A poly-silicon hot-film shear-stress sensor insulated by a vacuum-chamber underneath has been designed and fabricated by the surface micromachining technology. The sensor is operated at both constant current and constant temperature modes. The dynamic performance (including time constant and cut-off frequency) measurement, calibration, and temperature compensation of the sensor have been realized

Ho, Chih-Ming

Huang, Jin-Biao

Jiang, Fukang

Liu, Chang

Tai, Yu-Chong

Tung, Steve

Caltech Authors - Main

FLUIDIC SHEAR-STRESS MEASUREMENT USING SUWACE- 
MICROMACHINED SENSORS 
Jin-Biao Huang, Chang Liu*, Fukang Jiang", Steve Tung, Yu-Chong Tai*, and Chih-Ming Ho 
Center for Micro Systems, University of Califomia, Los Angeles 
Los Angeles, CA 90095-1597 
*Electrical Engineering Department, California Institute of Technology 
Pasadena, CA 91 125 
Abstract - A poly-silicon hot-film shear-stress sensor 
insulated by a vacuum-chamber underneath has been 
designed and fabricated by the surface micromachining 
technology. The sensor is operated at both constant current 
and constant temperature modes. The dynamic performance 
(including time constant and cut-off frequency) 
measurement, calibration, and temperature compensation of 
the sensor have been realized. 
I. INTRODUCTION 
Fluid flow over a solid wall generates a velocity 
gradient that produces shear stress at the wall. This wall 
shear stress is one of the important flow properties in 
aerospace engineering and fluid mechanics[ 11. Presently, 
there are many measurement techniques for shear stress 
[l]. However, none of them can simultaneously satisfy 
the operational requirements for turbulent boundary layer 
research: fine spatial resolution (- lOOpm), fast frequency 
response (>5kHz), and high sensitivity. With the help of 
micro-machining technology, the floating-element shear 
stress sensor has satisfied the requirement of spatial 
resolution[2-3]. But the other requirements remain to be a 
problem. 
Flush-mount hot-film anemometers are commonly used 
to measure wall shear stresses. The method of 
measurement is based on a simple heat transfer theory. 
The drawback of traditional hot-film anemometers is heat 
transfer to the substrate which results in low sensitivity. 
An new micromachined hot-film shear-stress sensor 
insulated by a vacuum-chamber underneath has been 
proposed and designed in the present study [6] for a 
distributed micro-electro-mechanical system (MEMS), 
which has high sensitivity and can achieve all the above 
requirements. The theory, circuit design, and more 
extensive experimental results of the sensor will be given 
in this paper. 
II. DESIGN AND FABRICATION 
Fig. 1 schematically shows the top and cross-sectional 
views of the micro hot-film sensor. By using 
micromachining technology, a vacuum chamber (cavity), 
the square part (dashed line) in Fig. 1, is piaced under a 
thin silicon nitride film. The typical size of the cavity is 
200x200~2 pm3. A poly-silicon strip (80-200 pm long, 2 
pm wide, and 0.45 pm thick) is deposited on the silicon 
nitride film and functions as the sensor element. Metal 
leads connect the sensor element to the outside through 
bonding pads. The flow direction is perpendicular to the 
length of the sensor strip. 
poly-Si resistor 
+l 
I
nitride 
silicon substrate 
Fig. 1 Schematic top (a) and cross-sectional (b) views of the 
shear stress sensor. 
The cavity is formed by sacrificial-layer (PSG, phospho- 
silicate glass) technique. Both silicon nitride and poly- 
silicon layers are deposited by LPCVD (low pressure 
chemical vapor deposition). The poly-silicon resistor is 
uniformly doped to a low sheet-resistance of typically 50 
!U*. The measured TCR (temperature coefficient of 
resistivity) of the sensor at this doping level is about 
O.O9%/"C. Typical resistance of the sensors is 2-5 162. 
The detailed process steps are given in [5-61. A SEM 
picture of the micro-fabricated sensors is shown in Fig. 2. 
0-7803-2624-5/95/$4.00 @ 1995 IEEE 
16 
Fig. 2 A SEM picture of the micro sensor. 
111. THEORY AND CIRCUITS 
Hot-film anemometer utilizes the convective heat 
transfer from the heated sensor to the above fluid to 
measure the shear stress generated by the fluid. The 
resistance of the sensing element R can be approximately 
related to its temperature T by a linear equation 
where R, and To are the average resistance and 
temperature at a reference condition which is usually the 
ambient condition, and a is the TCR (temperature 
coefficient of resistivity) of the sensor. An important 
parameter governing the operation of hot-film sensor is 
the overheat ratio defined as [8] 
where T is the temperature of the heated sensor. In 
operation, it is more practical to use a resistive overheat 
ratio defined by 
where R is the resistance of the heated sensor. The 
relationship between the two overheat ratios is aR= aT,aT. 
The heating power of a hot-film sensor operating in 
steady state can be correlated with wall shear stress 2, as 
follows[ 1 1  
R=R,[ l+a(T-To)] (1) 
aT=(T-T,)lT, (2) 
aR=(R-R,)IR, (3) 
i2R=( T-TJ(A+BT,’”) (4) 
where Tf is the temperature of the measured fluid, i is the 
heating current going through the sensor, A and B are 
calibration constants. The equation shows that the heating 
power is linearly proportional to the one third power of 
the shear stress. 
The usual operation mode for hot film sensor is either 
constant current (CC) or constant temperature (CT). Since 
the resistance of a micromachined hot-film sensor (>1 kQ) 
is generally higher than a traditional one (-5OQ), 
traditional anemometer circuits need to be modified for 
presenrcase. Figs. 3 (a) and (b) show the modified circuits 
for CC and CT operations, respectively, in which R 
represents the sensor and E.,,, is the output terminal. In 
Fig. 3 (b), Roh is used to adjust resistive overheat ratio, R, 
and C, are for compensation. Fig. 3 (a) is basically a 
voltage controlled current source and it can provide 
constant current to the sensor with resistance up to dozens 
of kilo-ohm. 
t1sv 
10k 
100 
6 
-15V 
L i  
t- I E out 
(b) 
Fig. 3 The CC(constant current) (a) and CT(constant 
temperature) (b) circuits of the sensor. 
IV. MEASUREMENTS 
1. Dynamic Performance 
Since suitable velocity fluctuations are not readily 
available, electronic test signals are usually used to 
determined the time constant of the sensor. According to 
both theoretical analyses[9] and experimental 
confirmation[7], the frequency response or time constant 
can be obtained by feeding either an electronic sine wave 
or a square wave into an anemometer circuit. The terminal 
Et in Fig. 3 is for this purpose. 
The measured time constant and cut-off frequency of 
the micro sensor at CC mode are typically 300 ps and 500 
Hz, respectively. By using feedback at CT mode, much 
better dynamic performance can be obtained. The 
measured time constant and cut-off frequency at CT mode 
are typically 72 ps and 1 1  kHz, respectivcly. A higher 
frequency response can be obtained by changing the 
overheat ratio of the sensor. Fig. 4 is a typical measured 
curve describing the cut-off frequency change vs. the 
resistive overheat ratio and it can be seen that a cut-off 
frequency of 70 kHz at CT mode can be reached. 
17 
0 0.05 0.1 0.15 0.2 0.25 0.3 
Ovemeat r d i o  a, 
Fig. 4 The cut-off frequency of the micro sensor vs. resistive 
overheat ratio at constant temperature mode. 
2. Shear Stress Calibration 
In order to correlate the output voltage with wall shear 
stress(z,), two calibration methods are usually used. In the 
first method, z, in a fully developed channel flow is 
related to the streamwise pressure gradient by[ 1 ,  101 
where P ,  is the local pressure, x is the stream-wise 
coordinate, and h is the height of the wind tunnel. In the 
second method, an empirical relationship between the free 
stream velocity and shear stress is used[5-61. Here the first 
method is used. 
The micro shear stress sensor is flush-mounted on the 
wall in the fully developed region of a wind tunnel. The 
calibration results for the same sensor at the same resistive 
overheat ratio of 0.2 but different operation mode are 
shown in Fig. 5.  The figure shows that the top curve at CT 
operation mode has a higher sensitivity than the bottom 
one at CC mode. If we replot the results in Fig. 6 as the 
heating power in the sensor divided by the temperature 
difference vs. the one third power of the shear stress, it 
can be seen that the calibration exhibits a linear 
relationship. This is consistent with the theoretical 
prediction by En.(4). Similar results can also be obtained 
for CC operation. 
2, = -OSh(dP,/dr) (5 )  
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Shear stress ‘F. (Pa) 
Fig. 5 The shear-stress calibration results of the sensor at the 
same overheat ratio of 0.2 but different operation mode, CC and 
CT, respectively. 
43.4 J I 
0.3 0.4 0.5 0.6 0.7 0.8 0.9 
(Pa‘”) 
Fig. 6 The replotted results of Fig. 5 at CT mode. 
3. Temperature Compensation 
The temperature effect of the micro sensors at a fixed 
free stream velocity (corresponding to a fixed shear stress) 
is observed. Figs. 7 (a) and (b) show the voltage output 
change vs. the flow temperature variation at different 
resistive overheat ratios for both CC and CT operation. In 
the figure, the slope for each case representing the 
temperature sensitivity of the sensor is also given. 
2oT ............................................................................................................................................ 
operation 
-=o 1 
63mVPC 
aR.O Ob 
3 7 mVPC 
04 I 
22.5 23 23.5 24 24.5 25 
Flow temperature T,  CC) 
(a) 
M) .................................. ~ ......................................................................................... 
a-4.05 CT ~ 
50 operation ~ -- 
47 mvpc 
F 
5 
-34 mVPC 
0 
10 
0 -  I 
23.8 24 24.2 24.4 24.6 24.8 25 
Flow temperature TI  CC) 
(b) 
Fig. 7 The temperature effect of the sensor at diXerent overheat 
ratio for both CC (a) and CT (b) operation. 
Based on the above temperature sensitivity results, the 
temperature effect can be compensated by either a 
software method or a specially-designed circuit as shown 
18 
in Fig. 8 for the CT operation. The main difference 
between this circuit and the previous one in Fig. 3 (b) is 
op-amps A2 and A3. The op-amp A3 is for the 
temperature compensation and A2 is for amplification and 
DC shifting. Another on-chip poly-silicon sensor (named 
cold-film sensor, it is operated at small current so that its 
heating effect is negligible) is used to pick up the flow 
temperature signal. This signal is fed to the circuit through 
op-amp A3 and then compensated with the signal from 
the brunch circuit Al .  The comparison results with and 
without temperature compensation at CT mode (resistive 
overheat ratio of 0.1) is shown in Fig. 9 and it can be seen 
that the absolute temperature sensitivity (the slope of the 
line) is decreased from 47 mVPC to 1 mVPC after the 
compensation. By tuning the gain between the input from 
the cold-film sensor and the output carefully, better results 
can be obtained. It should be pointed out that all output 
voltages have been normalized to the output E,,, of the 
first stage(A1). This compensation circuit is applicable to 
the multi-channel circuit operation. In other words, only 
one cold-film sensor is needed for multi-channel hot-film 
sensor operation. Similarly, this temperature 
compensation configuration is also suitable for CC 
operation. 
lbut 
A rl- 
Fk. 8 The temperature compensation circuit for the CT 
operation of the sensor. 
50 
without compensation CT 
uR=o.l slope: -47mVPC 
with compensation 
slope: 1 mVPC 
5‘ 
E 
5 
lu 30 
8 s 
- 
-- 
S 
0 20 
5 
-- 
5, 
0 10 -- 
04 
23.70 23.90 24.10 24.30 24.50 24.70 
Flow temperature TI (“C) 
Fig. 9 The temperature compensation results of the sensor at 
overheat ratio of 0.1 and the CT mode. 
V. CONCLUSIONS 
The micromachined hot-film shear-stress sensors have 
been designed and fabricated by micro-machining 
technology. Extensive experimental results show that the 
micro shear stress sensor at the constant-temperature 
operation mode can reach a cut-off frequency of 70 Wz, 
and a shear stress sensitivity of 70 mVRa. The 
temperature compensation of the sensor has also been 
characterized. 
ACKNOWLEDGMENT 
This work is supported by AFOSR URI project 
(University Research Initiative). 
[91 
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T. J. Hanratty and J. A. Cambell, “Measuiement of wall 
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19 


Fluidic shear-stress measurement using surface-micromachined sensors

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