Thin-film Resonators Research Articles

Study of the out-of-plane vibrational modes in thin-film amorphous silicon micromechanical disk resonators

Thin-film silicon micro resonators are fabricated by surface micromachining at temperatures that are CMOS and large area substrate-compatible. Disk resonators offer large working surfaces and a large number of vibrational modes. The vibrational modes of micromechanical disk resonators made from hydrogenated amorphous silicon thin films were studied in this work. The dynamic behavior of these structures is shown to be mechanically described to be in the transition between a membrane and a plate due to the influence of residual stresses generated during the film growth and to thermal mismatch with underlying layers. Non-degenerate modes are observed as a consequence of the radial symmetry and their effective stiffness is related to the anchor geometry and the parity of the number of diametric nodal lines. The experimentally measured frequencies were compared with the simulated values from finite element modeling with good agreement. Investigation of the intrinsic quality factors shows that there is a dependence of the energy dissipation per cycle with the mode order that is related to the clamping anchors. Thermal annealing experiments show that enhanced quality factors can be obtained using low temperature annealing for a limited period of time.

Localized and Propagating Plasmons in Metal Films with Nanoholes

The occurrence of plasmon resonances in thin (~20 nm) Al and Au films, perforated with nanoholes, was studied. In both metals, two plasmon resonances were observed: (i) A surface plasmon polariton mode associated with a maximum in extinction and (ii) a localized resonance in the nanohole associated with a minimum in extinction. By varying the diameter of the nanoholes, the scaling of the peak positions of the plasmon resonances was determined as a function of hole diameter. In the large nanohole limit, the plasmon peak positions depend only on the nanohole diameter being independent of the material. On the other hand, for small nanoholes the plasmon peak positions are material and size dependent. In contrast to Al films where the localized plasmons can be excited from the near-IR to the UV, no plasmon resonances were observed for Au at energies above the interband threshold (2.4 eV). The interaction between a distinct interband transition in Al at 1.5 eV and the localized plasmon resonance is considered in detail. We observe for the first time experimentally a noncrossing behavior of the interband transition and the localized plasmon resonance. The energy (size) dependence of surface plasmon peak width, being a measure for the decay/damping of the latter, is very different for the two metals. This can be explained by considering the different decay mechanisms active in the two metals. Apart from these basic plasmonics results, we test the potential of using the shifts of the plasmon resonances in perforated Al films to follow the atmospheric oxidation/corrosion kinetics of Al. The results are quantified by model calculations. The obtained kinetic law for the oxide growth is in good agreement with a previous XPS study on plain Al films. This suggests that the nanohole-induced plasmon resonances can be a sensitive and simple measure for Al corrosion and metal corrosion in general.

Continuous-film vs. device-level ferromagnetic resonance in magnetic tunnel junction thin films

We quantitatively compared film-level ferromagnetic resonance (FMR) measurements using standard vector network analyzer (VNA) techniques with device-level FMR measurements for both thermal FMR (T-FMR) and field-swept spin-torque FMR (FS-ST-FMR) techniques on magnetic tunnel junction (MTJ) thin films with in-plane magnetization. The film and FS-ST-FMR device determination of damping α are in agreement; however, α cannot be reliably determined by use of T-FMR device measurements due to bandwidth limitations. The device-level intercept of Hres vs. f is lower than film-level measurements of the effective magnetization (Meff) due to the demagnetizing field and exchange coupling of the patterned free layer. The intercept shows device-to-device variations due to a combination of size variation and local film variations. At the device level, the inhomogeneous broadening (ΔH0) is nearly zero, while in film-level measurements, μ0ΔH0 > 10 mT due to averaging of the local film variations detected explicitly in the intercept of Hres vs. f at the device level. These results suggest that continuous-film and FS-ST-FMR measurements on multiple devices can provide comparable information about thin-film Meff, α, and ΔH0 with minimal interpretation, but caution is necessary when using T-FMR to determine α or ΔH0.

Microcrystalline diamond micromechanical resonators with quality factor limited by thermoelastic damping

Thin-film microcrystalline diamond micromechanical resonators with mechanical quality factor limited by thermoelastic dissipation in the diamond film are demonstrated. Surface micromachined double ended tuning fork resonators were fabricated from in-situ boron doped microcrystalline diamond films deposited using hot filament chemical vapor deposition. Time-domain thermoreflectance measurements show thermal conductivity of 110 W m−1 K−1 for heat transport through the thickness of the diamond film. Measurement of the quality factor of resonators spanning a frequency range 0.5–10 MHz shows a maximum Q = 81 646 and demonstrates good agreement with quality factor limited by thermoelastic dissipation using 100 W m−1 K−1 for the in-plane thermal conductivity of the diamond film.

Mid-infrared surface plasmon resonance in zinc oxide semiconductor thin films

Surface plasmon resonance (SPR) in semiconducting materials at mid-infrared (mid-IR) energies offers the potential for new plasmonic functionalities and integration schemes. Mainstream semiconductors are transparent to mid-IR energies, thus a tightly integrated monolithic package for SPR sensing becomes feasible. We report mid-IR surface plasmon resonance in zinc oxide as a model material for semiconductors with 4 × 1019 to 8 × 1019 cm−3 carriers. The surface plasmon modes were characterized using spectroscopic IR-ellipsometry and compared to a reflectivity simulation. The data confirm the feasibility of mid-IR SPR, show a generic ability for plasmon tuning, and demonstrate the predictive power of the reflectivity model.

Promises and challenges of nanoplasmonic devices for refractometric biosensing

Optical biosensors based on surface plasmon resonance (SPR) in metallic thin films are currently standard tools for measuring molecular binding kinetics and affinities - an important task for biophysical studies and pharmaceutical development. Motivated by recent progress in the design and fabrication of metallic nanostructures, such as nanoparticles or nanoholes of various shapes, researchers have been pursuing a new generation of biosensors harnessing tailored plasmonic effects in these engineered nanostructures. Nanoplasmonic devices, while demanding nanofabrication, offer tunability with respect to sensor dimension and physical properties, thereby enabling novel biological interfacing opportunities and extreme miniaturization. Here we provide an integrated overview of refractometric biosensing with nanoplasmonic devices and highlight some recent examples of nanoplasmonic sensors capable of unique functions that are difficult to accomplish with conventional SPR. For example, since the local field strength and spatial distribution can be readily tuned by varying the shape and arrangement of nanostructures, biomolecular interactions can be controlled to occur in regions of high field strength. This may improve signal-to-noise and also enable sensing a small number of molecules. Furthermore, the nanoscale plasmonic sensor elements may, in combination with nanofabrication and materials-selective surface-modifications, make it possible to merge affinity biosensing with nanofluidic liquid handling.

Analysis of Thickness Vibrations of C-Axis Inclined Zig-Zag Multi-layered Zinc Oxide Thin Film Resonators

The free vibrations of a multilayer C-axis inclined zig-zag ZnO thin-film bulk acoustic wave resonator (FBAR) connected to external impedance have been analyzed; the frequency equation and mode shape for this resonator were derived based on the linear piezoelectric theory. The impedance characteristics of the FBAR are derived and compared with previous experimental results. The analytical result shows that as the layer number increases, the thickness shear mode remains stable while the longitudinal mode has shifted to a lower value. Sensitivity analysis has been performed to explain the discrepancy between our analytical result and previous experiment result. The analytical results provide an insight for the multi-layered zig-zag FBAR design and applications.

Correspondence - Analysis of thickness vibrations of c-axis inclined zig-zag two-layered zinc oxide thin-film resonators

The free vibrations of a two-layered C-axis inclined zig-zag ZnO thin-film bulk acoustic wave resonator (FBAR) connected to external impedance are analyzed. The frequency equation and mode shape for this resonator are derived based on the linear piezoelectric theory. The impedance characteristics of the FBAR are derived and compared with previous experimental results.

Electron spin resonance of thin films of organic light-emitting material tris(8-hydroxyquinoline) aluminum doped by magnesium

We have successfully observed electron spin resonance (ESR) signals of radical anions in thin films of tris(8-hydroxyquinoline) aluminum (Alq3), a compound widely used as electron transporting and luminescent layers in organic light-emitting diodes. To obtain definitely defined radical-anion states in Alq3, we doped Alq3 with Mg by co-evaporating these materials. The obtained g value and peak-to-peak ESR linewidth ΔHpp of Alq3 radical anions are 2.0030 and 2.19mT, respectively. Theoretical g value and hyperfine interactions were calculated by density functional theory method, which are in good agreement with the experimental results. A quantitative evaluation of doping concentration was performed. We confirmed that doped charges are localized at deep trapping sites by the lineshape analysis and temperature dependence of the ESR signals. Morphological investigation using transmission electron microscopy clarified that the co-evaporated Mg atoms form clusters.

Angular dependence of the photothermally modulated magnetic resonance in Gd thin films

In this paper we use electron spin resonance and photothermally modulated magnetic resonance techniques to investigate gadolinium thin films as a function of the orientation of the film surface with respect to the external magnetic field and of the temperature, around the magnetic phase transition temperature. We observe that, in the ferromagnetic phase, the resonance line is shifted up to higher external magnetic fields when the angle between the film surface and the field increases, revealing the magnetic anisotropy of the sample. At the same time, when the temperature is augmented to values higher than the phase transition temperature, the external field of the resonance collapses back to the expected value in the paramagnetic phase for all orientations. We also demonstrated that, even for the perpendicular orientation (magnetic field perpendicular to the sample surface), the photothermally modulated magnetic resonance signal is maximized near the magnetic phase transition temperature. Furthermore, in the ferromagnetic phase the photothermally modulated magnetic resonance intensity is very sensitive to the orientation, showing a significant enhancement in the perpendicular direction.

Quasi-thickness-shear waves in thin-film piezoelectric resonators of ZnO and AlN with tilted C-Axis

We study the propagation of Lamb waves in a piezoelectric plate of crystals of class 6mm with tilted c-axis. Dispersion relations for waves in ZnO and AlN plates with a few specific tilting angles of the c-axis are obtained. Displacement amplitude and phase angle distributions along the plate thickness are also calculated. It is shown that for certain values of the tilting angle of the c-axis, there exist long waves with a dominating thickness-shear component. The results further support the possibility of thin-film resonators operating with thickness-shear modes.

Surface acoustic wave driven ferromagnetic resonance in nickel thin films: Theory and experiment

We present an extensive experimental and theoretical study of surface acoustic wave-driven ferromagnetic resonance. In a first modeling approach based on the Landau-Lifshitz-Gilbert equation, we derive expressions for the magnetization dynamics upon magnetoelastic driving that are used to calculate the absorbed microwave power upon magnetic resonance as well as the spin current density generated by the precessing magnetization in the vicinity of a ferromagnet/normal metal interface. In a second modeling approach, we deal with the backaction of the magnetization dynamics on the elastic wave by solving the elastic wave equation and the Landau-Lifshitz-Gilbert equation selfconsistently, obtaining analytical solutions for the acoustic wave phase shift and attenuation. We compare both modeling approaches with the complex forward transmission of a LiNbO$_3$/Ni surface acoustic wave hybrid device recorded experimentally as a function of the external magnetic field orientation and magnitude, rotating the field within three different planes and employing three different surface acoustic wave frequencies. We find quantitative agreement of the experimentally observed power absorption and surface acoustic wave phase shift with our modeling predictions using one set of parameters for all field configurations and frequencies.

Size‐Controlled Synthesis of Cu2‐xE (E = S, Se) Nanocrystals with Strong Tunable Near‐Infrared Localized Surface Plasmon Resonance and High Conductivity in Thin Films

AbstractA facile method for preparing highly self‐doped Cu2‐xE (E = S, Se) nanocrystals (NCs) with controlled size in the range of 2.8–13.5 nm and 7.2–16.5 nm, for Cu2‐xS and Cu2‐xSe, respectively, is demonstrated. Strong near‐infrared localized surface plasmon resonance absorption is observed in the NCs, indicating that the as‐prepared particles are heavily p‐doped. The NIR plasmonic absorption is tuned by varying the amount of oleic acid used in synthesis. This effect is attributed to a reduction in the number of free carriers through surface interaction of the deprotonated carboxyl functional group of oleic acid with the NCs. This approach provides a new pathway to control both the size and the cationic deficiency of Cu2‐xSe and Cu2‐xS NCs. The high electrical conductivity exhibited by these NPs in metal‐semiconductor‐metal thin film devices shows promise for applications in printable field‐effect transistors and microelectronic devices.

Effect of photodiode angular response on surface plasmon resonance measurements in the Kretschmann-Raether configuration

We study the effect of photodiode angular response on the measurement of surface plasmon resonance (SPR) in metallic thin films using the Kretschmann-Raether configuration. The photodiode signal depends not only on the light intensity but also on the incidence angle. This implies that the photodiode sensitivity changes along the SPR curve. Consequently, the measured SPR spectrum is distorted, thus affecting fits and numerical analyses of SPR curves. We analyze the magnitude of this change, determine when it is significant, and develop a calibration method of the experimental setup which corrects for this type of spectral shape distortions.

Growth and ferromagnetic resonance of yttrium iron garnet thin films on metals

High-quality yttrium iron garnet (YIG) thin films were grown on a sandwich structure that consisted of a thick Cu layer and two thin cladding layers. The cladding layers were high entropy alloy nitrides (HEAN) and served as barriers to prevent Cu diffusion and oxidation during the YIG deposition. The Cu and HEAN layers were deposited by sputtering. The YIG films were grown by pulsed laser deposition. The YIG films had a thickness of several hundreds of nanometers, a surface roughness of several nanometers, and (111) orientation. The films showed a peak-to-peak ferromagnetic resonance linewidth of 1.1 Oe at 9.45 GHz.

An intermode-coupled thin-film micro-acoustic resonator

A novel concept for the development of thin-film micro-acoustic resonators based on the coupling between different plate acoustic modes is demonstrated. The basic principles for the design and fabrication of intermode-coupled plate acoustic wave resonators on c-textured thin aluminum nitride films are presented. More specifically, the lowest order symmetric S0 Lamb wave is excited and then coupled to the fundamental thickness shear bulk resonance by means of a metal strip grating with specific periodicity. The experimental results demonstrate that the grating-assisted intermode coupling can be employed in high-frequency resonators inheriting the low dispersive nature of the S0 mode in combination with the energy localization in the plate bulk typical for the fundamental thickness shear resonance.

Nonlocal feedback in ferromagnetic resonance

Ferromagnetic resonance in thin films is analyzed under the influence of spatiotemporal feedback effects. The equation of motion for the magnetization dynamics is nonlocal in both space and time and includes isotropic, anisotropic, and dipolar energy contributions as well as the conserved Gilbert and the nonconserved Bloch damping. We derive an analytical expression for the peak-to-peak linewidth. It consists of four separate parts originated by Gilbert damping, Bloch damping, a mixed Gilbert-Bloch component, and a contribution arising from retardation. In an intermediate frequency regime the results are comparable with the commonly used Landau-Lifshitz-Gilbert theory combined with two-magnon processes. Retardation effects together with Gilbert damping lead to a linewidth whose frequency dependence becomes strongly nonlinear. The relevance and the applicability of our approach to ferromagnetic resonance experiments are discussed.

Reliability and stability of thin-film amorphous silicon MEMS resonators

The stability of the resonance frequency (fres) characteristics of MEMS resonators upon long-term cycling is crucial for many applications. Thin-film silicon MEMS have been developed to take advantage of their low-temperature processing and large area deposition characteristics. A reliability and stability study of thin-film-doped hydrogenated amorphous silicon (n+-a-Si:H)-aluminum MEMS resonators fabricated on glass substrates at a maximum processing temperature of 110 °C is presented. Long-term cycling of thin-film silicon microbridge resonators with different top electrode configurations was performed in vacuum and in air using electrostatic actuation. The number of cycles to failure, the fres stability, the quality factor (Q) stability and the effect of measurement temperature are studied. The resonant bridges withstand the industry standard of 1011 continuous cycles at high load with no failure reported both in vacuum and air with fres shifts which depend on the resonator top electrode configuration. No Q degradation was observed. Frequency stability better than ±20 ppm was observed in vacuum after long-term cycling.

Unconventional rf photoresponse from a superconducting spiral resonator

Superconducting thin film resonators employing strip geometries show great promise in rf/microwave applications due to their low loss and compact nature. However, their functionality is limited by nonlinear effects at elevated rf/microwave powers. Here, we show that by using a planar spiral geometry carrying parallel currents in adjacent turns, this limitation can be minimized. We investigate the rf current distributions in spiral resonators implemented with Nb thin films via laser scanning microscopy. The rf current density profile along the width of the individual turns of the resonators reveals an unconventional trend: maximum current in the middle of the structure and decaying toward its edges. This unusual behavior is associated with the circular nature of the geometry and the cancellation of magnetic field between the turns, which is favorable for handling high powers since it allows the linear characteristics to persist at high rf current densities.

AlN/3C–SiC Composite Plate Enabling High‐Frequency and High‐Q Micromechanical Resonators

An AlN/3C-SiC composite layer enables the third-order quasi-symmetric (QS(3)) Lamb wave mode with a high quality factor (Q) characteristic and an ultra-high phase velocity up to 32395 ms(-1). A Lamb wave resonator utilizing the QS(3) mode exhibits a low motional impedance of 91 Ω and a high Q of 5510 at a series resonance frequency (f(s)) of 2.92 GHz, resulting in the highest f(s)·Q product of 1.61 × 10(13) Hz among the suspended piezoelectric thin film resonators reported to date.