6–20 GHz 30% ScAlN Lateral Field-Excited Cross-Sectional Lamé Mode Resonators for Future Mobile RF Front Ends

This article reports on 30% scandium-doped AlN (ScAlN) lateral field-excited (LFE) cross-sectional Lame’ mode resonators (CLMRs) with unprecedented performance in the 6–20 GHz range. By combining high-crystallinity 30% ScAlN piezoelectric thin films, a lithographic tunability of the resonance frequency, and a simple three-mask post-CMOS compatible fabrication process, we propose a technology platform that can enable the mass production of low-loss, wideband, and compact microacoustic filtering devices spanning a wide spectrum portion on the same chip for the next-generation radio frequency front ends (RFFEs) of handsets. This article demonstrates a successful scaling of the microacoustic technology well beyond the sub-6-GHz fifth-generation (5G) band, as well as the outstanding capabilities of high-crystallinity 30% ScAlN piezoelectric layers in delivering high-quality factor (<inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>) and high-electromechanical coupling (<inline-formula> <tex-math notation="LaTeX">${k}_{t}^{{2}}$ </tex-math></inline-formula>) resonators, notably exceeding the state of the art in terms of relevant figures of merit (FOMs). Furthermore, we experimentally investigate the impact of geometrical parameters, such as tethering configuration and width-over-length ratio on the devices’ 3-dB quality factor (<inline-formula> <tex-math notation="LaTeX">${Q}_{\text {3dB}}$ </tex-math></inline-formula>), power linearity (PL), and temperature coefficient of frequency (TCF). By adopting a statistical approach for data analysis, we determine the optimal geometry to maximize the <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> value. Moreover, we experimentally demonstrate that a fully tethered device’s configuration ensures superior PL, lower TCF, and higher device yield and select that as the best design tradeoff between all the variables under consideration. Finally, we discuss a further scaling of LFE CLMRs, both in terms of higher doping levels in the piezoelectric layer, in order to enhance the performance of microacoustic filters, and in terms of higher operation frequencies, in order to reach and cover the mm-wave spectrum.


I. INTRODUCTION
S INCE the advent of the first mobile handsets, wireless communication has become ubiquitous, radically changing our lifestyles in only a few decades.This unprecedented level of connectivity between individuals has paved the way for the new applications that are being developed at an always- The authors are with the Nano Systems Innovation (NanoSI), Northeastern University, Boston, MA 02115 USA (e-mail: giribaldi.g.@.northeastern.edu).
Digital Object Identifier 10.1109/TUFFC.2023.3312913increasing pace.Live video streaming, social networking, and virtual reality are only a few of the latest digital innovations that have emerged in recent years.In addition to that, machineto-machine communication and the Internet of Things are promising to technologize our surroundings, allowing humans to be more in control than has ever been.As the world becomes more and more connected, the always-increasing volume of transmitted data is supported by the ongoing rapid evolution of the wireless communication protocols, culminating in 2020 in a first mass deployment of its fifth generation (5G).Such novel technology promises remarkable improvements in key parameter indicators (KPIs) such as data rate, spectral efficiency, and latency compared to previous generations [1], [2].5G allocates the spectrum into two frequency bands: sub-6-GHz ( f < 6 GHz, FR-1) bands and mm-waves • Leveraging sputtered high-crystallinity ScAlN thin-films, record-breaking Q and k 2 t devices are presented, backed by statistical analysis on the measured data to identify the optimal device topology.
• The devices are poised to enable the synthesis of pass-band filters for mobile applications in the 5G FR-3 and 6G mid-band frameworks.
(24 GHz < f < 300 GHz, FR-2).The former is the one mobile phones are mainly relying on and consists, for the most part, of a refarming of 4G-LTE bands, while providing only marginal upgrades to the 4G-LTE KPIs.Moreover, sub-6-GHz 5G bands are already congested given the high number of daily users, especially in crowded areas and during largescale events.On the other hand, besides a few pilot use cases, the mm-wave spectrum remains untouched in the framework of mobile devices.The reason lies in the lack of compact and high-performance technological solutions for radio frequency front ends (RFFEs), and specifically for the passband filtering elements.In fact, the classic super-high frequency (SHF) solutions, such as cavity and waveguide filters, possess footprints in the tens of mm 2 range, preventing large-scale integration of multiple devices in handsets.Filters based on distributed elements were demonstrated and already commercialized [3], but the low quality factor of microstrip inductors limits the filter roll-off sharpness, undermining efficient spectrum usage.Moreover, the high-frequency carriers in the mm-waves are strongly attenuated by propagation losses, requiring a higher density of base stations and thereby increasing the overall cost of the technology deployment.
Recently, the 7-20 GHz band was proposed as a third 5G frequency range (FR-3) as an excellent tradeoff between network capacity and coverage.Moreover, it allows for less stringent technology requirements given the lower frequency of operation and therefore a potentially faster commercial mass roll-out compared to the mm-waves.Furthermore, such spectrum portion is foreseen to be repurposed as 6G midband, devoted to crowded urban-area coverage [4].In such a framework, the need for component carrier bandwidths (BWs) of 400 MHz or more requires RFFE filters with enhanced fractional BW (FBW).
Fig. 1 shows the building-block view of the receiver portion of a heterodyne RFFE [5].That system is constituted by an antenna, a passband filter, a low-noise amplifier (LNA), and a mixer with its local oscillator.The passband filter has the fundamental task of removing unwanted spectral components to allow for a higher signal-to-noise ratio (SNR) in the received carrier.Such components are currently implemented with acoustic passive technologies, thus reducing the overall power consumption of the RF module.Microelectromechanical (MEM) filters are generally synthesized as some sort of cascade [e.g., ladder scheme (Fig. 1)] of microacoustic resonators [6].In this sense, the state of the art is constituted by surface acoustic wave (SAW) [7] and bulk acoustic wave (BAW) [8] devices.SAW filters confine the resonant vibration on the surface of the piezoelectric active layer and constitute Fig. 1.Building block diagram describing the receiver portion of a heterodyne RFFE.The passive passband filter is shown in its most used topology, the ladder scheme.In the inset on the left, a visual representation of the frequency operation of the filter building blocks is given (simulated data).The inset on the right represents the resonator in its widely used mBVD model.In this work, the dielectric losses are represented by a resistor (R 0 ) in parallel to the static capacitance (C 0 ).Such losses can be arbitrarily described by a resistor in series or in parallel to C 0 , according to standard series-parallel impedance transformations.the first microelectromechanical system (MEMS) filters that were introduced in mobile phones [9].Usually, a singlecrystalline piezoelectric material (e.g., lithium niobate and lithium tantalate) is employed, thus providing high Q and k 2 t values.Moreover, SAW resonators possess a lithographic tunability of the resonance frequency and can be fabricated with simple and low-cost micromachining processes.Nevertheless, given the low phase velocity of SAW waves and the Q degradation at SHFs, they have been implemented only in the sub-4-GHz range (IHP SAWs [10]).
BAW devices, on the other hand, confine the resonant vibration in the whole resonator body, with their most successful implementation being the thin-film bulk acoustic resonator (FBAR) [11].Devices using a similar concept are the solidly mounted resonator (SMR) [12] and the single-crystal bulk acoustic resonator (XBAW) [13].BAW devices are currently implemented as filter building blocks in the higher frequency bands in mobile handsets and rely on piezoelectric aluminum nitride (AlN) or lightly Scandium-doped AlN (ScAlN) thin films.Such materials can be sputtered while maintaining excellent piezoelectric properties, and their micromachining is compatible with standard CMOS fabrication processes.Nevertheless, given these devices' reliance on a purely vertical excitation and mode shape, bulk modes do not provide a lithographic tunability of the resonance frequency, notably increasing the cost of manufacturing.In fact, in order to achieve on-chip frequency diversity, the industry relies on multiple mass-loading and trimming steps with nanometer precision, which may become unpractical at higher frequencies ( f > 8 GHz), i.e., when the dimensions of electrodes and piezo-layer start approaching the few hundreds or even tens of nanometers.To circumvent FBARs' limitations, Lamb wave resonators (LWRs) were introduced, relying on the excitation of an acoustic standing Lamb wave via interdigitated transducer (IDT) electrodes [6].Such resonators, though not yet commercialized for mobile filtering, have gathered conspicuous interest in research environments, with several different explored designs and materials [14], [15], [16], [17], [18].Among LWRs, the AlN-based cross-sectional Lame' mode resonator (CLMR) [19] represents a promising solution to substitute BAWs in future mobile RFFEs.CLMRs attained high Q (>1000) values and high k 2 t (>7%) values, given the reliance on a bidimensional resonant mode.Nevertheless, for the purpose of a scaling toward the 5G FR-3 and the mm-waves, the CLMR topology employing a double IDT [thickness field-excited (TFE)] results unpractical due to the fabrication complexity, including the growth of a thin piezoelectric film on a patterned bottom electrode.Lateral field-excited (LFE) CLMRs (see Fig. 2), on the other hand, rely on a single top electrode IDT, providing lithographic tunability of the resonance frequency and a reduced-complexity micromachining process.The main issue with LFE CLMRs is the modest piezoelectric response of AlN, which limits the maximum achievable k 2 t to 3% [19], a value that does not allow the synthesis of filters fulfilling the stringent FBW requirements of the 6G midband.
From the work of Akiyama et al. [20], there has been an increased interest in ScAlN as an alternative to pure AlN, given the enhancement of the piezo-coefficient due to the doping process [21].Thanks to high scandium concentrations, LFE CLMRs attain k 2 t values in excess of 7% [22], making this technology viable for the next-generation passive passband filters.In fact, they combine high-performance, lithographic tunability of the resonance frequency, and a post-CMOS compatible and low-complexity micromachining process, which can be ideally carried out with only two lithographic masks.
In this work, we present the first comprehensive analysis of 30% ScAlN LFE CLMRs ranging from 6 to 20 GHz of operation frequency, successfully demonstrating a scaling of the microacoustic technology well beyond the sub-6-GHz spectrum, as well as unprecedented performance in terms of quality factor and electromechanical coupling in this frequency range.Such results can enable the synthesis and mass production of wideband, low-loss, and compact microacoustic filters in the 5G FR-3 and 6G midband, to be used in cost-efficient RFFEs of handsets.
Section II provides an overview of CLMR operation with focus on the LFE configuration, along with their modeling.In Section III, a detailed description of the optimization of In particular, the horizontal acoustic wavelength (λ), the pitch (p), the electrode width (W el ), and the piezoelectric thickness (h).Moreover, the CLMR mode shape, obtained via COMSOL multiphysics FEM simulation, is given.
ScAlN thin films and of the micromachining process employed to fabricate the devices of this work is given.In Section IV, experimental results in the 6-11 and 14-20 GHz ranges are provided, along with a comparison with 2-D finite element modeling (FEM) COMSOL1 simulations.In Section V, we experimentally investigate the impact of key geometrical dimensions and of the tethering structure on the quality factor of CLMRs operating in the 6-11 GHz range.By applying a pseudo-analysis of variance (ANOVA) statistical method and combining its output with power linearity (PL) tests, we define an optimal CLMR structure.Finally, Section VI provides a technical discussion on the future outlooks of the LFE CLMR technology.Such devices can be scaled with an increased doping level in the piezoelectric layer in order to enhance the filter performance and in terms of a higher frequency of operation, in order to reach the mm-wave spectrum.

II. CROSS-SECTIONAL LAME' MODE RESONATORS
Since the work of Piazza et al. [14], AlN-based LWR with intrinsic lithographic tunability of the resonance frequency was extensively explored.Moreover, it was found that for certain ratios of the thickness of the piezoelectric layer (h) and the horizontal acoustic wavelength (λ), k 2 t is maximized [23], [24] (see Fig. 3).In fact, due to the hybridization of the S 0 and S 1 symmetric resonant modes, a bidimensional mode shape arises in the cross section of the AlN plate [19], allowing to harness both the d 33 and d 31 piezoelectric coefficients to transduce the resonant vibration.Said CLMRs were, therefore, able to demonstrate enhanced k 2 t values in excess of 2% and 7% in AlN when using a single and double IDT configurations, respectively, while maintaining high Q value.Fig. 3(a) shows the COMSOL simulated displacement at resonance for three CLMR topologies [25], including the floating bottom electrode (FBE) structure which employs a single IDT and an FBE to better drive the electric field with respect to the LFE configuration and relaxes the fabrication constraints compared to the TFE one [25].Fig. 3(b) shows the simulated k 2 t versus h/λ curve for an LFE CLMR with aluminum electrodes in AlN and 30% ScAlN as in this work.Such curve shows that k 2 t can be traded off for a lithographic tunability of the resonance frequency.According to the nomenclature detailed in [19], the resonator employing the optimal h/λ ratio is named nondegenerate CLMR, being characterized by equal displacement in the in-plane and vertical dimensions.On the other hand, resonant modes further from the optimum, but still attaining higher k 2 t compared to the 1-D Lamb wave fundamental modes, are named degenerate CLMRs.The ab initio equations of [21], describing the evolution of the mechanical, electrical, and piezoelectric properties of ScAlN with respect to the doping level, were used for the purpose of FEM simulations.

A. Thin-Film Optimization for Devices
Sc-doping of AlN films changes their properties by softening the material and by increasing the dielectric (ϵ r ) and piezoelectric coefficients d 31 and d 33 , which translates to a higher k 2 t of resonators.In [21], ab initio equations derived from the density functional theory describing the evolution of said parameters with the scandium level are reported.Given the nonlinear trend of the values with the doping, the highest grade of improvement is achieved for the highest impurity concentrations (Sc [%] ≥ 30%).
Nevertheless, the local lattice deformation caused by the high-atomic number scandium atoms makes the growth of highly c-axis-oriented ScAlN not trivial [26].In fact, the local stresses created by the scandium atoms in the Wurtzite lattice are relaxed by tilting of the c-axis during the growth, promoting the generation of abnormally oriented grains (AOGs) [27].Such AOG formation is a stochastic process, worsening with higher Sc concentrations and/or thicknesses and hindering the performance of microacoustic devices, both in terms of Q and k 2 t [28].
For the films' sputtering, an industrial-grade Evatec Clusterline 1 II [see Fig. 4(a)] was employed.Such a tool allows for extremely low base pressures ( p < 5 × 10 −8 torr), since this parameter is known to greatly influence the quality and repeatability of the reactive sputtering process.A 12 ′′ 30% AlSc compound casted target was used [see Fig. 4(a)].
The sputtering recipe was carefully optimized in order to achieve the highest crystal quality on target 280 [thin film 1 (TF1)] and 150 nm [thin film 2 (TF2)] films deposited on 200-mm high-resistivity Si⟨100⟩ wafers.Such a value is quantified by the X-ray diffractometry (XRD) full-width halfmaximum (FWHM) [see Fig. 4(c) and (d)].During the growth, AOGs are less prone to originate when only nitrogen (e.g., no Argon) is used as a carrier gas [29], [30].Moreover, the deposition pressure was seen as the main player in influencing the film's crystallinity.Such a value is directly controlled by the gas flow.The other parameters affecting the crystal quality are the power applied to the target and the deposition temperature, while the RF power to the substrate acts as a stress tuner.Observations have shown a strong correlation between the FWHM and compressive stresses, and the best FWHM values were found in films with stress values that were too high to allow the fabrication of suspended structures.Therefore, a tradeoff between crystallinity and stress was found.In Fig. 4(b), a scanning electron microscope (SEM) top surface micrograph of the 280 nm film is reported, showcasing a near-zero density of AOGs.The 150-nm film's surface has AOGs with a similar density, but with an almost negligible size given the smaller thickness.The final recipe parameters used for the TF1 and TF2 films are: 1) power applied to the casted target of 5 kW; 2) nitrogen flow of 30 sccm; 3) deposition temperature of 350 • C; 4) RF power to the substrate of 10 W; and 5) substrate-target distance of 20 mm.The films' inplane stress was measured with a Tencor-Flexus tool.The final values were compressive 30 and 600 MPa for the 280 and 150 nm films, respectively.

B. Device Fabrication
The LFE CLMRs were fabricated with a low-complexity three-mask micromachining process [22], [31].First, the Sc-doped AlN film was deposited on 200 mm high-resistivity Si⟨100⟩ wafers.Then, the film was etched in order to define the resonant plate and to expose the silicon underneath for the release step.In order to obtain straight sidewalls, a SiO 2 hard mask was deposited via plasma-enhanced chemical vapor deposition (PECVD) and etched via reactive ion etching (RIE) with fluorine chemistry.Then, the ScAlN was etched in an Oxford inductively coupled plasma (ICP) RIE tool.In order to etch ScAlN, high Argon, RF, and ICP powers were used, along with a mild chlorine-based chemical gas flow (Cl 2 and BCl 3 ).The etch recipe is reported in the caption of Fig. 5. Finally, the oxide mask was stripped via wet etch in 49% hydrofluoric acid (HF).The top electrode was then patterned in two subsequent lithographic steps.The first lithography was made with an electron-beam lithography (EBL) tool (Elionix ELS-F125) to define the very narrow finger electrodes required to reach the high frequencies of operations: 117-350 nm for Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the 6-11 GHz range and 75-144 nm for the 14-20 GHz one.A ZEP20A positive-tone photoresist (PR) was utilized and O-Xylene was used as developer.The aluminum electrodes were then deposited via thermal evaporation, with thicknesses of 95 and 43 nm for the two batches, respectively, as those values were found via FEM simulations to maximize k 2 t with the used material stack.After that, the PR was removed in Microposit Remover 1165 heated at 85 • C. In order to ease the low-throughput and high-cost EBL step, the pads were then defined via a direct writer and deposited with sputtering.The TF1 batch had pads made with 200 nm of aluminum, while the TF2 one used 5/200 nm of titanium/gold.In the vision of a possible commercialization and mass production of the devices, the two steps can be merged together with the aid of an Extreme UV stepper, combining high resolution and high throughput [32], in order to bring the process to a true two-mask one.Finally, the devices were released in XeF 2 isotropic etching.Fig. 5 shows the fabrication flow, while Fig. 6 depicts SEM micrographs of fabricated devices.

IV. EXPERIMENTAL RESULTS
The devices were characterized in laboratory conditions in a two-port configuration using a vector network analyzer (Keysight N5244B), two low-loss coaxial RF cables, a probe station, and two cascade ground-signal-ground (GSG) probes with 150 µm pitch.The calibration step took advantage of the transmission-reflection-line (TRL) standard, demonstrated to be more precise than the short-open-load-through (SOLT) one when approaching higher frequencies [33].Fig. 7 reports showcase resonators from this work, fabricated in the TF1 (6-11 GHz) and TF2 (14-20 GHz) batches.As it can be seen from the excursion of the admittance from the resonance to the antiresonance, the devices showcase high Q•k 2 t figures of merit (FOMs), unprecedented in this frequency range (see Table I).The single-mode electromechanical coupling is defined as where f s and f p represent the resonance and antiresonance frequencies, respectively, which is reported also in Fig. 8(a) as a function of the h/λ ratio, together with the COMSOL 2-D simulation results, as in Fig. 3.In Fig. 8(b), the agreement between the simulations and the measured data in terms of resonance frequency as a function of the devices' λ is reported.Regarding the quality factor, the 3 dB Q value, with equation where BW 3 dB is the 3 dB BW, which is reported in Table I for the devices of Fig. 7.The decrease in Q 3 dB for the TF2 batch is explained by the lower quality of the piezoelectric layer (FWHM of 2.7 • versus 2.1 • ) as demonstrated in [22], also showing that more room for improvement of such devices exists.Moreover, given the much smaller device dimensions, fabrication nonidealities such as overlay errors and IDT finger artifacts are more pronounced, impacting negatively the Q value.
To estimate the motional quality factor (Q m ) that can be obtained with 30% ScAlN films, the devices were also fit with a modified Butterworth-Van Dyke (mBVD) model, taking into account the parasitic resistance coming from the top electrode (R s ) and the dielectric losses (R 0 ).R s was computed using the analytical model reported by Colombo et al. [34], to which the experimentally extracted contact resistance was added, resulting in values comprised between 4 and 7 .The values of Q m are also reported in Table II.
In Fig. 9, the admittance responses of two of the best resonators of the two batches are reported, both in magnitude and in phase, along with their mBVD fittings.In the plots, the motional Q and the k 2 t values are also shown.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The device of Fig. 9(c) and (d) is matched to an impedance around 300 , but given the high frequency of operation, this results in a very small static capacitance (C 0 = 31 fF).Such a small value reduces the measured k 2 t due to the impact of the feedthrough capacitance (C f ) between the two signal pads.The value of C f was extracted from open measurements and quantified averaging on three different results as 9.4 fF.Since C f is roughly one-third of C 0 and the two capacitances are in parallel, the mBVD equation for the k 2 t becomes

TABLE II RESULT OF THE PSEUDO-ANOVA ANALYSES PERFORMED WITH MATLAB
where C m is the motional capacitance.Therefore, to have a more accurate estimation of the k 2 t , the feedthrough capacitance was deembedded, resulting in the value also reported in Fig. 9(c).
The metrics and FOM reported in Table I are among the highest ever demonstrated in their frequency range, while some of them are record-breaking.In particular, some devices of this work achieved the highest k 2 t , Q, and Q •k 2 t above 8 GHz.The highest, or some of the highest, t values ever demonstrated were also achieved.In Fig. 10, scatter plots comparing the performance of the devices of this work in terms of Q • k 2 t product with others found in the literature t are taken as metrics, the resonators from other works can have some sort of deembedding, depending on the data availability in the respective publications.In the legend, "LN" is lithium niobate and "uni."means unidimensional.
As shown in Fig. 7 and Fig. 9(a) and (b), the devices suffer from the presence of spurious modes between resonance and antiresonance.Such unwanted resonances pose issues when synthesizing filters, as they create ripples in the passband, thus distorting the device group delay.The spurious responses are identified as transversal modes from FEM simulations, well known to originate in CLMRs [44].In order to solve the issue, common techniques such as IDT electrode apodization can be utilized [44].

V. DESIGN ANALYSIS VIA PSEUDO-ANOVA AND ANCHORED-ALL-AROUND TOPOLOGY
While the k 2 t of the devices is set by the piezo-and electrode materials [25], as well as by the resonant mode, the quality factor, per same design and materials, is a strong function of the device geometry.In this section, we provide an experimental statistical study performed with a pseudo-ANOVA [45] statistical method, with the aim of finding the best LFE CLMR geometry to maximize Q 3 dB .We refer to it as pseudo-ANOVA because of the lack of enough degrees of freedom to make it a canonical ANOVA [45].In the analysis, 304 resonators employing the same TF1 piezoelectric layer but fabricated in three different batches were taken into account.The explored variations include the batch number, in order to confirm the repeatability of the results, the W/L ratio, since devices matched to the same impedance can have more or less IDT fingers, with different lengths, the presence or not of side Bragg reflectors in order to confine the resonant vibration and their electrical boundary condition (floating or shorted), and the tether configuration, namely multianchors (MAs) or full anchors (FAs) (Fig. 11).The devices without reflectors have the classic LWR design, in which the interface with the air is responsible to confine the standing wave.The Bragg reflectors were fabricated together with the IDTs and have the same pitch and metal thickness.
The devices possess different resonance frequencies in the 6-11 GHz range.The results of the pseudo-ANOVA, performed with MATLAB, are reported in Table II.The p-value is an index of how much a certain variable impacts on the parameter under investigation (PUI).Only the variables with a p-value < 0.05 are statistically significant for the PUI.In order to obtain an experimental equation for Q 3 dB , a general linear model (GLM) is applied on the data, resulting in the following equation: where AType (anchor type) is equal to 1 for MA and to 2 for FA.From the analysis, it is concluded that the batch number does not impact Q 3 dB , confirming the repeatability of the micromachining process.Moreover, the W/L ratio has a small impact, and in particular wider and shorter devices showcase better Q 3 dB .This can be explained by the fact that longer IDT fingers have higher resistance, while for a larger number of shorter fingers, the IDT resistance is lower, being the electrodes all in parallel.Also, the longer the fingers, the larger is a parasitic series inductance, introducing nonidealities to the mBVD model [17].Additionally, the presence or not of reflectors does not impact Q 3 dB , as well as their electrical boundary conditions.This result opens the possibility of fabricating devices with side Bragg reflectors in order to relax the impact of X -axis misalignment between the plate and the top electrodes.Moreover, since the resonant vibration is confined by the metal reflectors, the plate sidewall becomes less critical, notably reducing the impact of fabrication nonidealities.Finally, the anchoring configuration has a major impact, with the FA showcasing lower Q 3 dB .This can be explained by the higher degree of energy leakage through the tethers, well known to lead to quality factor degradation in lower frequency resonators [46], even though with a less dramatic effect in this frequency range.The above-mentioned results offer a design guideline for which larger and shorter devices with MA are the absolute best to maximize the quality factor.Nevertheless, Q 3 dB is not the only important parameter in a microacoustic resonator, and other performance metrics such as the robustness to fabrication nonidealities, the temperature coefficient of frequency (TCF), and the PL should be taken into account by the designer, as they would negatively impact the yield and performance of a commercial microacoustic filter.As demonstrated in [47], resonators having more anchoring surface showcase a higher degree of PL, since they allow to the excess heat to flow into the substrate.Therefore, by trading off the quality factor, a fully tethered geometry is proposed, namely the anchoredall-around one (see Fig. 12).Such a topology anchors the resonator on all sides with FA and Bragg reflectors, while the etch pits needed to release the device are further away from the active area.To experimentally verify the impact of the tethering structure on the PL, resonators with similar Q • k 2 t products were tested with powers ranging from −8 to 6 dBm, and the relative frequency shift in ppm is reported in Fig. 12.The frequency shift f shift,ppm was computed as where the quantity between parenthesis is the input power sent with the VNA.As shown in the figure, the investigated geometries were MA and FA without reflectors and AAA CLMRs, and each data point is the average on four different Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
resonators.From this analysis, the best configuration for the PL is the AAA one, showcasing 55% and 25% less frequency drift compared to the geometries employing MA and FA without reflectors, respectively.Another advantage of this geometry is the extremely high tolerance to overlay errors on both the X -and Y -directions, making these devices more robust to fabrication nonidealities, thereby allowing for a higher fabrication yield.Furthermore, the sturdiness of the AAA configuration allows for the fabrication of suspended CLMRs on stressy substrates.In fact, the TF2 batch employed the AAA geometry and was able to withstand an in-plane compressive stress of 600 MPa.Finally, temperature tests were performed to quantify the impact of the anchor configuration on the TCF.To do so, six identical copies of CLMRs with MA, FA, and AAA configuration were frequency tested from 20 • C to 140 • C, with 20 • C intervals, and the frequency drift was recorded and averaged between the results from identical samples.The extracted TCF was found to be −45.3ppm/K for the MA case and −36.1 and −35.6 ppm/K for the FA and the AAA ones, respectively.The results highlight that the biggest contribution to the TCF is the isolation of the resonator's active area via the anchors, while the presence or not of the reflectors plays a minor role.Nevertheless, the AAA topology proves superior also for the TCF, while further improvement of thermal stability can be achieved via a silicon-dioxide deposition on the active area [48].

VI. DISCUSSION ON A FURTHER CLMR SCALING
The current section provides a technical discussion about the further scaling of the super high-frequency LFE CLMR technology.In particular, the focus is on increasing the Sc-doping level of the piezoelectric layer in order to enhance filter performance and, on reducing it, in order to enable the fabrication of resonators in the mm-waves.

A. Increasing the Doping Level
As already mentioned, the nonlinear nature of the mechanical, piezoelectric, and dielectric coefficients as a function of the Sc-doping level results in a larger performance enhancement for the highest dopings.In particular, the higher the impurity concentration, the higher is k 2 t and the lower is the operating frequency per same geometry.Therefore, when the goal is to increase the BW of a filter, directly proportional to the resonators' k 2 t , higher Sc-doping levels are preferred, as long as the minimum feature sizes allow to reach the target frequency.The possibility of synthesizing devices with wider FBW will prove to be fundamental for the purpose of using LFE CLMRs in midband 6G RFFEs, given the component carrier BW of 400 MHz or more [4].Additionally, the insertion loss of a filter is inversely proportional to the resonators' k 2 t through the motional resistance; therefore, a higher Sc-doping level enables lower losses with respect to lower ones when the same Q is considered.Fig. 13 shows the COMSOL 2-D simulation of devices employing the same geometrical dimensions of the best resonator from this work [see Fig. 9(a) and (b)], but with higher t is also reported.
doping levels, up to 42%, as well as their k 2 t .A motional quality factor of 500 was assumed in the simulations.

B. Increasing the Operation Frequency
Conversely, when the goal is to reach higher frequencies (e.g., the mm-wave bands, n257-n260), a possible solution is to decrease the Sc-doping level, in order to increase the resonant modes' phase velocity.In this way, a higher resonance is achieved per same pitch, thus relaxing the lithographic constraints.Moreover, the mm-wave bands possess channel BW requirements not exceeding 400 MHz, requiring filters with FBWs ranging from 1.6% (lower end of the n257 band) to 0.9% (higher end of the n259 band).To prove the potential of CLMRs to reach the mm-waves, COMSOL 2-D simulations of LFE devices employing a minimum feature size of 80 nm and Sc-doping levels ranging from 0% to 30% are shown in Fig. 14(a), confirming that a further scaling is possible.Fig. 14(b) FEM-simulated resonance frequency as a function of IDT finger sizes is reported for different doping levels, up to 30%.The mm-wave bands are highlighted, and as it can be observed, they are all reachable with the present technology.The considered minimum feature size of 50 nm is achievable both with conventional EBL tools like the one used in this work as well as with state-of-the-art industrial Extreme UV steppers [32], able to combine high resolution and high throughput.
Finally, in Fig. 14(c), the S 21 response of filters using FEM-simulated resonators as building blocks is provided.The devices are 50--matched third-order ladder filters, and two examples are provided per Sc concentration.The first uses the resonator of Fig. 14(a) as series element, while the second employs a device with finger size of 50 nm.The other geometrical parameters are listed in the caption.The frequency bands are also highlighted.The simulation results shown in Fig. 14 employ Sc-doped AlN films of 100 and 130 nm, therefore thinner than the ones presented in this work.Their purpose was to prove the concept of using LFE CLMRs for mm-wave filters in mobile RFFEs.More research work has to be made by the authors to reduce the piezoelectric film thickness while maintaining good crystallinity.The goal of the present results is therefore to show the limits and capabilities of the CLMR technology and to demonstrate by a theoretical and simulation standpoint their suitability for covering the commercial mm-wave bands.

VII. CONCLUSION
This work demonstrated the outstanding capabilities of the 30% Sc-doped AlN LFE CLMR platform in delivering microacoustic resonators with operating frequencies well beyond the sub-6-GHz 5G band.An optimized sputtering recipe was developed for target thicknesses of 280 and 150 nm, and resonators in the 6-11 and 14-20 GHz range were fabricated on them.The devices showcased unprecedented Q 3 dB , k 2 t , Q m , and their product FOMs in this frequency range, together with an on-chip wide-frequency tunability that comes without any complication of the micromachining process, carried out on MEMS foundry-standard 200-mm Si wafers.The present devices enable the synthesis of compact and wideband passive passband filters in the 6-20 GHz range and look toward a possible mass production, aided by the low-complexity fabrication process and the high device yield.Finally, the future outlooks of the LFE CLMR platform are discussed, showing its potential to fill the technology gap for 5G FR-2, FR-3, and 6G midband filters in cellular radios.

Manuscript received 31
July 2023; accepted 1 September 2023.Date of publication 7 September 2023; date of current version 13 October 2023.This work was supported in part by the United States Department of Defense, Defense Advanced Research Projects Agency (DARPA) MTO COFFE Program, under Grant HR001121S0031; and in part by the PM Ben Griffin.(Corresponding author: Gabriel Giribaldi.)

Highlights•
This work scales the microacoustic technology to the 6-20 GHz range with excellent performance, simple and post-CMOS compatible manufacturing techniques, and lithographic definition of the resonance.

Fig. 2 .
Fig. 2. 3-D and 2-D view of an LFE CLMR, with highlighted relevant dimensions.In particular, the horizontal acoustic wavelength (λ), the pitch (p), the electrode width (W el ), and the piezoelectric thickness (h).Moreover, the CLMR mode shape, obtained via COMSOL multiphysics FEM simulation, is given.

Fig. 3 .
Fig. 3. (a) COMSOL simulated mode shape at resonance for TFE, LFE, and FBE CLMRs.A TFE CLMR employs top and bottom IDTs to maximize k 2 t but has an increased fabrication complexity.An LFE CLMR trades off electromechanical coupling in favor of a two-mask fabrication process, while an FBE CLMR uses an FBE to increase k 2 t while keeping the fabrication complexity lower compared to a TFE one.(b) h/λ curve for an LFE CLMR with Al electrode and AlN or 30% ScAlN piezoelectric layer.

Fig. 5 .
Fig. 5. 3-D view of the micromachining process used to fabricate the devices of this work.Step 1 is ScAlN thin-film sputtering; step 2 is ScAlN etching; step 3 is top electrode deposition; and step 4 is device's release.The ScAlN etching recipe employed an RF power of 300 W, an ICP power of 600 W, and a Cl 2 /BCl 3 /Ar flow of 10/6/28 sccm.The etching pressure was 10 mT.

Fig. 6 .
Fig. 6.SEM micrographs of fabricated devices.(a) Overview of a chip with multiple resonators.(b) Device tethered with MAs.(c)-(f) Anchored all-around CLMR (see Section V) is shown from the pad structure to the interdigitated electrodes.

Fig. 8 .
Fig. 8. (a) Measured single-mode electromechanical coupling as a function of the h/λ ratio for the devices from Fig. 7, together with the COMSOL 2-D simulated one.(b) Measured resonance frequency as a function of the horizontal acoustic wavelength is reported, as well as the COMSOL 2-D simulated one.

Fig. 9 .
Fig. 9. Fittings of the best resonators of (a) and (b) TF1 batch and (c) and (d) TF2 one, including the measured admittance in both magnitude and phase.

Fig. 10 .
Fig. 10.Scatter plots comparing the devices of Fig. 7 plus other LFE CLMRs fabricated in the same batches with the resonators reported in the literature operating above 8 GHz.While for the present devices, the Q 3 dB and a raw-data k 2t are taken as metrics, the resonators from other works can have some sort of deembedding, depending on the data availability in the respective publications.In the legend, "LN" is lithium niobate and "uni."means unidimensional.

Fig. 11 .
Fig. 11.Visual representation of the geometrical variations investigated in the pseudo-ANOVA statistical analysis.

Fig. 12 .
Fig. 12.(a) Visual representation of the three different tether configurations for which the PL is studied.The AAA CLMR is introduced for the first time as the geometry showcasing the highest linearity and (b) measured admittance versus frequency for a showcase resonator as a function of input power to show the frequency drift in the investigated input power range.

Fig. 13 .
Fig. 13.COMSOL 2-D simulated resonators with the same geometrical dimensions of the best device from this work [see Fig. 9(a) and (b)] but with higher Sc-doping levels.The k 2t is also reported.

Fig. 14 .
Fig. 14.(a) COMSOL FEM simulations of resonators with a finger width of 80 nm, 130 nm of piezoelectric layer, 20 nm of Al top electrode thickness, and 500 of mechanical Q.(b) Resonance frequency of CLMRs is plotted as a function of their finger width, in order to visualize the limits of the technology.A piezoelectric layer thickness of 100 nm was used.(c) Passband filters are shown.The parallel-to-series static capacitance ratio is equal to 2. There are two filters per Sc-doping level: the lower frequency one uses the device of (a) as series resonator, while the higher frequency filter employs a device with 50 nm electrode width.The FBWs as a function of the Sc-doping level are reported.

TABLE I TABLE REPORTING THE
MAIN METRICS AND FOM OF THE DEVICES OF FIG. 7. THE TF1 AND TF2 BATCHES ARE SEPARATED BY A LINE