Pis’ma v ZhETF, vol. 109, iss. 4, pp. 254 - 255

February 25

On-chip piezoelectric actuation of nanomechanical resonators

containing a two-dimensional electron gas

A. A. Shevyrin⁺¹⁾, A. K. Bakarov^+∗, A. A. Shklyaev^+∗, A. S. Arakcheev^∗×, M. Kurosu^◦∇, H. Yamaguchi^◦∇,

A. G. Pogosov^+∗

⁺Rzhanov Institute of Semiconductor Physics Siberian Branch of the Russian Academy of Sciences,

630090 Novosibirsk, Russia

^∗Novosibirsk State University, 630090 Novosibirsk, Russia

^×Budker Institute of Nuclear Physics Siberian Branch of the Russian Academy of Sciences,

630090 Novosibirsk, Russia

^◦NTT Basic Research Laboratories, Atsugi-shi, 243-0198 Kanagawa, Japan

^∇Department of Physics, Tohoku University, 980-8578 Sendai, Japan

Submitted 5 December 2018

Resubmitted 7 December 2018

Accepted 7 December 2018

DOI: 10.1134/S0370274X19040106

Micro- and nanomechanical resonators provide a

lengths L are 8 and 10 µm, respectively. Thicknesses h

versatile platform for creation of various sensors [1]

of both resonators are 166 nm. The width of the res-

and for fundamental studies [2]. Their downsizing can

onators equals W₀ = 2 µm near the clampings. During

be desirable, but it often complicates the actuation.

the experiment, the samples were placed in a vacuum

Among the piezoelectric materials used for fabrica-

chamber with optical access. Amplitude and phase of

tion of nanomechanical resonators, especially inter-

the vibrations were measured using a Doppler vibrom-

esting are the AlGaN/GaN and AlGaAs/GaAs [3-5]

eter combined with a vector signal analyzer. The vibra-

heterostructures containing a two-dimensional electron

tions were piezoelectrically driven by application of an

gas (2DEG). These systems are integrable with high-

ac voltage between the top gate and the 2DEG.

electron-mobility transistors within a single chip. More-

Figure 1c, d shows the measured frequency depen-

over, at low temperatures, the coupling between me-

dences of the amplitude of flexural vibrations. The ex-

chanical motion and electron transport makes it pos-

perimentally measured responsivities (u₀/V₀)_exp, i.e.,

sible to study the transport phenomena under unusual

the ratios of the resonant amplitude u₀ to the driv-

conditions and to trace electron-transport processes by

ing voltage V₀ are 790 nm/V for the cantilever and

precise measuring the change in the resonant frequency

20 nm/V for the bridge. When V₀ increases, the resonant

[4], thus widening the range of existing experimental

curves characterizing the bridge are tilted to the left (see

techniques. Previously, the piezoelectric actuation has

the inset in Fig. 1d), indicating softening nonlinearity.

been successfully used [4,5] for driving the flexural vi-

This behavior is typical for buckled and bent bridges

brations of micromechanical AlGaAs/GaAs-based res-

[3], while initially straight bridges usually demonstrate

onators with a 2DEG. In the present paper, we experi-

hardening due to the beam elongation at high ampli-

mentally show that this technique is suitable for driving

tudes. Figure 1e, f shows the amplitude and phase cor-

flexural and torsional vibrations of smaller (0.166 nm-

responding to the second vibrational mode of the can-

thick) resonators in the MHz frequency range at room

tilever. The presented data confirm that the observed

temperature. We also show that, due to the buckling and

mode is torsional.

static bending of axially-loaded thin resonators, their

The maximal expected amplitude of flexural vibra-

piezoelectric actuation has important features which

tions u₀ and its ratio to the voltage amplitude V₀ can

should be taken into account for the driving to remain

be estimated as

effective.

(u₀)

e₁₄Q

=α

(1)

We studied two types of resonators, namely, a can-

V₀

ρL²Ω²

theor

tilever and a bridge shown in Fig. 1a, b. Their total

where the non-dmen∕∫al coefficient α is

dΨ



¹ W(x)

(x)

α=



Ψ²

(2)



¹⁾e-mail: shevandrey@isp.nsc.ru

8 d(x/L)

W₀

x=Lg

254

Письма в ЖЭТФ том 109 вып. 3 - 4

2019

On-chip piezoelectric actuation of nanomechanical resonators. . .

255

to the frequency, rather than by mechanical effects. This

attenuation is caused by finite resistance of the contacts

and 2DEG, as well as by the distributed parasitic ca-

pacitance between the gate and the 2DEG, which tends

to equalize their electrical potentials. The obtained ef-

ficiencies can be considered as high in comparison to

those derived from the existing papers [5].

The buckling of the bridge affects the vibrations. As

shown in inset in Fig. 1h, the static bending changes the

modal shape Ψ(^xL ) included in Eq. (2). At a moderate

axial load T, the shape of the fundamental mode has

one peak at the beam center. According to Eq. (2), the

gate ending at the center, where^dΨdx = 0, cannot drive

the vibrations, since the bending moments piezoelectri-

cally induced in the oppositely curved regions cancel

each other. At a large T, the modal shape becomes a

function with two peaks. If the gate ends at these two

additional points, the vibrations are also suppressed.

The estimated longitudinal compression in our case is

T ≈ 1.2T_cr. The solid black line Fig.1g shows coefficient

α calculated as a function of T. It can be seen that, at

this compression, α is reduced by only 6 % in compari-

son to the case of a non-compressed beam. Thus, in our

case, the buckling influence is small and can be neglected

when estimating the actuation efficiency. However, it

would be of great importance for long and thin beams

which buckle at small critical load T_cr. Figure 1h shows

the optimal L_g maximizing the vibrations. The dashed

red line in Fig.1g shows the corresponding α values. It

can be seen that the gate shortening makes it possible

Fig. 1. (Color online) Images of the studied cantilever (a)

to largely eliminate the buckling-induced suppression.

and bridge (b). Below (c), (d) are the corresponding ampli-

The work is partially supported by Russian Foun-

tudes of the piezoelectrically-driven flexural vibrations. At

dation for Basic Research grant # 16-32-60130, State

the driving voltage of 400 mV, the doubly-clamped beam

Programme (Grant

#0306-2016-0015) and MEXT

demonstrates softening nonlinearity indicating buckling

Grant-in-Aid for Scientific Research on Innovative

(see the inset in (d)). Amplitude (e) and phase (f) of the

Areas “Science of hybrid quantum systems” (Grant #

cantilever torsional vibrations. (g) - The dependence of co-

JP15H05869 and JP15K21727). The theoretical part of

efficient α determining the vibrations amplitude on com-

work is supported by Russian Science Foundation grant

pression. The solid black curve corresponds to gate length

#18-72-10058.

Lg = L/4, and the dashed red curve is calculated for op-

Full text of the paper is published in JETP Letters

timal Lg(T ) values, shown in (h)

journal. DOI: 10.1134/S0021364019040052

Here e₁₄ is the piezoelectric constant, Q is the qual-

1. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali,

ity factor, L is the resonator length, Ω₀ is the resonant

and A. Bachtold, Nat. Nanotechnol. 7, 301 (2012).

frequency, Ψ(x) is the normalized mode shape and W

2. K. Moskovtsev and M. I. Dykman, Phys. Rev. B 95,

is the resonator width. These equations give estimates

085426 (2017).

u₀/V₀

= 1800 nmV^-1 and 160 nmV^-1 for cantilever

3. A. A. Shevyrin, A. G. Pogosov, M. V. Budantsev,

A. K. Bakarov, A. I. Toropov, S. V. Ishutkin, E. V. Shes-

and bridge, respectively. Comparing these values with

terikov, and A. S. Arakcheev, Appl. Phys. Lett. 103,

the experimentally measured responsivities, we obtain

131905 (2013).

the actuation efficiencies 13 % for the bridge and 44 %

4. Y. Okazaki, I. Mahboob, K. Onomitsu, S. Sasaki, and

for the cantilever. Their ratio is close to the resonant fre-

H. Yamaguchi, Nat. Commun. 7, 11132 (2016).

quencies inverse ratio. This speaks in favour of the fact

5. I. Mahboob, N. Perrissin, K. Nishiguchi, D. Hatanaka,

that the efficiency is largely determined by the driving

Y. Okazaki, A. Fujiwara, and H. Yamaguchi, Nano Lett.

voltage attenuation which should be also proportional

15, 2312 (2015).

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2019