Novel synthesis design of a 3DOF silicon piezoresistive micro accelerometer

Proceedings of the 4th IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems January 5-8, 2009, Shenzhen, China

Novel Synthesis Design of a 3-DOF Silicon Piezoresistive Micro Accelerometer Tan D. Tran1, Minh D. Nguyen2, Long T. Nguyen1, Tue H. Huynh3, and Thuy P. Nguyen1 1

2

MEMS and Microsystems Department, College of Technology, VNUH, VIETNAM Inorganic Materials Science, MESA+ Institute for Nanotechnology, University of Twente, NETHERLANDS 3 Bac Ha International University, VIETNAM

Abstract — This paper presents the novel synthesis design of a three-degree of freedom silicon piezoresistive accelerometer. The purpose of this novel synthesis design is to achieve the high performance device. The design synthesis has been performed based on considerations of mechanical and electronics sensitivities, noise and thermal effects, respectively. The mechanical sensitivity is optimized due to combination of a FEM software and a MNA one. The electronics sensitivity, noise and thermal effect can be determined by thermal, mechanical and piezoresistive coupled-field simulations. The dimension of sensor is as small as 1.5 mm2, so it is suitable for many immerging applications. Keywords — optimization; piezoresistive; accelerometer

I.

coupled-field

simulations;

INTRODUCTION

During the last decades, miniaturized multi-axis of accelerometers is a high demand in various applications due to their very small size, minimum energy consumption as well as their low cost [1]. There is an extensive research on silicon piezoresistive accelerometer to improve its' performance and further miniaturization [2,3]. However, a comprehensive design and analysis considering the optimization of sensitivity, noise and thermal effect has not been reported. This paper presents the full design of a 3-DOF micro accelerometer in two phases: coupling ANSYS and SUGAR to optimize the structure of the device; and coupled analyzing for thermal – mechanical – piezoresistive fields to evaluate the sensor performance. The results are very helpful to improve and optimize the performance of the device.

II.

Figure 1. 3D model of 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 deflection of the proof mass. When a vertical acceleration (Az), i.e. Z component, applies to the sensor the mass will move vertically up and down. Similarly, when the X or Y component of 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 the piezoresistor doped on the surface of the beam structure [3]. 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. These p-type piezoresistors were chosen to diffuse on the surface of these four beams because they can provide the maximal resistance variations. These piezoresistors

WORKING PRINCIPLE

High sensitivity and small cross-axis sensitivity are important requirements for the 3-DOF accelerometer. It is known that the resonant of the structure determines the mechanical sensitivity. To get high sensitivity, we have to pay a low bandwidth by reducing the resonant frequency. We proposed a configuration as shown in Fig.1 to trade-off between these critical characteristics. It consists of a seismic mass suspended by four beams which have long and highly symmetric configuration.

_

were aligned with the crystal directions and of n-type silicon (100). These piezoresistors were designed to be identical and fabricated by diffusion method. III.

DESIGN AND ANALYSIS

In the first phase of the synthesis design, the structure of the accelerometer was optimized by combining the finite element method (FEM) with ANSYS and modified nodal analysis (MNA) method with SUGAR [7].

© 2009 IEEE

108

Proceedings of the 4th IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems January 5-8, 2009, Shenzhen, China

Fig.2 shows the synthesis flow that was used to obtain the target design. We used SUGAR to quickly sketch out the structure of the accelerometer. Design goal for our configuration to get the first resonant frequency at 1500 Hz. After iterating in SUGAR and small manual tuning to converge towards this goal, an acceptable preliminary design was brought to ANSYS for FEM verification. Afterward, the model is brought to the second phase of the synthesis process.

TABLE I.

Rz1 Az + Ay Ax -

Y N

Design Constraints

Desired Conditions

1

RESISTANCE VALUES CHANGES WITH THREE COMPONENTS OF ACCELERATION

Rz2 0 -

Rz3 Rz4 Ry1 + + 0 + + 0

Ry2 + +

Ry3 +

Ry4 Rx1 Rx2 Rx3 Rx4 + 0 + + 0 0 + - +

To predict the other characteristics of the piezoresistive sensor [5,6], multiphysics analyze are needed in the 2nd phase.

6

The model

2

Finite Analysis Method (ANSYS) 5

Modified SUGAR library

3

N

Nodal Analysis in MATLAB/SUGAR and Auto Refinement

Y

Manual Tuning and Synthesis

4

Thermal Analysis

Structural Analysis

Piezoresistive Analysis

Figure 2. The first phase of the synthesis design

The most important aspect of our design process which requires FEA is the analysis of the stress distribution in the flexure beams. Based on this distribution, piezoresistors are positioned to eliminate the cross-axis sensitivities and to maximize the sensitivities to the three acceleration components. Stress analysis is then performed to determine the stress distribution in the beams (Fig.3). Based on the stress distribution in the flexure beams, twelve piezoresistors are placed to maximize sensitivity to the three components of acceleration and eliminate cross-sensitivity. The sensing principle of the sensor is based on the characteristic of the ptype piezoresistor [4]. The resistance decreases when the sensor is exerted by a compressive stress and increases when it is exerted by a tensile stress. Table 1 summarizes the increase (+), decrease (-), or invariance (0) in resistance of piezoresistors due to application of accelerations Ax, Ay, and Az. These identical piezoresistors are diffused on the surface of the beams to form three Wheatstone bridges [3].

Fabrication & Test Figure 4. The second phase of the synthesis design

Conventionally, two different software models are used for computation of the temperature distribution and structural sensitivity. This conventional technique is time consuming and errors might be produced during the transfer between the two models. Obviously, the coupled-field analysis method is more efficient than the conventional one because a unique model is built within a single software tool and the related data can be transferred easily between elements because of the unique FEA mesh. The ANSYS SOLID87 and SOLID92 elements were used for such thermal and structural calculations, respectively. From the thermal distribution, the thermal stress on the sensor can now be calculated. Figure 5. shows the stress distribution in along the X, Y and Z of the first beam caused by the acceleration Az and thermal effect, concurrently. This analysis appropriately mimicks the real operating conditions of the sensor.

Figure 3. Stress distribution of a beam caused by vertical acceleration Az.

109

Proceedings of the 4th IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems January 5-8, 2009, Shenzhen, China 0.0015 Az Ay to Az 0.001

Ax to Az Az to Ay Ax to Ay

output (V)

0.0005

Ay

0 -15

-10

-5

0

5

10

15

-0.0005

-0.001

-0.0015 acceleration (g)

Figure 7. The sensing and crosstalk voltages obtained by the ANSYS

Figure 5. The stress distribution on the first beam due to the vertical acceleration and thermal effect

The sensing chip was fabricated by micromachining process. The sensing chip was fabricated by micromachining process. Starting material is a multi layers SOI wafer. Thermal diffusion is performed to form p-type Si, EB lithography and RIE to create piezoresistors, metallization process to make interconnection, and deep RIE to define the beam and proof mass. Figure 8. and 9 shows the respectively the photographs of fabricated sensing chip.

Coupling to the structural – piezoresistive analysis, the resistors volumes are modeled using the piezoresistive option of the coupled-field solid SOLID227 and the structural part of the beam is modeled using SOLID92. The resistors are connected into a Wheatstone bridge arrangement by coupling the VOLT degrees of freedom on area sides of the resistors (Figure 6. ). The mechanical analysis is applied to find out the optimal locations for the piezoresistors in order to sense accelerations minimum cross-talks. Then, the piezoresistive effect is analyzed in order to obtain the sensing output voltage and the corresponding crosstalk voltages.

Figure 8. Micrograph of a fabricated chip

Figure 6. The Wheatstone bridge of the AZ acceleration circuit formed by SOLID227 and SOLID92 elements

The applied acceleration results in stress redistribution, leading to the variation of the piezoresistors, giving rise to an output voltage that depends on the input acceleration as shown in Figure 7. Figure 9. Zooming in the first corner of the sensing chip: fabrication and mask design

The static sensitivity of the fabricated sensor is characterized by rotating the accelerometer’s sensitive axes around the earth’s gravitational vector from 90o to -90o. By normalizing the sensitivity at 1 g, the steady state response of the voltage is shown in Figure 11.

110

Proceedings of the 4th IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems January 5-8, 2009, Shenzhen, China

between theoretical and experimental results as have been reported in [6]. The novel analysis can give us more informative and reliable results than the previous one and it is necessary optimize the parameters of the sensor. IV.

CONCLUSION

This paper presents a novel synthesis design of a specific MEMS accelerometer. The structure of the sensor was optimized by combining of SUGAR and ANSYS. The piezoresistive effect was used as sensing principle of the sensor. ANSYS software was utilized as the basis to simulate the thermal, mechanical, and piezoresistive properties of the silicon based accelerometer. This analysis is necessary to improve and optimize the performance of the device. ACKNOWLEDGMENT This work is supported from the Ministry of Science & Technology, project No. 410506.

Figure 10. The output response of the accelerometer vs. orientation to gravity

In order to determine the linearity of this sensor, we assume that the offset voltage is zero. Hence, the relationship between acceleration input and voltage output can be obtained as shown in Figure 11.

REFERENCES [1] [2]

[3]

[4]

[5]

[6]

[7] Figure 11. The static response of the AZ orient acceleration

By comparing the simulated and experimental results, it can be seen that the different is not more than 15%. This result is quite acceptable because this difference falls in the gap

111

Yozo Kanda, “Piezoresistance Effect of Silicon”, Sensors and Actuators, Vol. A 28, pp. 83-91, 1981. T. D. Tran, Dzung V.D, T. T. Bui, L. T. Nguyen, T. P. Nguyen, Sugiyama. S, “Optimum Design Considerations for a 3-DOF Micro Accelerometer Using Nanoscale Piezoresistors”, in Proceedings of the 3rd IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems, 2008, China, pp. 770-773 . Dzung V.D, Toriyama. T, and Sugiyama. S, “Noise and Frequency Analyses of a Miniaturized 3-DOF Accelerometer Utilizing Silicon Nanoscale Piezoresistors”, in The 3rd Int'l Conference on Sensors 2004, vol. 3, pp. 1464-1467. Y. Kanda, “Graphical representation of the piezoresistance coefficients in Si shear coefficients in plane”, Japanese J. Appl. Phys., vol. 26, No. 7, pp. 1031-1033, 1987. Sekalski, P. Pons, and P. Napieralski, “Finite elements simulations of piezoresistive sensor of blood pressure”, in Proceedings of the 7th International Conference 2003, pp. 509- 512. C.Pramanik, S.Banerjee, D.Mukherjee, and H.Saha, “Development of SPICE Compatible Thermal Model of Silicon MEMS Piezoresistive Pressure Sensor for CMOS- MEMS Integration”, in IEEE SENSORS 2006, pp. 761 – 764. J. Clark, N. Zhou, S. Brown, and K.S.J. Pister, "Nodal analysis for MEMSdesign using SUGAR v0.5”, Proc. 1998 International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM 98), pp. 308-313.