# Prediction of Cross-Axis-Sensitivity of Inertial Micro-Sensor Through Modeling and Simulation

Prediction of Cross-axis-sensitivity of inertial micro-sensor through modeling and simulation B. P. Joshi1, A. B. Joshi2, A. S. Chaware2 , S.

**Prediction of Cross-Axis-Sensitivity of Inertial Micro-Sensor Through Modeling and Simulation**

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A. Gangal*2 1 Armament Research & Development Establishment (ARDE), DRDO Ministry of Defence, Dr Homi Bhabha Road, Pashan Pune-411021, India Ph. No. +91-20-2588 4795, Fax No. +91-20-2589 3102 E-mail:[email protected] org 2 Department of Electronic Science, University of Pune, Pune-411 007, India Abstract: In addition to sensitivity and bandwidth, the cross-sensitivity is an important design parameter for acceleration/ inertial sensor design.

In this paper prediction of cross-axis sensitivity of cantilever type of piezoresistive accelerometer is discussed. The effect of variation in geometrical parameters such as width and thickness of flexure & proof mass (PM) on crosssensitivity are studied. Optimization of cross-sensitivity by varying geometrical parameters has been attempted. This paper deals with simulations of skewed type (Flexure perpendicular to proof mass) and planar type (Flexure in plane with Proof mass) structure for cross-axis sensitivity analysis. The simulation and modeling has been carried using Coventorware MEMSCAD software.

Keywords: Inertial sensor, Cross-sensitivity, MEMSCAD, FEM. 1 Introduction Micromachined accelerometers are widely used in many applications. Large number of scientists all over the world are working on MEMS based acceleration sensors that are mostly either capacitive or of piezoresistive type. A piezoresistive type of acceleration sensor basically consists of a proof-mass attached to a micro-cantilever (Flexure) all made out of silicon. [1-4]. For piezoresistive accelerometer sensitivity S is defined as relative change in resistance per unit of acceleration.

Following mathematical equation defines relation between sensor dimensions and its sensitivity [5]. Equation for sensitivity can be written as: S = K . g . L t 2 (In Pa. ) …… Eq. 1 Where, S is the sensitivity [stress level], g is the applied acceleration, t is thickness of flexure in µm, L is length of flexure in µm, K is the constant of proportionality. An accelerometer is expected to have only one sensitive axis. However, cantilever type of accelerometer is also sensitive in other direction. This undesired sensitivity is called as cross axis sensitivity.

Cross axis sensitivity is the maximum sensitivity in the plane perpendicular to the sensitive direction relative to the sensitivity in the measuring direction. It is calculated as the geometric sum of the 1 sensitivities in two perpendicular directions in this plane [6]. If Z is sensitive axis then cross sensitivity is defined as ……Eq 2 Where suffix (x, y, z) denotes axis in which sensitivity is measured. Effect of cross sensitivity is one of the most important design considerations. Many attempts have been made to reduce cross sensitivity by the accelerometer designers. 7-8]. Since it is a structure deflecting under influence of inertial force, stress is developed in the flexure due to its bending. Therefore it can be stated that if the width of flexure is much greater than its thickness the cross axis sensitivity will be low. Different types of mechanical designs and structures have been tried by designers to reduce cross-sensitivity effect. Efficient use of four-piezoresistors in bridge structure is mostly tried structure [7]. Another way to reduce cross sensitivity is multi flexure accelerometer [8].

However, all these structures have a major drawback, that is, they require more processing steps as well as larger size on chip. In this paper, single cantilever type piezoresistive accelerometer is presented. The crosssensitivity is analysis is carried out by varying width as well as thickness of flexure and proof mass. Paper discusses simulations carried out for skewed and planner structure accelerometer using Coventorware software. 2 Simulations Cantilever (Flexure) type of piezoresistive accelerometer is modeled and simulated using Coventorware 2003 software. Fig. shows Skewed type acceleration sensor structure, in which Flexure is perpendicular to proof mass and sensitive axis is Y-axis. The sensor is modeled with proof mass having dimension of 2000µm X 400µm X 200µm (LxWxH) and flexure is having dimensions of 100µm X 50µm X 12µm (LxWxH). In this structure, flexure width is in Z-axis and flexure thickness is in Y-axis. Fig. 2 shows the planar type of accelerometer of the above dimension, in which flexure is in plane with Proof Mass. In this case, flexure width in Y-axis, thickness is in Z-axis. Z-axis is sensitive axis.

Simulation is carried out using MemMech solver. The Max stress values are considered for discussion in terms of sensitivity. Z Y X Fig 1: Skewed piezoresistive Accelerometer Fig 2: Planar Piezoresistive Accelerometer 2 Simulations are carried out to find cross-axis sensitivity by varying flexure thickness & flexure width. Simulations are also carried out to find cross-axis sensitivity by varying thickness and width of proof mass. 3 Results and discussions 3. 1 Skewed structure (Fig 1) Simulations were carried out on skewed type of structure (of dimension mentioned in simulations above) by varying its lexure thickness. Flexure thickness is varied from 50 µm to 200 µm and flexure width is kept as 12 µm. Skew structure response for variation in flexure thickness is shown in table No. 1. Here sensitive axis is Y-axis. Table 1: Cross axis sensitivity w. r. to variation in Flex thickness for skewed structure Flexure thickness In µm 50 100 150 200 Sz Sx Sy (In MPa) (In MPa) (In MPa) 82 6. 5 340 22 1. 5 170 9. 8 0. 52 110 5. 6 0. 19 81 % Cross-Sensitivity 24. 19 12. 97 8. 92 6. 92 Thickness to width ratio 4. 17 8. 33 12. 50 16. 67

It is observed that as the flexure thickness is increased while keeping the width same, cross axis sensitivity decreases but at the cost of sensitivity, which is not acceptable. To minimize this undesirable cross-sensitivity effect, structure is modified. In modified structure, flexure is in plane with proof mass. [Fig no. 2] Further simulations are carried out with Planner structure. 3. 2 Planar Accelerometer Planner accelerometer of above-mentioned dimensions was simulated. Varying geometrical parameters like thickness & width of proof mass as well as flexure simulations were carried out.

The results are given in following paragraphs. Here sensitive axis is Z-axis. 3. 2. 1 Variations in flexure width(FW) Simulations are carried out in MEMMECH Solver by varying flexure width from 12µm to 30 µm while keeping flexure thickness same as 50 µm. Following table shows effect of flexure width on sensitivity as well as cross-sensitivity. Table 2: Cross axis sensitivity for various flexure widths of planar structure Flexure Width (In µm) 12 18 24 30 Sensitivity Sx Sy Sz(In MPa) (In MPa) (In MPa) 330 28 25. 2 150 13 11. 29 83 7. 4 6. 34 54 4. 9 4. 07 % Cross axis Sensitivity 11. 42 11. 48 11. 74 11. 80 Thickness to width ratio 4. 7 2. 78 2. 08 1. 67 3 It can be seen from the above results that as thickness to width ratio reduces cross-sensitivity marginally increases but effecting drastic reduction in sensitivity of the sensor. 3. 2. 2 Variation in flexure thickness (FT) Simulations are carried out in MEMMECH solver by varying flexure thickness from 50 to 125 µm. Following table shows effect of flexure thickness on sensitivity as well as cross-sensitivity. Table 3: Cross axis sensitivity for various flexure thickness of planar structure Flexure Width (In µm) 50 75 100 125 Sensitivity Sx Sy Sz(In MPa) (In MPa) (In MPa) 330 28 25. 220 19 14 160 14 8. 8 130 11 5. 9 % Cross sensitivity 11. 42 10. 73 10. 34 9. 60 Thickness to width ratio 4. 17 6. 25 8. 33 10. 42 The simulation results show noticeable reduction in cross-sensitivity as the thickness to width ratio increases. This is because as the flexure becomes more and more stiff, cross-sensitivity decreases. 3. 2. 3 Variation in Prof mass width (PMW) Simulations are carried out in MEMMECH solver by varying proof mass width. It is varied from 400µm to 1000µm. Here the flexure dimensions are kept original as 100µm X 50µm X 12µm (LxWxH).

Following table shows the effect of proof mass width on sensitivity as well as crosssensitivity. Table 4: Effect of Proof-Mass Width variation on cross sensitivity of planar structure PM Width (In µm) 400 600 800 1000 Sensitivity Sz(In MPa) 330 490 660 830 Sx (In MPa) 28 41 54 66 Sy (In MPa) 25. 2 37. 8 50. 5 63. 2 % Cross axis Sensitivity 11. 42 11. 38 11. 20 11. 01 It can be seen from above results that Variations in Proof mass width have negligible effect on cross sensitivity but helps to increase the sensor sensitivity by many folds. This is due to increase in proof-mass weight. 3. 2. Variation of Prof mass thickness (PMT) Simulations are carried out in MEMMECH solver by varying proof-mass thickness. It is varied over from 50µm to 200µm. Here also the flexure dimensions are kept as 100µm X 50µm X 12µm (LxWxH). Following table shows effect of proof mass thickness on sensitivity as well as cross-sensitivity. 4 Table 5: Effect of Proof-Mass thickness variation on cross sensitivity of planar structure PM Thickness (In µm) 200 150 100 50 Sensitivity Sz(In MPa) 330 250 160 82 Sx (In MPa) 28 16 6. 8 1. 6 % Cross axis Sy Sensitivity = RMS of Sx (In MPa) &Sy / Sz 25. 2 11. 42 13. 57 8. 39 5. 47 5. 45 0. 95 2. 27

It can be seen from above results that cross-sensitivity decreases considerably with decrease in Proof Mass thickness but at the heavy cost of sensitivity. This due to decrease in proof mass weight. Fig No. 3 gives summary of variation in cross-sensitivity with respect to each of the above discussed parameters. Cross Axis Sensitivity for various geometrical parameters. 14. 00 12. 00 % cross-sen. 10. 00 8. 00 6. 00 4. 00 2. 00 0. 00 1 2 3 4 FT PMW FW PMT Fig 3: Graph of summary of variation in cross-sensitivity for geometrical parameters The proof mass width and flexure thickness doesn’t have much impact on cross sensitivity.

In case of flexure width variation, cross sensitivity decreases along with increase in flexure width. The bending stress caused by transverse acceleration in X, Y direction is much less then stress caused by desired acceleration in Z direction. Thus for low cross-sensitivity, Ratio of width to thickness should be high. These results have good agreements with earlier reported results [7-8] 4) Conclusions A cross sensitivity effect is studied by varying geometrical parameter like thickness as well as width of flexure and proof mass. Following conclusions can be drawn from all of the above simulation Skewed structure has much higher cross-sensitivity as compared to planar type of structure for the same thickness to width ratio of flexure. (Compare values of in table 1 and 2 for thickness to width ratio of 4. 17). But they have similar sensitivity. When Thickness to Width ratio is increased to 8. 33 in case of skewed structure its crosssensitivity drastically reduces but is still higher than plan structure. One can safely increase sensor sensitivity by increasing proof mass weight by increasing width in planar structure. Variations in flexure thickness and Proof Mass width doesn’t affect cross ensitivity. For better low cross-sensitivity, thickness to width ratio of flexure for planar type of design should be as low as possible and further sensitivity can be enhanced by increasing proof mass width. 5 Acknowledgements The authors thank ARDE, Pune, Ministry of Defence for funding the research work on development of micro accelerometer at University of Pune. Shri BP Joshi, Scientist ‘F’, would like to thank Director ARDE for giving opportunity to work on the project and also to Dr. S. K. Salwan (Guide for Ph. D. ) for his valuable guidance and suggestions. References 1. J.

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