Experimental Details

Resonance Frequency (MHz)

5.3 Experimental Details

The monocrystalline 3C-SiC epitaxial layer is grown on monocrystalline silicon substrate by atmospheric pressure chemical vapor deposition (APCVD) [24], reinforced by newly developed surface roughness control and improvement techniques [25].

Doubly-clamped beam resonator devices are fabricated with a process specifically suitable for UHF SiC NEMS [8,17]. Shown in Fig. 5.3 are SEM images of a typical UHF 3C-SiC resonator. The doubly-clamped beam design simplifies understanding of device size and dimensional effects, and also minimizes the influence of complexities in, and variations from, the fabrication processes. Metallization consisting of 10nm titanium (Ti) atop a 30nm aluminum (Al) layer is deposited onto the SiC structural material. This enables patterning devices read out by magnetomotive excitation, and also detection [26]of the beam resonance from the in-plane flexural fundamental mode.

The measured sheet resistance of the metallization film is 1.5Ω/□ at ~20K and 6.7Ω/□ at room temperature, with a proximately linear temperature dependency in this range. The device samples are secured in high vacuum (≤10^-7Torr) in a liquid He cryostat. The sample temperature is monitored by a thermometer, and controlled by a resistive heater, both mounted on the gold-plated sample stage. Feedback control of sample temperature is applied and for each measurement temperature fluctuation is limited to be within 1mK, to minimize the instantaneous resonant frequency variation due to the temperature fluctuation.

Fig. 5.3 Scanning electron micrographs of a typical single-crystal 3C-SiC UHF NEMS resonator.

Main: Oblique view (scale bar: 1μm). Inset: Top view (scale bar: 2μm).

Network analysis techniques for two-port systems are used to detect the transduced magnetomotive effect from the NEMS devices and to measure the resonant frequencies and quality factors. Because the strength of the magnetomotive effect decreases as the frequency scales up and in the UHF band it is easily overwhelmed by the embedding and parasitic impedances of the system, it has been a challenge to attain large and clean resonance signals out of the electrical background. With our recently developed techniques of background suppression for UHF NEMS over wide frequency spans [27], now resonance signals with very large signal-to-background ratios (also known as

“resonance on-to-off ratios”, typically 5~10dB [27], as compared to previously typical values of ~0.1dB) are reliably attained and thus quality factors can be accurately extracted from the resonance signals free from competing or even dominant response due to embedding and parasitic impedances. Alternatively, albeit less convenient, quality factors can also be measured by a direct time-domain damped ring-down process of the resonators, which has been calibrated and verified to attain <5% discrepancy for extracted Q’s as compared to those from fitting resonance curves in the network analysis

method [28]. In the present work, network analysis with elaborately minimized background response ensures better confidence for accurate extraction of Q’s.

426 427 428 429 430 0

2 4 6

8

^(b)

1 10

3 4 5 6 7 8 9

Dissipation Q-1 / 10-4

Magnetic Field B (T)

424 426 428 430 432 2.0

2.5 3.0 3.5 4.0 4.5 5.0 5.5

Resonance Signal (μV)

Frequency (MHz)

T = 20 K B = 8 Tesla 10MHz Span

B = 8T B = 7T B = 6T B = 5T B = 4T B = 3T B = 2T B = 1T

N E M S Re sona nce (dB)

Frequency (MHz)

(a)

Fig. 5.4 Resonance signal of a 428MHz NEMS resonator, at various magnetic field conditions, as measured by a microwave network analyzer, utilizing detailed balancing and nulling techniques with a bridge circuitry scheme. Inset (a): The magnetomotive damping effect. Inset (b): A typical UHF resonance signal over a 10MHz wide frequency span.

Fig. 5.4 shows the measured resonance signal of the 428MHz device, as the magnetic field B is ramped up from 0T to 8T, with the background response signal at 0T subtracted.

At B=8T, the signal-to-background ratio is 8dB at the resonance peak. The right-hand side inset of Fig. 5.4 shows the resonance signal referred to the input of the preamplifier, in which both the background signal and the resonance are shown in linear scale (in μVolts, 8dB at peak if converted into dB, exactly corresponding to the dB plot in Fig. 5.4;

but here in the linear scale plot the absolute level of the flat background, ~2.25μV, i.e., -100dBm, is clearly indicated), and a fit based on the Lorentzian approximation of the power signal perfectly matches the resonance data in a wide span of 10MHz.

Fig. 5.5 shows the measured dissipation as a function of temperature for the 3C-SiC 428MHz and 482MHz NEMS resonator devices. The radio frequency (RF) drive power, the magnetic field and the electronic detection system settings are kept the same in all these measurements, leaving temperature the only variable. Magnetic field B=6T with enough RF power (-33dBm) is calibrated and used to attain large enough resonance signals (approaching the top regime of the dynamic range) for accurate extraction of Q’s in all these temperature-dependent measurements. As shown in Fig. 5.5, the measured dissipation increases with increasing temperature, with a temperature dependency of about Q^-1∝T^0.3 for both devices. It should be pointed out that this dissipation temperature-dependency phenomenon is not unique for these SiC resonators. In Table 5-1 we list seemingly similar temperature dependency reported for micro- and nanomechanical resonators made of Si, GaAs, diamond and carbon nanotube, with none of their temperature dependencies clearly understood. Because dissipation in resonant devices is complicated and associated with various energy loss mechanisms, how to understand the data requires examinations of all possible dissipation processes.

Assuming that the dissipation from different origins is additive and uncorrelated, the possible important mechanisms that may contribute to the measured dissipation include the 3C-SiC NEMS structure layer’s intrinsic dissipationQ₀⁻¹, magnetomotive damping

−1

Qmag , thermoelastic damping Q_ted⁻¹ , clamping losses Q_clamp⁻¹ , metallization layer dissipation Q_metal⁻¹ , surface loss Q_surf⁻¹ , etc.,

⋅⋅

⋅ + +

+ + +

=

surf metal

clamp ted

mag Q Q Q Q

Q Q Q

1 1

1 1

1 1 1

0

(5-1)

We neglect the air viscous damping effect since all our measurements are performed in UHV condition. We now explore all these possible mechanisms to find out the implications of these data.

20 40 60 80 100 10

^-4

10

^-3

10 100

10^-6 10^-5 10^-4

TED Max, (Qted -1)max

Temperature (K)

428 MHz 482 MHz T ^0.3 Fitting

Diss ipati o n Q

-1

Temperature (K)

Fig. 5.5 Measured dissipation as a function of temperature for the selected 428MHz and 482MHz NEMS resonators. The dashed lines show the Q^-1∝T ^0.3 approximation to guide the eyes. Inset:

Theoretical estimation of maximum possible thermoelastic dissipation as a function of temperature.

Table 5-1 Temperature dependency of Q^-1 in various micro- & nanomechanical resonators.

Material L (μm) w (nm) t (nm) Resonant Frequency Temperature

Dependency Method 3C-SiC

(this work) 1.55, 1.65 120 80 Flexural, in-plane, 428MHz, 482MHz

Q^-1~T ^0.3 (20~85K) Si [21] 5~25 1000 200~360 Flexural, out-of-plane,

12.4MHz, 4.7MHz

Q^-1~T ^0.3 (4~10K)

GaAs [21] 6~25 400~2000 ~800

Torsional, 0.62, 1.02, 1.28, 2.75MHz Flexural, out-of-plane, 13MHz

Q^-1~T ^0.25

(4~40K)

Diamond [28] 2.5, 3, 4,

and 8 80 40

Flexural, in-plane, 13.7MHz, 55.1MHz, 110.1MHz, 157.3MHz

Q^-1~T ^0.2 (5~30K)

Experimental

Network Analysis

Single-Walled Carbon Nanotube [22]

0.003μm

(3nm) d=0.35nm d=0.35nm Flexural, 300GHz Q^-1~T ^0.36 (50mK~293K)

Molecular dynamics simulation of ring-down process