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This work reports an acoustic solidly mounted resonator (SMR) at 18.64 GHz, among the highest operating frequencies reported. The device is built in scandium aluminum nitride (ScAlN) on top of silicon dioxide (SiO2) and tantalum pentoxide (Ta2O5) Bragg reflectors on silicon (Si) wafer. The stack is analyzed with X-ray reflectivity (XRR) and high-resolution X-ray diffraction (HRXRD). The resonator shows a coupling coefficient (k2) of 2.0%, high series quality factor (Qs) of 156, shunt quality factor (Qp) of 142, and maximum Bode quality factor (Qmax) of 210. The third-order harmonics at 59.64 GHz is also observed with k2 around 0.6% and Q around 40. Upon further development, the reported acoustic resonator platform can enable various front-end signal-processing functions, e.g., filters and oscillators, at future frequency range 3 (FR3) bands., Comment: 5 pages, 9 figures, 5 tables

This work reports the procedure for modeling piezoelectric acoustic resonators and filters at millimeter wave (mmWave). Different from conventional methods for lower frequency piezoelectric devices, we include both acoustic and electromagnetic (EM) effects, e.g., self-inductance, in both the circuit-level fitting and finite element analysis, toward higher accuracy at higher frequencies. To validate the method, thin-film lithium niobate (LiNbO3) first-order antisymmetric (A1) mode devices are used as the testbed, achieving great agreement for both the standalone resonators and a fifth-order ladder filter. Upon further development, the reported acoustic and EM co-modeling could guide the future design of compact piezoelectric devices at mmWave and beyond., Comment: 6 pages, 11 figures, submitted to IEEE JMEMS

As 5G connectivity proliferates, signal processing applications at 6G centimeter bands have gained attention for urban wireless capacity expansion. At sub-5 GHz, acoustic resonators operating in the fundamental symmetric (S0) Lamb mode hold significant promise if frequency scaled to the 6G centimeter bands. Concurrently, the lateral wavelength dependency and the traveling wave nature of S0 mode enable monolithic multi-frequency fabrication, transversal filters, correlators, and other compact signal processing components. In this work, we present thin-film lithium niobate (LN) S0 resonators scaled up to 16 GHz. Specifically, we study the characteristics of the S0 mode as the wavelength is minimized and showcase a device at 14.9 GHz with a Bode Q maximum of 391, a k2 of 6%, and a figure of merit (FoM) of 23.33, surpassing the state-of-the-art (SoA) in its frequency range., Comment: 4 pages, 8 figures, to be presetned in Hilton Head 2024,the 19th in the series of Hilton Head Workshops on the science and technology of solid-state sensors, actuators, and microsystems

Acoustic devices offer significant advantages in size and loss, making them ubiquitous for mobile radio frequency signal processing. However, the usable bandwidth is often limited to the achievable electromechanical coupling, setting a hard limit using typical transducer designs. In this work, we present an ultra-wideband transducer design utilizing a tapered electrode configuration to overcome this limitation. The design is realized on a lithium niobate (LN) on silicon carbide platform, utilizing a combination of first and higher order shear-horizontal modes to generate the ultra-wideband response. The implementation shows a fractional bandwidth (FBW) of 55% at 2.23 GHz with an associated insertion loss (IL) of 26 dB for the measured 50 ohm case. Upon improved impedance matching, this performance could be improved to 79% FBW and an IL of 16.5 dB. Upon further development, this ultra-wideband design could be reasonably scaled towards improved FBW and IL trade off to enable improved usability for cases where bandwidth should be prioritized., Comment: 4 pages, 5 figures, to be presetned in Hilton Head 2024,the 19th in the series of Hilton Head Workshops on the science and technology of solid-state sensors, actuators, and microsystems

This work reports the first study of periodically poled piezoelectric film (P3F) lithium niobate (LiNbO3) resonators at cryogenic temperatures. We experimentally investigate the temperature dependency of resonant frequencies and quality factor (Q) of higher-order Lamb modes up to 20 GHz between 80{\deg}K and 297{\deg}K, using a tri-layer P3F LiNbO3 resonators as the experimental platform. The supported thickness-shear Lamb modes between second-order symmetric (S2) and eleventh-order antisymmetric (A11) modes show temperature coefficients of frequency (TCF) averaging -68.8 ppm/K. Higher Q and more pronounced spurious modes are observed at lower temperatures for many modes. Upon further study, the cryogenic study will be crucial for identifying dominant loss mechanisms and origins of spurious modes in higher-order Lamb wave devices for millimeter-wave applications., Comment: 4 pages, 4 figures, submitted to IEEE IMS 2024

In this work, we demonstrate a C-band shear-horizontal surface acoustic wave (SH-SAW) resonator with high electromechanical coupling (kt2) of 22% and a quality factor (Q) of 565 based on a thin-film lithium niobate (LN) on silicon carbide (SiC) platform, featuring an excellent figure-of-merit (FoM = kt2*Q ) of 124 at 6.5 GHz, the highest FoM reported in this frequency range. The resonator frequency upscaling is achieved through wavelength ($\lambda$) reduction and the use of thin aluminum (Al) electrodes. The LN/SiC waveguide and synchronous resonator design collectively enable effective acoustic energy confinement for a high FoM, even when the normalized thickness of LN approaches a scale of 0.5$\lambda$ to 1$\lambda$. To perform a comprehensive study, we also designed and fabricated five additional resonators, expending the $\lambda$ studied ranging from 480 to 800 nm, in the same 500 nm-thick transferred Y-cut thin-film LN on SiC. The fabricated SH-SAW resonators, operating from 5 to 8 GHz, experimentally demonstrate a kt2 from 20.3% to 22.9% and a Q from 350 to 575, thereby covering the entire C-band with excellent performance., Comment: 4 pages, 5 figures, 1 table

This paper reports the first piezoelectric acoustic filter in periodically poled piezoelectric film (P3F) lithium niobate (LiNbO3) at 23.8 GHz with low insertion loss (IL) of 1.52 dB and 3-dB fractional bandwidth (FBW) of 19.4%. The filter features a compact footprint of 0.64 mm2. The third-order ladder filter is implemented with electrically coupled resonators in 150 nm bi-layer P3F 128 rotated Y-cut LiNbO3 thin film, operating in second-order symmetric (S2) Lamb mode. The record-breaking performance is enabled by the P3F LiNbO3 platform, where piezoelectric thin films of alternating orientations are transferred subsequently, facilitating efficient higher-order Lamb mode operation with simultaneously high quality factor (Q) and coupling coefficient (k2) at millimeter-wave (mmWave). Also, the multi-layer P3F stack promises smaller footprints and better nonlinearity than single-layer counterparts, thanks to the higher capacitance density and lower thermal resistance. Upon further development, the reported P3F LiNbO3 platform is promising for compact filters at mmWave., Comment: 4 pages, 7 figures, IEEE Microwave and Wireless Technology Letters

In this work, we investigate the frequency scaling of shear-horizontal (S.H.) surface acoustic wave (SAW) resonators based on a lithium niobate on insulator (LNOI) substrate into the centimeter bands for 6G wireless systems. Prototyped resonators with wavelengths ranging between 240 nm and 400 nm were fabricated, and the experimental results exhibit a successful frequency scaling between 9.05 and 13.37 GHz. However, a noticeable performance degradation can be observed as the resonance frequency (fs) scales. Such an effect is expected to be caused by non-ideal helec/{\lambda} for smaller {\lambda} devices. The optimized LNOI SH-SAW with a {\lambda} of 400 nm exhibits a fs of 9.05 GHz, a keff2 of 15%, Qmax of 213 and a FoM of 32, which indicates a successful implementation for device targeting centimeter bands., Comment: 4 pages, 7 figures, 1 table, submitted to IEEE IC-MAM 2024

This work describes sputtered scandium aluminum nitride (ScAlN) thin-film bulk acoustic resonators (FBAR) at millimeter wave (mmWave) with high quality factor (Q) using platinum (Pt) electrodes. FBARs with combinations of Pt and aluminum (Al) electrodes, i.e., Al top Al bottom, Pt top Al bottom, Al top Pt bottom, and Pt top Pt bottom, are built to study the impact of electrodes on mmWave FBARs. The demonstrated FBAR with Pt top and bottom electrodes achieve electromechanical coupling (k2) of 4.0% and Q of 116 for the first-order symmetric (S1) mode at 13.7 GHz, and k2 of 1.8% and Q of 94 for third-order symmetric (S3) mode at 61.6 GHz. Through these results, we confirmed that even in the frequency band of approximately 60 GHz, ScAlN FBAR can achieve a Q factor approaching 100 with optimized fabrication and acoustic/EM design. Further development calls for stacks with better quality in piezoelectric and metallic layers., Comment: 4 pages, 7 figures, accepted by IEEE MEMS 2024

This paper reports the first high-performance acoustic filters toward millimeter wave (mmWave) bands using transferred single-crystal thin film lithium niobate (LiNbO3). By transferring LiNbO3 on the top of silicon (Si) and sapphire (Al2O3) substrates with an intermediate amorphous Si (aSi) bonding and sacrificial layer, we demonstrate compact acoustic filters with record-breaking performance beyond 20 GHz. In the LN-aSi-Al2O3 platform, the third-order ladder filter exhibits low insertion loss (IL) of 1.62 dB and 3-dB fractional bandwidth (FBW) of 19.8% at 22.1 GHz, while in the LN-aSi-Si platform, the filter shows low IL of 2.38 dB and FBW of 18.2% at 23.5 GHz. Material analysis validates the great crystalline quality of the stacks. The high-resolution x-ray diffraction (HRXRD) shows full width half maximum (FWHM) of 53 arcsec for Al2O3 and 206 arcsec for Si, both remarkably low compared to piezoelectric thin films of similar thickness. The reported results bring the state-of-the-art (SoA) of compact acoustic filters to much higher frequencies, and highlight transferred LiNbO3 as promising platforms for mmWave filters in future wireless front ends., Comment: 4 pages, 8 figures, accepted by IEEE MEMS 2024

In this work, a 38.7 GHz acoustic wave ladder filter exhibiting insertion loss (IL) of 5.63 dB and 3-dB fractional bandwidth (FBW) of 17.6% is demonstrated, pushing the frequency limits of thin-film piezoelectric acoustic filter technology. The filter achieves operating frequency up to 5G millimeter wave (mmWave) frequency range 2 (FR2) bands, by thinning thin-film LiNbO3 resonators to sub-50 nm thickness. The high electromechanical coupling (k2) and quality factor (Q) of first-order antisymmetric (A1) mode resonators in 128 Y-cut lithium niobate (LiNbO3) collectively enable the first acoustic filters at mmWave. The key design consideration of electromagnetic (EM) resonances in interdigitated transducers (IDT) is addressed and mitigated. These results indicate that thin-film piezoelectric resonators could be pushed to 5G FR2 bands. Further performance enhancement and frequency scaling calls for better resonator technologies and EM-acoustic filter co-design., Comment: 4 pages, 6 figures, accepted by IEEE MTT-S International Microwave Filter Workshop (IMFW) 2024

This work reports a millimeter wave (mmWave) thin-film bulk acoustic resonator (FBAR) in sputtered scandium aluminum nitride (ScAlN). This paper identifies challenges of frequency scaling sputtered ScAlN into mmWave and proposes a stack and new fabrication procedure with a sputtered Sc0.3Al0.7N on Al on Si carrier wafer. The resonator achieves electromechanical coupling (k2) of 7.0% and quality factor (Q) of 62 for the first-order symmetric (S1) mode at 21.4 GHz, along with k2 of 4.0% and Q of 19 for the third-order symmetric (S3) mode at 55.4 GHz, showing higher figures of merit (FoM, k2xQ) than reported AlN/ScAlN-based mmWave acoustic resonators. The ScAlN quality is identified by transmission electron microscopy (TEM) and X-ray diffraction (XRD), identifying the bottlenecks in the existing piezoelectric-metal stack. Further improvement of ScAlN/AlN-based mmWave acoustic resonators calls for better crystalline quality from improved thin-film deposition methods., Comment: 3 pages, 7 figures, submitted to JMEMS

Radio frequency (RF) acoustic resonators have long been used for signal processing and sensing. Devices that integrate acoustic resonators benefit from their slow phase velocity (vp), in the order of 3 to 10 km/s, which allows miniaturization of the device. Regarding the subject of small form factor, acoustic resonators that operate at the so-called fundamental antisymmetric mode (A0), feature even slower vp (1 to 3 km/s), which allows for smaller devices. This work reports the design and fabrication of A0 mode resonators leveraging the advantages of periodically poled piezoelectricity (P3F) lithium niobate, which includes a pair of piezoelectric layers with opposite polarizations to mitigate the charge cancellation arising from opposite stress of A0 in the top and bottom piezoelectric layers. The fabricated device shows a quality factor (Q) of 800 and an electromechanical coupling (k2) of 3.29, resulting in a high figure of merit (FoM, Q times k2) of 26.3 at the resonant frequency of 294 MHz, demonstrating the first efficient A0 device in P3F platforms. The proposed A0 platform could enable miniature signal processing, sensing, and ultrasound transducer applications upon optimization., Comment: 4 pages, 6 figures, accepted by IEEE IUS 2023

Recently, piezoelectric power conversion has shown great benefits from replacing the bulky and lossy magnetic inductor in a traditional power converter with a piezoelectric resonator due to its compact size and low loss. However, the converter performance is ultimately limited by existing resonator designs, specifically by moderate quality factor (Q), moderate electromechanical coupling (kt2), and spurious modes near resonance. This work reports a spurious-free lithium niobate (LiNbO3) thickness-extensional mode bulk acoustic resonator design, demonstrating Q of 4000 and kt2 of 30% with a fractional suppressed region of 62%. We first propose a novel grounded ring structure for spurious-free resonator design, then validate its performance experimentally. Upon further work, this design could be extended to applications requiring spurious suppression, such as filters, tunable oscillators, transformers, etc., Comment: 4 pages, 6 figures, presented at IEEE IFCS 2023

This work reports a 50.74 GHz lithium niobate (LiNbO3) acoustic resonator with a high quality factor (Q) of 237 and an electromechanical coupling (k2) of 5.17% resulting in a figure of merit (FoM, Q x k2) of 12.2. The LiNbO3 resonator employs a novel bilayer periodically poled piezoelectric film (P3F) 128 Y-cut LiNbO3 on amorphous silicon (a-Si) on sapphire stack to achieve low losses and high coupling at millimeter wave (mm-wave). The device also shows a Q of 159, k2 of 65.06%, and FoM of 103.4 for the 16.99 GHz tone. This result shows promising prospects of P3F LiNbO3 towards mm-wave front-end filters., Comment: 4 pages, 5 figures, published in 2023 Joint Conference of the IEEE International Frequency Control Symposium & European Frequency and Time Forum (IEEE IFCS 2023)

This work reports an acoustic filter at 23.5 GHz with a low insertion loss (IL) of 2.38 dB and a 3-dB fractional bandwidth (FBW) of 18.2%, significantly surpassing the state-of-the-art. The device leverages electrically coupled acoustic resonators in 100 nm 128{\deg} Y-cut lithium niobate (LiNbO3) piezoelectric thin film, operating in the first-order antisymmetric (A1) mode. A new film stack, namely transferred thin-film LiNbO3 on silicon (Si) substrate with an intermediate amorphous silicon (a-Si) layer, facilitates the record-breaking performance at millimeter-wave (mmWave). The filter features a compact footprint of 0.56 mm2. In this letter, acoustic and EM consideration, along with material characterization with X-ray diffraction and verified with cross-sectional electron microscopy are reported. Upon further development, the reported filter platform can enable various front-end signal-processing functions at mmWave., Comment: 4 pages, 8 figures, submitted to IEEE JMEMS

Implementing microelectromechanical system (MEMS) resonators calls for detailed microscopic understanding of the devices, such as energy dissipation channels, spurious modes, and imperfections from microfabrication. Here, we report the nanoscale imaging of a freestanding super-high-frequency (3 ~ 30 GHz) lateral overtone bulk acoustic resonator with unprecedented spatial resolution and displacement sensitivity. Using transmission-mode microwave impedance microscopy, we have visualized mode profiles of individual overtones and analyzed higher-order transverse spurious modes and anchor loss. The integrated TMIM signals are in good agreement with the stored mechanical energy in the resonator. Quantitative analysis with finite-element modeling shows that the noise floor is equivalent to an in-plane displacement of 10 fm/sqrt(Hz) at room temperatures, which can be further improved under cryogenic environments. Our work contributes to the design and characterization of MEMS resonators with better performance for telecommunication, sensing, and quantum information science applications., Comment: 19 pages, 6 Figures

We report direct visualization of gigahertz-frequency acoustic waves in lithium niobate phononic circuits. Primary propagation parameters, such as the power flow angle (PFA) and propagation loss (PL), are measured by transmission-mode microwave impedance microscopy (TMIM). Using fast Fourier transform, we can separately analyze forward and backward propagating waves and quantitatively evaluate the propagation loss. Our work provides insightful information on the propagation, diffraction, and attenuation in piezoelectric thin films, which is highly desirable for designing and optimizing phononic devices for microwave signal processing., Comment: 12 pages, 4 figures

This paper is the first report of the high-temperature characteristics of a laterally vibrating piezoelectric lithium niobate (LiNbO$_{3}$) MEMS resonator array up to 500{\deg}C in air. After a high-temperature burn-in treatment, device quality factor (Q) is enhanced to 508 and the resonance shifts to a lower frequency and remains stable up to 500{\deg}C. During subsequent in situ high-temperature testing, the resonant frequencies of two coupled shear horizontal (SH0) modes in the array are 87.36 MHz and 87.21 MHz at 25{\deg}C and 84.56 MHz and 84.39 MHz at 500{\deg}C, correspondingly, representing a -3% shift in frequency over the temperature range. Upon cooling to room temperature, the resonant frequency returns to 87.36 MHz, demonstrating recoverability of device performance. The first- and second-order temperature coefficient of frequency (TCF) are found to be -95.27 ppm/{\deg}C and 57.5 ppb/{\deg}C$^{2}$ for resonant mode A, and -95.43 ppm/{\deg}C and 55.8 ppb/{\deg}C$^{2}$ for resonant mode B, respectively. The temperature-dependent quality factor (Q) and electromechanical coupling coefficient ($k_{t}^{2}$) are extracted and reported. Device Q decreases to 334 after high-temperature exposure, while $k_{t}^{2}$ increases to 12.40%. This work supports the use of piezoelectric LiNbO$_{3}$ as a material platform for harsh environment radio-frequency (RF) resonant sensors (e.g. temperature and infrared).

We present the first group of acoustic delay lines (ADLs) at 5 GHz, using the first-order antisymmetric (A1) mode in Z-cut lithium niobate thin films. The demonstrated ADLs significantly surpass the operation frequency of the previous works with similar feature sizes, because of its simultaneously fast phase velocity, large coupling coefficient, and low-loss. In this work, the propagation characteristics of the A1 mode in lithium niobate is analytically modeled and validated with finite element analysis. The design space of A1 ADLs is then investigated, including both the fundamental design parameters and those introduced from the practical implementation. The implemented ADLs at 5 GHz show a minimum insertion loss of 7.94 dB, an average IL of 9.1 dB, and a fractional bandwidth around 4%, with delays ranging between 15 ns to 109 ns and the center frequencies between 4.5 GHz and 5.25 GHz. The propagation characteristics of A1 mode acoustic waves have also been extracted for the first time. The A1 ADL platform can potentially enable wide-band high-frequency passive signal processing functions for future 5G applications in the sub-6 GHz spectrum bands., Comment: 16 pages, 27 figures

This paper presents a new class of micro-electro-mechanical system (MEMS) C-band filters for 5G front-ends. The filter is comprised of resonators based on the first-order asymmetric Lamb wave (A1) mode in thin film lithium niobate. Two filters have been demonstrated at 4.5 GHz with sharp roll-off, flat in-band group delay, and spurious-free response over a wide frequency range. The first design shows a fractional bandwidth (FBW) of 10%, an insertion loss (IL) of 1.7 dB, an out-of-band (OoB) rejection of -13 dB, and a compact footprint of 0.36 mm2, while the second design shows an FBW of 8.5%, an IL of 2.7 dB, an OoB rejection of -25 dB, and a footprint of 0.9 mm^2. The demonstrations herein mark the largest fractional bandwidth (FBW) achieved for acoustic-only filters at 5G frequencies., Comment: 3 pages, 7 figures

This paper presents the first voltage-controlled MEMS oscillator (VCMO) based on a Lithium Niobate (LiNbO3) lateral overtone bulk acoustic resonator (LOBAR). The VCMO consists of a LOBAR in a closed loop with 2 amplification stages and a varactor-embedded tunable LC tank. By adjusting the bias voltage applied to the varactor, the tank can be tuned to change the closed-loop gain and phase responses of the oscillator so that Barkhausen conditions are satisfied for a particular resonance mode. The tank is designed to allow the proposed VCMO to lock to any of the ten overtones ranging from 300 to 500 MHz. Owing to the high-quality factors of the LiNbO3 LOBAR, the measured VCMO shows a low close-in phase noise of -100 dBc/Hz at 1 kHz offset from a 300 MHz carrier and a noise floor of -153 dBc/Hz while consuming 9 mW. With further optimization, this VCMO can lead to direct radio frequency (RF) synthesis for ultra-low-power transceivers in multi-mode Internet-of-Things (IoT) nodes.

This work presents a new class of micro-electro-mechanical system (MEMS) resonators toward Ka band (26.5-40GHz) for fifth-generation (5G) wireless communication. Resonant frequencies of 21.4 and 29.9 GHz have been achieved using the fifth and seventh order asymmetric (A5 and A7) Lamb-wave modes in a suspended Z-cut lithium niobate (LiNbO3) thin film. The fabricated device has demonstrated an electromechanical coupling (kt2) of 1.5% and 0.94% and extracted mechanical Qs of 406 and 474 for A5 and A7 respectively. The quality factors are the highest reported for piezoelectric MEMS resonators operating at this frequency range. The demonstrated performance has shown the strong potential of LiNbO3 asymmetric mode devices to meet the front-end filtering requirements of 5G., Comment: 5 pages, 7 figures, 2018 IEEE International Frequency Control Symposium

This work demonstrates the first non-reciprocal network based on switched low-loss acoustic delay lines. The 4-port circulator is built upon a recently reported frequency-independent, programmable, non-reciprocal framework based on switched delay lines. The design space for such a system, including the origins of the insertion loss and harmonic responses, is theoretically investigated, illustrating that the key to better performance and low-cost modulation signal synthesis lies in a large delay. To implement a large delay, we resort to in-house fabricated low-loss, wide-band lithium niobate (LiNbO3) SH0 mode acoustic delay lines employing single-phase unidirectional transducers (SPUDT). The 4-port circulator, consisting of two switch modules and one delay line module, has been modularly designed, assembled, and tested. The design process employs time-domain full circuit simulation and the results match well with measurements. A 18.8 dB non-reciprocal contrast between insertion loss (IL = 6.6 dB) and isolation (25.4 dB) has been achieved over a fractional bandwidth of 8.8% at a center frequency 155 MHz, using a record low switching frequency of 877.19 kHz. The circulator also shows 25.9 dB suppression for the intra-modulated tone and 30 dBm for IIP3. Upon further development, such a system can potentially lead to future wide-band, low-loss chip-scale nonreciprocal RF systems with unprecedented programmability., Comment: 13 pages, 23 figures

This work demonstrates the first non-reciprocal network based on switched low-loss acoustic delay lines. A 21 dB non-reciprocal contrast between insertion loss (IL=6.7 dB) and isolation (28.3 dB) has been achieved over a fractional bandwidth of 8.8% at a center frequency 155MHz, using a record low switching frequency of 877.22 kHz. The 4-port circulator is built upon a newly reported framework by the authors, but using two in-house fabricated low-loss, wide-band lithium niobate (LiNbO3) delay lines with single-phase unidirectional transducers (SPUDT) and commercial available switches. Such a system can potentially lead to future wide-band, low-loss chip-scale nonreciprocal RF systems with unprecedented programmability., Comment: 4 pages, 7 figures

Passive and linear nonreciprocal networks at microwave frequencies hold great promises in enabling new front-end architectures for wireless communication systems. Their nonreciprocity has been achieved by disrupting the time-reversal symmetry using various forms of biasing schemes, but only over a limited frequency range. Here we demonstrate a framework for synthesizing theoretically frequency-independent multi-port nonreciprocal networks. The framework is highly expandable, and can have an arbitrary number of ports while simultaneously sustaining balanced performance and providing unprecedented programmability of non-reciprocity. A 4-port circulator based on such a framework is implemented and tested to produce broadband nonreciprocal performance from 10 MHz to 900 MHz with a temporal switching effort at 23.8 MHz. With the combination of broad bandwidth, low temporal effort, and high programmability, the framework could inspire new ways of implementing multiple input multiple output (MIMO) communication systems for 5G., Comment: 10 pages, 6 figures