Advances in Natural Sciences, Vol. 10, No.2 (2009) (187-192)

Nanosciences and Nanotechnology

FULL ANALYSIS AND FABRICATION OF A PIEZORESISTIVE
THREE DEGREE OF FREEDOM ACCELEROMETER
Tran Duc Tan, Nguyen Thang Long, and Nguyen Phu Thuy
Faculty of Electronics and Telecommunication,
College of Technology, Vietnam National University,
144 Xuan Thuy Road, Hanoi, Vietnam
Dao Viet Dung and Bui Thanh Tung
Research Organization for Science and Engineering,
Ritsumeikan University, Shiga, Japan
Received January 26, 2009

Abstract. In this paper, a miniaturized piezoresistive three-degree of freedom accelerometer has
been developed and fabricated using MEMS (micro electromechanical systems) technology. We
proposed a flexure configuration in order to meet requirements of small cross-axial acceleration,high and linear sensitivity. The overall chip dimension is 1.5×1.5×0.5 mm3 (L×W×T) and thebeam size is 950×80×10 µm3 (L×W×T). Twelve piezoresistors are diffused on the surface of beam
structure. Three simple Wheatstone bridges are formed directly on this sensor by interconnecting
these piezoresistors to sense three components of acceleration independently. This sensor isdesigned to have the bandwidth of 200 Hz with a cross-axis sensitivity drops to below 3%. A
completed simulation and analysis were performed in which the real conditions in fabrication
are considered. The full analysis proposed in this paper is capable to eliminate the discrepancy
between simulation results and experimental data. The measured sensitivity is 0.2 mV/G (Vin= 3 V). Experimental results show that the sensor is suitable for applications in sign language
or patient monitoring with a high accuracy.
Keywords: MEMS, piezoresistive effect, design
PACS number: 85.85.+j

1. INTRODUCTION
During last decades, MEMS technology has been rapidly developed with the successin fabricating miniaturized mechanical structures and integrating them with microelectronic components. In order to commercialize MEMS products effectively, one of the key
factors is to optimize the design process. In this paper, we focused on the design aspectsof a typical MEMS device: a piezoresistive accelerometer.
Although piezoresistive accelerometers suffer from the dependence of temperature,they have DC response, simple readout circuits, ability to meet the requirement of highsensitivity, high reliability and low cost in addition to the potential for mass production.

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The full simulation and analysis proposed in this paper can give the results which are very
close to experimental data.
2. WORKING PRINCIPLE
The three-degree of freedom accelerometer always requires small cross-axial acceleration, high and linear sensitivity. We proposed a flexure configuration that is shown in
Fig. 1 in order to meet these critical designs.

Fig. 1. The 3-DOF Piezoresistive accelerometer.

The operation of the device is based on Newton’s second law of motion. An external
acceleration results in a force being exerted on the mass. This force results in a deflectionof the proof mass. When a vertical acceleration (Az ), i.e. Z component, applies to thesensor, the mass will move vertically up and down. Similarly, when the X or Y componentof transversal acceleration acting on the sensor, the mass will move laterally. The deflection of the proof mass causes stresses in four beams, resulting in resistance variation of thepiezoresistor doped on the surface of the beam structure [1]. This variation was converted
into electrical signals by using three imbalance Wheatstone bridge circuits. These Wheatstone bridge circuits were built by interconnecting twelve p-type piezoresistors. Thesep-type piezoresistors were chosen to diffuse on the surface of these four beams because
they can provide the maximal resistance variations. These piezoresistors were alignedwith the crystal directions <110> and <11̄0> of n-type silicon (100). These piezoresistors
were designed to be identical and fabricated by diffusion method.
The phenomenon that resistance of crystal material is varied when subjected tomechanical stresses is called piezoresistance effect. It caused by the anisotropic characteristics of the energy resolution in crystal space. In silicon material, there are only three
independent coefficients π11 , π12 and π44 . The longitudinal piezoresistance coefficient πlis defined in the case when the stress parallels with the direction of the electric filed andcurrent density. Similarly, the transverse piezoresistance coefficient πt is defined in thecase when the stress is perpendicular with the direction of the electric filed and current
density. In directions <110> and <11̄0> of n-type silicon (100), we can find these two

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coefficients from to three independent coefficients π11 , π12 and π44 by using relations:1(π11 + π12 + π44 ) ,2
1πt = (π11 + π12 − π44 ) .
2πl =(1)From simulation results in Fig. 3 (section 3), we found that two normal stresses
σ2 and σ3 are rather smaller when comparing to σ1 . This phenomenon will affect thesensitivity of the sensor. To eliminate this effect, we should avoid placing piezoresistorsnear the fixed end and the start of the beam. Thus, we can calculate the relative changeof resistance due to the normal stress as follows:∆R= πl σl + πt σt .
(2)R
3. DESIGN AND ANALYSIS BY USING ANSYS
At first, the structural analysis of the sensing chip was done by modified nodal
analysis (MNA) method for a quick estimation of sensor dimensions based on the required
ranges of acceleration and the dimensions of the beam. Then, the finite element method(FEM) is applied to perform analyses of the stress distribution in the flexure beams. Basedon the stress distribution, piezoresistors are placed to eliminate the cross-axis sensitivities
and to maximize the sensitivities to three components of acceleration. The finite element
model of the sensing chip was analyzed by using ANSYS software.
Figure 2 shows the mesh generation for analysis, and the stress distribution on thebeam is shown in Fig. 3. Figure 4 shows the stress distribution in the X-oriented, Yoriented and Z oriented of the first beam caused by the acceleration Az . Clearly, thestress distribution in the direction along the beam is much larger than the others’.

Fig. 2. The dense mesh generation of the FEM model.

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Fig. 3. The stress distribution on the beams
caused by the acceleration Az .

Fig. 4. The stress distribution on the first beam.

Based on the stress distribution in the flexure beams, twelve piezoresistors are placed
to maximize the sensitivities to three components of acceleration and eliminate the crosssensitivity. The sensing principle of the sensor is based on the characteristic of the p-typepiezoresistor. These identical piezoresistors are diffused on the surface of the beams toform three Wheatstone bridges [2].
4. SENSITIVE ERROR ANALYSIS
In the previous section, we have performed design and simulation on the sensor withidealization constraints. The full analysis in this section is capable to eliminate the discrepancy between simulation results and experimental data. The mechanical sensitivitiesof each components of acceleration can be respectively expressed as:i
Sstress=σi, i = 1, 2, 3,ai(3)iwhere Sstressand σ i are mechanical sensitivity to the acceleration ith component ai andlongitudinal stress, induced by the application of this acceleration, respectively. The
electronic sensitivity can be given by∆RVouti=Vin = πl Sstress
Vin ,(4)Si =aiR

where Si and Vout are the sensitivity to the ith acceleration component and output voltage,respectively. The longitudinal stress σ i in Eq. (3) obtained from the stress analysis byutilizing ANSYS software. This value is the stress at the center point of the piezoresistor
and on the surface of the beam. We have to recalculate it by the stress analysis along thelength, width and thickness of the piezoresistor. Figure 4 represents the stress distribution
when the Az is applied to the sensor. The Az piezoresistors are placed onto this transverse
beam in order to sense this acceleration component. We can see that the stress is not thesame along length of the piezoresistor. The stress analysis along the width and thickness
can give the similar results. We now can define αl , αw , and αt as the stress factors

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in length, width, and thickness of the piezoresistor, respectively. These values can beevaluated as follows:
ZLZWZT
i −1ii −1ii −1αl = Lσlσ (l) dl, αw = W σlσ (w) dw, αt = T σlσ i (t) dt, (5)000where σ i (l), σ i (w) and σ i (t) are the stress along the length, width, and thickness (L,W and T) of the piezoresistor caused by the ith acceleration ai . They can be obtained
by ANSYS stress analysis technique. Finally, the value of the longitude stress can becorrected by using following formula_i

σ = αl αw αt σ i_1(6)_2_3

After stress correction processes, we derived σ = 0.73σ 1 , σ = 0.73σ 2 , and σ = 0.75σ 3 .
Recalculation of (4) can give us the more correct analysis. This correction is avery important step because this stress error is a major error compared to fabrication or
readout circuit ones.

Fig. 5. The ratio S i (T ) /S i (T0 ) at the impurity
concentration of 5.1019 atoms/cm3 .

Fig. 6. Microphotograph of fabricatedaccelerometer.

In order to differentiate between the temperature sensitivity of the piezoresistors andthe piezoresistive coefficient π1 , the impurity concentration was controlled at about 5.1019
atoms cm−3 to get π1 = 35.10−5 MPa [3]. However, we will investigate the sensitivity
error that this choice still brings about. Temperature affects the piezoresistive coefficientthrough a change in the mobility and carrier concentration (N ) in the respective bands[4]. The dependence of the piezoresistive coefficient on the impurity concentration at agiven temperature (T ) can be obtained by multiplying the piezoresistive factor P (N, T )by the PR coefficient at room temperature (T0 ) as follows:
π (T ) = π (T0 ) P (N, T ) ,0(EF /kT )300 Fs+0.5,P (N, T ) =T Fs+0.5 (EF /kT )

(7)
(8)

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where k is Boltzmann constant and T is temperature. The Fermi integral is the function oftemperature and the Fermi energy EF [5]. We observe that the ratio between the sensitivity at environment temperature to the sensitivity at the room temperature S i (T ) /S i (T0 )by substituting Eq. (7) into Eq. (4) (see Fig. 5).
The big gap between simulation and experimentation can be reduced effectively
by these full analyses. The measured sensitivity is 67 µV/V/G while the theoreticalsensitivity is 82 µV/V/G. Experimentation results show that the sensor (Fig. 6) is suitable
for applications in sign language or patient monitoring.
5. CONCLUSION
This paper presents a full design and analysis for a specific MEMS accelerometer.
The piezoresistive effect was used as the sensing principle of the sensor. The design results
can be closest to fabrication condition by sensitivity error analysis.
ACKNOWLEDGMENTS
This work is supported by the Ministry of Science and Technology, project No.
410506.
REFERENCES
1. Yozo Kanda, Sensor. Actuat. A 28, 64 (1991).
2. Dao Viet Dzung, Toshiyuki Toriyama, John Wells, and Susumu Sugiyama, Sensor. Mater. 15,113 (2003).
3. Dao Viet Dzung, T. Toriyama, and S. Sugiyama, The 3rd Int’l Conference on Sensors, Vienna
University of Technology, Vienna, Austria, IEEE Sensors Council, 2004, p. 1464.
4. Y. Kanda, Jpn. J. Appl. Phys. 26, 1031 (1987).
5. C. Pramanik, H. Saha, and U. Gangopadhyay, J. Micromech. Microeng. 16, 1340 (2006).
Corresponding author: Tran Duc Tan, Faculty of Electronics and Telecommunication, Collegeof Technology, Vietnam National University, 144 Xuan Thuy Road, Hanoi, Vietnam. E-mail:tantd@vnu.edu.vn