We have fabricated doubly clamped beams from GaAs/AlGaAs quantum-well heterostructures containing a high-mobility two-dimensional electron gas (2DEG). Applying an rf drive to in-plane side gates excites the beam's mechanical resonance through a dipole–dipole mechanism. Sensitive high-frequency displacement transduction is achieved by measuring the ac emf developed across the 2DEG in the presence of a constant dc sense current. The high mobility of the incorporated 2DEG provides low-noise, low-power, and high-gain electromechanical displacement sensing through combined piezoelectric and piezoresistive mechanisms

Bichler, M.

Huang, X. M. H.

Roukes, M. L.

Tang, H. X.

Wegscheider, W.

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 20 11 NOVEMBER 2002Two-dimensional electron-gas actuation and transduction for GaAs
nanoelectromechanical systems
H. X. Tang, X. M. H. Huang, and M. L. Roukesa)
Condensed Matter Physics 114-36, California Institute of Technology, Pasadena, California 91125
M. Bichlerb) and W. Wegscheider
Institut fu¨r Experimentelle und Angewandte Physik, Universita¨t Regensburg, D-93040 Regensburg, Germany
~Received 7 March 2002; accepted 30 August 2002!
We have fabricated doubly clamped beams from GaAs/AlGaAs quantum-well heterostructures
containing a high-mobility two-dimensional electron gas ~2DEG!. Applying an rf drive to in-plane
side gates excites the beam’s mechanical resonance through a dipole–dipole mechanism. Sensitive
high-frequency displacement transduction is achieved by measuring the ac emf developed across the
2DEG in the presence of a constant dc sense current. The high mobility of the incorporated 2DEG
provides low-noise, low-power, and high-gain electromechanical displacement sensing through
combined piezoelectric and piezoresistive mechanisms. © 2002 American Institute of Physics.
@DOI: 10.1063/1.1516237#Thin, suspended two-dimensional electron gas ~2DEG!
heterostructures have been recently perfected, and have sub-
sequently been employed for nanoscale conducting
devices.1,2 In this letter, we present a high-resolution dis-
placement readout that is based upon our ability to achieve
very high mobility suspended quantum wires. Molecular
beam epitaxial ~MBE! grown materials are directly patterned
and in-plane gates are used to excite the vibration. No met-
allization is needed, hence high Q values can be obtained.
The starting material was a specially designed, MBE-
grown, 2DEG heterostructure similar to that used in Ref. 1.
The structural layer stack comprises seven individual layers
having a total thickness of 115 nm. The top and bottom are
thin GaAs cap layers preventing oxidation of the
Al0.3Ga0.7As:Si donor layers in between. The central 10-nm-
thick GaAs layer forms a quantum well sustaining a high
mobility 2DEG located 37 nm below the top surface and
surrounded by two AlGaAs spacer layers. Below the struc-
tural layer stack is a 400 nm Al0.8Ga0.2As sacrificial layer.
The structure was intentionally made asymmetric to avoid
neutralizing the piezoelectric effect of GaAs.
After ohmic contacts were deposited, a thick layer of
poly-methyl-methacrylate ~PMMA! is spun on the chip, fol-
lowed by a single electron-beam lithography step to expose
trenches in PMMA that isolate the beam from its side gates.
PMMA was then employed as a direct mask against a low
voltage electron cyclotron reactor etch performed to further
etch the trenches to the sacrificial layer. After stripping off
the PMMA, final structure relief is achieved by removing the
sacrificial layer beneath the beams with diluted HF. To mini-
mize the damage to the 2DEG from dry etching, a Cl2 /He
plasma was chosen because of its excellent etching charac-
teristics, such as smooth surface morphology and vertical
sidewall. A stable etching speed at 35Å /s is obtained under
a!Author to whom correspondence should be addressed; electronic mail:
roukes@caltech.edu
b!Walter-Schottky-Institut der Technischen Universita¨t Mu¨nchen, Am Cou-
lombwall, 85748 Garching, Germany.3870003-6951/2002/81(20)/3879/3/$19.00
Downloaded 25 Feb 2006 to 131.215.240.9. Redistribution subject toconditions of less than 150 V self-bias ~20 W constant rf
power!, Cl2 and He flow rate ratio 1:9, 3 mTorr pressure, and
300 W microwave power. With the same method, we have
also fabricated suspended Hall bars and extensively charac-
terized the resulting suspended 2DEG. Before processing,
the initial mobility and density after illumination are 5.1
3105 cm2/Vs, 1.2631012 cm22, respectively. With our im-
proved low damage etching, the mobility can be maintained
at 2.03105 cm2/Vs, while the electron density is somewhat
reduced to 4.531011 cm22. We observed well-developed
quantum Hall plateaus in the etched structure even with
channel width as small as 0.35 mm. In longitudinal resistance
measurements, we detected a low field maximum, corre-
sponding to maximal boundary scattering when the electron
cyclotron motion diameter matches the electrical width of
the suspended wire.3 From the position of this peak, we are
able to deduce the depletion to be 0.1 mm on each side of the
wire. We also confirmed ballistic behavior of electrons from
transport measurement on the Hall cross-junction. Both ‘‘last
Hall plateau’’ and ‘‘negative bendresistance’’ 4 are present in
all of the devices. The transport mean free path was found to
be approximately 2 mm.
A typical device is shown in Fig. 1. The beams are 0.5
mm wide and 6 mm long, having a calculated spring constant
of 0.25 N/m. When cooled to liquid helium temperature,
their two-terminal resistance is about 100 kV. After illumi-
nation, this drops to about 5 kV ~including contact and lead
resistances!. The electrical width of the beam is about 0.3
mm with Rh5170 V .
In nanoelectromechanical system ~NEMS!, both the in-
duction and the detection of motion pose important chal-
lenges. In our devices, the actuation is relatively trivial and
very effective. The rf drive is supplied directly to one of the
side gates, which is a large area of 2DEG connected to the
output of a network analyzer through alloyed ohmic contact.
All the trenches have a width of 0.5 mm. The devices are first
measured at 4.2 K in vacuum. A constant dc sensing current
ranging from 0 to 26 mA is supplied to the vibrating beam
through a 10 mH rf choke, whose value is chosen large9 © 2002 American Institute of Physics
 AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
3880 Appl. Phys. Lett., Vol. 81, No. 20, 11 November 2002 Tang et al.enough to avoid loss of the small signal that is induced. The
oscillatory signal is picked up by a low temperature amplifier
placed in close proximity to the device. Before connecting
the signal to the input of the network analyzer, a room tem-
perature amplifier is used to improve signal-to-noise ratio.
The combined amplifiers have a voltage gain of about 200 in
the frequency range of these experiments.
We observed a very strong signal around the first me-
chanical resonance. The magnitude response curves at vari-
ous driving amplitudes are shown in Fig. 2~a!. Calculations
confirm this resonance corresponds to the first out-of-plane
vibrational mode. When the drive amplitude is increased
above 45 mV, the response curve becomes nonlinear and
assumes an asymmetric shape. In the linear response region,
the amplitude at resonance is proportional to the ac gate volt-
age amplitude.
To clarify the origin of the observed signal, we fixed the
drive at 10 mV and then varied the dc bias current from
226 mA to 0 and then to 26 mA. The response amplitude
versus drive amplitude at resonance is presented in Fig. 2~b!.
Two features are evident from this data. First, at the highest
currents close to 20 mA, the signal becomes saturated for two
reasons: ~a! Joule heating of the small beam, and ~b!, satu-
ration of the drift velocity at high applied electrical fields
(;15 kV/m). Second, at intermediate current the signal
strength at resonance is proportional to the dc bias current, as
indicated in the inset of Fig. 2~b!. In addition, when we re-
verse the current direction, we also find that the induced
signal changes its sign (180° phase change!. Therefore, we
conclude that the dominant contribution to the observed sig-
nal is a change of resistance due to beam vibration. This
appears to originate from both piezoresistive effect of bulk
GaAs and transverse piezoelectric charge gating of 2DEG.
Note that a small signal is observed even for zero current
bias. From the slope of the linear part in the inset of Fig.
2~b!, a nominal drive of 10 mV induces a resistance change
of about 10 V in the device.
We now estimate the sensitivity of this technique. By
looking at the critical amplitude at the onset of nonlinearity,
we can determine the amplitude of vibration of the resonat-
ing beam. This critical displacement amplitude depends only
on the geometry of the beam, and is approximately given as5
xc; (2h)/A0.5Q(12n2), where h is the thickness of the
FIG. 1. ~a! SEM image of a doubly clamped beam. The in-plane gates are
formed by the 2DEG. ~b! Sketch of measurement setup. A constant dc bias
current (Ib) is sent through a large rf choke (;10 mH). Gate drive voltage
consists of both dc and rf components: Vg5Vg(0)1vgeivt. The induced sig-
nal can be expressed as V5V (0)1veI(vt1w), where the dc voltage V (0)
5IbRdc is blocked by a capacitor C , and the oscillating component is am-
plified.Downloaded 25 Feb 2006 to 131.215.240.9. Redistribution subject tobeam in the vibration direction, and n is Poisson’s ratio for
GaAs. Plugging in measured values of Q52600 and n
50.31, we obtain xc56 nm, which is attained at a drive
level of about 45 mV. The minimum resolvable signal is
achieved at 0.1 mV drive and about 5 mA sensing current.
Hence, at the highest possible current of 20 mA, we can
detect a resonance at xc/450/450.03 Å, or 3
31023 Å/AHz, which is consistent with our estimate based
on Johnson noise from beam resistance at 4.2 K. The corre-
sponding force sensitivity is 75 fN/AHz, comparable with
previous schemes to detect small NEMS resonators by opti-
cal interferometry6 and the magnetomotive method.7 The re-
quired force to drive the beam to the nonlinearity threshold is
1.5 nN. The displacement resolution can be improved by
using 2DEG heterostructures with even higher mobility, or
by operating at ;100 mK with a state-of-the-art low tem-
perature preamplifier.
Note that in Fig. 2, all the driving force results from the
applied ac gate voltage. We did not find any significant
change of resonant frequency or magnitude with dc bias on
the gate. This is indicative of a coupling mechanism different
from electrostatic force between the gates and the beam.
Electrostatic force is proportional to the product of dc and ac
components of gate potential so that the response should
directly scale with the dc gate voltage.8 This assumes a direct
Coulomb interaction between coupling plates. In our in-
plane-gate configuration, the net charge on the beam is
C(Vg(0)1vgeivt). The capacitance between coplanar 2DEG
areas has an estimated value of 18 aF/mm,9 which is very
small compared to parallel plates. With a nominal 1 V dc
gate voltage, there are only a few hundred induced electron
charges on the beam. The upper bound of the electric field
FIG. 2. Voltage drop across the beam as it is driven to its lowest mechanical
resonance with increasing drive amplitudes. The dc bias current is fixed at 5
mA. Inset: The peak response as a function of driving amplitude in the linear
regime. ~b! Magnitude response vs dc bias current. Inset: The signal ampli-
tude at resonance with sensing current increased from 226 to 26 mA. AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
3881Appl. Phys. Lett., Vol. 81, No. 20, 11 November 2002 Tang et al.applied on the gate is (Vg(0)1vgeivt)/d , d is the beam–gate
separation ~Fig. 3!. Thus, the total electrostatic force applied
on the beam with angular frequency v is f
5CVg
(0)vge
ivt/d . Only a projection of this force drives the
beam along the out-of-plane (y) direction. A reasonable es-
timate of the effective y-component of this force is
f y5CVg(0)vgeivty0 /d2, ~1!
where y0 is a static offset due to, for example, uncontrolled
asymmetry of suspended beam. A 10 nm misalignment of the
beam with respect to gate should be observable in our de-
vices ~but is not seen!. Therefore, we take this number as the
upper limit in our estimation of y0 . At a nominal 1 V dc gate
voltage, 45 mV ac gate voltage, the force originating from
the electrostatic drive mechanism is calculated to be f y
’0.2 pN. This is four orders of magnitude smaller than the
force required to drive the beam into nonlinear response.
Given the absence of direct electrostatic forces, we pro-
pose a new driving mechanism, a short–range dipole-dipole
interaction. This dipole–dipole interaction potential can be
expressed as U5*(1/4p«0) (p2dp1/r3) , which can be un-
derstood as rf coupling between two dipole moments dp1
and p2 . Here dp1 is the dipole momentum of a slice of the
gate, dp15«r«0Lvgeivtdr , and p2 is the fixed dipole mo-
ment due to the piezoelectric effect within the strained beam.
y is the beam displacement, p253EdAwt2y /L , and L , w ,
and t are beam length, width and thickness, respectively
~Fig. 3!. «r is dielectric constant of GaAs. Here, E
;85 Gpa is Young’s modulus and dA;3.8 pC/N is the pi-
ezoelectric constant of AlGaAs.10 The resulting force along y
direction is
f y5
]U
]y 5
3«r
4p ~EdA!S wt
2
d2 D vgeivt. ~2!
This dynamic force is independent of the dc gate voltage,
consistent with our observation. After structural relief, the
suspended beams are intrinsically stressed due to the hetero-
structure’s asymmetry and other factors. Therefore, a static
dipole moment exists on the beam and yields the out-of-
plane vibration. At 45 mV ac gate voltage drive, f y is esti-
mated to be 1.2 nN from this mechanism, four orders of
magnitude higher than the direct Coulomb interaction. This
is consistent with the force we observe at the onset of non-
linearity. Because of its short-range characteristics, this
dipole–dipole interaction is unique to NEMS and is insig-
nificant in microelectromechanical systems.
FIG. 3. A cross-sectional schematic of the dipolar actuation mechanism,
showing dipole formation on the beam (p1) and on the driving gate (dp2).Downloaded 25 Feb 2006 to 131.215.240.9. Redistribution subject toWe have also studied the temperature dependence of our
strain sensitive devices. Measurements were performed at
three different temperatures in vacuum. The results are
shown in Fig. 4. The devices perform exceptionally well at
liquid helium and nitrogen temperatures, but at room tem-
perature, the response is diminished. The decay of signal
strength with temperature can be attributed to the significant
reduction of 2DEG mobility. At elevated temperature the in-
creased two-terminal beam resistance acts as a large voltage
divider, and only a small fraction of induced signal voltage is
available.
We gratefully acknowledge support from DARPA,
through Grant No. DABT63-98-1-0012, and the NSF via
grant ECS-0089061. We also thank F. G. Monzon and J.
Casey for early contributions to this work, and J. Y. T. Yang
and K. Cooper for help with the low temperature amplifier.
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FIG. 4. ~a! SEM image of a doubly clamped beam. The in-plane gates are
formed by the 2DEG. ~b! Sketch of measurement setup. A constant dc bias
current (Ib) is sent through a large rf choke (;10 mH) before reaching the
beam. Gate drive voltage consists of both dc and rf components: Vg5Vg(0)
1vge
ivt
. The induced signal can be expressed as V5V (0)1veI(vt1w),
where the dc voltage potential V (0)5IbRdc is blocked by a capacitor C , and
the oscillating component is amplified at both liquid helium and room tem-
perature. AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp


Two-dimensional electron-gas actuation and transduction for GaAs nanoelectromechanical systems

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Two-dimensional electron-gas actuation and transduction for GaAs nanoelectromechanical systems

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