low-loss devices to quantify the damping mechanisms are critical. An open question is whether surface passivation techniques that have shown benefits for both electronic⁶⁷ and photonic⁶⁸ devices have any role to play in PnICs.

As outlined above in Sec. III, exerting effective dynamic control^50,52 on propagating acoustic fields in waveguide geometries is critical for a range of applications. While a number of methods can be used to tune acoustic wave propagation, given the focus on harnessing AE effects in this paper, we use AE effects as the model mechanism to illustrate some of the key challenges that need to be addressed and the inherent tradeoffs involved.

In a piezoelectric semiconductor, the local carrier density (more generally, the local conductivity) affects the acoustic wave propagation by screening the associated electric field and thereby affecting the piezoelectric stiffening.⁶⁹ The carriers induce both a dispersive (phase shift) and a dissipative (attenuation) effect with no DC bias applied.³¹ To minimize the acoustic dissipation one needs to increase the carrier density significantly (⁠ $>1015/cm2$⁠). If one works with a FinFET-style⁴⁴ architecture with a 2D electron gas layer on top of the acoustic waveguide, this requires effectively gating the carrier concentration with a metal electrode without incurring excessive IL due to acoustic damping and scattering. More generally, harnessing AE effects (like gain) in waveguide geometries require making low resistance Ohmic contacts to 2D electron gas layers in geometries with large topographical variation, where the contact area needs to be minimized to mitigate excess IL. One can in principle try and inject carriers from the side (with a lateral pin diode) as is common in active integrated photonics, but unlike in optics, the acoustic field is not confined to the central region because of the surface mode issues outlined in the IL section above. This is one of the main reasons why all current AE demonstrations have been limited to plane wave (quasi-1D) geometries, even though it has been recognized that moving to confined geometries can result in significant performance improvements³⁶ for the nonlinear interactions. This general trade-off between effective modulation of small volumes and excess IL also applies to other modulation mechanisms like temperature, strain, and electric field.

Progress in nanoscale devices always places a requirement on the development of new metrology methods⁷⁰ and PnICs are no different. Traditional methods for monitoring acoustic wave propagation in devices need to be updated to visualize acoustic wave propagation⁷¹ in tightly confined geometries and use the measurements to iteratively feedback on the device design. A key restriction of most traditional acoustic wave imaging techniques is that they are sensitive mainly to surface displacement. With guided modes, there is a significant fraction of the acoustic energy that is confined below the surface. Therefore, methods that can accurately map the 3D acoustic energy distribution⁷² sensitively, with nanometer spatial and nanosecond temporal resolution would revolutionize PnIC design and characterization. Especially for tackling the IL problem, it is hard to optimize device geometries if one is forced to rely only on S-parameter measurements. Local mapping techniques are critical for understanding energy loss and the effect of phononic bandgap structures on acoustic wave propagation.

We have shown that strong transverse confinement of gigahertz acoustic fields to wavelength (micrometer)-scale waveguides and resonators in piezoelectric platforms provides significant advantages for a wide range of applications in sensing, communication, and signal processing. To realize these benefits, the excess insertion loss facing such phononic integrated circuits needs to be addressed, which boils down to the question: can gigahertz acoustic fields be injected into and extracted from wavelength scale devices with near-unity efficiency?

I would like to thank the members of my research group, particularly Mahmut Bicer, Stefano Valle, Jacob Brown, Fahad Malik, and Ankur Khurana for their contributions to this research program, and John Haine, Martin Cryan, Martin Kuball, Bruce Drinkwater, Mark Beach, and John Rarity for valuable feedback on various aspects of this work. I gratefully acknowledge funding support from the European Research Council (SBS3-5, 758843) and the UK's Engineering and Physical Sciences Research Council (EP/V005286/1).

The author has no conflicts to disclose.

Krishna Coimbatore Balram: Conceptualization (lead); Funding acquisition (lead); Investigation (lead); Writing – original draft (lead).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.