IOP PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING
J. Micromech. Microeng. 17 (2007) 1657–1663 doi:10.1088/0960-1317/17/8/032
A silicon straight tube fluid density sensor
M Najmzadeh
1
, S Haasl
2
and P Enoksson
1
1
Department of Microtechnology and Nanoscience, Chalmers University of Technology,
SE-412 96, Gothenburg, Sweden
2
Imego AB, Arvid Hedvalls Backe 4, SE-411 33, Gothenburg, Sweden
E-mail: najmzade@student.chalmers.se
Received 2 April 2007, in final form 21 June 2007
Published 20 July 2007
Online at stacks.iop.org/JMM/17/1657
Abstract
In this paper, a new and simple silicon straight tube is tested as a fluid
density sensor. The tube structure has a hexagonal cross section. The
fabrication process consists of anisotropic silicon etching and silicon fusion
bonding. A tube structure with a length of 2.65 cm was tested. The sample
volume is 9.3 µL. The first three modes of vibrations were investigated with
a laser Doppler vibrometer for air and five liquid mixtures. The fluid density
sensitivity of each mode was measured and the average was −256 ±
6 ppm (kg m
−3
)
−1
around the density of water. The density of an unknown
fluid can be continuously monitored using this sensor by measuring the
resonance frequency of one of the vibration modes and extracting the
density from the calibration curves.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
A resonant densitometer is a sensor for measuring fluid density
where a change in density results in a change in the mass
loading of the resonator structure and thus a change in the
resonance frequency [1].
The first micromachined tube structure used as a fluid
density sensor was a free–free double-loop resonating structure
[1]. The corners in the structure, however, required corner
compensation techniques that complicated the fabrication.
Two fixed-free resonating structures have also been presented
[2, 3]. All the structures have shown good liquid density
sensitivity which according to theory is a function of the ratio
of the cross-sectional area of the tube to the cross-sectional area
of the fluid, but they had corners. Corners add an additional
pressure drop in the tube system and increase the risk of
trapping gas bubbles.
Corner compensation techniques can be used to create
convex corners in KOH etching. These techniques, however,
are time-stopped and sensitive to overetching. Overetching
causes the tube walls to be thinner at these corners, reducing
the burst pressure. Sharp corners are furthermore risk zones
for clogging by gas bubbles or particles. Clogged gas bubbles
can affect the accuracy of the density sensor by shifting the
resonance frequency, reducing the vibration amplitude of the
tube and reducing the Q-factor due to changes in the moment
of inertia, as the gas bubbles move up and down in the liquid
when the tube is in resonance [4].
Other techniques like using quartz tuning forks,
vibrating microdiaphragms, membranes, cantilevers and using
magnetoelastic thin or thick films have been presented [5–10].
The advantages of using tubes lie in the low sample volume
and the possibility of continuously monitoring the density of
a fluid with high resolution.
In [5], a titanium diaphragm was divided into smaller parts
by a 10 µm nickel, gold and polymer microstructure to create
an array of 10 µm wide and 1–3 µm thick microdiaphragms.
By placing this array in a liquid bath and detecting the
echo of an ultrasonic pulse emitted toward this passive array,
the resonance frequency of the diaphragms, depending on
parameters such as viscosity and density of the medium, could
be measured. The relationship between the density and the
resonance frequency was linear for this sensor.
In [6], a piezoelectric unimorph cantilever was made of
steel foil partially coated with piezo-electric PbO · ZrO
2
· TiO
2
(PZT). The cantilever was clamped at the PZT-coated end,
and the non-coated end of the cantilever was immersed in
the liquid. The resonance spectra of the cantilever could be
obtained using an impedance analyzer. The viscosity and
the density of the liquid could be measured simultaneously
by observing the measured resonance frequency and the peak
width of the phase-angle spectra.
0960-1317/07/081657+07$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1657
M Najmzadeh et al
In [7], the resonance frequency and Q-factor of a vibrating
silicon plate immersed in a fluid provided a measure of the
fluid’s density and viscosity, respectively. The plate was
excited by placing a permanent magnet beneath it and passing
an ac current through a coil on the plate. The plate was
fabricated from an SOI wafer with a 20 µm thick device
layer using a multi-layer lithography process. The maximum
inaccuracy in the measurements was ±1.5% for fluid’s density
between 0.5 and 1.5 g mL
−1
and ±10% for fluid’s viscosity
between 0.4 and 100 cP showing that the sensor could function
accurately in extreme environments over a wide density and
viscosity range. The sensor was shown to withstand up to
1500 MPa pressure and 200
◦
C temperature, allowing it to be
used in the harsh down-hole environment found in oil wells.
In [8], a plate-wave device based on a silicon nitride
membrane with piezoelectric ZnO interdigital transducers was
used as a density and viscosity sensor. The membrane acted as
a passive acoustic delay line whose properties were affected
by placing a drop of liquid in the 6 µL well formed by the
KOH-etched silicon substrate supporting the membrane. Both
the viscous dissipation in the liquid and the mass loading due
to the effective mass in the viscous boundary layer cause a
wave attenuation in the plate-wave delay line, allowing the
density and viscosity of the liquid to be determined.
In [9], a commercially available quartz tuning fork was
glued to a PZT rectangular plate and placed in a liquid bath.
The resonance frequency of the arms of the fork, which are two
cantilevers, was detected by applying an ac driving voltage to
the PZT actuator and measuring the amplitude of the voltage,
generated in the tuning fork due to the piezoelectric effect,
and finding the maximum of the f –V curves. The fork’s
resonance frequency and its amplitude of vibration decrease
for increasing ambient fluid density, because of the damping
contribution to its dynamic behavior. By this sensor, the
density of non-conductive solutions was measurable by an
error in the order of 20 kg m
−3
.
In [10], two magnetoelastic sensors (30 mm × 3mm×
30 µmFe
40
Ni
40
P
14
B
6
Metglas
TM
thick-film sensors, alloy
2826 MB) with different surface roughness were tested. Two
sides of one sensor were covered with a TiO
2
layer to make the
surface smoother. By immersing the sensor in a liquid bath,
liquid was trapped in the surface-roughness features causing
an increase of the effective loading mass independent of the
viscosity of the fluid. The resonance frequency of each sensor
could be detected by applying an external magnetic field and
detecting the generated magnetic flux from the mechanically
deformed sensors by a pickup coil. The difference between the
frequency responses of the two sensors was proportional to the
density of the liquid. After finding the density, the viscosity
could be evaluated from the data.
In this paper, we present the design of a fixed–fixed
straight-tube resonating structure (see figure 1). The sample
volume is just 9.3 µL. The design consists of one resonant
element, a straight tube and a silicon frame. Having no corners
leads to less flow restriction and less risk of trapping gas
bubbles in the sensor. In this sensor, the resonant element
is a fixed–fixed resonating tube. The silicon frame supports
the tube mechanically and serves as an electrical interface.
The frame was glued to an aluminum fixture. This fixture
mechanically supports the moving part of the sensor and it
Figure 1. Straight tube densitometer.
allows an external tube system to be connected to the inlet and
outlet of the sensor. Electrodes were patterned in an etched
recess of a glass slide. The fixture clamps the glass slide
close to the vibrating element. The recess depth, and thus the
electrode distance, was 6 µm.
The fabrication consists of etching two silicon wafers in
KOH to produce a pair of half tubes. These two wafers are
bonded together by silicon fusion bonding. Another KOH
etching step is used to release the tubes.
In this work, important performance parameters of the
densitometer such as the Q-factor and the density sensitivity
are investigated and calculated for the first three resonance
modes of the sensor.
The ability of the sensor to measure the density
of multiphase fluids and provide accurate results almost
independently of other fluid parameters such as viscosity,
allows it to be used varying fields such as the food
industry, perfume industry as well as the biomedical,
pharmaceutical and petrochemical industries. In the medical
field, for example, possible applications of the sensor can
be to characterize blood (e.g. hematocrit) or urea. Other
applications can be the measurement of alcohol levels or fuel
grade monitoring.
2. Theory
The resonance frequencies of a clamped–clamped tube can be
calculated by [11]
f
i
=
λ
2
i
2πL
2
EI
m
(1)
where I is the area moment of inertia, E is Young’s modulus
of Si, L is the length of the tube and m is the total mass of
the resonant element (tube and fluid) per unit length. λ
i
is a
constant related to the mode of vibration. For i = 1to3,itis
equal to 4.730, 7.853 and 10.996, respectively.
m, the total mass of fluid and tube per unit length, is equal
to
m = ρ
t
A
t
+ ρ
f
A
f
. (2)
By rewriting equation (1) and simplifying all geometric
parameters into one constant C
i
,f
i
can be written as
f
i
= C
i
E
ρ
t
A
t
+ ρ
f
A
f
, (3)
where C
i
depends on the tube dimensions and the vibration
mode. ρ
t
and ρ
f
are the densities of the tube and the fluid,
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Silicon straight tube fluid density sensor
Figure 2. The straight tube design parameters (all the dimensions
are in µm).
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
x/L
W(x)
Figure 3. The first three vibration modes of a clamped–clamped
beam system. L is the length of the beam and W(x) is the
normalized deflection.
respectively. A
t
and A
f
are the cross-sectional areas of the
tube walls and the fluid.
Fluid density sensitivity for this sensor can be written as
S ≡
1
f
i
∂f
i
∂ρ
f
=−
1
2
ρ
f
+
A
t
A
f
ρ
t
. (4)
Therefore, by decreasing A
t
/A
f
ratio, the density
sensitivity will be increased. The A
t
/A
f
design ratio is 0.535
(see figure 2), yielding a theoretical fluid density sensitivity
of −223 ppm (kg m
−3
)
−1
at the density of water for each
resonance mode (at room temperature and 1 atm pressure, ρ
t
and ρ
f
are equal to 2329 and 997 kg m
−3
, respectively [12]).
Vibration modes were detected using a laser Doppler
instrument. Figure 3 shows the first three vibration modes.
Figure 4 shows the theoretical dependence of the first
resonance frequency, f
1
, versus the density of the fluid inside
the tube.
3. Design and fabrication
The main steps of the fabrication process were KOH etching
and silicon–silicon fusion bonding shown in figure 5.Inthis
section, the side on which the wafer is bonded is called the
inside side of the wafer.
75 mm (1 0 0)-silicon wafers were thermally oxidized at
1050
◦
C in an oven for 25 min to produce 300 nm oxide.
LPCVD at 770
◦
C was used to deposit 100 nm nitride. After
0 200 400 600 800 1000
6500
7000
7500
8000
8500
9000
9500
ρ
f
(kg/m
3
)
f
1
(Hz)
Figure 4. Theoretical dependence of the first resonance frequency
versus the fluid’s density.
Support frame
Silicon tube
Nitride
Si Oxide
(
a
)
(
b
)
(
c
)
Figure 5. Main steps in the fabrication process.
photolithography, RIE was used to create a nitride mask on
the inside side of the wafers. In this step, a Plasma Therm
Batchtop PE/RIE m/95 was used with the following recipe—
power: 100 W, chamber pressure: 25 mT, gas flows: 32 sccm
CF
4
, 4 sccm H
2
.
Another photolithography and RIE step was used to create
a nitride pattern on the outside mask of the wafers to be able
to align two such wafers in the bonding step. KOH etching
was used to create the interior of the tubes (at 80
◦
C; 35 wt%
KOH).
The pre-bonding process was used to create a hydrophilic
and clean silicon surface suitable to bond. Two such wafers
were soaked in a Piranha solution (1:3 solution of H
2
O
2
37 wt% : H
2
SO
4
96 wt%) for 10 min. A Karl-Suss BA6 bond
aligner was used to align the wafers together using alignment
marks on the inside and outside sides of the wafers. The
aligned wafers were pressed together using a substrate bonder
(Karl-Suss SB6) for 5 min with a force of 7 kN at 50
◦
C. The
pressed wafers were annealed in an oven at 700
◦
Cfor1h.
After the silicon–silicon fusion bonding step, KOH was
used to etch the exterior of the tubes to release the structures
(at 80
◦
C; 35 wt% KOH). Finally, the wafer was diced to create
10 mm × 28.5 mm sensor structures.
1659
M Najmzadeh et al
Figure 6. Dimensions of the silicon sensor (top); cross section
A–A
of a glued sensor in the fixture (bottom).
Figure 6 shows the dimensions of the sensor and the cross
section of the glued sensor in the fixture.
4. Measurements
For evaluation, the sensor was glued to an aluminum fixture
using an epoxy glue. The fluid was led to the tube by steel
tubes. The electrodes, which are parallel to the resonant tube,
are sputtered through a shadow mask in an etched recess of a
glass slide. The slide was placed and fixed under the sensor by
the fixture. The gap between the electrode and the sensor was
6 µm. Because of chip bow, the distance between the center
of the sensor and the electrode was smaller than the nominal
gap. The bow direction was used to assist exciting the tube
with a lower amplitude of voltage.
By focusing the laser beam from the laser Doppler head
on the resonant tube, the spectrum of vibrations could be
detected by the vibrometer (see figure 8). Table 2 shows
the resonance frequency and the Q-factor for each vibration
mode for different fluids in the tube, at an ambient pressure of
2 × 10
−4
mbar. Figure 9 shows a typical spectrum obtained
from the LDV. Figure 10 illustrates the typical movements
detected by the LDV. To calibrate the densitometer, different
mixtures of water and 2-propanol were used to detect the first
three resonance frequencies. The density of the tested mixtures
was measured using a scale and a volumetric flask. Table 1
Figure 7. SEM picture of a cross section of a fabricated sensor (not the evaluated tube).
Laser spot on the tube
Inlet-outlet
Wires
Figure 8. Evaluating the density sensor by using a laser Doppler
vibrometer.
0 10 20 30 40 50
0
0.5
1
1.5
2
2.5
3
3.5
frequency (kHz)
Amplitude of vibration (nm)
Figure 9. The spectrum of vibrations of a water-filled tube detected
by the LDV (average of 30 points along the sensor; using a periodic
chirp signal to excite the sensor).
shows the practical evaluation results of changing resonance
frequencies with different mixtures of water and 2-propanol
(IPA) at 2 × 10
−4
mbar (frequency resolution: 1 Hz).
Figures 11–13 show the change of resonance frequencies
with varying liquid density. The regression line related to the
least-squares approximation between measurements is drawn
in each figure.
In figure 14, the resonance frequencies of an air-filled tube
are added to the statistical data and the regression lines are
passed through the points using least-squares approximation
(chamber pressure: 2×10
−4
mbar; air pressure inside the tube:
1 bar). The calibration curves with more experimental data
are being used to do statistical calculations in the discussion.
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Silicon straight tube fluid density sensor
Figure 10. Detected movements of a water-filled tube by the LDV (the measurement points are marked on the sensor).
Table 1. Measurements of the density and the resonance
frequencies at a chamber pressure of 2 × 10
−4
mbar.
x
V
(W) x
V
(IPA) ρ (kg m
−3
) f
1
(Hz) f
2
(Hz) f
3
(Hz)
1.00 0.00 997.70 7127 19 661 38 125
0.75 0.25 958.92 7176 19 822 38 452
0.50 0.50 912.19 7254 20 027 38 800
0.25 0.75 853.70 7381 20 337 39 370
0.00 1.00 779.11 7567 20 847 40 440
Air – 1.2047 10 104 28 402 54 100
x
V
(W): approximate volumetric fraction of water in the mixture.
x
V
(IPA): approximate volumetric fraction of 2-propanol in the
mixture.
Table 2. Q-factor measurements for different vibration modes of
three fluids at a chamber pressure of 2 × 10
−4
mbar.
Fluid Q
1
Q
2
Q
3
Water 61 72 97
2-Propanol 54 70 93
Gas
∗
138 157 244
* The pressure inside the tube is
equal to the chamber pressure.
5. Discussion
5.1. Q-factor
Table 2 shows that mode 1 has the lowest Q-factor. In this
mode, the center of mass of the vibrating element moves up
and down, causing the frame to vibrate as well. Mode 2 is
mass balanced but because of momentum instability, the frame
vibrates transversely. In mode 3, the center of gravity of the
vibrating tube goes up and down but it is less than mode 1.
These frame movements, induced by the movement of center
of gravity and the momentum instability, together with the
observed fact that the frame is stiffer at higher frequencies,
can cause the frame loss to be lower at higher mode numbers.
This evolution of increasing Q-factors with increasing mode
shapes, together with the observation that the Q-factor is higher
for a gas-filled tube than for a liquid-filled (and thus heavier)
tube, leads the authors to speculate that the main source of the
losses resulting in these limited Q-factors is a high loss through
the glue used to attach the vibrating element, generally called
clamping loss. In comparison with a gas-filled tube, the drop
750 800 850 900 950 1000
1700
1750
1800
1850
1900
1950
2000
1/fr
2
(Hz
*10 )
ρ
f
(kg/m
3
)
Figure 11. Calibration curve: shift of f
1
with varying fluid density.
750 800 850 900 950
230
235
240
245
250
255
1/fr
2
(Hz *10 )
ρ
f
(kg/m
3
)
Figure 12. Calibration curve: shift of f
2
with varying fluid density.
of the Q-factor in a liquid-filled tube can also be due to the
internal liquid damping that was also observed in encapsulated
tube systems [4].
The suggested solution is to use a stiffer glue or to
encapsulate the sensor with more rigid methods such as anodic
bonding. Prior presented designs were reported to have higher
Q-factors [1–3, 14]. In [1], this is due to the fact that the
double-tube micromachined tube is a free–free resonating
system while for [2, 14] the size of the single-tube sensor
(U-tube [2]) is much smaller than the stiff encapsulation,
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