Investigations on the Q's and energy dissipations in NEMS resonators, especially those working in the VHF/UHF/Microwave ranges, are crucial. On one hand, in almost all the potential applications promised by NEMS, both high operating frequencies and high Q's are desirable; on the other hand, the scaling laws of resonance frequency and Q on the device dimensions trade off. Hence it has been very challenging to attain VHF/UHF/Microwave frequencies, and to retain very high Q's at the same time.

For instance, we have measured the Q's of generations of doubly-clamped beam VHF/UHF/Microwave SiC NEMS resonators, and have observed a steady decrease of Q as the resonance frequency is increased. These devices have been fabricated by following the same process and with the same level of precision in defining and controlling the device dimensions, and the frequency is scaled up only by changing the beam length. The resonance frequency-Q tradeoff has also been identified in our experiments with HF/VHF NEMS resonators made from GaAs, Si, and heavily-doped Si.

Figure 1. Scaling of devices and the trade-off between resonance frequency and the measured quality factors (Q's) of a number of VHF/UHF/microwave NEMS resonators made of SiC (top panel). Measured dissipation (Q-1) with respect to the cubic power of the aspect ratios of the devices (bottom panel, please see Refs. 2, 3, 5).

We have also found the measured Q's of the NEMS devices are correlated to the surface roughness of the thin film material from which the devices have been patterned and fabricated via surface nanomachining processes. We have been investigating the energy dissipation mechanisms in these NEMS resonators. We measure and model effects such as magnetomotive damping effect (eddy-current damping) associated with magnetomotive transduction, thermoelastic damping, clamping losses, viscous damping, surface and interface losses, etc. For NEMS devices of the same material and same nanofabrication processes, we have found that the clamping losses are very important and account for the observed change in Q's when the resonance frequency is scaled up in the VHF/UHF/Microwave ranges.

Figure 2. Nanofabrication and design using FEM tools (e.g., FEMLAB, later COMSOL, and CFDRC) of free-free beam UHF NEMS resonators to reduce clamping losses and attain higher Q's (see Ref. 1).

We are developing Q-engineering technologies to boost up Q's for VHF/UHF/Microwave NEMS resonators. Various techniques can be devised to engineer the device fabrication processes and transduction schemes to alleviate a certain kind of the aforementioned damping or dissipation effects. For example, for the clamping losses which are significant for VHF/UHF/Microwave NEMS resonators, we have designed and implemented free-free beam resonators to minimize the clamping losses, as compared to conventional doubly-clamped beam structures.

Besides the Q studies and Q-engineering for high performance devices applications, the dissipation mechanisms in NEMS itself compose an intriguing research topic. By developing sophisticated and ingenious measurement techniques, and experimenting with possibly the smallest mechanical resonators, we expect to probe the origins of the energy dissipation sources.

Personnel
 Philip X. L. Feng, Henry X.M. Huang and Michael L. Roukes

Funding
DARPA/MTO and SPAWAR

References

1. Huang XMH, Feng XL, Zorman CA, Mehregany M, Roukes ML, "VHF, UHF and Microwave Frequency Nanomechanical Resonators" (invited), New J. Phys., Vol. 7, Art. No. 247 (2005).
2. Feng XL, Zorman CA, Mehregany M, Roukes ML, "Dissipation in Single-Crystal 3C-SiC Ultra-High Frequency Nanomechanical Resonators", Tech. Digest, Solid-State Sensors, Actuators and Microsystems Workshop (Hilton Head’06),342-346, South Carolina, June 4-8 (2006).
   [see also: http://arxiv.org/abs/cond-mat/0606711]
3. Feng XL, He RR, Yang PD, Roukes ML, "Very High Frequency Silicon Nanowire Electromechanical Resonators", Nano Letters, Vol. 7, No. 7, 1953-1959 (2007).
4. Lifshitz R, Roukes ML, "Thermoelastic Damping in Micro- and Nanomechanical Systems", Phys. Rev. B 61, 5600-5609 (2000).
5. Cross MC, Lifshitz R, "Elastic Wave Transmission at An Abrupt Junction in a Thin Plate with Application to Heat Transport and Vibrations in Mesoscopic Systems", Phys. Rev. B 64, Art. No. 085324 (2001). 

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