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S U P P O R T I N G I N F O R M A T I O N
1
Large-scale integration of nanoelectromechanical
systems for gas sensing applications
I. Bargatin
1,2†
, E.B. Myers
1
, J.S. Aldridge
1‡
, C. Marcoux
2
, P. Brianceau
2
, L. Duraffourg
2
,
E. Colinet
2
, S. Hentz
2
, P. Andreucci
2
, M.L. Roukes
1
1
Kavli Nanoscience Institute and Department of Physi
cs, Caltech, Pasadena, CA
2
CEA/LETI - MINATEC, Grenoble, France
Fabrication Procedure
The NEMS arrays employed in this work were fabricat
ed from CMOS-compatible materials
using state-of-the-art microelectronic lithography
and etching techniques with nanoscale
alignment. The high-frequency (HF) NEMS arrays were
fabricated from a 200-mm SOI
wafer with 160-nm-thick silicon layer (resistivity
10

.cm) and 400-nm-thick buried
oxide layer. The metal film — a proprietary alloy f
ully compatible with CMOS — was
deposited by sputtering technique at 175°C. Its thi
ckness varied between 45 and 70 nm
depending on the design. Optical deep ultraviolet (
248 nm wavelength) lithography was
then used to pattern the thin-film metal features:
wirebonding pads, lead-frame, and the
NEMS array itself. We were able to achieve a better
than 200-nm resolution in a
reproducible way using a positive resist and a bott
om anti-reflective coating (BARC).
The exposed areas of the metal film were etched usi
ng reactive ion etching (RIE) in boron
trichloride (BCl
3
)
and argon (Ar) plasma. The resulting metallization
layer served as a mask
for the subsequent CF
4
plasma etching of the 160-nm-thick silicon structu
ral layer down to
the buried oxide. In some designs, additional litho
graphy steps were performed to define
bare-silicon (metallization-free) areas on beams or
cantilevers before the final silicon
etching. In this case, the accuracy of alignment be
tween the lithography levels was better
than 30 nm (Fig. S1). In some designs, the metal la
yer on the bonding pads and lead-frames
was thickened to 650 nm to facilitate the wirebondi
ng procedure, decrease the access
resistance, and improve the impedance matching.
Finally, the NEMS cantilevers or beams were suspend
ed using a vapor HF etch step that was
carefully timed to minimize the undercut of the anc
hors. The arrays were typically etched
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
2
for 6 hours at 32 °C in HF vapor concentration of a
pproximately 10%, resulting in silicon
dioxide etching rate of 1.2 nm/min. The vapor HF di
d not significantly attack the metal
layer, with the etch rate being only 1nm/hour.
With this process, we were able to produce the firs
t 200-mm wafers of NEMS VLSI, each
containing more than 3.5 million NEMS. The arrays d
escribed in the main text contained 2
800 NEMS cantilevers and occupied an area 0.14 mm b
y 1.0 mm. Other arrays we fabricated
contained up to 6800 resonant NEMS cantilevers on a
rea of 0.2 mm by 0.6 mm, achieving an
integration density of approximately 60 000 NEMS/mm
², and a functional device yield of
approximately 95%.
In future designs and process runs, advanced lithog
raphy techniques can be employed to
decrease the minimum feature size of the arrays eve
n further. Modern 193-nm DUV dry
lithography can potentially achieve resolution of 7
0-80 nm on 200 mm wafers with 15 nm
overlay. Hybrid lithography that combines e-beam an
d DUV processes can achieve 50-nm
minimum feature size while keeping the total lithog
raphy process reasonably fast for 200-
mm wafers. In this process, the relatively slow e-b
eam is used to define the smallest
features, such as 50-nm-wide metallic lines, while
the fast DUV lithography defines all
larger features. Variable Shape Beam e-beam lithogr
aphy has been demonstrated to achieve
35-nm half-pitch size and overlay of between 15 and
7 nm depending on the field size. The
3.5 million NEMS of our current wafers could be wri
tten in just 3 hours (simulated writing
time). With these advanced lithography techniques,
one could achieve integration density
exceeding 100.000 NEMS/mm².
Fig. S1.
Scanning electron micrographs of fully released c
antilevers with one or two metal loops. The two-
loop type of cantilever were not used in the array
configuration, but its image illustrates the accura
cy of
the lithography process. Note that the accuracy of
mask alignment (overlay) was better than 30 nm.
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
3
Balanced two-port measurement scheme for thermoelas
tic actuation and
piezoresistive detection
The combination of thermoelastic actuation and piez
oresistive downmixing described in
Ref. 1 uses two separate metal loops for actuation
and detection—a total of four
measurement ports. The same combination of thermoel
astic actuation and piezoresistive
downmixing can be used when only one loop is availa
ble, as for example in the case of a
simple two-legged cantilever or an array of such ca
ntilevers. Figure S2 shows the schematic
of the resulting two-port measurement setup. The dr
ive voltage oscillating at frequency
ω
d
/2 creates temperature variations at frequency
ω
d
, which induces cantilever motion
.
The
bias voltage frequency
ω
b
is offset from the drive frequency,
ω
b
=
ω
d
-
, typically by less
Fig. S2.
(a) Schematic of two-port measurement of an array
using thermoelastic actuation and
piezoresistive detection. DC is the directional cou
pler, FD is the frequency doubler, HPF is the high-
pass
filter, LPF is the low-pass filter. (b) Same with b
alanced detection of two arrays. PS is the 180-degr
ee
power splitter.
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
4
than 100 kHz. Both the drive and bias voltages are
combined using an RF power combiner
and sent into the metal loop. On the other side of
the loop, a relatively large RF capacitor
C
RF
= 6 nF is connected to ground and therefore creates
a virtual ground at high frequencies, f
>> (2
π×
50
6 nF)
-1
500 kHz. This ensures that both the drive and bias
voltages
primarily drop across the metal loop of the resonat
or rather than elsewhere in the circuit. A
low-pass filter ensures that only the downmixed sig
nal, and not the RF drive and bias
voltages are transmitted into the low-noise amplifi
er.
One difference between the four-port measurement de
scribed in Ref.
1
and the two-port
measurement is the existence of a significant backg
round in the two-port case. This
background arises because the resistance of the pie
zoresistor depends not only on strain
but also on the temperature. Since thermoelastic ac
tuation relies on temperature variations
to drive the cantilever, we cannot easily avoid thi
s type of background. This effect produces
a background signal at the downmixed frequency beca
use the variations in resistance due
to changing temperature and those due to the cantil
ever motion occur at the same
frequency, and therefore mix down to the same frequ
ency
. The magnitude of the
background signal can be estimated as
V
b
~
V
b
α
R

T
/2, where
α
R
is the temperature
coefficient of resistance (of the order of 4
×
10
-3
K
-1
for most pure metals) and

T
is the
amplitude of temperature variations. In practice, f
or resonators with quality factors on the
order of one thousand, this background and the reso
nant signal were roughly of the same
order of magnitude. As a result, the two-port measu
rement is relatively easy to use for
vacuum measurements, where the signal is usually co
mparable to the background, and
more difficult in air, where the quality factor can
be of the order of 100 or less and
resonance signal can be orders of magnitude smaller
than the background.
One way to reduce this type of background would be
to fabricate the loop from specialty
alloys like nichrome, constantan, or manganine, whi
ch are designed to have temperature
coefficients of resistance up to two orders of magn
itude smaller than those of pure metals.
Another way to reduce this background is to use two
separate, thermally isolated loops for
actuation and detection, as illustrated by the cant
ilever in Fig. S1.
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
5
A two-port measurement also differs from a four-por
t measurement in that each
mechanical resonance produces not one but two peaks
during wide frequency sweeps, as
shown in Fig. S3. The first one appears at the expe
cted position, where the voltages are
applied at the frequencies
ω
1
=
ω
d
/2=
ω
R
/2 and
ω
2
=
ω
b
=
ω
R
, where
ω
R
is the resonance
frequency. There is, however, a second peak that ap
pears when one voltage is applied at the
frequency
ω
1
=
ω
R
+
and another at
ω
2
=2
ω
R
+
. To understand how this peak forms,
note that when we apply both of these voltages to t
he same loop, they will mix and produce
Fig. S3.
Wide frequency sweep for a two-port measurement o
f a single 1.6-μm-long cantilever with the
fundamental out-of-plane resonance frequency of 62.
11 MHz. The sweep exhibits one resonance peak at
the expected resonance frequency and another at rou
ghly twice the expected frequency. The large
oscillating background is due to RF cable resonance
effects. Lorentzian fits of these two peaks produc
e
resonance frequencies of 62.11 MHz and 124.32 MHz,
quality factors of +1000 and -1000, and amplitudes
of 0.75 mV and 1.45 mV, respectively. The frequency
offset was 44 kHz for this measurement.
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
6
temperature variations at the difference frequency
ω
2
ω
1
=
ω
R
, therefore driving the
resonance. The resistance variations at frequency
ω
R
can then mix with the applied voltage
at frequency
ω
1
=
ω
R
+
to produce a signal at the expected downmixed freq
uency
. The
net result is that another peak appears in the grap
h at roughly twice the frequency of the
expected peak. Figure S3 shows a typical two-port f
requency sweep showing a peak at the
expected frequency and an additional peak at roughl
y twice the expected frequency.
Surprisingly, the amplitude of the additional peak
is twice bigger than that of the expected
peak. This can be explained by considering the alge
braic relationships of the various
voltage-mixing processes involved. If we apply a su
m of two voltages oscillating at
frequencies
ω
1
and
ω
2
, the heating is proportional to the square of tota
l voltage:
(
)
(
)
K
+
+
+
=
+
+
=
+
=

t
V
t
V
V
t
V
t
V
t
t
V
V
t
V
t
V
t
V
T
2
2
2
2
1
2
1
1
2
1
2
2
2
2
2
1
2
1
1
2
2
1
2
2
2
1
1
2
cos
2
1
cos
2
cos
2
1
cos
cos
cos
2
cos
cos
cos
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
(S1)
Therefore, the temperature variations at frequency
ω
2
ω
1
are twice as big as those at
frequency
ω
1
, and therefore drive the cantilever motion twice h
arder. The additional mixing
process that produces the downmixed signal at frequ
ency
does not change that
conclusion: the amplitude of “double-frequency” pea
k is twice that of the “regular” peak.
In addition to the twofold difference in amplitude,
the phase of the resonance response of
the additional peak is flipped with respect to that
of the expected peak for reasons similar
to those described as in the preceding section. As
a result, the regular peaks are fitted with
positive quality factors, while additional “double-
frequency” peaks, with negative. This
turns out to be helpful when analyzing data from wi
de measurement sweeps that contain
peaks from multiple mechanical resonances: if the f
itted quality factor
Q
is positive, then
there is indeed a mechanical resonance at the expec
ted frequency
ω
e
=
ω
1
=
ω
2
+
; however,
if the fitted Q is negative, the real mechanical re
sonance happens at the frequency
ω
e
/2–
.
In sensing applications, it is often more convenien
t to work with this “double-frequency”
resonance peak since its signal-to-noise ratio is u
sually twice better for the same amount of
heating.
Piezoresistive signal from series-parallel arrays
If we assume that with no excitation all piezoresis
tors have identical resistances
R
0
, the
resistance of the entire array without excitation i
s given by
R
arr
=
R
0
×
m
/
l
, where
m
is the
number of columns in the array, and
l
is the number of rows. If the resonators are excit
ed
into motion, the resistance of a piezoresistor in r
ow
i
and column
j
will become
R
ij
=
R
0
(1+
δ
ij
),
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
7
where
δ
ij
is the relative change in its resistance due to th
e motion-related deformation. The
resistance of the entire array in this case is give
n by
( )
+
+
=
∑∑
= =
=
=
l
i
m
j
ij
m
j
l
i
ij
arr
lm
l
m
R
R
R
1 1
0
1
1
1
0
1
1
1
1
δ
δ
,
(S2)
where the Taylor expansion is justified because the
relative changes in the resistance of
piezoresistors are generally small,
δ
ij
<<1. When using piezoresistive detection, the signa
l is
proportional to the applied bias voltage
V
b
:
=
=
=

=
m
l
j
i
ij
b
arr
arr
b
arr
lm
V
R
R
V
V
,
1
,1
2
2
1
δ
.
(S3)
If all resonators respond in exactly identical ways
,
δ
ij
=
δ
0
, the formula for the array signal
reduces to that of an individual resonator:
0
,
1
,1
2
1
2
δ
δ
b
m
l
j
i
ij
b
arr
V
lm
V
V
=
=
=
=
.
(S4)
The maximum drive that can be applied to an individ
ual piezoresistive resonator is limited
either by the nonlinearity of mechanical response o
r the maximum tolerable level of
heating. In our experiments, the maximum tolerable
temperature increase due to heating
was typically on the order of 100 K, corresponding
to maximum dissipated power on the
order of
P
max
~ 100 μW for an individual resonator. If this maxim
um power is applied to
each resonator in the array, the total dissipated p
ower will naturally scale as the number of
array elements,
N
=
lm
. In contrast, the bias signal,
V
b
, and the maximum signal that can be
obtained from the array,
V
arr
, will scale as the number of columns,
m
.
It would seem then that an array consisting of just
one row would be the most economical
way to leverage the signal of individual resonators
. However, having an array of just one
row would mean that the array resistance scales lin
early with the number of array
elements,
R
arr
=
R
0
×
N
, and may reach excessively large values for arrays
of thousands of
resonators. In experiments, it is often desirable t
o keep the resistance of the total array
close to some fixed value, usually 50 Ohm for high-
frequency applications. In addition, a
single-row array is very vulnerable to electrical d
efects since the breaking of the conducting
path in just one piezoresistor would render the ent
ire array inoperable. As a result, it is
preferable to scale the number of rows proportional
ly to the number of columns, so that the
arrays remain robust with respect to defective indi
vidual resonators and have
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
8
approximately constant resistance. In this case, th
e piezoresistive signal scales
proportionally to
m
and therefore proportionally to the square root of
the total number of
array elements, √
N
. At the same time, Johnson noise and thermoelastic
noise—the
fundamental sources of noise in such measurement—do
not depend on
N
at all. The signal-
to-noise ratio then also scales as the square root
of the number of elements, √
N
, and, of the
total dissipated power, √
N
P
max
. This situation, where the signal-to-noise ratio i
ncreases
proportionally to the square root of the total diss
ipated power, is very commonly
encountered in electrical engineering.
Note, however, that the scaling of signal as √
N
is the best-case scenario. In reality, different
resonators will not respond to the drive in identic
al ways for a number of reasons. The first
one to consider is that the phase and amplitude of
the drive may not be the same for all
resonators. For example, in the case of piezoshaker
drive, the phases and amplitudes of the
surface motion will vary due to the interference of
ultrasound waves inside the bulk of the
resonator chip. The length scale of such variations
is on the order of the bulk acoustic
wavelength corresponding to the resonator’s frequen
cy, ~ 350 μm for a 25 MHz resonator
on silicon substrate, which is smaller than the dim
ensions of the typical arrays we used in
our experiments.
If we assume, for the sake of argument, that the dr
ives for different resonators of the array
have completely random phases
φ
d
but the same amplitude, then the array signal will
take
the form
d
i
m
l
j
i
ij
b
arr
e
V
lm
V
φ
δ
=
=
=
,
1
,1
2
1
(S5)
The addition of such signals with random phase is e
quivalent to a random walk in the
complex plane, which implies that the expected magn
itude of the sum will scale as the
square root of the total number of terms in the sum
:
0
0
2
1
2
1
δ
δ
b
b
arr
V
N
N
N
V
V
=
=
.
(S6)
Since the bias signal
V
b
normally scales as
√N
, the use of arrays does not offer any
advantages with respect to the use of an individual
device in this case. It is therefore crucial
to keep the drive phase the same for all the resona
tors in the array. Maintaining such phase
coherence of the drive is difficult with piezoshake
r drive but is much easier with integrated
actuators, such as the thermoelastic actuators.
Even if the drives of all resonators in the array a
re perfectly in sync, the response of
individual resonators may not be the same because t
hey all have slightly different
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
9
mechanical properties, in particular different reso
nance frequencies. This effect of the
frequency dispersion is considered in the following
section.
Effect of frequency dispersion
The finite resolution of e-beam and optical lithogr
aphy introduces slight variations in the
dimensions of the fabricated resonators. As a resul
t, all resonators in the array will have
slightly different mechanical properties, and in pa
rticular different resonance frequencies.
A simple way to judge whether this dispersion in re
sonance frequency is significant is by
comparing it to the natural width of the resonance
under typical operating conditions. For
example, nanoscale resonators shown in Figure S1 ha
ve a typical quality factor on the order
of 100 in air at atmospheric pressure, correspondin
g to a resonance width that is 1% of the
resonance frequency. Therefore, if the dispersion o
f resonance frequency is much smaller
than 1%, the individual resonance curves will stron
gly overlap and the Lorentzian-response
term of individual resonators may be treated as the
same, leading to the summed array
response being Lorentzian as well. In this case, we
obtain the maximum possible amplitude
of the array response. Conversely, if the dispersio
n of the frequencies is much larger than
1%, the sum of the individual Lorentzian response c
urves will be much broader than an
individual resonance, and the peak array signal wil
l be much reduced with respect to the
maximum possible signal.
In order to quantify this qualitative argument, we
need to consider the problem of adding
up many Lorentzian resonance curves with randomly d
istributed resonance frequencies.
The normal or Gaussian probability distribution is
a common choice in such simulations;
however, we have found that in reality the distribu
tion of resonance frequencies has long
and “fat” tails, i.e., the probability of finding r
esonance frequencies far off the mean is much
larger than would be expected in a Gaussian distrib
ution. The large number of outliers is
illustrated by the data in Figs. 3(b) and 4(a).
To model this large number of outliers, it is more
appropriate and convenient to use the
Cauchy distribution, which has the probability dens
ity function similar to the Lorentzian:
2
0
0
0
/
2
1
2
/
)
(
+
=
distr
R
disrt
R
Q
Q
p
ω
ω
ω
πω
ω
,
(S7)
where
ω
0
is the center frequency of the distribution and
Q
distr
characterizes the width of the
distribution, similarly to the way that a quality f
actor characterizes the width of a
Lorentzian curve. The Cauchy distribution more accu
rately describes the long tails of the
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
10
frequency distribution that we observe in practice
and has the added advantage that the
expected form of the array response can be calculat
ed analytically, as shown below.
The response of a forced, damped harmonic oscillato
r is given by
Q
i
Q
A
s
D
R
D
R
R
D
/
/
)
(
2
2
2
ω
ω
ω
ω
ω
ω
+
=
,
(S8)
where
A
is the amplitude of the resonance signal,
ω
R
is the resonance frequency,
Q
is its
quality factor, and
ω
D
is the frequency of the drive. If the quality fact
or of an individual
resonator is large, Q >> 1, the response near the r
esonance can be approximated by the
complex Lorentzian
)
2
/(
/
)
(
Q
i
Q
A
s
R
D
R
R
D
ω
ω
ω
ω
ω
+
=
.
(S9)
The expected signal from one array cantilever with
a randomly distributed resonance
frequency is then a convolution of the complex Lore
ntzian response with the Cauchy
distribution:
+
+
=
+
×
+
Q
Q
i
Q
A
d
Q
Q
Q
i
Q
distr
R
D
R
distr
R
disrt
R
D
R
R
1
1
2
2/
/
2
1
2/
2
/
)
s(
0
0
2
0
0
0
ω
ω
ω
ω
ω
ω
ω
ω
πω
ω
ω
ω
ω
ω
,
(S10)
which is simply the complex Lorentzian response wit
h a new effective quality factor
Q
eff
= 1/(
Q
-1
+
Q
distr
-1
) and a new effective amplitude
A
eff
=
AQ
eff
/
Q
. The expected signal of the
entire array will have the same form, since it is e
ssentially the sum of the expected signals
of individual cantilevers and we assume all cantile
vers in the array to be described by the
same Cauchy probability distribution. In addition,
for a large array, N >> 1, the typical
response generally will not deviate far from the ex
pected response as the random
variations introduced by individual resonances will
largely average out. Therefore, the
frequency dispersion effectively has the same resul
t as an additional source of damping,
corresponding to a quality factor
Q
distr
, which reduces the effective quality factor of the
array from
Q
to
Q
eff
= 1/(
Q
-1
+
Q
distr
-1
).
To illustrate this effect of the resonance frequenc
y dispersion on the shape of the array
response, we have performed numerical simulations f
or an array consisting of 2800
elements (Fig. S3(a)) In the simulations, all reson
ators assumed to have a quality factor of
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
11
100, corresponding to experimental value in air, an
d the width of the Cauchy distribution
was varied, starting from a distribution width much
smaller than the natural width of the
resonance,
Q
distr
>>
Q
, and ending with a distribution width much larger
than the natural
width of the resonance,
Q
distr
<<
Q
. As expected, increasing the width of the frequenc
y
distribution broadens the resonance peak of the ent
ire array and reduces its amplitude.
In Fig. S3(a), the simulated response curves do not
deviate significantly from the perfect
Lorentzian curves due to the large number of the el
ements in the array and their relatively
low quality factors. However, the fact that the ove
rall response curves of the array consist of
many narrow lines corresponding to individual reson
ators becomes evident if the quality
factors of individual resonances are high enough, a
s shown in Fig. S3(b). These curves
simulate the response of actual arrays used in expe
riments in air and vacuum. The
Fig. S4.
(a) X and Y quadratures of the simulated response
of an array of 2800 cantilevers with
Q
= 100
and
Q
distr
of 400, 100, and 25. The effective quality factors
Q
eff
in these cases are (400
-1
+100
-1
)
-1
80, (100
-
1
+100
-1
)
-1
50, and (25
-1
+100
-1
)
-1
20, respectively. (b) Same for
Q
distr
= 100 and
Q
of 100 and 1000,
which approximately corresponds to the frequency di
spersion and quality factors in air and vaccum of
actual arrays used in experiments.
“Large-scale integration of nanoelectromechan
ical systems for gas sensing applications”
I. Bargatin, E.B. Myers, et al.
(Supporting Information)
12
frequency distribution width of the typical arrays
we have worked with were on the order
of 1%, corresponding to
Q
distr
= 100, and the quality factors of individual reson
ances were
on the order of 100 and 1000 in air and vacuum, res
pectively. As a result, the experimental
curves in vacuum had more “fine structure” than tho
se in air due to the response of
individual cantilevers.
The differences between different resonators in the
array are, of course, not limited to the
variations in the drive phase and resonance frequen
cies. The quality factors and the
amplitudes of response of individual resonators wil
l also vary. However, we have found in
our experiments that these variations are relativel
y insignificant and have a negligible effect
on the overall response of the arrays.
1
I. Bargatin, I. Kozinsky, M.L. Roukes,
Efficient electrothermal actuation of multiple mode
s of high-frequency
nanoelectromechanical resonators
, Appl. Phys. Lett.
90
, 093116 (2007).