Voltage tunable RF/microwave integrated ME inductors

As one of the three fundamental components for electronic circuits, inductors have been used extensively in a variety of RF applications. However, it has been challenging to achieve enhanced inductance and quality factor (Q = ω × maximum energy stored/power loss, ω is the angular frequency) at RFs, particularly for GHz frequencies. Gao demonstrated high-Q integrated magnetic inductors based on a solenoid structure with multilayer FeGaB/Al₂O₃ films.^{Reference Gao, Zardareh, Yang, Nan, Zhou, Onabajo, Liu, Aronow, Mahalingam, Howe, Brown and Sun14} The high-quality factor was obtained because of the demonstrated eddy-current loss reduction, lower out-of-plane anisotropy, and higher permeability in comparison with a single FeGaB layer of the same thickness. The inductors exhibit significantly enhanced and flat inductance, as well as a high-quality factor at 0.5–2.5 GHz, showing great potential for RF integrated circuit (RFIC) applications. Figure 1a–b shows the frequency dependence of the inductance and quality factor, respectively, for two different lengths of magnetic film (200 and 500 μm).^{Reference Gao, Zardareh, Yang, Nan, Zhou, Onabajo, Liu, Aronow, Mahalingam, Howe, Brown and Sun14} Nearly constant inductance across 0.1 to 3 GHz with a high-quality factor of 19 at 0.5 GHz are presented, where the Q is normally around 10 at this frequency range for integrated RF inductors. The lower resistance loss and higher quality factor are due to the increased coil winding width needed for the increased magnetic core length. Because the number of turns to cover the core and the gap between two neighboring coils remain constant, a longer core length necessitates a wider coil, and with the wider coil, the current can pass more easily, thus lowering the resistance.

Figure 1.

Comparison between different lengths of the FeGaB/Al₂O₃ film (200 μm and 500 μm): (a) Inductance, L, and (b) quality factor, Q. The inset shows the optical image of the inductor. (c) By applying various electric fields to the Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ slab, high tunability of inductance, which reaches up to 150% in approximately 2–3.5 GHz, can be achieved.^{Reference Gao, Zardareh, Yang, Nan, Zhou, Onabajo, Liu, Aronow, Mahalingam, Howe, Brown and Sun14}

In order to directly transfer the strain to the inductor and enhance the performance, deep reactive-ion etching was applied to remove the Si substrate on the back side, and the inductors were bonded with ethyl cyanoacrylate glue to one piezoelectric single crystal of the Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ (PMN-PT) slab poled along its thickness direction (thickness of ∼0.5 mm).^{Reference Gao, Zare, Onabajo, Li, Zhou, Nan, Yang, Liu, Mahalingam, Howe, Jones and Sun15} Due to the strain-mediated magnetoelectric coupling, large inductance tunability (up to 150%) from 2 GHz to 3.5 GHz was achieved in the inductors with an applied E-field ranging from 0 to 8 kV/cm across the thickness direction of the PMN-PT slab, as shown in Figure 1c. The ME inductor showed good high-frequency performance with a wide operation frequency range, in which the inductance is more than 2 nH and the peak quality factor is close to 20. This shows great promise for voltage tunable inductance in RFIC.

Dual magnetic- and electric-field tunable nanoelectromechanical systems ME bandpass filters

RF bandpass filters based on thin-film bulk acoustic resonators (FBARs) show a high-quality factor, compact size, low loss, preferable temperature stability, and processing compatible with the complementary metal oxide semiconductor (CMOS) integrated circuit, which are widely used in smartphones and e-readers. However, these FBAR-based bandpass filters have a fixed frequency of operation, which lead to bulky and expensive electronics for reconfigurable communication systems. Here, high-quality factor miniaturized RF bandpass filters (device or circuit that allows signals between two specific frequencies to pass, but discriminates against signals at other frequencies) with dual electric (E-) and magnetic (H-)field tunability based on ME nanoelectromechanical systems (NEMS) coupled FBARs using a five-mask microfabrication process were fabricated.^{Reference Lin, Nan, Qian, Gao, Hui, Wang, Guo, Belkessam, Shi, Rinaldi and Sun16} Due to the strong ME effect between the piezomagnetic multilayer FeGaB/Al₂O₃ films and piezoelectric AlN thin film, the acoustic wave could be strongly coupled with the electromagnetic wave. The resonance of coupled resonators, which are excited in the fundamental, longitudinal mode, and the transmission from port one to port two along the in-plane direction, are due to the contour mode, or in-plane mode, which is mainly determined by the width of the resonator.

An 11.15 dB return loss, the loss of power in the returned/reflected signal, and 3.57 dB insertion loss, the loss of signal power resulting from the insertion, with a high-quality factor of 252 can be achieved at 93.165 MHz at zero-bias field, as shown in Figure 2a.^{Reference Lin, Nan, Qian, Gao, Hui, Wang, Guo, Belkessam, Shi, Rinaldi and Sun16} The bandpass filters have a sensitive dependence on the magnetic field with ∼0.5% magnetic field tunability (∼50 kHz/10 Oe) of the operation frequency as seen in Figure 2b. The delta-E effect, which is a change in the Young’s modulus causing a change in frequency, is determined by the total anisotropy that includes the shape anisotropy and the induced anisotropy. This reached a maximum under ∼95 Oe applied magnetic field. Figure 2c shows a voltage tunability of 2.3 kHz/1 V. The shift in the frequency due to ME coupling is relatively small compared with the delta-E effect, since the magnetostriction coefficient of FeGaB, 70 ppm, is much smaller than the delta-E effect induced percentage change in Young’s modulus of magnetostrictive soft magnetic films, which can be up to 20–30%. The tunable RF bandpass filters based on NEMS magnetoelectric FBARs are compact and power efficient. They readily integrate with CMOS technology and will definitely be the future highlight in RF and microwave systems.

Figure 2.

(a) Measured return loss S ₁₁ and insertion loss S ₂₁ at zero-bias field. An 11.15 dB return loss and 3.57 dB insertion loss with a high-quality factor of 252 can be achieved at 93.165 MHz. (b) Resonance frequency as a function of DC magnetic field, and the change of Young’s modulus, which affects the resonance frequency, reached the maximum under ∼95 Oe applied magnetic field. (c) Resonance frequency as a function of DC electric field. The inset shows the optical image. The tunability of 2.3 kHz/1V is achieved as shown in Figure 6. (d) Scanning electron microscope image of the coupled resonators with silicon substrate released.^{Reference Lin, Nan, Qian, Gao, Hui, Wang, Guo, Belkessam, Shi, Rinaldi and Sun16}

Integrated nanomechanical ME sensors

One open challenge has been in sensing weak DC and low-frequency alternating current (AC) magnetic fields. The DC magnetic field dependence of ME coupling can be used for DC magnetic field sensing. However, an AC magnetic field is needed to drive the ME sensors at a certain frequency for sensing the DC magnetic field using ME coupling.^{Reference Dong, Zhai, Li and Viehland17} The large power consumption for generating AC magnetic fields and comparatively low sensitivity make sensing DC magnetic fields for ME sensors challenging. Nan^{Reference Nan, Hui, Rinaldi and Sun18} demonstrated a self-biased NEMS ME sensor for application as a magnetometer that was based on piezomagnetic (FeGaB/Al₂O₃) multilayer nanoplate resonator at 215 MHz. The electromechanical resonance frequency change was attributed to the change in Young’s modulus, which was induced by the bias magnetic field in FeGaB, or the delta-E effect. In Figure 3a,^{Reference Nan, Hui, Rinaldi and Sun18} the sensitivity of this sensor can be observed from the admittance curve (the reciprocal of the impedance) versus the frequency at different DC bias magnetic fields (0 Oe, 15 Oe, and 60 Oe) applied along the length direction of the resonator, showing an electromechanical resonance frequency of 215 MHz at zero bias. Both resonance frequency, f _r, and peak admittance amplitude, Y, at the resonance frequency exhibited similar trends with the DC bias magnetic field, as shown in Figure 3b, reaching minimum values at a bias field of 15 Oe. Both quantities then increase until the FeGaB/Al₂O₃ multilayer was saturated at 50∼60 Oe. The quality factor, Q, follows the same trend as the Young’s modulus, indicating that it may be strongly related to the magnetic anisotropy and magnetic domain wall. Under a high magnetic field, Q is largely enhanced, which could be due to the elimination of magnetic domain walls and a decrease in magnetic losses.

Figure 3.

(a) Admittance curve of the nanoelectromechanical systems (NEMS) sensor at various bias direct current (DC) magnetic fields, showing an electromechanical resonance frequency of 215 MHz. (b) Resonance frequency and admittance amplitude at the resonance frequency as a function of DC magnetic field. Both resonance frequency, f _r, and peak admittance amplitude, Y, exhibited similar trends with the DC bias magnetic field, which reaches minimum values at a bias field of 15 Oe. (c) The sensitivity and linearity of the DC magnetic field sensor with DC bias magnetic field of 5 Oe. The inset shows the zoomed-in part (green box) ranging from 50 pT to 4 nT in a magnetically unshielded environment. The red/orange/brown lines are for reference of linearity. The measurement value of the admittance amplitude starts to scatter at 300 pT, indicating the ultrasensitive magnetic sensor with a detection range starting from ∼300 pT. (d) Sensitivity and linearity of the DC magnetic field sensor at zero-bias magnetic field in a magnetically unshielded environment showing a limit of detection as low as 600 pT under the self-bias condition. The red/orange/brown lines are for reference of linearity. Note: H, magnetic field; Q, quality factor; pT, pTesla.^{Reference Nan, Hui, Rinaldi and Sun18}

A fixed 5 Oe DC bias magnetic field was used to tune the magnetic materials to reach the maximum slope of the electromechanical resonance frequency versus magnetic field, as shown in Figure 3c. The inset in Figure 3c shows an enlarged view with the small DC magnetic field ranging from 50 pT to 4 nT. The measurement value of the admittance amplitude starts to scatter at 300 pT, indicating the detection range starts at ∼300 pT. The limit of detection as low as 600 pT is measured under the self-bias condition shown in Figure 3d, which is comparable to 300 pT results (Figure 1c inset). The integrated RF NEMS ME sensor is compact, power-efficient, and represents a new class of ultrasensitive magnetometers for DC and low-frequency AC magnetic fields.

Acoustically actuated NEMS ME antennas

One of the key challenges for state-of-the-art conventional antennas lies in their miniaturization. Conventional antennas rely on an electromagnetic wave resonance, and therefore, typically have a size of more than one-tenth of the electromagnetic wavelength, λ₀. The limitation for antenna size miniaturization has made it challenging to achieve compact antennas and antenna arrays particularly at very high frequency (30–300 MHz) band and ultrahigh frequency (0.3–3 GHz) band. Antennas are basically an array of conductors that generate an oscillating electric field and magnetic field through an oscillating electric current, required to ensure a large radiation amplitude. However, there is another path to attain radiation power since electricity and magnetization are always coupled together, which indicates the magnetic current also generates an electromagnetic wave. Multiferroics have been studied for ME antennas for more than five years.^{Reference Yao and Wang19–Reference Domann and Carman23} Strong ME coupling, if realized dynamically at RFs in ME heterostructures, could enable voltage-induced RF magnetic currents that radiate electromagnetic waves and acoustically actuated nanoscale ME antennas with a new receiving and transmitting mechanism.^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24}

The antennas are based on a bulk acoustic wave resonator to transfer dynamic strain across the piezoelectric layer and magnetostrictive layer. Two proposed antennas shown in Figure 4, nanoplate resonators (NPRs) and FBARs,^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24} have the same excitation, but have different resonance modes, providing a variety of frequency coverage. From the transmitting aspect, an RF electric field induces an alternating strain wave/acoustic wave that can induce a dynamic change in magnetization due to converse ME coupling and generate a magnetic current for radiation. Reciprocally, from the receiving aspect, the RF magnetic field component of the electromagnetic wave can be detected and induce a dynamic voltage/charge due to the direct ME coupling. The acoustic wavelength is approximately five orders shorter than the electromagnetic wavelength at the same frequency. Therefore, since the ME antennas are operating at the acoustic resonant frequency instead of the electromagnetic wave resonant frequency, the antennas can dramatically shrink to hundreds to thousands of times smaller dimensions.

Figure 4.

(a) Optical images of the fabricated (left) nanoplate resonators (NPRs) and (right) thin-film bulk acoustic resonators (FBARs). (b) Scanning electron microscope image of the fabricated (top) NPRs and (bottom) FBARs. Note: VHF, very high frequency; UHF, ultrahigh frequency.

A ground plane is a flat or nearly flat horizontal conducting surface. The ground plane plays a major role in determining radiation characteristics, including gain. However, the imaging current, induced in the metal while a current passes, flowing in the opposite direction of the planar antennas, can cancel out the radiation from the antennas. This is why most large-profile antennas are in a vertical position and perpendicular to the surface, such as a vertical quarter-wave dipole, where the imaging current serves as part of the antenna for in-phase radiation. The ME antennas use magnetic currents for radiation instead of electric currents. The in-phase imaging current provides 3 dB gain enhancement while attaching to the ground. This ground-plane immunity property can enable a variety of applications on metallic surfaces and on the human body, which is also considered as a ground plane.

All antenna devices in this study^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24} were fabricated with the same five-mask fabrication process on one small chip that includes thousands of antennas. The resonance frequency, f _r, of various devices were measured with different design principles and geometries via a network analyzer. Figure 5 plots f as a function of 1/w (w = width) for NPRs and 1/t (t = thickness) for FBARs.^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24} As shown, the f of NPR devices is inversely proportional to w for NPRs, and f is inversely proportional to the AlN thickness for FBAR. This indicates that the frequency of the antenna is simply defined by the resonator geometry. This indicates that by using a simple device geometry design, we can achieve a wide frequency band from tens of MHz to tens of GHz on only one chip. A bank of multifrequency MEMS resonators can be connected to a CMOS oscillator circuit for the realization of reconfigurable ME antenna arrays.

Figure 5.

Measured resonance frequency, f _r, as a function of 1/w (w is width) for nanoplate resonators (NPRs) and 1/t (t is thickness) for thin-film bulk acoustic resonators (FBARs) resonators. By using a simple device geometry design, we can achieve a wide frequency band from tens of MHz to tens of GHz on only one chip.^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24}

For antenna gain measurements, a calibrated linear polarization standard horn antenna and an ME antenna were connected to a vector network analysis device, which is an essential RF and microwave measurement tool. The resonance frequency was found to be 2.53 GHz by measuring the return loss (S ₂₂), as shown in Figure 6a, with a peak return loss of 10.26 dB. In Figure 6b, a nonmagnetic control device with Al/AlN was also tested with the same experimental setup and at the same resonance frequency near 2.5 GHz. The control device exhibited a similar S ₂₂ as the ME antenna, which indicates similar power is transferred into both antennas. The receiving and transmitting behavior of ME antennas corresponds to the S ₂₁ and S ₁₂ parameters, respectively, as shown in Figure 6c. The antenna gain for the ME antenna is calculated to be −18 dBi through the gain comparison method. However, as seen in Figure 6d, no clear resonance peak was observed in the control antenna measurements, which is ∼20 dB lower than the performance of ME antenna. The ME coupling effect likely dominates the performance of the antenna transmission.

Figure 6.

(a) Return loss (S ₂₂) of magnetoelectric thin-film bulk acoustic resonators (ME FBAR). The inset shows the simulated out-of-plane displacement of the circular disk at resonance peak position indicating the thickness direction resonance. (b) Return loss (S ₂₂) curve of the nonmagnetic Al/AlN control FBAR. Both magnetic and nonmagnetic devices had similar return loss curves indicating that the same energy transferred into the both devices. (c) Transmitting and receiving behavior (S ₁₂ and S ₂₁, respectively) of the ME FBAR. (d) Transmitting and receiving behavior (S ₁₂ and S ₂₁, respectively) of the nonmagnetic Al/AlN control FBAR. The curves in the nonmagnetic device are ∼20 dB lower than the performance of those in the magnetic device. Therefore, we can suggest that the ME coupling effect dominates the performance of the antenna transmission.^{Reference Nan, Lin, Gao, Matyushov, Yu, Chen, Sun, Wei, Wang, Li, Wang, Belkessam, Guo, Chen, Zhou, Qian, Hui, Rinaldi, McConney, Howe, Hu, Jones, Brown and Sun24} Note: f _r, resonance frequency; Q, quality factor.