JOURNAL OF SEMICONDUCTOR TECHNOLOGY AND SCIENCE, VOL.19, NO.6, DECEMBER, 2019 ISSN(Print) 1598-1657 https://doi.org/10.5573/JSTS.2019.19.6.600 ISSN(Online) 2233-4866

Manuscript received Oct. 22, 2019; accepted Nov. 26, 2019 1Interdisciplinary Program in Creative Engineering 2School of Mechatronics Engineering, Korea University of Technology and Education, Cheonan, Korea E-mail : bllee@koreatech.ac.kr

Time Efficient Evaluation of Multi-axis MEMS Gyroscope Using Three-dimensional Test Methodology

Faisal Iqbal1, Hussamud Din2, and Byeungleul Lee2,*

Abstract—Recently, the demand for micro-electromechanical systems (MEMS) based inertial sensors has been increased due to a wide range of application in consumer electronics; however, high volume production remains a major challenge for the MEMS industry. This paper proposes a new three dimensional (3-D) test methodology for the time-efficient evaluation of multi-axis MEMS gyroscopes. A mathematical model for the proposed 3-D test method was derived based on the coordinates transformation. The 3-D test methodology was validated experimentally using three-axis MEMS gyroscope from ST Microelectronics and the results were compared with the conventional one dimensional (1-D) test method. The experimental results revealed that the measurement error between the conventional 1-D and the proposed 3-D test was less than 1%, whereas the test time was decreased three times. Finally, the error sources and limitations of the proposed 3-D test method was highlighted. Index Terms—MEMS, 3-D test method, gyroscope evaluation

I. INTRODUCTION

Micro-electromechanical systems (MEMS) inertial sensors, such as accelerometers and gyroscopes, are used in a wide variety of applications including automotive

and industrial applications. The demand for MEMS-based inertial sensors in consumer electronics has increased rapidly in the past few years due to their low power consumption, small size, and light weight [1-5].

MEMS gyroscopes are used to measure the angular rate. Apart from designing and fabrication, testing and/or evaluation of MEMS devices consumes a great deal of money. Several cross-sectional studies have shown that 1/3 of the product cost goes to test setup. To reach the market demand, high volume production at a lower cost is an issue for the MEMS industry [6-8].

The product development flow for MEMS gyroscope sensor is shown in Fig. 1. The development of the sensors starts with the design of mechanical structure, which is validated by finite element analysis (FEA) simulations. The FEA simulations help the designer to improve the mechanical structure for better performance, followed by fabrication and initial evaluations at wafer-level [9, 10]. Wafer-level automatic test equipment and parallel test architecture have been used to reduce the test time and increase the throughput as reported in [11]. After the wafer-level test, the fabricated devices are packaged, and reliability tests are conducted. Finally, the devices are evaluated for the functional test, and calibration is performed on each single device for appropriate usage.

The functional test includes the evaluation of the scale factor, bias errors, and noise performance [12]. The bias stability and noise performance are evaluated at zero rate input in the case of gyroscope, whereas the scale factor is measured by applying external physical stimuli (angular rate) in the respective axis. To increase the accuracy in the scale factor measurement, the gyroscope sensors are evaluated at different angular rates where

JOURNAL OF SEMICONDUCTOR TECHNOLOGY AND SCIENCE, VOL.19, NO.6, DECEMBER, 2019 601

multi-point results are linearly fitted using linear regression.

For cost effectiveness, a uniaxial rate table is used to evaluate the MEMS gyroscope, which provides the external angular rate in single axis. To determine the rate output, the sensor is attached to a test fixture and the primary axis of the sensor and/or fixture is aligned to the rate table. Although this method is highly accurate, however, in case of multi-axes gyroscope evaluation, the sensor needs to be rotated three times for each single axis, which is time-consuming.

In this manuscript, a 3-D test method is proposed for the fast evaluation of multi-axis MEMS gyroscope. The proposed 3-D method reduces the evaluation time by three times and eventually reducing the test cost. The article is arranged as follows. In section 2, a proper mathematical model for MEMS gyroscope evaluation using 1-D test method and the proposed 3-D test method are presented. The experimental results of the proposed 3-D method are compared with the 1-D test method in section 3. Also, the limitations of the proposed method are highlighted. Finally, the conclusions are given in section 4.

II. METHODOLOGY

To evaluate scale factor of multi-axis MEMS gyroscope, the output to external physical stimuli can be modeled as:

s,x x ,0u s . x xu u= + . (1) s,y y ,0u s .y yu u= + . (2) s,z z ,0u s .z zu u= + . (3)

where xs , ys , z s are the scale factors, ,0 ,0 ,0, ,x y zu u u

are the bias offset and y z, , and uxu u are the input

physical stimuli (angular rate in case of gyroscope). The scale factor of the gyroscope is evaluated by

measuring the corresponding output to external angular rate. In the case of gyroscope evaluation, the gyroscope is attached to the test fixture and mounted to the rate table. We define the absolute coordinate system as

[ ]0 X Y Z in which angular rate is applied, and the

fixture coordinates as ' ' 0 X Y Z¢é ùë û , assuming that the

gyroscope and test fixture has same coordinates. We also assume that both the fixture and absolute coordinates have the same origin at 0. The angular rate provided by the rate table in absolute coordinates can be related to the fixture coordinates by rotation matrix R as:

=f wU RU . (4)

where 00T

w gU Fé ù= ë û is a vector in absolute coordinate

system and gF is angular rate along the z-axis of

uniaxial rate table. Whereas, [ ] Tf X Y ZU u u u¢ ¢ ¢= is a

vector in fixture coordinates and the rotation matrix R . The matrix R , having an unsigned angle q , between the two coordinates axis can be defined by direction cosine matrix as:

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )

, , ,

, , ,

, , ,

cos cos cos

cos cos cos

cos cos cos

X X X Y X Z

Y X Y Y Y Z

Z X Z Y Z Z

R

q q q

q q q

q q q

¢ ¢ ¢

¢ ¢ ¢

¢ ¢ ¢

é ùê ú

= ê úê úê úë û

where for example ,X Zq ¢ be the angle between

Fig. 1. MEMS sensors development and test flow.

602 FAISAL IQBAL et al : TIME EFFICIENT EVALUATION OF MULTI-AXIS MEMS GYROSCOPE USING THREE-DIMENSIONAL …

axisX ¢ - and .Z axis-

1. Conventional 1-D Test Method The 1-D test method for gyroscope evaluation is

shown in Fig. 2(a). For a uniaxial rate table offering the angular rate along Z axis- , the single axis gyroscope can be evaluated by aligning the fixture and/or gyroscope axis to the absolute .Z axis- In case of z-axis

gyroscope, where , 0Z Zq ¢ = , be the angle between

Z axis¢ - and Z axis- , will yield, 00

X

f Y

Z g

uU u

u F

¢

¢

¢

é ùé ùê úê ú= = ê úê úê úê úë û ë û

,

As explained above that both the sensor and fixture have same coordinates. While neglecting the bias offset, we can re-write Eqs. (1-3) as:

s,xu 0= . (5) s,yu 0= . (6) s,zu s .z gF= . (7)

The terms s,xu and s,yu are usually not zero and

represent the cross-axis sensitivity, whereas s,zu is the

measured output of the sensor to externally applied

angular rate gF .

2. Proposed 3-D Test Method

The proposed 3-D test method is shown in Fig. 2(b).

The rotation matrix R defines the orientation of the fixture. Unlike the 1-D test method for which the fixture is rotated each time to evaluate every single axis of the multi-axis MEMS gyroscope, this paper exploits the Euler angles such that each sensor will experience the same angular rate and can be evaluated simultaneously. The rotation matrix can be defined by three plane rotations, involving rotation angles ( , , ψ).q f The

rotation matrix for sequence zyzR with Euler angles

( , , ψ)q f can be written as:

zyz

c c c s s c s c c s c sR c s c c s c c c s s s s

c s s s c

q f y q y y q q f y q fq y f y q q y f q y q f

y f f y f

- - -é ùê ú= + -ê úê ú-ë û

where c and s represents cosine and sine functions respectively.

Using Euler angle rotation matrix sequence zyzR , we

re-define Eq. (4) as:

( ) ( )( ) ( )

( )

cos .sin sin .sin .

cos

X

f Y g

Z

uU u F

u

q fq f

f

¢

¢

¢

é ùé ùê úê ú= = ê úê úê úê úë û ë û

(8)

where q and f represent the angle between fixture and absolute coordinates. As each axis will experience the same force in the 3-D test method, we solve Eq. (8) for “q ” and “f ” for all X Y Zu u u¢ ¢ ¢= = .

1tan X

Y

uu

q - ¢

¢

æ ö= ç ÷

è ø.

45q = ° . ( ) ( )1 cos sin

tan X Y

Z

u uu

q qf ¢ ¢

¢

- +æ ö= ç ÷

è ø.

54.74f = ° . Putting back the values of “q ¢ and “f ” in equation

10 will yield:

13 0

1 03

13

X

f Y

Z g

uU u

u F

¢

¢

¢

é ùê úê ú é ùé ùê ú ê úê ú= = ê ú ê úê úê ú ê úê úë û ë ûê úê úë û

(9) Based on the above discussion, it is clear that if the

designed test fixture with the derived angles, each axis of the gyroscope will experience equal angular rate. Finally, the output of the gyroscopes sensor can be re-written as:

s,x xxu s .3gF

=Ö

. (10)

s,yu s . .3g

y

F=

Ö (11)

s,zu s .3g

z

F=

Ö. (12)

where gF is the external angular rate experienced by

the sensors

JOURNAL OF SEMICONDUCTOR TECHNOLOGY AND SCIENCE, VOL.19, NO.6, DECEMBER, 2019 603

III. EXPERIMENTAL RESULTS AND

DISCUSSION

Experimental setup for the 3-D test method is shown in Fig. 3. The sensor was mounted on the designed 3-D fixture and attached to the rate table AC1120. The experiment was performed on ST Microelectronic device, LSM9DS0 sensor, having 3-axis gyroscope, 3-axis accelerometer, and 3-axis magnetometers [13]. The LSM9DS0 was evaluated using STEVAL-MKI109V2 daughter board. The block diagram is shown in Fig. 4. The device was evaluated at different input rates in the range of 200± degrees per second (dps) and linearly fit using linear regression to determine the scale factor of the device.

Fig. 5 and 6 show the experimental results of 1-D and the proposed 3-D test method respectively. The measured scale factor (SF) for ,x y , and z gyroscope using 1-D test setup was 109.98 / ,LSB dps 111.38 / ,LSB dps and

114.28 / ,LSB dps respectively, whereas the 3-D test

results show a scale factor of 110.99 / ,LSB dps

112.13 / ,LSB dps and 115.58 /LSB dps for ,x y and z gyroscope respectively. The percentage error between 1-D and 3-D test method was measured and is summarized in Table 1.

( )

1 3 % 100

1

Measured D SF Measured D SF

ErrorMeasured D SF

-

= ´ .

(13)

The experimental results reveal that the errors were less than 1% for the x and y gyroscopes; however, the z gyroscope correspond to an error of 1.15%. The

(a)

(b)

Fig. 2. (a) 1-D test method, (b) 3-D test method.

Fig. 3. Experimental setup of 3-D test method for gyroscope evaluation using uniaxial rate table (AC1120).

X

Y

Z

ADC

ADC

ADC

Signal Condition:Registers,

FIFO

Gyroscope

C/V

C/V

LSM9DS0

Fig. 4. Block diagram of LSM9SO and MKI109 motherboard.

604 FAISAL IQBAL et al : TIME EFFICIENT EVALUATION OF MULTI-AXIS MEMS GYROSCOPE USING THREE-DIMENSIONAL …

errors in the measurement results are either the coupling of the cross-axis sensitivity to the primary axis or errors in the 3-D test fixture designs. Further, experiments and analysis were carried out to highlight the error sources in the proposed 3-D test method.

1. Effect of Cross Axis Sensitivity

First, the cross-axis sensitivity of the gyroscope was

measured using 1-D test setup, and its effect on the 3-D test setup was further analyzed. The main sources of the cross-axis coupling are the test fixture misalignment with the absolute coordinates, MEMS itself, and die placement errors [14]. The cross-axis for gyroscope was calculated as:

( )2 2

, / % 100ij iki j k

ii

S SS

S+

= ´ . (13)

where the first subscript represents the primary axis in which the angular rate was measured, and the second subscript represents the axis in which the external angular rate was applied. The measured cross axis sensitivity for ,x y and z gyroscope was 1.75%, 1.67%, and 0.37% respectively. Next, the effect of cross-axis on the primary axis was measured as:

2 2 2 overll ii ij ikS S S S= + + . (14)

where overallS is the overall sensitivity, iiS , ijS , and

ikS represent the primary axis sensitivity and the cross-axis sensitivity terms. Table 2 summarized the measurement errors along with the cross-axis sensitivity. The results show that the cross-axis sensitivity has an effect of only 0.02%. Also, with the improvement in the MEMS fabrication and design technology, most of the

(a) (b) (c)

Fig. 5. Measured scale factor of gyroscope using 1-D test method (a) x-gyroscope, (b) y-gyroscope, (c) z-gyroscope.

(a) (b) (c)

Fig. 6. Measured scale factor of gyroscope using 3-D test method: (a) x-gyroscope, (b) y-gyroscope, (c) z-gyroscope.

Table 1. Measured scale factor using 1-D and 3-D test.

Scale factor (LSB/dps) Percentage (%) Error Test Method

x-gyro y-gyro z-gyro x-gyro y-gyro z-gyro

1-D Test 109.980 111.390 114.280

3-D Test 110.990 112.140 115.590 0.92% 0.67% 1.15%

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devices have a cross-axis sensitivity less than 2% [1, 15, 16] which means that the 3-D measurement test results will affect the scale factor with an error of 0.02%.

2. Effect of 3-D Fixture Design

From the above discussion, it was cleared that the

actual cross-axis sensitivity has less than 0.02% effect on the measured scale factor, which means that most of the errors are raised from the 3-D test fixture design, where the input rate directly depends on the 3-D fixture design angles. Fig. 7 shows the scale factor errors induced due to angle “q ” and “f ”. It can be seen that 1-degree error

in angle f will result to 2.5% scale factor error in z axis- and 1.21% error in x axis- respectively. Based on the above discussion, it can be concluded that the measurement errors in the test setup are mainly because of the designed test fixture angles.

4. CONCLUSION

In this paper, a study on 3-D test method was conducted to evaluate the scale factor of multi-axis MEMS gyroscope. A mathematical model for the proposed 3-D test model was established. The

experimental results were compared with the conventional 1-D test method showing that the measurement errors were less than 1%. Although the 1-D test method is highly accurate, however, in case of multi-axis gyroscope evaluation, the method is not efficient in terms of time. By exploiting the 3-D test method, the throughput of the test system can be increased three times.

Furthermore, the limitation of the proposed 3-D test method was highlighted. One source of the weakness in this method was the cross-axis coupling of the secondary axis to the primary axis, which contributed only 0.02% to measurement errors. Moreover, it was found that the main source of measurement errors was fixture design and the corresponding angles. Ensuring the reduction in fixture angle errors will further improve the measurement results.

ACKNOWLEDGMENT

This work is supported by the R&D program of the Ministry of Trade, Industry, and Energy (MOTIE)/Korea Evaluation Institute of Industrial Technology (KEIT). [10084665, Development of IMU Embedded 6-axis, 10-axis compound navigation system integrating highly reliable inertial measurement unit (IMU), Global Navigation Satellite System (GNSS), Magnetometer, and altimeter for maned / unmanned aircraft]. This work was also partially supported by the Education and Research Program of KoreaTech in 2019.

REFERENCES

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Table 2. Measured scale factor using 1-D and 3-D test with cross-axis sensitivity

Scale factor (LSB/dps) Percentage ( )% Error Test Method

x-gyro y-gyro z-gyro x-gyro y-gyro z-gyro

1-D Test 109.990 111.140 114.281

3-D Test 110.99 112.14 115.59 0.89% 0.65% 1.13%

Fig. 7. Induced scale factor error with test fixture angles.

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Faisal Iqbal received B.S. degree in Telecommunication Engineering from University of Engineering and Technology, Peshawar, Pakistan, and M.S. degree in Interdisciplinary Program in Creative Engineering from Korea University of Tech-

nology and Education, Republic of Korea, in 2009 and 2017 respectively. He is currently pursuing Ph.D. degree in Interdisciplinary Program in Creative Engineering at Korea University of Technology and Education, Republic of Korea. His research interests include MEMS inertial sensors.

Hussamud Din received B.S. degree in Electronics Engineering from International Islamic University Islamabad, Pakistan in 2011, and M.S. degree in Electrical Engineering from Center for Advanced Studies in Engineering, Islamabad, Pakistan in

2016. He is currently pursuing Ph.D. degree at Korea University of Technology and Education in Mechatronics Engineering. His research interests include MEMS inertial sensors.

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Byeungleul Lee is Professor at Korea University of Technology and Education. He received B.S. degree in Electronics Engineering from the Hanyang University and M.S. degree in Electrical and Electronics engi-neering from Korea Advanced

Institute of Technology, in 1989 and 1991 respectively. He obtained his Ph.D in Electrical Engineering and Computer Science from the Seoul National University in 2004. From 1991 to 2008, he worked for Samsung Electronics as a principal researcher for MEMS development. His research interests include semicon-ductor transducer and MEMS applications.