Ultra-High Frequency NEMS Resonators with Low-Noise Phase-Locked Loops
4.5 Roadmaps of UHF NEMS Resonators and Performance
Based on the foregoing measurements and milestones achieved, we have been able to build roadmaps of the characteristics and performance of these generations of UHF NEMS devices. These roadmaps are very important and meaningful. They also have a lot of implications for the achievable scaling capabilities of UHF NEMS, and on the routes toward the ultimate goals of UHF-NEMS-based sensing and communication applications.
For the family of UHF NEMS devices operating in the range of 300~500MHz, all characterized in the PLL system with resonances read out by bridge scheme, their basic specs (device dimensions, mass, frequency, Q), achieved dynamic range (DR) and measured frequency stability performance (Allan deviation) are listed in Table 4-1.
We carefully examine the noise floor and onset of nonlinearity of each of these devices to estimate their ideal, intrinsic dynamic ranges. Since in these measurements the readout preamplifier noise is not matched to the intrinsic noise floor of the device, the practical dynamic range is compromised. Fig. 4.10 shows the scaling of both the intrinsic and achievable dynamic ranges of UHF devices we have made so far. In the analyses, some
of the UHF devices demonstrated in pushing the 1GHz operating frequency barrier are also included [23]. For these devices, the dimensions, resonance frequency and Q’s have been measured but their noise floor and dynamic ranges have not been examined.
Table 4-2 presents the roadmaps of the noise floor and dynamic range for the UHF NEMS devices working in the range of 400MHz~1GHz.
400 600 800 1000
-220 -200 -180 -160 -140 -120 -100 -80 -60
Measured Onset of Nonlinearity Refer to the Input of Preamp
Achieved DR
Ideal Device Noise Floor (thermomechanical) Refer to the Input of Preamp
Power Level RTI of P reamp (dBm)
Resonance Frequency (MHz)
Ideal Onset of Nonlinearity Refer to the Input of Preamp
Noise Floor of Preamp (RTI) Ideal
DR
Fig. 4.10 Ideally intrinsic dynamic range and practically achievable dynamic range specifications of the UHF NEMS resonators.
As illustrated in Chapter 2, the power handling capability of a resonator device is another very important metric that is especially crucial for communication and signal processing applications. So we have also built an extended roadmap of the power handling for all the VHF/UHF/microwave NEMS resonator devices we have so far demonstrated, as shown in Table 4-3. For VHF NEMS resonators (with f0 100MHz or so), typically we have the RF power sent to the devices in nanowatt (nW) range, about or over 90% of which is dissipated as heat on the DC resistance for the devices; the power goes to the mechanical resonance, thus the power handling of the NEMS resonator, is in
picowatt (pW) range (note that Q always plays a role in determining the exact numbers, as the Q trades off with power handling). As the rules of thumb, we have:
(i) For 10−100MHz VHF NEMS resonators, Pdrive,max: 0.1−10nW range; and power handling PC: 1−100pW range.
(ii) For 300MHz−1GHz UHF NEMS resonators, Pdrive,max: 0.1−100μW range; and power handling PC: 0.1−100nW range.
These typical numbers are confirmed by the typical total driving power level seen in our experiments, and the mechanical domain calculations and the estimations based on the circuit model are of the same orders of magnitudes.
Note all the calculations and analyses of the specifications and metrics of UHF NEMS are based on the theoretical foundations and formulae discussed in Chapter 2.
Table 4-1 UHF NEMS resonator devices specs and performance NEMS Device Dimensions
Resonance Frequency
(MHz) L (μm) w (nm) t (nm)
Device Mass (fg, 10-15g)
Meff
(fg) Q DR (dB)
σA
(τ=1sec)
Mass Sensitivity (1zg=10-21g) 295 2.65 180 80 160.2 118 ~3000 80 4.7×10-8 15 zg 420 1.8 150 100 111.1 82 ~1200 90 3.1×10-7 67 zg 411 1.7 120 80 72.3 53 ~2600 85 6.6×10-8 10 zg 428 1.65 120 80 75.5 54 ~2500 90 2.5×10-8 4 zg 482 1.55 120 80 70.9 52 ~2000 98 2.1×10-8 3 zg
Table 4-2 Dynamic range specs of UHF NEMS resonators Resonance
Frequency (MHz)
(μm) L w (nm)
t (nm)
Device Mass
(fg)
RF Q
Intrinsic Noise Floor Displacement
(fm)
Intrinsic Noise Floor (Voltage, pV)
Intrinsic Noise Floor (dBm)
Intrinsic Dynamic
Range (dB)
Achieved Dynamic Range in Measurements
(dB) 428 1.65 120 80 75.5 2500 1.44 51.0 -192 120 90 482 1.55 120 80 70.9 2000 1.11 41.7 -197 128 98 339 1.6 140 80 71.3 3600 2.52 68.7 -190 109 N.A.
357 1.55 160 80 78.9 3000 2.02 56.2 -192 112 N.A.
480 1.32 140 80 61.3 1600 1.07 34.2 -196 120 N.A.
488 1.31 150 80 60.8 1600 1.05 33.8 -196 120 N.A.
590 1.6 140 80 71.2 1700 0.75 35.8 -196 132 N.A.
712 1.55 160 80 78.9 900 0.39 21.8 -200 137 N.A.
1014 1.11 120 80 44.2 500 0.23 13.0 -205 142 N.A.
1029 1.09 120 80 43.4 500 0.23 12.8 -205 142 N.A.
Thermal noise of preamp: -177dBm
Table 4-3 Power handling specs of 3C-SiC VHF/UHF NEMS resonators
Resonance Frequency (MHz)
(μm) L w (nm)
t (nm)
Device Mass
(fg)
Effective Mass
Meff
(fg)
Measured Q
Critical Displacement
(amplitude) aC (nm)
Effective Stiffness keff (N/m)
Resonator Mechanical
Energy at the Critical Amplitude
(fJ)
Power Handling
124 2.5 200 80 177.2 130.2 1300 1.47 79.0 0.085 50.9 pW 133 2.35 150 80 124.9 91.8 5000 0.71 64.1 0.016 2.7 pW 190 2.35 150 100 145.0 106.6 5200 0.99 151.9 0.075 17.2 pW 199.6 3.1 180 100 229.5 168.7 7500 1.51 265.3 0.30 50.6 pW 240.5 1.8 150 100 111.1 81.6 1500 1.37 186.4 0.18 176.8 pW 295.4 2.66 170 80 160.2 117.8 3000 2.60 405.7 1.37 850.2 pW 420 1.8 150 100 111.1 81.6 1200 2.68 568.4 2.04 4.5 nW 395 1.75 120 80 74.4 54.7 2600 1.65 336.8 0.46 455.3 pW 411.4 1.7 120 80 72.3 53.1 2600 1.62 355.0 0.47 482.7 pW 428 1.65 120 80 75.5 55.5 2500 1.66 401.3 0.55 644.4 pW 482 1.55 120 80 70.9 52.1 2000 1.77 478.0 0.75 1.1 nW 339 1.6 140 80 71.3 52.4 3600 0.99 237.8 0.12 68.5 pW 357 1.55 160 80 78.9 58.0 3000 1.07 291.8 0.17 124.4 pW 480 1.32 140 80 61.3 45.1 1600 1.43 409.8 0.42 785.6 pW 488 1.31 150 80 60.8 44.7 1600 1.43 420.1 0.43 821.0 pW 590 1.6 140 80 71.2 52.3 1700 2.50 719.1 2.25 4.9 nW 712 1.55 160 80 78.9 58.0 900 3.89 1160.6 8.78 43.6 nW 1014 1.11 120 80 44.2 32.5 500 3.81 1318.7 9.58 122.0 nW 1029 1.09 120 80 43.4 31.9 500 3.73 1333.4 9.27 119.9 nW
Black: tested by the author (the work on the 124MHz, 133MHz, 190MHz in collaboration with Jack) Blue: data from X.M.H. Huang’s thesis work for resonance frequencies, dimensions and Q’s.
The UHF NEMS resonators roadmaps are encouraging and stimulating. For example, as shown in Tables 4-1 and 4-2, for the close to 500MHz devices, we have experimentally achieved ~100dB dynamic range and the excellent frequency fluctuation noise floor (Allan deviation) leads to a mass sensitivity of 3zg. This manifests that probably the most intriguing promise of these UHF NEMS-PLL systems is that the measured frequency stability is translated into unprecedented mass sensitivity if the devices are used as inertial mass sensors, based on the analyses in [9]. For all the devices measured with the PLL scheme, the mass sensitivity values go deep into the zeptogram (10-21g) scale. In fact, given 1zg≈0.6kDalton, the demonstrated mass sensitivity indicates that we have already had the capability of weighing biomolecules with mass in the 10-100kDalton ranges, and distinguishing some of them with fine enough resolution. Further, this suggests that single-molecule mass detection with single-Dalton sensitivity becomes possible and applicable with UHF NEMS.
It is also clearly verified by the roadmaps that frequency stability and thus the overall mass sensing performance relies on a combination of high frequency and high Q.
Therefore, scaling up operating frequency and simultaneously retaining high Q remains a great challenge for NEMS mass sensor engineering. Besides, we note that to fully understand the origin and mechanism of the deteriorating long-term stability (long-term drifting) shown in Fig. 4.7, and to develop techniques for optimizing both short-term and long-term stability, study upon various possible drifting and aging effects in the system is needed. Realistically, long-term drifting mechanisms may be unavoidable as they persist in many other conventional time bases, but it would be still very valuable if the Allan deviation can be engineered so that the σA∼1/√τ and/or flat regions are wide enough to cover the averaging time range of interest. Or equivalently, the noise is thermal noise or 1/f noise limited and the knee point between 1/f noise and 1/f 2 noise is really low at offset frequency, i.e., really close to carrier.