Sezawa Mode Research Articles

Acoustofluidic Diversity Achieved by Multiple Modes of Acoustic Waves Generated on Piezoelectric-Film-Coated Aluminum Sheets.

Excitation of multiple acoustic wave modes on a single chip is beneficial to implement diversified acoustofluidic functions. Conventional acoustic wave devices made of bulk LiNbO3 substrates generally generate few acoustic wave modes once the crystal-cut and electrode pattern are defined, limiting the realization of acoustofluidic diversity. In this paper, we demonstrated diversity of acoustofluidic behaviors using multiple modes of acoustic waves generated on piezoelectric-thin-film-coated aluminum sheets. Multiple acoustic wave modes were excited by varying the ratios between IDT pitch/wavelength and substrate thickness. Through systematic investigation of fluidic actuation behaviors and performances using these acoustic wave modes, we demonstrated fluidic actuation diversities using various acoustic wave modes and showed that the Rayleigh mode, pseudo-Rayleigh mode, and A0 mode of Lamb wave generally have better fluidic actuation performance than those of Sezawa mode and higher-order modes of Lamb wave, providing guidance for high-performance acoustofluidic actuation platform design. Additionally, we demonstrated diversified particle patterning functions, either on two sides of acoustic wave device or on a glass sheet by coupling acoustic waves into the glass using the gel. The pattern formation mechanisms were investigated through finite element simulations of acoustic pressure fields under different experimental configurations.

Spatial analysis of multi-frequency SAW beams excited by slanted IDTs on ZnO-SiC heterostructures

Slanted (or fan-shaped) interdigital transducers (IDTs) with broadband response allow the selective excitation of surface acoustic waves (SAWs) with narrow beam widths and pathways controlled by the excitation frequency. Such SAW-based spatial and frequency control is important for applications in microfluidics, as well as in emerging applications in semiconductor nanostructures. In this contribution, we generate both Rayleigh and Sezawa modes with slanted IDTs on a 4H-SiC substrate coated with a piezoelectric ZnO film. We directly measure the phase wavefronts of narrow SAW beams in the 1200–1260 MHz frequency bandwidth using high-resolution ( <1μm ) optical interferometry, and discuss the mechanisms that directly affect the propagation direction and phase profiles of the SAW beams. The combination of multimodal and multi-frequency SAW delay lines provides rich opportunities for SAW-based control of low-dimensional systems, such as electrons in epitaxial graphene or spin centers near the surface of the SiC substrates.

S-band acoustoelectric amplifier in an InGaAs-AlScN-SiC architecture

Here, we report on an acoustoelectric slab waveguide heterostructure for phonon amplification using a thin Al0.58Sc0.42N film grown directly on a 4H-SiC substrate with an ultra-thin In0.53Ga0.47As epitaxial film heterogeneously integrated onto the surface of the Al0.58Sc0.42N. The aluminum scandium nitride film grown directly on silicon carbide enables a thin (∼850 nm thick) piezoelectric film to be deposited on a thermally conductive bulk substrate (370 W/m K for 4H-SiC); the high thermal conductivity of the substrate, large mobility of the semiconductor (∼7000 cm2/V s), and low carrier concentration (∼5 × 1015 cm−3) yield low self-heating. A Sezawa mode with optimal overlap between the peak of its evanescent electric field and the semiconductor charge carriers is supported. The high velocity of the heterostructure materials allows us to operate the Sezawa mode amplifier at 3.05 GHz, demonstrating a gain of 500 dB/cm (40 dB in 800 μm). Additionally, a terminal end-to-end radio frequency gain of 7.7 dB and a nonreciprocal transmission of 52.6 dB are achieved with a dissipated DC power of 2.3 mW. The power added efficiency and acoustic noise figure are also characterized.

Analysis of Sezawa mode Rayleigh-type SAWs on ScAlN film/floated electrode layer/ScAlN film/high velocity substrates

Surface acoustic wave (SAW) devices for frequency filters are increasingly required to have high performance in future mobile communications. The coupling factors K 2 for Rayleigh-type SAW (RSAW) on ScAlN film/high velocity substrate structures can be enhanced by introducing polarization-reversal structure into the ScAlN film. However, the growth of polarization-reversal ScAlN films with high crystal orientation would be very difficult. In this study, the Sezawa mode RSAWs on layered structures consisting of ScAlN films with floated intermediate electrode layer/high velocity substrates were analyzed by using Farnell and Adler’s SAW propagation analysis and finite element method. We found that the K 2 values of the Sezawa modes were enhanced by inserting the floated intermediate electrode layer without using polarization reversal structure, which were higher than those of the polarization-reversal ScAlN films/high velocity substrates. The enhancement of K 2 would be due to the improvement of the SAW energy concentration at the ScAlN film surface.

Experimental Analysis of Rayleigh and Sezawa Modes Resonance Frequencies in SAW Devices Manufactured on Sc0.3Al0.7N/Si†

GHz operating single port SAW resonators have been manufactured on Sc0.3Al0.7N/Si substrate. The thickness of the ScAlN thin layer was 0.8 μm. Advanced nano‐lithographic techniques have been developed for devices manufacturing. Rayleigh and Sezawa modes have been evidenced on Sc0.3Al0.7N/Si structure. The targeted applications are temperature sensors for harsh environmental operations. The sensitivity and temperature coefficient of frequency (TCF) of the manufactured devices have been experimentally determined and analyzed. The mode shapes of the resonances that appear in the devices supported on Sc0.3Al0.7N/Si substrate were evidenced by finite element method (FEM) simulations. A technique that combines FEM with Coupling of Modes (COM) was used for the determination of the resonance frequencies. Simulations performed for the temperature dependence of the resonance frequency led to results close to the experimental ones for the Rayleigh mode as well as for the Sezawa mode for devices supported on Sc0.3Al0.7N/Si substrate. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Analysis of the Effects of Parameters on the Performance of Resonators Based on a ZnO/SiO2/Diamond Structure

With the development of communications technology, surface acoustic wave (SAW) and bulk acoustic wave (BAW) devices have become hotspots of the competitive research in the frequency band above GHz. It imposes higher requirements on the operating frequency, temperature coefficient of frequency (TCF), and electromechanical coupling coefficient (k2) of SAW devices. In this work, we reported on a novel ZnO/SiO2/diamond-layered resonator structure and systematically investigated its propagation characteristics by using finite element methods. A comparative study and analysis of k2 and acoustic velocity (vp) for both the excited Rayleigh mode and the Sezawa mode were conducted. By selecting the appropriate ZnO piezoelectric film, SiO2, and electrode thickness, the Sezawa mode was chosen as the main mode, effectively improving both k2 and vp. It was observed that the k2 of the Sezawa mode is 7.5 times that of the excited Rayleigh mode and nearly 5 times that of piezoelectric single-crystal ZnO; vp is 1.7 times that of the excited Rayleigh mode and nearly 1.5 times that of piezoelectric single-crystal ZnO. Furthermore, the proposed multilayer structure achieves a TCF close to 0 while maintaining a substantial k2. In practical applications, increasing the thickness of SiO2 can compensate for the device’s TCF reduction caused by the interdigital transducer (IDT). Finally, this study explored the impact of increasing the aperture width and IDT pairs on the performance of the single-port resonator, revealing the changing patterns of quality factor (Q) values. The results reported here show that the structure has great promise for the fabrication of high-frequency and low-TCF SAW devices.

Electromechanical sensitivity of ZnO thin films at high-pressure regime for SAW strain sensor applications

This paper employs Density Functional Theory (DFT) to investigate the influence of high hydrostatic pressure on the piezo-elastic properties of ZnO with a specific focus on its repercussions for Surface Acoustic Wave (SAW) devices. Our findings reveal a significant enhancement in the piezoelectric coefficient d33 under high-pressure conditions, particularly reaching 13.09 pC/N at 8 GPa compared to the unpressurized state. This noteworthy improvement directly contributes to an overall enhancement in the electromechanical coupling coefficients (K2), emphasizing for the first time the potential of high-pressure conditions to positively influence the performance of ZnO/Al2O3 SAW devices. To confirm that, we utilized the Finite Element Method (FEM) to analyze the performance of a Surface Acoustic Wave (SAW) device based on ZnO for both propagating modes, namely Rayleigh and Sezawa, under elevated pressure conditions. We observed an improvement in the electromechanical coupling factor (K2) for the Rayleigh and the Sezawa modes, with enhancements of approximately 23% and 52%, respectively, under an applied pressure of 8 GPa compared to 0 GPa. Furthermore, we found that the Sezawa mode exhibits eight times greater sensitivity to pressure variations compared to the Rayleigh mode. These findings provide designers with a better understanding of the electromechanical responsivity and sensitivity of the ZnO-SAW devices to high level of applied pressure.

Simulation and Optimization of Surface Acoustic Wave Devices With High Electromechanical Coupling Factor and Zero Temperature Coupling Coefficient by Pattern Piezoelectric Layer

Recently, a more popular patterned surface acoustic wave (SAW) device with better performance was proposed. This structure has a large electromechanical coupling factor. To make surface acoustic wave devices easy to be applied to integrated circuit technology, a multilayer structure based on patterned Al/ZnO/Si is designed by using finite element method (FEM). Firstly, dependence of ZnO piezoelectric material on electromechanical coupling factor is studied systematically. The results show that Al/ZnO/Si structure excites Rayleigh mode and Sezawa mode with high electromechanical coupling factor. The patterning of piezoelectric materials could be achieved by etching. The electromechanical coupling factor of Rayleigh mode is as high as 7.98%, and the electromechanical coupling factor of Sezawa mode is up to 9.68%. As we all know, temperature will affect the characteristics of SAW devices. Therefore, the temperature characteristics based on this structure are systematically studied. To achieve zero temperature coupling coefficient, SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is used as an intercalation layer for temperature compensation. The structure of Rayleigh mode and Sezawa mode with the thinner SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer is easier to achieve zero temperature coupling coefficient than that of conventional structure. Meanwhile, the electromechanical coupling factor of Sezawa mode based on patterned Al/ZnO/SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Si structure does not change significantly with the increase of SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> thickness, with the maximum value of 10.78%, and the minimum value of 10.62%, which is 1.1% larger than that of structure without SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .

Super-High-Frequency Low-Loss Sezawa Mode SAW Devices in a GaN/SiC Platform.

This paper presents a comprehensive study of the performance of Sezawa surface acoustic wave (SAW) devices in SweGaN QuanFINE® ultrathin GaN/SiC platform, reaching frequencies above 14 GHz for the first time. Sezawa mode frequency scaling is achieved due to the elimination of the thick buffer layer typically present in epitaxial GaN technology. Finite element analysis (FEA) is first performed to find the range of frequencies over which the Sezawa mode is supported in the grown structure. Transmission lines and resonance cavities driven with Interdigital Transducers (IDTs) are designed, fabricated, and characterized. Modified Mason circuit models are developed for each class of devices to extract critical performance metrics. We observe a strong correlation between measured and simulated dispersion of the phase velocity (vp) and piezoelectric coupling coefficient (k2). Maximum k2 of 0.61% and frequency-quality factor product (f.Qm) of 6×1012 s-1 are achieved for Sezawa resonators at 11 GHz, with a minimum propagation loss of 0.26 dB/λ for the two-port devices. Sezawa modes are observed at frequencies spanning up to 14.3 GHz, achieving a record high in GaN microelectromechanical systems (MEMS) to the best of the authors' knowledge.

SAW Resonators and Filters Based on Sc0.43Al0.57N on Single Crystal and Polycrystalline Diamond.

The massive data transfer rates of nowadays mobile communication technologies demand devices not only with outstanding electric performances but with example stability in a wide range of conditions. Surface acoustic wave (SAW) devices provide a high Q-factor and properties inherent to the employed materials: thermal and chemical stability or low propagation losses. SAW resonators and filters based on synthetized by reactive magnetron sputtering on single crystal and polycrystalline diamond substrates were fabricated and evaluated. Our SAW resonators showed high electromechanical coupling coefficients for Rayleigh and Sezawa modes, propagating at 1.2 GHz and 2.3 GHz, respectively. Finally, SAW filters were fabricated on /diamond heterostructures, with working frequencies above 4.7 GHz and ~200 MHz bandwidths, confirming that these devices are promising candidates in developing 5G technology.

Guided waves in stratified media: Observing multiple Sezawa modes

Appearance of multiple Sezawa (M2,2) modes and the related interfacial Stoneley waves at propagation of Lamb wave in a stratified medium containing several layers obeying Wiechert condition is observed. Possible appearance of the multiple high frequency Stoneley and Sezawa modes may have importance in various applications starting from micro and nanomechanics to geophysics along with developing the nondestructive acoustic methods for qualitative and quantitative assessment of the high frequency asymptotics. The analysis is based on Cauchy sextic formalism.

Properties of higher-order surface acoustic wave modes in Al1−xScxN/sapphire structures

In this work, surface acoustic wave (SAW) modes and their dependence on propagation directions in epitaxial Al0.68Sc0.32N(0001) films on Al2O3(0001) substrates were studied using numerical and experimental methods. In order to find optimal propagation directions for higher-order SAW modes, phase velocity dispersion branches of Al0.68Sc0.32N on Al2O3 with Pt mass loading were computed for the propagation directions &amp;lt;112¯0&amp;gt; and &amp;lt;11¯00&amp;gt; with respect to the substrate. Experimental investigations of phase velocities and electromechanical coupling were performed for comparison with the numerical results. Simulations carried out with the finite element method and a Green function approach allowed identification of each wave type, including Rayleigh, Sezawa, and shear-horizontal wave modes. For the propagation direction &amp;lt;11¯00&amp;gt;, significantly increased wave guidance of the Sezawa mode compared to other directions was observed, resulting in enhanced electromechanical coupling (keff2=1.6%) and phase velocity (vphase=6km/s). We demonstrated that selecting wave propagation in &amp;lt;11¯00&amp;gt; with high mass density electrodes results in increased electromechanical coupling without significant reduction in phase velocities for the Sezawa wave mode. An improved combination of metallization, Sc concentration x, and SAW propagation direction is suggested that exhibits both high electromechanical coupling (keff2&amp;gt;6%) and high velocity (vphase=5.5km/s) for the Sezawa mode.

Dynamic humidity response of surface acoustic wave sensors based on zinc oxide nanoparticles sensitive film

ZnO nanoparticles/quartz surface acoustic wave (SAW) humidity sensors were fabricated, and their sensing performance was investigated. The pristine ZnO deposited on ST-cut quartz substrates by radio frequency magnetron sputtering is nanoparticles with grain sizes of 20–50 nm. The comparative analysis for humidity sensing applications of SAW-Love devices based on ZnO sensitive layers with different deposition pressures (0.25 Pa, 0.5 Pa, 1.0 Pa) was conducted, and their properties such as sensor sensitivity, response and recovery were studied. The sensors exhibit a good sensitivity in relative humidity (RH) from ~ 1% RH to 95% RH. Rayleigh mode and Sezawa mode frequency responses of the sensors increase with increasing humidity. The Sezawa mode shows 2–3 times higher humidity sensitivity than its Rayleigh mode counterpart for different RH. Rayleigh and Sezawa mode of 0.5 Pa ZnO nanoparticles-based SAW-Love sensor obtains a higher average sensitivity of 237.4 Hz/% RH and 388.1 Hz/% RH, respectively. Furthermore, the measured response frequencies values decrease rapidly and returned to near the initial state after moisture off. This comparative study demonstrates that the SAW-Love based on Sezawa mode has a great potential for applications in chemo-sensors.

Highly coupled leaky surface acoustic wave on hetero acoustic layer structures based on ScAlN thin films with a c-axis tilt angle

In this paper, we present hetero acoustic layer (HAL) structures based on ScAlN thin films with a c-axis tilt angle. The surface acoustic wave (SAW) excitation modes and their propagation characteristics for different Euler angles (0°, θ, ψ) of the ScAlN thin film are analyzed using the finite element method. We find that the acoustic field distribution of HAL structures can be adjusted by rotating their Euler angles and that normal SAWs are suppressed; however, leaky SAWs (LSAWs) with significantly improved electromechanical coupling coefficients (K 2) are excited. A maximum K 2 of 14% can be obtained for shear horizontal (SH)-type LSAWs, which is almost 7 times larger than that of the previously reported normal SAW Sezawa mode. Moreover, the optimized HAL structure consisting of (0°, 90°, 60°) ScAlN thin film/SiO2/AlN/Si simultaneously possesses a larger K 2, a wider bandwidth, and a higher Q value, which is promising for the design and application of wideband SAW devices with high performance.

Surface acoustic wave pressure sensor on ScAlN/3C-SiC/Si layer structure incorporating biomimetic microcantilever: modelling and performance enhancement

This paper presents a bio-inspired cantilever-type SAW pressure sensor based on Scandium-doped AlN (ScAlN)/3CSiC/Si layer structure. The proposed biomimetic microcantilever is configured with stress concentration region (SCR) comprising of a series of narrow slits. For a given depth, by properly setting the number and the width of those slits for a given depth, homogeneous stress/strain distribution in vicinity of SCR are achieved. Furthermore, multi-physics finite element modeling for evaluating the pressure coefficient of frequency (PCF) of a one-port SAW resonant sensor is performed and validated. Then the PCF for the proposed SAW pressure sensor with the optimized biomimetic microcantilever is analyzed. The dependence of ScAlN thin film thickness h ScAlN and scandium-doped concentration r of Sc r Al1-r N thin film on PCF for different SAW modes including Rayleigh mode and Sezawa mode are calculated. The investigation results show that the maximum PCF of −111 ppm bar−1 can be achieved for Rayleigh mode, which is 2.4 times larger than that of the previously reported ZnO/Si structure. In addition, its PCF has weak dependence on h ScAlN, which are quite favorable for manufacturing pressure sensors with good reproducibility. The conceived bio-inspired cantilever-type SAW devices based on ScAlN/3 CSiC/Si structure will open the door to develop pressure sensors with a stable and reliable performance and enhanced sensitivity.

Experimental and Theoretical Study of Multifrequency Surface Acoustic Wave Devices in a Single Si/SiO2/ZnO Piezoelectric Structure.

The propagation of surface acoustic waves (SAWs) along a ZnO/SiO2/Si piezoelectric structure is experimentally and theoretically studied. Six surface acoustic modes were experimentally detected in the 134 to 570 MHz frequency range, for acoustic wavelength λ = 30 μm, and for SiO2 and ZnO layers with a thickness of 1 and 2.4 μm. The numerical and three-dimensional (3D) finite element method analysis revealed that the multilayered substrate supports the propagation of Rayleigh and Sezawa modes (Rm and Sm), their third and fifth harmonics at λ/3 and λ/5. The velocity of all the modes was found in good agreement with the theoretically predicted values. Eigenfrequency, frequency domain, and time domain studies were performed to calculate the velocity, the electroacoustic coupling coefficient, the shape of the modes, the propagation loss, and the scattering parameter S21 of the SAW delay lines based on the propagation of these modes. The sensitivity to five different gases (dichloromethane, trichloromethane, carbontetrachloride, tetrachloroethylene, and trichloroethylene) was calculated under the hypothesis that the ZnO surface is covered by a polyisobutylene (PIB) layer 0.8 µm thick. The results show that the modes resonating at different frequencies exhibit different sensitivities toward the same gas. The multi-frequency ZnO/SiO2/Si single device structure is a promising solution for the development of a multiparameters sensing platform; multiple excitation frequencies with different sensing properties can allow the parallel analysis of the same gas with improved accuracy.

Surface Acoustic Waves-Localized Plasmon Interaction in Pillared Phononic Crystals

We study numerically the interaction of surface acoustic waves propagating at the surface of a multilayer structure (the so-called Sezawa waves) with localized surface plasmons at the bottom of metallic pillars deposited on the substrate. The pillars are made of gold and the multilayer structure is constituted by a layer of gold on a silicon substrate and covered by a thin spacer of dielectric material. We are interested in localized plasmons, which are the analog of metal-dielectric-metal surface plasmons. The physical characteristics of these plasmons, such as their eigenvalues and absorption or reflection spectra, are modulated by surface acoustic waves due to deformation of the structure in the vicinity of the pillars. The surface waves are generated in the area in front of the pillars deposited on the substrate. Two types of acoustic modes are envisioned to interact with the localized plasmons, namely, confined modes associated with the local resonances of the pillars and the propagating Sezawa modes that deform the structure in the vicinity of the surface. We discuss the efficiency of phonon-plasmon coupling for both types of modes and select those that can be useful for an experimental realization based on this platform. Also, we show that, besides the plasmon frequency, the phonon-plasmon coupling magnitude strength is sensitive to the distance between the pillars, which reveals the role of interactions between the pillars on the coupling. The geometrical parameters are chosen such that the acoustic waves are in the sub-GHz range and the plasmons are around the telecommunication wavelength of 1.55 mu m. This work may help with the design of optomechanical devices that can be controlled by fast coherent acoustics and facilitate applications involving enhanced sound-light interactions, such as light modulation.

Theoretical analysis of high electromechanical coupling surface acoustic wave propagating on lead-free Na0.5Bi0.5TiO3–BaTiO3 single crystal

The propagation properties of surface acoustic wave (SAW) on the Na0.5Bi0.5TiO3–BaTiO3 (NBBT) substrate with different crystal cuts were theoretically analyzed by Finite Element Method (FEM). The calculated results, for the NBBT with the optimized electrode type and thickness, indicate the existence of Rayleigh and Sezawa modes with high electromechanical coupling factor K2 ~18% and ~6.8% respectively, which are considerably higher than that of the conventional lithium niobate (LiNbO3) single crystal for SAW applications. The research provides a comprehensive understanding of the SAW propagation characteristics of lead-free NBBT, and explores the promising applications of NBBT in wideband SAW devices.

Numerical Investigation of Rayleigh, Sezawa and Love Modes in C-Axis Tilted ZNO/SI for Gas and Liquid Multimode Sensor

ABSTRACTFinite element analysis is carried out to investigate the characteristics of Rayleigh, Sezawa and Love surface acoustic modes travelling along c-axis tilted ZnO layer on Si (001) half-space. The phase velocity dispersion curves, electromechanical coupling, reflectivity and mass loading sensitivity are studied for different electroacoustic coupling configurations and c-axis tilt angles θ. The behavior of Rayleigh and Sezawa modes operating as gas sensor, was simulated under the hypothesis that the ZnO free surface is covered with a thin polyisobutylene (PIB) film, 0.2 μm thick, able to selectively adsorb volatile gases at atmospheric pressure and room temperature. The sensor sensitivity to gas concentration in air, i.e. the frequency shifts per unit gas concentration, is studied and compared to some common materials used in literature. The obtained results, demonstrate the feasibility of high-frequency multimode micro-sensor based on the c-axis tilted ZnO piezoelectric thin film and operating in both liquid and gaseous environments.

Giant Reflection Coefficient on Sc0.26Al0.74N Polycrystalline Diamond Surface Acoustic Wave Resonators

Since the commercialization of surface acoustic wave (SAW) devices, the technology is steadily increasing the device performances without compromising their power handling, size and price. Herein, one‐port SAW resonators are fabricated on scandium aluminum nitride (Sc0.26Al0.74N)/polycrystalline diamond heterostructures. SAW propagation properties are studied using three different piezoelectric thin‐film thicknesses within the heterostructure. The Rayleigh and Sezawa resonance frequencies are above 1.5 and 2.5 GHz, respectively, achieving Sezawa mode reflection coefficients below −50 dB. The polycrystalline diamond substrate is synthesized by microwave plasma chemical vapor deposition (MPCVD) on top of a 500 μm‐thick Si (001) substrate. The Sc0.26Al0.74N thin films are synthesized by reactive sputtering at nominally room temperature. The thin film's composition is analyzed by Rutherford backscattering spectrometry (RBS). The full width at half maximum (FWHM) of the X‐ray diffraction (XRD) ω scans below 3° indicates that the synthesized Sc0.26Al0.74N thin films are highly c‐axis oriented. The electromechanical coupling coefficient, quality factor, and dielectric loss parameters are computed by curve fitting the device electrical measurements to the simulation results of a modified Butterworth Van Dyke (mBVD) model implemented in the advance design system (ADS) tool.