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Ultra-High Frequency Nanomechanical Piezoresistive Amplifiers for Direct Channel-Selective Receiver Front-Ends Alireza Ramezany, and Siavash Pourkamali Nano Lett., Just Accepted Manuscript • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018
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Ultra-High Frequency Nanomechanical Piezoresistive Amplifiers for Direct ChannelSelective Receiver Front-Ends Alireza Ramezany * and Siavash Pourkamali University of Texas at Dallas, Richardson, Texas, 75080, USA
ABSTRACT Channel-selective filtering and amplification in ultra-high frequency (UHF) receiver front-ends are crucial for realization of cognitive radio systems and the future of wireless communication. In the past decade, there have been significant advances in the performance of microscale electromechanical resonant devices. However, such devices have not yet been able to meet the requirements for direct channel selection at RF. They also occupy a relatively large area on the chip making implementation of large arrays to cover several frequency bands challenging. Electromechanical piezoresistive resonant devices, on the other hand, are active devices that have recently shown the possibility of simultaneous signal amplification and channel-select filtering at lower frequencies. It has been theoretically predicted that if scaled down into the nanoscale, they
*
Corresponding author, Email:
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can operate in the UHF range with a very low power consumption. Here, for the first time, nanomechanical piezoresistive amplifiers with active element dimensions as small as 50nm×200nm are demonstrated. With a device area of less than 1.5um2 a piezoresistive amplifier operating at 730MHz shows gains as high as 10dB and effective quality factor (Q) of 330,000 for a 250Ω load, while consuming 189μW of power. Based on the measurement results, it is shown that for piezoresistor dimensions of 30nm×100nm it is possible to get a similar performance at 2.4GHz with device foot-print of less than 0.2um2.
Keywords: NEMS, Narrow Band filtering, RF-MEMS, High Quality Factor Resonators, Thermal Actuation
With the ever-growing number of wireless users and the narrowing gap between supply and demand, one of the biggest imminent challenges in the future of wireless communications is the spectrum crisis1. The global efficiency can be greatly improved by systems capable of dynamic frequency spectrum allocation replacing the current fixed spectrum allocation system. For example, in opportunistic spectrum access, an unlicensed secondary user is temporarily allowed spatial and geographic reuse of a part of the spectrum that normally belongs to a licensed user1,2. Such solutions fall inside the general umbrella of Cognitive Radio System (CRS), a system able to dynamically and autonomously adapt its operational parameters and protocols and to learn from its previous experiences3,4. CRS utilizes Software Defined Radio (SDR) transceivers that are able to use any available band, adapt to multiple access methods and adaptive modulation schemes1. Therefore, the RF transceiver section needs to be particularly flexible. Dependence of the current derivatives of conventional super-heterodyne RF front-end architecture on intermediate frequency (IF) hardware does not fit effectively within such
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requirements. In current configurations, signal from the antenna must be filtered, amplified and down-converted to IF before it is sent to an analog-to-digital converted (ADC)5. Expansion of such architecture to CRS will require tremendous increase in the number of such components to cover various frequency bands. To meet the demands of CRS, direct RF sampling approach has been proposed as the only practical architecture for SDR systems5,6. In direct sampling, the signal chain from the antenna is directly fed to a high-performance RF sampling ADC, thus significantly reducing the complexity of the RF front ends. Ideally, a true SDR would not require any specific front-end hardware between the antenna and the ADC. However, processing a large portion of the spectrum without any filtering would require a wide dynamic range for the ADC leading to impractical ADC power consumptions (e.g. 80W for GSM network as calculated in6). A more practical solution, is to allow the software to select the desired channel by accessing and enabling a narrow-band (Q>30,000) filter in a large filter bank6. Currently available RF filters (e.g. SAW and FBAR), do not offer such sharp filtering characteristics7. Over the past two decades, Micro-Electromechanical Systems (MEMS) have offered innovative enabling technologies for timing and frequency-selection applications. However, the majority of such efforts have focused on piezoelectric and capacitive resonators that are passive electrical components8–14. Reaching the required Q for channel selection at RF while minimizing insertion loss has proven to be a formidable challenge. While capacitive resonant devices can offer large Qs they introduce significant loss to the filtered signal (e.g., 50-60dB 11,12). Piezoelectric devices, on the other hand, provide a significantly lower insertion loss but lack in quality factor (e.g., 50040008,10,15). There have been recent efforts to develop on-chip active resonant components by
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integrating field effect transistors (FETs) within electromechanical devices16–20. Such devices have not been able to meet the SDR performance requirements either. Electromechanical piezoresistive amplifiers are relatively simple devices comprised of a monolithic conductive structure. Being active electronic elements, they can perform both amplification and narrowband filtering simultaneously within a single structure. Lower frequency versions of such devices (0.3GHz) with significantly reduced power consumption are demonstrated. The nanomechanical piezoresistive amplifier essentially consists of a piezoresistive Nanobeam connected to two suspended masses as shown in Figure 1a. In the in-plane resonant mode of interest, the masses vibrate back and forth in opposite directions periodically stretching and compressing the nanobeam. A pair of clamped-clamped beams are used for anchoring purpose keeping the structure suspended and electrically connected to wire-bond pads. Upon arrival of an RF signal the nanobeam undergoes a periodic thermal expansion and contraction due to Joule heating. If the RF signal contains frequency components close to the natural resonance frequency of the structure, the resonance mode is excited and the nanobeam undergoes significant periodic strain. In presence of a DC bias across the nanobeam, due to the piezoresistive effect, this vibration turns into a filtered output RF signal only containing frequency components within the resonator passband. Strain modulated electrical resistance of the beam along with the DC bias leads to an additional internal source of thermal excitation power component. If in phase with the thermal excitation from the incoming RF signal (determined by the piezoresistive coefficient polarity and thermal response time of the nanobeam), the additional excitation can significantly increase the vibration amplitude and therefore the output signal amplitude. In this manner, similar to a
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Expansion
Piezoresistive Nanobeam
PMMA
Si
Masses Supports
e.
Si
SiO2
50nm Trench
200nm
200nm
Cr Hard Mask
f. 1µm
Si
Handle Layer
d.
c.
b.
a.
Cr
200nm Buffer Oxide
g. 1µm
f0 = 400MHz 200nm
f0 = 750MHz 800nm
Figure 1. a) Schematic view showing the structure and in-plane resonant mode shape of a nanomechanical piezoresistive amplifier; b) The patterned device shape including a 50nm wide trench on PMMA using EBL at 20KeV; c) The Cr hard mask after the liftoff process; d) etching the device pattern onto the Si device layer and buffer oxide layer using chlorine based plasma; e) Released structure after HF dip; f, g) Different views of the completed devices with operating frequency of 400MHz and 750MHz. transistor, such device can absorb power from a DC bias source and use it to amplify an AC signal. Basically, in presence of significant internal thermal excitation (adequate DC bias), the nanobeam behaves like a spring that cools down when expanded and therefore retracts with a larger force in the next half-cycle of its resonance, and vice versa. This process is referred to as “internal amplification”21. In theory, scaling down the dimensions of the piezoresistor and masses not only raises the resonance frequency, but also reduces the power consumption needed to achieve the same strength of internal amplification. Therefore, in this work two devices with similar 200nm×50nm piezoresistive Nanobeams are fabricated on a silicon on insulator (SOI) substrate with a 300nm thick silicon device layer and a 400nm thick buffer oxide. Square shaped masses with dimensions
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of 1.5µm and 800nm are chosen leading to operating frequencies of approximately 400MHz and 750MHz. In order to reach such small dimensions, Electron Beam Lithography (EBL) was used to pattern a 240nm thick Poly Methyl Methacrylate (PMMA) E-Beam resist (Figure 1b). A 50nm layer of Cr was then evaporated on to the sample to form a hard mask via lift-off (Figure 1c). This was followed by chlorine based inductively coupled plasma etching of the device patterns onto the Si device layer (Figure 1d). Finally, to suspend the devices, the substrate is exposed to 49% Hydrofluoric acid, where the buffer oxide layer underneath the patterned silicon (Figure 1e) is removed. Figures 1f and 1g show scanning electron micrographs of the fabricated devices. Figure 2a shows the electrical model used to predict the S21 frequency response. The piezoresistive beam acts as the parallel combination of its electrical resistance RA, and its frequency dependent motional current source im(f). The motional transconductance (gm(f)=im(f)/vac) is comprised of three frequency dependent transfer functions: thermal, mechanical and piezoresistive. The detailed derivation of each individual transfer function is discussed in 14. Ideally, the thermal response of the piezoresistive beam resembles that of a periodically charging and discharging RC circuit as shown in figure 2a, where Cth and Rth are the thermal capacitance and resistance of the beam, respectively. As discussed in14, when the thermal time constant is much larger than the mechanical time constant i.e., ω0 >> (RthCth)-1, the AC temperature generated across the beam (Tac) will lag behind the AC voltage (vac) by a desirable ~90º. Along with an inherent 90º lag of the mechanical resonance response at resonance frequency ω0, and 180º phase from the negative piezoresistive coefficient of n-type doped silicon, the motional current im at resonance frequency will be in phase with the incoming RF signal and can form a positive feedback to
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increase the vibration amplitude (i.e., internal amplification). In other words, at resonance, the piezoresistive beam acts as the parallel combination of its electrical resistance RA, and its motional
kΩ
Figure 2. a) The electrical model of the nanomechanical amplifier consisting of thermal, mechanical and piezoresistive components. b) Finite element analysis of temperature distribution across the device. c) Plots of AC temperature on the nanobeam showing a 45º lag of temperature across the piezoresistor. d) Real part of the device impedance marking the overall resistance of the device at resonance and the active region where gain is possible. e) Calculated S21 response of the device based on the FEM results. resistance Rm where |Rm|=|1/gm|@ω0 and is negative (due to the negative direction of the im compared to vac).
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However, as the dimensions are scaled down, the individual thermal time constants of the masses and the support beams become comparable to that of the piezoresistor, and the ideal model for thermal response is no longer valid. Therefore, finite element method (FEM) was used to predict the thermal response of the piezoresistive beam. Figure 2b, shows the simulated DC and AC temperature distribution across the device. Combination of a 1V DC voltage and a 10mV AC signal at 750MHz were supplied as inputs, while temperature fluctuations at the center and ends of the piezoresistor were monitored at steady state (figure 2c). According to simulations, on average the AC temperature across the piezoresistor, lags behind vac by only 45º at resonance frequency as opposed to the 90º commonly achieved for larger devices. Therefore, the motional current will no longer align with the incoming signal at resonance frequency ω0, and the remaining 45º required for the internal amplification must be compensated by the rapid phase change in the mechanical response beyond the resonance frequency ω0. Figures 2d and 2e show numerical calculations of the model in figure 2a using the FEM results and assuming piezoresistive coefficient (πl) of -10-10Pa-1. While the maximum gm value occurs at ω0 (i.e.,
�𝐾𝐾�𝑀𝑀), the
internal amplification can only take place at the internal frequency ωI, where
the gm has zero phase but a smaller magnitude. Figure 2d shows the real part of the device impedance ZD including the overall device resistance RD at resonance, i.e., Real(ZD)|@ωI. Increasing the DC bias current increases the absolute value of gm at resonance (ω0 and ωI), and eventually the overall device resistance RD becomes negative. At this point, the S21 phase at resonance changes from 0° to 180º. The device must be matched to the proper load (RL) to provide gain (Gain=RL/(RL+RD)). Ideally, the device resistance must satisfy RL < |RD|< 2RL to yield Gain >1 21
. For a larger load, a smaller gm and power consumption can maintain the same gain as long as
RL 50 Ω), larger effective quality factor and signal transmission at resonance can be achieved for a smaller gm and DC power. However, the gm values that can satisfy the gain condition (i.e., RL < |RD|< 2RL) can now be obtained in a smaller range of DC currents (lower downward peaks in figure 2d). Also, as discussed in11, at very large loads (RL>> RA) the device is ultimately loaded by its own physical resistance RA, and can be pushed to an unstable region (i.e., self-sustained oscillation) if |1/gm| < RA. Therefore, as long as the stability condition is satisfied, the maximum attainable quality factor is limited by the smallest matching range the load can provide as well as the fluctuations in DC
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a.
b.
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c.
400MHz
d.
730MHz
e.
Figure 3. a and b) The measured S21 response of the fabricated devices that include the loading effects of the parasitic elements as well as the 50Ω termination of the network analyzer showing minimal insertion loss with large quality factors. c) The measured motional transconductance as a function of DC power. d) The S21 response after elimination of parasitic elements. e) Loop gain, a measure of internal amplification strength plotted vs. DC power consumption for measured devices as well as possible loop gains for a 2.4GHz device. Assuming same material parameters (e.g., πl, α, E), the 2.4GHz device shows similar loop gains for a reasonable range of power consumption even with a lower mechanical quality factor. power that can change the value of device resistance RD. Further down scaling of the Nanobeam will lead to a stronger internal amplification while the device consumes similar power at higher
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frequencies. The strength of the internal amplification, i.e., the voltage gain induced across the piezoresistor by the motional current im, is determined by the product of gm and RA, referred to as loop gain: 𝑉𝑉𝑎𝑎𝑎𝑎,𝑚𝑚
𝑉𝑉𝑎𝑎𝑎𝑎,𝑖𝑖𝑖𝑖
=
𝑖𝑖𝑚𝑚 .𝑅𝑅𝐴𝐴 𝑣𝑣𝑎𝑎𝑎𝑎
= 𝑔𝑔𝑚𝑚 𝑅𝑅𝐴𝐴 ∝ 𝛼𝛼. 𝜋𝜋𝑙𝑙 . 𝑄𝑄𝑚𝑚 . 𝑉𝑉 −1 𝑓𝑓 −1 . 𝑃𝑃𝐷𝐷𝐷𝐷
(1)
Where Vac,in is the initial AC voltage across the beam, Vac,m is the voltage induced by the motional current and α, πl, Qm, V and f are the thermal expansion coefficient, piezoresistive coefficient, mechanical quality factor, beam volume, and operating frequency. As shown in figure 3e, due to the fact that the two devices have similar beam dimensions with mechanical quality factors of 1000 and 5000 at 400MHz and 730 MHz, respectively, the two devices show similar loop-gains. To achieve the same level of loop-gain at higher frequencies, under the same mechanical quality factor, the beam dimensions must be reduced. Assuming similar parameters (e.g., α, πl, etc.), a device fabricated on a 150nm device layer with 30nm×100nm beam dimensions and 0.09um2 mass area can potentially deliver a similar loop-gain at 2.4GHz (for GSM and CDMA standards). It is hard to precisely predict mechanical quality factor of such device; therefore, the loop-gains are plotted for mechanical quality factors of 500, 1000, and 2000 to predict the hypothetical required DC power consumption at such frequency. In conclusion, it was shown that as predicted by the theory, nanomechanical piezoresistive amplifiers can offer sharp filtering characteristics along with active signal amplification in the UHF range. Having dimensions in the nanoscale is crucial for such devices to reach accepable performance, a trait that most electromechanical devices do not share. Table 1 shows a comaprison of the presented device with other state of the art miniaturized electromechanical UHF resonator technologies.
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Frequency tuning range and noise performance of the nanomechanical amplifiers require further study. Tuning of the resonance frequency to cover a wider range of freqeuncies can be accomplished by controling the DC bias current. As shown in figure 3, at high gains a slight change Table 1. Comparison of the state of the art microscale UHF electromechanical resonant devices a Device Type
Material
Area Size (um2)
Capacitive
Diamond
870
800MHz
77,000
Passive
-54
[12]
Piezoelectric
Lithium Niobate
12,800
750MHz
300
Passive
-4
[10]
Capacitive/ Piezoelectric
Aluminum Nitride
2,800
1.2GHz
3,000
Passive
-20
[13]
Piezoelectric/ AlGaN/GaN 25,000 HEMT
900MHz
8,350
