Two-dimensional (2D) materials are promising for atomic-scale, ultralow-power, and highly tunable resonant nanoelectromechanical systems (NEMS) in sensing, communications, and computing. Toward these applications, a broad and controllable linear dynamic range (DR) is desirable for increasing the signal-to-noise ratio (SNR) and reliability. Here, we develop a comprehensive strain-enhanced DR model for 2D NEMS resonators, which is experimentally verified through the tuning of DRs in 2D molybdenum disulfide (MoS2) and molybdenum ditelluride (MoTe2) NEMS resonators using gate-induced strain. We find that the resonance frequency, quality factor, and nonlinear coefficient are all tuned by the gate voltage, which enhance the DR together. Through the guidance of the DR tuning model, we demonstrate DR enhancement by up to 26.9 dB (from 69.5 to 96.4 dB) in a 2D MoS2 NEMS resonator by properly tuning the gate voltage, leading to a theoretical mass resolution of 26 yg (1 yg = 10−24 g). To accurately extract the DR, we further differentiate the quality factors for thermomechanical resonances and for resonances at the largest linear amplitude. This gate-enhanced DR model is also verified using a MoTe2 resonator, with DR enhancement of 7 dB (91.2 to 98.2 dB). The results provide a promising pathway for accurately predicting and optimizing the DRs in NEMS resonators, toward enhanced sensitivity and SNR in mass sensing, radio frequency signal processing, memory, and computing applications.

1.
S.
Bertolazzi
,
J.
Brivio
, and
A.
Kis
, “
Stretching and breaking of ultrathin MoS2
,”
ACS Nano
12
,
9703
9709
(
2011
).
2.
A.
Bachtold
,
M.
Joel
, and
M. I.
Dykman
, “
Mesoscopic physics of nanomechanical systems
,”
Rev. Mod. Phys.
94
,
045005
(
2022
).
3.
B.
Xu
,
P.
Zhang
,
J.
Zhu
,
Z.
Liu
,
A.
Eichler
,
X.-Q.
Zheng
,
L.
Jaesung
,
A.
Dash
,
S.
More
,
S.
Wu
,
Y.
Wang
,
H.
Jia
,
A.
Naik
,
A.
Bachtold
,
R.
Yang
,
P. X.-L.
Feng
, and
Z.
Wang
, “
Nanomechanical resonators: Toward atomic scale
,”
ACS Nano
16
,
15545
15585
(
2022
).
4.
J.
Lee
,
Z.
Wang
,
K.
He
,
J.
Shan
, and
P. X.-L.
Feng
, “
High frequency MoS2 nanomechanical resonators
,”
ACS Nano
7
,
6086
6091
(
2013
).
5.
C.
Chen
,
S.
Rosenblatt
,
K. I.
Bolotin
,
W.
Kalb
,
P.
Kim
,
I.
Kymissis
,
H. L.
Stormer
,
T. F.
Heinz
, and
J.
Hone
, “
Performance of monolayer graphene nanomechanical resonators with electrical readout
,”
Nat. Nanotechnol.
4
,
861
867
(
2009
).
6.
Z.
Wang
,
R.
Yang
, and
P. X.-L.
Feng
, “
Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators
,”
Nanoscale
13
,
18089
18095
(
2021
).
7.
S.
Manzeli
,
D.
Dumcenco
,
G.
Migliato Marega
, and
A.
Kis
, “
Self-sensing, tunable monolayer MoS2 nanoelectromechanical resonators
,”
Nat. Commun.
10
,
4831
(
2019
).
8.
F.
Ye
,
J.
Lee
, and
P. X.-L.
Feng
, “
Glowing graphene nanoelectromechanical resonators at ultra-high temperature up to 2650 K
,” in
IEEE International Electron Devices Meeting (IEDM)
(
IEEE
,
2018
), pp.
87
90
.
9.
J.
Zhu
,
B.
Xu
,
F.
Xiao
,
Y.
Liang
,
C.
Jiao
,
J.
Li
,
Q.
Deng
,
S.
Wu
,
T.
Wen
,
S.
Pei
,
J.
Xia
, and
Z.
Wang
, “
Frequency scaling, elastic transition, and broad-range frequency tuning in WSe2 nanomechanical resonators
,”
Nano Lett.
22
,
5107
5113
(
2022
).
10.
T.
Mei
,
J.
Lee
,
Y.
Xu
, and
P. X.-L.
Feng
, “
Frequency tuning of graphene nanoelectromechanical resonators via electrostatic gating
,”
Micromachines
9
,
312
(
2018
).
11.
X.
Song
,
M.
Oksanen
,
M. A.
Sillanpää
,
H. G.
Craighead
,
J. M.
Parpia
, and
P. J.
Hakonen
, “
Stamp transferred suspended graphene mechanical resonators for radio frequency electrical readout
,”
Nano Lett.
12
,
198
202
(
2012
).
12.
L.
Wang
,
P.
Zhang
,
Z.
Liu
,
Z.
Wang
, and
R.
Yang
, “
On-chip mechanical computing: Status, challenges, and opportunities
,”
Chip
2
,
100038
(
2023
).
13.
L.
Wei
,
X.
Kuai
,
Y.
Bao
,
J.
Wei
,
L.
Yang
,
P.
Song
, and
X.
Wang
, “
The recent progress of MEMS/NEMS resonators
,”
Micromachines
12
,
724
(
2021
).
14.
R. D.
Alba
,
F.
Massel
,
I. R.
Storch
,
T. S.
Abhilash
,
A.
Hui
,
P. L.
McEuen
,
H. G.
Craighead
, and
J. M.
Parpia
, “
Tunable phonon-cavity coupling in graphene membranes
,”
Nat. Nanotechnol.
11
,
741
746
(
2016
).
15.
J. P. R.
Mathew
,
N.
Patel
,
A.
Borah
,
R.
Vijay
, and
M. M.
Deshmukh
, “
Dynamical strong coupling and parametric amplification of mechanical modes of graphene drums
,”
Nat. Nanotechnol.
11
,
747
751
(
2016
).
16.
X.
Zhang
,
K.
Makles
,
L.
Colombier
,
D.
Metten
,
H.
Majjad
,
P.
Verlot
, and
S.
Berciaud
, “
Dynamically-enhanced strain in atomically thin resonators
,”
Nat. Commun.
11
,
5526
(
2020
).
17.
V.
Singh
,
S. J.
Bosman
,
B. H.
Schneider
,
Y. M.
Blanter
,
A.
Castellanos-Gomez
, and
G. A.
Steele
, “
Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity
,”
Nat. Nanotechnol.
9
,
820
824
(
2014
).
18.
M.
Will
,
M.
Hamer
,
M.
Müller
,
A.
Noury
,
P.
Weber
,
A.
Bachtold
,
R. V.
Gorbachev
,
C.
Stampfer
, and
J.
Güttinger
, “
High quality factor graphene-based two-dimensional heterostructure mechanical resonator
,”
Nano Lett.
17
,
5950
5955
(
2017
).
19.
R.
Yang
,
S. E. H.
Yousuf
,
J.
Lee
,
P.
Zhang
,
Z.
Liu
, and
P. X. L.
Feng
, “
Raman spectroscopic probe for nonlinear MoS2 nanoelectromechanical resonators
,”
Nano Lett.
22
,
5780
5787
(
2022
).
20.
H.
Xie
,
S.
Jiang
,
D. A.
Rhodes
,
J. C.
Hone
,
J.
Shan
, and
K. F.
Mak
, “
Tunable exciton-optomechanical coupling in suspended monolayer MoSe2
,”
Nano Lett.
21
,
2538
–−
2543
(
2021
).
21.
M.
Muruganathan
,
F.
Seto
, and
H.
Mizuta
, “
Graphene nanomechanical resonator mass sensing of mixed H2/Ar gas
,”
Int. J. Autom. Technol.
12
,
24
28
(
2018
).
22.
D.-H.
Shin
,
H.
Kim
,
S. H.
Kim
,
H.
Cheong
,
P. G.
Steeneken
,
C.
Joo
, and
S. W.
Lee
, “
Graphene nano-electromechanical mass sensor with high resolution at room temperature
,”
iScience
26
,
105958
(
2023
).
23.
P.
Weber
,
J.
Güttinger
,
A.
Noury
,
J.
Vergara-Cruz
, and
A.
Bachtold
, “
Force sensitivity of multilayer graphene optomechanical devices
,”
Nat. Commun.
7
,
12496
(
2016
).
24.
R.
Yang
,
Z.
Wang
, and
P. X.-L.
Feng
, “
All-electrical readout of atomically-thin MoS2 nanoelectromechanical resonators in the VHF band
,” in
29th International Conference on Micro Electro Mechanical Systems
(
IEEE
,
2016
), pp.
59
62
.
25.
X.
Fan
,
F.
Forsberg
,
A. D.
Smith
,
S.
Schröder
,
S.
Wagner
,
H.
Rödjegård
,
A. C.
Fischer
,
M.
Östling
,
M. C.
Lemme
, and
F.
Niklaus
, “
Graphene ribbons with suspended masses as transducers in ultra-small nanoelectromechanical accelerometers
,”
Nat. Electron.
2
,
394
404
(
2019
).
26.
J. N.
Kirchhof
,
Y.
Yu
,
D.
Yagodkin
,
N.
Stetzuhn
,
D. B.
de Araújo
,
K.
Kanellopulos
,
S.
Manas-Valero
,
E.
Coronado
,
H.
van der Zant
,
S.
Reich
,
S.
Schmid
, and
K. I.
Bolotin
, “
Nanomechanical absorption spectroscopy of 2D materials with femtowatt sensitivity
,”
2D Mater.
10
,
035012
(
2023
).
27.
M.
Kumar
and
H.
Bhaskaran
, “
Ultrasensitive room-temperature piezoresistive transduction in graphene-based nanoelectromechanical systems
,”
Nano Lett.
15
,
2562
2567
(
2015
).
28.
A.
Blaikie
,
D.
Miller
, and
B. J.
Alemán
, “
A fast and sensitive room-temperature graphene nanomechanical bolometer
,”
Nat. Commun.
10
,
4726
(
2019
).
29.
C.
Chen
,
S.
Lee
,
V. V.
Deshpande
,
G.-H.
Lee
,
M.
Lekas
,
K.
Shepard
, and
J.
Hone
, “
Graphene mechanical oscillators with tunable frequency
,”
Nat. Nanotechnol.
8
,
923
927
(
2013
).
30.
J.
Lee
and
P. X.-L.
Feng
, “
Self-sustaining MoS2 nanomechanical oscillators and feedback cooling
,”
Appl. Phys. Lett.
119
,
243506
(
2021
).
31.
P.
Zhang
,
Y.
Jia
,
Z.
Liu
,
Y.
Zhang
,
M.
Xie
, and
R.
Yang
, “
Nanoelectromechanical memories based on nonlinear 2D MoS2 resonators
,” in
35th International Conference on Micro Electro Mechanical Systems
(
IEEE
,
2022
), pp.
208
211
.
32.
A.
Dash
,
S. K.
More
,
N.
Arora
, and
A. K.
Naik
, “
Ultra-sensitive charge detection and latch memory using MoS2-nanoresonator-based bifurcation amplifiers
,”
Appl. Phys. Lett.
118
,
053105
(
2021
).
33.
K. L.
Ekinci
,
Y. T.
Yang
, and
M. L.
Roukes
, “
Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems
,”
J. Appl. Phys.
95
,
2682
2689
(
2004
).
34.
S. K.
Roy
,
V. T. K.
Sauer
,
J. N.
Westwood-Bachman
,
A.
Venkatasubramanian
, and
W. K.
Hiebert
, “
Improving mechanical sensor performance through larger damping
,”
Science
360
,
eaar5220
(
2018
).
35.
M. M.
Parmar
,
P. R. Y.
Gangavarapu
, and
A. K.
Naik
, “
Dynamic range tuning of graphene nanoresonators
,”
Appl. Phys. Lett.
107
,
113108
(
2015
).
36.
P.
Zhang
,
Y.
Jia
,
Z.
Liu
,
X.
Zhou
,
D.
Xiao
,
Y.
Chen
,
H.
Jiao
, and
R.
Yang
, “
Probing linear to nonlinear damping in 2D semiconductor nanoelectromechanical resonators toward a unified quality factor model
,”
Nano Lett.
23
,
9375
9382
(
2023
).
37.
T.
Kaisar
,
J.
Lee
,
D.
Li
,
S. W.
Shaw
, and
P. X.-L.
Feng
, “
Nonlinear stiffness and nonlinear damping in atomically thin MoS2 nanomechanical resonators
,”
Nano Lett.
22
,
9831
–−
9838
(
2022
).
38.
A.
Eichler
,
J.
Moser
,
J.
Chaste
,
M.
Zdrojek
,
I.
Wilson-Rae
, and
A.
Bachtold
, “
Nonlinear stiffness and nonlinear damping in atomically thin MoS2 nanomechanical resonators
,”
Nat. Nanotechnol.
6
,
339
–−
342
(
2011
).
39.
J.
Molina
,
J. E.
Escobar
,
D.
Ramos
,
E.
Gil-Santos
,
J. J.
Ruz
,
J.
Tamayo
,
Á.
San Paulo
, and
M.
Calleja
, “
High dynamic range nanowire resonators
,”
Nano Lett.
21
,
6617
6624
(
2021
).
40.
H. W. C.
Postma
,
I.
Kozinsky
,
A.
Husain
, and
M. L.
Roukes
, “
Dynamic range of nanotube- and nanowire-based electromechanical systems
,”
Appl. Phys. Lett.
86
,
223105
(
2005
).
41.
J.
Lee
,
Z.
Wang
,
K.
He
,
R.
Yang
,
J.
Shan
, and
P. X.-L.
Feng
, “
Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range
,”
Sci. Adv.
4
,
eaao6653
(
2018
).
42.
P.
Zhang
,
Y.
Jia
,
M.
Xie
,
Z.
Liu
,
S.
Sheng
,
J.
Wei
, and
R.
Yang
, “
Strain-modulated dissipation in two-dimensional molybdenum disulfide nanoelectromechanical resonators
,”
ACS Nano
16
,
2261
2270
(
2022
).
43.
P.
Zhang
,
Y.
Jia
,
S.
Shen
, and
R.
Yang
, “
Strain-modulated equivalent circuit model and dissipation model for 2D MoS2 NEMS resonators
,” in
34th International Conference on Micro Electro Mechanical Systems
(
IEEE
,
2021
), pp.
658
661
.
44.
C.
Samanta
,
N.
Arora
,
V.
Kumar
,
S.
Raghavan
, and
A. K.
Naik
, “
The effect of strain on effective Duffing nonlinearity in the CVD-MoS2 resonator
,”
Nanoscale
11
,
8394
8401
(
2019
).
45.
J.
Zhu
,
P.
Zhang
,
R.
Yang
, and
Z.
Wang
, “
Analyzing electrostatic modulation of signal transduction efficiency in MoS2 nanoelectromechanical resonators with interferometric readout
,”
Sci. China Inf. Sci.
65
,
122409
(
2022
).
46.
I. M.
Datye
,
A.
Daus
,
R. W.
Grady
,
K.
Brenner
,
S.
Vaziri
, and
E.
Pop
, “
Strain-enhanced mobility of monolayer MoS2
,”
Nano Lett.
22
,
8052
8059
(
2022
).
47.
M.
Manzeli
,
A.
Allain
,
A.
Ghadimi
, and
A.
Kis
, “
Piezoresistivity and strain-induced band gap tuning in atomically thin MoS2
,”
Nano Lett.
15
,
5330
5335
(
2015
).
48.
R.
Yang
,
A.
Islam
, and
P. X.-L.
Feng
, “
Electromechanical coupling and design considerations in single-layer MoS2 suspended-channel transistors and resonators
,”
Nanoscale
7
,
19921
19929
(
2015
).
49.
R.
Yang
,
X.-Q.
Zheng
,
Z.
Wang
,
C. J.
Miller
, and
P. X.-L.
Feng
, “
Multilayer MoS2 transistors enabled by a facile dry-transfer technique and thermal annealing
,”
J. Vac. Sci. Technol. B
32
,
061203
(
2014
).
50.
A. M.
Van der Zande
,
R. A.
Barton
,
J. S.
Alden
,
C. S.
Ruiz-Vargas
,
W. S.
Whitney
,
P. H. Q.
Pham
,
J.
Park
,
J. M.
Parpia
,
H. G.
Craighead
, and
P. L.
McEuen
, “
Large-scale arrays of single-layer graphene resonators
,”
Nano Lett.
10
,
4869
4873
(
2010
).
51.
L.
Kumar
,
L. V.
Jenni
,
M.
Haluska
,
C.
Roman
, and
C.
Hierold
, “
Mechanical stress relaxation in adhesively clamped carbon nanotube resonators
,”
AIP Adv.
8
,
025118
(
2018
).
52.
X.
Yao
,
D.
Hoch
, and
M.
Poot
, “
Relaxation and dynamics of stressed predisplaced string resonators
,”
Phys. Rev. B
106
,
174109
(
2022
).
53.
P.
Hernández López
,
S.
Heeg
,
C.
Schattauer
,
S.
Kovalchuk
,
A.
Kumar
,
D. J.
Bock
,
J. N.
Bolotin
,
B.
Kirchhof
,
K.
Höfer
,
D.
Greben
,
L.
Yagodkin
,
F.
Linhart
,
F.
Libish
, and
K. I.
Bolotin
, “
Strain control of hybridization between dark and localized excitons in a 2D semiconductor
,”
Nat. Commun.
13
,
7691
(
2022
).
54.
Y.
Xie
,
J.
Lee
,
Y.
Wang
, and
P. X.-L.
Feng
, “
Straining and tuning atomic layer nanoelectromechanical resonators via comb-drive MEMS actuators
,”
Adv. Mater. Technol.
6
,
2000794
(
2021
).
55.
A.
Chiout
,
C.
Brochard-Richard
,
L.
Marty
,
N.
Bendiab
,
M. Q.
Zhao
,
A. C.
Johnson
,
F.
Oehler
,
A.
Ouerghi
, and
J.
Chaste
, “
Extreme mechanical tunability in suspended MoS2 resonator controlled by Joule heating
,”
npj 2D Mater. Appl.
7
,
20
(
2023
).
56.
I.
Kozinsky
,
H. W. C.
Postma
,
I.
Bargatin
, and
M. L.
Roukes
, “
Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators
,”
Appl. Phys. Lett.
88
,
253101
(
2006
).
57.
Z.
Wang
and
P. X.-L.
Feng
, “
Dynamic range of atomically thin vibrating nanomechanical resonators
,”
Appl. Phys. Lett.
104
,
103109
(
2014
).
58.
S.
Schmid
,
K. D.
Jensen
,
K. H.
Nielsen
, and
A.
Boisen
, “
Damping mechanisms in high-Q micro and nanomechanical string resonators
,”
Phys. Rev. B
84
,
165307
(
2011
).
59.
R. J.
Dolleman
,
P.
Belardinelli
,
S.
Houri
,
H. S. J.
van der Zant
,
F.
Alijani
, and
P. G.
Steeneken
, “
High-frequency stochastic switching of graphene resonators near room temperature
,”
Nano Lett.
19
,
1282
1288
(
2019
).

Supplementary Material

You do not currently have access to this content.