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High Q electromechanics with InAs nanowire quantum dotsHari S. Solanki, Shamashis Sengupta, Sudipta Dubey, Vibhor Singh, Sajal Dhara et al. Citation: Appl. Phys. Lett. 99, 213104 (2011); doi: 10.1063/1.3663631 View online: http://dx.doi.org/10.1063/1.3663631 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i21 Published by the American Institute of Physics. Related ArticlesInfluence of the temperature dependent nonlinearities on the performance of micromechanical resonators Appl. Phys. Lett. 99, 194102 (2011) High-Q silica microcavities on a chip: From microtoroid to microsphere Appl. Phys. Lett. 99, 181123 (2011) Surface chemical modification for exceptional wear life of MEMS materials AIP Advances 1, 042141 (2011) Localized non-contact manipulation using artificial bacterial flagella Appl. Phys. Lett. 99, 174101 (2011) Mass sensing based on a circuit cavity electromechanical system J. Appl. Phys. 110, 083107 (2011) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors
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High Q electromechanics with InAs nanowire quantum dots
Hari S. Solanki,1,a) Shamashis Sengupta,1,b) Sudipta Dubey,1 Vibhor Singh,1 Sajal Dhara,1
Anil Kumar,1 Arnab Bhattacharya,1 S. Ramakrishnan,1 Aashish A. Clerk,2,c)
and Mandar M. Deshmukh1
1Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research,Homi Bhabha Road, Mumbai 400005, India2Department of Physics, McGill University, Montreal, Quebec, Canada H3A 2T8
(Received 11 August 2011; accepted 31 October 2011; published online 22 November 2011)
In this report, we study electromechanical properties of suspended InAs nanowire resonators. At
low temperatures, the nanowire acts as the island of a single electron transistor, and a strong
coupling between electron transport and mechanical modes is observed for resonant mechanical
driving. Further, as a function of the mechanical drive frequency, the conductance exhibits a Fano
lineshape. This arises from the interference between two contributions to potential of the single
electron transistor coming from capacitively induced charges and the mechanical oscillation. The
quality factor (Q) of these devices is �105 at 100 mK. VC 2011 American Institute of Physics.
[doi:10.1063/1.3663631]
Nano electromechanical systems (NEMS) are of interest
for single charge,1 single spin,2 and spin torque3 detection
studies as well as to measure mass4–6 and forces.7,8 NEMS
have also demonstrated continuous position measurements
near the fundamental limits set by the uncertainty princi-
ple.7,9 All these experiments require both a strong electrome-
chanical coupling between mechanical motion and electronic
degrees of freedom as well as low-dissipation mechanical
resonances; achieving both these goals in the same system
can be challenging. We demonstrate both these features
(strong electromechanical coupling and high mechanical Q)
in an InAs nanowire (NW) resonator.
High Q is the key to achieving high NEMS sensitivity.
Researchers have measured Q� 105 at low temperatures
using carbon nanotubes and graphene10,11 as an active part
of the NEMS. In comparison to carbon nanotubes and gra-
phene, NWs offer a unique possibility to control dimensions,
composition, and doping during the growth process. InAs is
known for its high electron mobility12 and strong spin-orbit
interaction,13 which makes it a promising material for high
speed electronic and spintronic devices. The InAs resonators
in our experiments have a Q value of �105 at 100 mK. At
low temperatures, the wire acts as a single-electron transis-
tor, and we observe sequential single electron tunneling
while the wire resonates. The mechanical motion causes a
modification of Coulomb blockade current peaks; we discuss
and analyze this in detail in what follows. Further, we find
that the tunneling at a Coulomb blockade current peak results
in an appreciable reduction of the mechanical resonant fre-
quency. Both these features are indicative of a strong cou-
pling between electron transport and mechanical degrees of
freedom. In addition, we observe Fano resonances in the
conductance as a function of mechanical driving frequency;
these result from an interference between the change in con-
ductance due to mechanical motion of the wire and a direct
electrostatic gating. These resonances are in good quantita-
tive agreement with a simple model describing this
interference.
Our InAs NWs are 50–150 nm in diameter and a few lm
long.14 We fabricate suspended single InAs NW resonator
devices in a field effect transistor (FET) geometry.15 Fig. 1(a)
shows a typical device, where a NW of length �3 lm and di-
ameter �80 nm is suspended �200 nm above the substrate
(the capacitance between the NW and the gate is �65 aF).
Fig. 1(b) shows the conductance variation with applied DC
gate voltage ðVDCg Þ displaying FET behavior at room tempera-
ture and low temperature. Room temperature measurements
of mechanical resonance are done using a heterodyne mixing
technique.14–17 Voltages of two different frequencies,
(xþDx) and x, are applied to the source and gate, respec-
tively. Consequently, the current through the device has dif-
ferent frequency components. The component at the
difference frequency (Dx) is called the mixing current (Imix),
and its magnitude depends upon the amplitude of mechanical
motion. Imix ¼ dGdVgðAnx þ BÞ, where G is the conductance, Vg
Vsd
I
Vg
Gate Voltage (V)-30 -15 0 15 30
32
27
22Freq
uenc
y (M
Hz)
Gate Voltage (V)
1
15
I mix(n
A)
(a)
Con
duct
ance
(µS) 60
40
20
0-30 -15 0 15 30
at 5 K at 300 K
(b)
8
(c)
FIG. 1. (Color online) (a) Scanning electron microscope image of a typical
device with circuit diagram used for characterization (scale bar corresponds
to 1 lm). (b) Tunability of NW transistor’s conductance as a function of
VDCg at two temperatures. (c) 2D plot of mixing current shows dispersion of
resonant frequency with VDCg at room temperature.
a)Electronic mail: [email protected])Electronic mail: [email protected])Electronic mail: [email protected].
0003-6951/2011/99(21)/213104/3/$30.00 VC 2011 American Institute of Physics99, 213104-1
APPLIED PHYSICS LETTERS 99, 213104 (2011)
Downloaded 22 Nov 2011 to 132.206.186.62. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
the gate voltage, nx the amplitude of mechanical oscillation at
driving frequency, x, applied to gate, and A and B are factors
depending upon the magnitude of voltages applied to the
source and drain. Imix as a function of actuating frequency (x)
shows a sharp change at mechanical resonance due to a large
amplitude of motion allowing us to track the electromechani-
cal resonance. Fig. 1(c) shows a 2D plot of Imix as a function
of frequency (x/2p) and VDCg at 300 K. We observed a non-
monotonic dependence of mechanical resonant frequency of
the NW on VDCg as well as mode mixing14 similar to an earlier
report.15 The estimated resonant frequency (using beam equa-
tion14) of our typical device is�28 MHz.
At low temperatures, the resonant frequency of the devices
increases, as expected. This is due to the variation in tension
that results from the relative contraction of NW and metal elec-
trodes. This has been seen in other NEMS devices as well.18
Fig. 2(a) (data from device 1) shows a 2D plot of mixing cur-
rent as a function of driving frequency (x/2p) and VDCg at 5 K.
We observe that at low temperatures, resonance features cannot
be detected using the mixing technique after the NW FET turns
off (towards the left of sharp vertical line in Fig. 2(a) around
��20 V). This vertical line is a natural consequence of the
mixing current being proportional to the change in conductance
with gate voltage.15,16 As the gate voltage is swept from the
off-state to the on-state of the device, the conductance changes
from a negligibly small value to a large value. This leads to
negligible mixing current below the on-off transition of the de-
vice. Fig. 2(b) shows a slice of the data shown in Fig. 2(a) at
VDCg ¼ �4 V and fit that gives a quality factor of 8709 at 5 K.
Typically, for all our devices, the Q increases by two orders of
magnitude from 300 K (Q� 100) to 5 K (Q� 10 000).
In addition, at low temperatures, our system acts as a
quantum dot, exhibiting familiar Coulomb blockade features
(Fig. 2(c), data taken on device 2). At Coulomb blockade
peaks, current flows through the NW by sequential single
electron tunneling.19,20 Fig. 2(d) shows Coulomb diamonds
in the current through the NW as a function of source-drain
and gate voltages. From the Coulomb diamonds (Fig. 2(d)),
the charging energy is estimated to be �1 meV at 100 mK.
From Fig. 2(a), we see that these NW devices are
mechanically resonating and also, from Figs. 2(c) and 2(d),
they act as single electron transistors (SETs). Combining
these two effects allow us to study the coupling between me-
chanical and charge degrees of freedom.19,20 First, we use a
rectification technique19,21 to probe Coulomb blockade
physics at mechanical resonance.14 Fig. 3(a) shows a 2D plot
of conductance through the device at a small bias voltage
(Vsd¼ 100 lV) at 1.4 K with VDCg and frequency (x/2p) of
mechanical driving signal (this figure shows data from de-
vice 1). In Fig. 3(a), shading indicates the region where the
driving frequency is approximately resonant with the me-
chanical motion; note that this line is not horizontal because
of the frequency pulling effect previously described (see
Figs. 1(c) and 2(a)). We also use vertical dashed lines to
indicate the position of Coulomb blockade current resonan-
ces. The Coulomb blockade resonances are strongly modi-
fied when the mechanical driving frequency (x) equals the
resonant frequency of the NW. Due to mechanical reso-
nance, the Coulomb peaks become broader irrespective of
frequency and gate voltage sweep direction. We now show
that this can be fully accounted for using a simple model.
As the wire oscillates, its capacitive coupling with the
back gate also changes at the same frequency, thereby modu-
lating the dimensionless gate voltage (or number of induced
carriers) N in the wire.
NðtÞ ¼ CgðtÞVgðtÞ=e ¼ N0 þ dNðtÞ;
Gtotal ¼ G0 þ Grect ’ G0 þ1
2
d2G
dN2ðdNðtÞÞ2;
(1)
Freq
uenc
y (M
Hz)
Gate Voltage (V)
0.5
0.4
0.3
37.637.537.4Frequency (MHz)
I mix(n
A)
0.2
1.5
2.8
-20 0 20
37.5
36.5
35.5
Q = 8709
(b)
-940 -930 -920
2
0
-2-9
-4
1
Log(
|Cur
rent
(nA
)|)
Gate Voltage (mV)
Vsd
(mV
)
180
110
40Cur
rent
(pA
)
-940 -930 -920Gate Voltage (mV)
(c)
(a)
(d)
FIG. 2. (Color online) (a) 2D mixing current plot as a function of driving
frequency and VDCg at 5 K. This is data from device 1. (b) Line plot of mixing
current as a function of driving frequency from (a). Shows Q of device to be
8709 at 5 K and VDCg ¼ �4V. (c) Coulomb blockade peaks in current
through the NW which corresponds to sequential single electron tunneling at
100 mK. This is data from device 2. (d) 2D plot of DC current (on loge scale)
with source-drain voltage Vsd and VDCg (Coulomb diamonds). Charging
energy of the system �1 meV at 100 mK.
-21.40 -21.14 -20.88
39.32
39.26
39.20
Gate Voltage (V)
Freq
uenc
y (M
Hz)
0.10
0.65
1.20
-920 -910 -900
53.688
53.684
53.680
Gate Voltage (mV)
-10
03
16
29
Cur
rent
(pA
)
Q = 96073
16
14
12
108
20-2
Freq
uenc
y (M
Hz)
Frequency (f-f0, kHz)
(d)
0.17
0.12
0.07Con
duct
ance
(µS)
39.3239.2639.20Frequency (MHz)
(b)(a)Q = 822
qx = -1.9± 28
± 0.1
± 7140
(c)
FIG. 3. (Color online) (a) Plot of the rectified signal through the device as a
function of driving frequency and VDCg at 1.4 K. This is data from device 1.
(b) Line plot of conductance of the device as a function of frequency at fixed
VDCg (�21.36 V) (shown by a vertical dotted line in (a)). On the left and right
sides, far from the resonant frequency, rectification signal is not same. Blue
trace shows the fitting for Fano resonance. Right at Coulomb blockade peak
Q reduces to �800 from �5000. (c) Modulated current through the device
with frequency and VDCg sweep at 100 mK temperature (this shows data
from device 2—the same device whose Coulomb blockade features have
been shown in Figs. 2(c) and 2(d)). (d) Measured Q at 100 mK and
VDCg ¼ �905:48 mV (shown by a vertical dotted line in (c)) comes out to be
�105 and resonant frequency, f0 is 53.6838 MHz.
213104-2 Solanki et al. Appl. Phys. Lett. 99, 213104 (2011)
Downloaded 22 Nov 2011 to 132.206.186.62. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
where N0 is its value at zero actuating voltage, i.e., Vac¼ 0.
The change in the number of induced carriers (N) in the QD
can be written as dN¼CdV gþVgdC, where C is the gate ca-
pacitance, Vg is the total voltage applied at the gate, and dC
is proportional to the mechanical amplitude. ðdNðtÞÞ2denotes time averaged quantities (see supplemental material
for detailed calculation14). When an ac voltage is applied to
the gate (in addition to the dc gate voltage VDCg ) and the wire
oscillates, both dVg and dC vary at the same frequency of
applied ac voltage (x). These two contributions add coher-
ently to dN(t) and contribute to the rectified conductance. As
dC will be phase shifted with respect to dVg (depending on
the detuning of the x from the mechanical resonance fre-
quency), one naturally obtains a Fano lineshape22,23:
Grectð~xÞ ¼ GD
j~x þ qx þ iqyj2
~x2 þ 1; (2)
where ~x ¼ x�x0
c=2, GD ¼ 1
2d2GdN2
C0
e
� �2jVacj2, qx ¼ � 1C0
dCdz
� �
VDCg
dFdVg
� �Q
kosc; and qy¼ 1 (the quantity (qxþ iqy) is known as
the Fano factor). Here x0 is the resonant frequency, x is the
frequency of the applied ac signal, c is the mechanical damp-
ing rate, z is the separation between NW and substrate which
depends upon the amplitude of oscillation, kosc is spring con-
stant of the resonator (kosc ¼ mx20, m is mass of resonator),
and F is the driving force on it. Fig. 3(b) shows the conduct-
ance, right at the Coulomb blockade peak, as a function of
frequency at fixed VDCg ¼ �21:36 V. By fitting Eq. (1) to
Fig. 3(b) (blue curve), we get the real part of Fano factor (qx)
as �1.9, while its calculated14 value is �2.7. There is, thus,
a good agreement between our data and calculations. Note
that as a consequence of Fano-lineshape described in Eq. (2),
the magnitude of Coulomb-blockade peak current is different
above and below the mechanical resonance (see Fig. 3(b)).
Having discussed how mechanical motion affects the
conductance of the NW, we now discuss the complementary
phenomena of how the electronic degrees of freedom affect
the mechanics (often described as “backaction”). First, we
find (similar to19,20,24) that electromechanical coupling results
in a dramatic modification of the mechanical damping. Con-
sider the Coulomb blockade peak at VDCg ¼ �21:36 V in Fig.
3(a). When the dot is tuned at this Coulomb blockade peak,
we find a mechanical Q of �800, whereas far away from any
Coulomb blockade peak, the Q is �5000. This enhanced
damping due to single-electron tunneling indicates a strong
electromechanical coupling and is expected from theory.25
In another set of complementary measurements at lower
temperatures, we measured the dependence of the mechanical
resonance frequency with VDCg using a frequency modulation
(FM) mixing technique11,26 and found a dip in the mechanical
resonant frequency at each Coulomb blockade peak. Fig. 3(c),
data from device 2, shows a 2D plot of mixing current through
the device measured using an FM technique which shows dip
in mechanical resonant frequency (this can also be seen by
subtracting the background from the data shown in Fig.
3(a)14). Similar frequency shifts, due to tunneling, have been
seen in carbon nanotubes19,20 as well. We are in a coupling re-
gime where electron tunnel rate (C) is �15 times that of me-
chanical resonance frequency of the dot. Fig. 3(d) shows a
fitting function for mixing current (using FM technique)
through the device which shows a Q of �105 at 100 mK, com-
parable to the highest Q seen in synthesized nanostructures.24
In summary, we have studied InAs NW resonator FETs.
At low temperatures, when charging energy dominates over
thermal energy, the NW acts as the island of a SET. In this re-
gime, Coulomb blockade peaks are strongly affected due to
mechanical resonance. At the same time, due to sequential
electron tunneling, the mechanical resonant frequency shifts
down at each Coulomb-blockade current peaks. Fano resonan-
ces are observed in the rectified conductance through the NW
as a function of gate-voltage frequency due to a simple classi-
cal interference effect. All these measurements suggest a
strong coupling between electron charge and mechanical
motion of the NW. The Q of these devices at low tempera-
tures is observed to be �105. Along with strong spin-orbit
interaction and a large g factor of InAs, these high Q and
strong electro-mechanical coupling devices may allow study
of coupling mechanism between spin of electron and mechan-
ical degree of freedom.
We acknowledge Government of India and
AOARD–104141 for support.
1H. Krommer, A. Erbe, A. Tilke, S. Manus, and R. H. Blick, Europhys.
Lett. 50, 101 (2000).2D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, Nature 430, 329
(2004).3G. Zolfagharkhani, A. Gaidarzhy, P. Degiovanni, S. Kettemann, P. Fulde,
and P. Mohanty, Nat Nano 3, 720 (2008).4K. Jensen, K. Kim, and A. Zettl, Nat Nano 3, 533 (2008).5B. Lassagne, D. Garcia-Sanchez, A. Aguasca, and A. Bachtold, Nano Lett.
8, 3735 (2008).6H.-Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, Nano Lett. 8,
4342 (2008).7J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K.
W. Lehnert, Nat Nano 4, 820 (2009).8H. J. Mamin and D. Rugar, Appl. Phys. Lett. 79, 3358 (2001).9T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk, and
K. C. Schwab, Nature 463, 72 (2010).10A. K. Huttel, G. A. Steele, B. Witkamp, M. Poot, L. P. Kouwenhoven, and
H. S. J. van der Zant, Nano Lett. 9, 2547 (2009).11A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, and A.
Batchtold, Nat Nano 6, 339 (2011).12S. A. Dayeh, D. P. R. Aplin, X. Zhou, P. K. L. Yu, E. T. Yu, and D. Wang,
Small 3, 326 (2007).13S. Nadj-Perge, S. M. Frolov, E. P. A. M. Bakkers, and L. P.
Kouwenhoven, Nature 468, 1084 (2010).14See supplementary material at http://dx.doi.org/10.1063/1.3663631 for
details.15H. S. Solanki, S. Sengupta, S. Dhara, V. Singh, S. Patil, R. Dhall, J. Parpia,
A. Bhattacharya, and M. M. Deshmukh, Phys. Rev. B 81, 115459 (2010).16V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T. A. Arias, and P. L.
McEuen, Nature 431, 284 (2004).17R. Knobel, C. S. Yung, and A. N. Cleland, Appl. Phys. Lett. 81, 532 (2002).18V. Singh, S. Sengupta, H. S. Solanki, R. Dhall, A. Allain, S. Dhara, P.
Pant, and M. M. Deshmukh, Nanotechnology 21, 165204 (2010).19G. A. Steele, A. K. Huttel, B. Witkamp, M. Poot, H. B. Meerwaldt, L. P.
Kouwenhoven, and H. S. J. van der Zant, Science 325, 1103 (2009).20B. Lassagne, Y. Tarakanov, J. Kinaret, D. Garcia-Sanchez, and A. Bach-
told, Science 325, 1107 (2009).21S. Rosenblatt, Pushing the Limits of Carbon Nanotube Transistors, Ph.D.
dissertation (Cornell University, 2006).22A. A. Clerk, X. Waintal, and P. W. Brouwer, Phys. Rev. Lett. 86, 4636 (2001).23D. A. Rodrigues, Phys. Rev. Lett. 102, 067202 (2009).24L. Cockins, Y. Miyahara, S. D. Bennett, A. A. Clerk, S. Studenikin, P.
Polle, A. Sachrajda, and P. Grutter, PNAS 107, 9496 (2010).25A. A. Clerk and S. Bennett, New J. Phys. 7, 238 (2005).26V. Gouttenoire, T. Barois, S. Perisanu, J.-L. Leclercq, S. T. Purcell, P.
Vincent, and A. Ayari, Small 6, 1060 (2010).
213104-3 Solanki et al. Appl. Phys. Lett. 99, 213104 (2011)
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