Abstract—A novel silicon capacitive temperature sensor implemented with micromachined multilayer cantilevers is presented. The multi-layered sensor structure has been fabricated with SOI wafers by a 4-mask process. Using this structure, the low-power dissipation and wide temperature range can be achieved. For the present sensor, the temperature range is from -70℃ to 100℃ with the sensitivity of 7fF/℃. This makes it suitable to serve as a temperature sensor for low-power and wide temperature range applications.
INTRODUCTION Thermal sensors form the largest class of microsensors today. Temperature is one of the most important parameters in the thermal sensors. Many kinds of temperature sensors have been reported. Usually, the silicon-based temperature sensors make use of the well-defined temperature dependence of silicon bipolar transistors, PN junction or electrical resistivity. The substrate bipolar transistor, as a CMOS compatible intergrated temperature sensor, operates at two different emitter currents; the difference in base-emitter voltage is proportional to absolute temperature (PTAT). The application area of PTAT temperature sensor is the thermal management in large digital systems and, however, cannot operate in the range of -90℃ to -60℃ [1]. For low power application, a capacitive temperature sensor is recently reported [2], [3]. In this sensor, one movable electrode of the capacitance is a polysilicon-gold bimorph beam fabricated with a surface-micromachined process. The other electrode is placed on glass substrate. This MEMS-based temperature sensor produces a sensitivity of 15 fF/℃ from 20 to 100 ℃. Such a capacitive device shows nonlinear characteristic and limited temperature range, as the capacitance value is inversely proportional to the distance between the two electrodes. Furthermore, the special bonding process was required to form a cavity between the two electrodes.
Although a vast selection of thermometers exists, there is no simple solution for all applications. For example, the Pt resistor as a typical thermistor is still used in radiosonde for temperature measurement which cannot satisfy the demand of modern weather monitoring [4]. With the development of
MEMS technology, the temperature sensor with wide temperature range, low cost, high-accuracy, low-power dissipation for harsh environmental monitoring is desired. MEMS technology has generated a significant amount of interest due to the potential performance and cost advantages with micro-scale devices fabricated based on silicon processing technology.
In this paper, a capacitive temperature sensor is proposed with a multilayer cantilever [5]. The physical effect of strain on the dielectric property, together with the effect of thermal expansion coefficient mismatch is used as the basic operation principle of the proposed cantilever device. The capacitive transduction mechanism, compared with optical, piezoresistive detection methods used in cantilever-based sensors, has the advantage of low-power dissipation, and the sensitivity of the sensor keeps constant with the scaled-down of the structure. To enhance the performance of the capacitive sensor, the strain/dielectric response of materials, the so-called dielectrostriction effect, has been introduced for pressure, stress, strain and tactile sensor [6], [7]. The variation of dielectric properties with deformation is considered to be the fundamental phenomenon in dielectric material [8]. It has been reported that the dielectric property is related to the mechanical strain in many materials including the silicon [9] and SiO2 [10], and even an initially isotropic material can become anisotropic in the deformed state [8].
STRUCTURE AND THERMO-MECHANICAL ANALYSIS
A. Structure and principle A schematic of a proposed capacitive temperature sensor
is shown in Fig.1. A micro composite cantilever consists of four layers. The top and bottom layers are aluminum and silicon, respectively, which are also used as the electrodes of the sensing capacitor. The center dielectric layers are silicon nitride and silicon oxide. When temperature varies, thermal stresses are introduced due to mismatches of the thermal expansion coefficient between adjacent thin films within the multilayer structure. Resultant moment can be easily generated from the stresses. Thus, the cantilever is bent concave or downward as temperature decreases or increases, causing the change of the sensing capacitance.
The capacitance C of a parallel-plate capacitor with an area A and thickness of dielectric layer h between the electrode plates is
ACh
ε= (1)
where ε is the permittivity of dielectric layer between the parallel electrode plates. Therefore, the relative capacitance change of the flexible parallel-plate capacitor can be expressed as
/ / h / hC A AC
ε εΔ = Δ + Δ − Δ (2)
The terms /A AΔ and h / hΔ present the effect of the geometry variation on capacitance change. It is obvious that these two terms have the opposite sign when the proposed structure is subjected to temperature. Thus, the geometry effect on capacitance change is weakened. The term /ε εΔ shows the relative variation of the dielectric property of dielectric layer with strain. Electrostriction and flex electricity are believed to contribute to this change [6], [11]. The following analysis is focused on the mechanical deformations of the temperature sensor due to the temperature change. However, by taking into account the dielectric effects of dielectric materials due to deformation, the output of the capacitive sensor can be enlarged.
B. Modeling and simulation Timoshenko was first to develop the fundamental
mechanics of a bimaterial (or bimetallic strip) subjected to a uniform temperature difference [12]. Based on Timoshenko’s theory, the following major assumptions were made: the layers are perfectly elastic and homogeneous; and the beam is narrow enough, so that both stress and strain in the width direction can be neglected. The temperature distribution within the cantilever is uniform as it is used as air temperature sensor. And a linear elastic material model and constant properties was assumed for all materials on the cantilever over the entire temperature range.
Fig.2 shows the forces and moments acting on the cross-section of a segment along the length of the composite beam as the temperature is decreased. The internal stress over the
cross-section of material ( i ) on the concave can be represented by an axial tensile force iF and bending moment
iM . Due to the fact there are no external forces, all forces acting over any cross-section of the beam must be in equilibrium, therefore,
0m
ii
F =∑ (3)
11 2
1 2 1tt t
( ) (t ) ( t )2 2 2
m mm
i m ii i
M F F F−
− = + + + + +∑ ∑ (4)
Based on beam theory, the radius of curvature of each layer ir is given by
i ii
i
E Ir
M= (5)
where iE is the Young’s modulus, and iI is the moment of inertia.
Noting the fact that the thickness is much less than the curvature of the cantilever, the curvature radius of each layer approximately yield ir r= . As a result, Eq. (4) becomes:
11 2
1 2 1tt t1 ( ) (t ) ( t )
2 2 2
m mm
i i m ii i
E I F F Fr
−
− = + + + + +∑ ∑ . (6)
Assuming the interface bonding between different layers is perfect, thus the total strain on the bearing surface of two adjacent layers i and 1i + must be equal, which is given by superposition of the strains due to the thermal expansion, axial force and bending, therefore,
1 1i+1
1 1
t tT T
2 2i i i i
ii i i i
F FA E r A E r
α α + +
+ +
Δ + − = Δ + + , (7)
for 1 1i to n= − ， Where iα is the thermal expansion coefficient of i th layer.
When the ambient temperature is changed by TΔ , the in plane deflection of a cantilever beam at its free end is:
2
2LLr
Δ = (8)
for L<< r, where L is the initial length of the beam.
Fig.2. Forces and moments acting on the cross section.
Fig.1. Structure of the capacitive temperature sensor.
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With Eqs. (3), (6) and (7), the radius of curvature of the micromachined cantilever, r, and all axial tensile forces, iF , can be solved as the function of thermal expansion coefficient, Young’s Modulus and thickness of each layers, but not the function of width. In this case, this developed model from Timoshenko formula is verified by ANSYS software. The results obtained from finite-element analysis agreed with these analytical solutions well.
The strain of each layer can be easily obtained after the forces and curvature radius are solved. With the above model, the stress, strain and deflection can be predicted. Fig. 3 is a three-dimensional plot of the strain of Si3N4 layer as a function of the thicknesses of aluminum (t1) and silicon layer (t4). Fig. 4 shows the strain of dielectric layer (SiO2) and tip deflection as a function of the thicknesses of the top and bottom layers.
FABRICATION AND TEST
C. Fabrication The process flow of the cantilever-type sensor is shown in
Fig. 5. A SOI wafer was chosen as the substrate material. Firstly, a 0.3μm dry thermal oxide was grown as the first dielectric layer. Then low-pressure chemical-vapor deposition (LPCVD) Si3N4 with a thickness of 0.15μm was double-sided deposited as the second dielectric layer, and meanwhile as the mask for silicon back etching. Next, the SiO2 and Si3N4 in the front side of the wafer were patterned. Subsequently, a 2μm Al layer was sputtered on the wafer front side and then was patterned leaving the area for bottom electrode contact and the top electrode. Si3N4 and SiO2 on the back side of the wafer were then patterned to expose the back-etching window using double-sided aligner. After that, the wafer was mounted in the Teflon holder to protect the front side of the wafer from etching, and immersed in the 40 wt% KOH solutions at 80℃, the wafer begun to back etch the exposed silicon with the etching rate about 60μm/h. The etch stops at the SiO2 layer edge. Finally, after the embedded SiO2 layer of SOI was etched by RIE, inductive coupled plasmas (ICP) was used to release the cantilever structure. Cantilever devices with different length and widths were designed and fabricated. A capacitive sensor with 1200 µm length and 300µm width is shown in Fig. 6.
Fig.4. Strain of SiO2 layer as a function of the thicknesses of Si and Al layer.
Fig.6. SEM photo of a sensor structure.
Fig. 5. Fabrication process flow chart of the sensors.
Fig.3. Strain of Si3N4 layer as a function of the thicknesses of Si layer and Al layer.
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D. Measurement The developed measurement system is illustrated in Fig.
7. The test was carried out by putting the device inside a temperature control chamber, VT7004 by Vötsch, monitoring the temperature with a PT100 thermometer closed to the device and a multimeter of high resolution, Keithley 2001 when the temperature changes. The temperature of the chamber was changed between -70 to 100℃. The capacitance of the sensor was measured by HP4284A Precision LCR meter at 10 kHz frequency, 0V applied bias. The temperature and corresponding capacitance were all recorded with PC data acquisition system. Therefore, a quasi-automatic test can be performed in such a system.
The experimental results are shown in Fig. 8. The responses of two typical sensors indicate that the capacitance varies monotonically with the ambient temperature. The test average sensitivities of the two devices are about 7fF/� and 3.2 fF/� for the area 2000μm by 500μm and 1500μm by 300μm, respectively. The test results also show that nonlinearity over the full range is less than 2.1% to the overall capacitance, while the maximum hysteresis error occurs in the temperature range of -20 to 10� and the error is about 1.6%.
CONCLUSION A micromachined silicon capacitive temperature sensor based on a multilayer cantilever is proposed, designed and fabricated. The experimental results show that the performance of the sensor is suitable to applications for the wide temperature range and low power consumption. The presented capacitive sensor provides sensitivity about 7pf/℃ from -70 ℃ to 100 ℃ . The dielectric effect contributes dominantly to the sensitivity enhancement. This sensor has some favorable features, such as micro size owing to its micromechanical structure, high sensitivity owing to its working principle, CMOS compatible technology. Such sensor is a capacitor, resulting in low energy consumption and no heat dissipation. This makes it suitable to act as temperature sensor in radiosonde.
ACKNOWLEDGMENT The project is supported by the Hig-Tech Research and
Development of China under contract No. 2007AA04Z306.
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Fig.7. Measurement system setup.
Fig.8. Capacitance variation as a function of temperature.
