Design and simulation of non-resonant 1-DOF drive mode and anchored 2-DOF sense mode gyroscope for implementation using UV-LIGA process Payal Vermaa,b*, Ram Gopalb, M. A. Butta, Svetlana N. Khoninaa,c, Roman V. Skidanova,c a Samara State Aerospace University, 34, Moskovskoye Shosse, Samara, 443086, Russia; b MEMS and Micro-sensors Group, CSIR – Central Electronics Engineering Research Institute, Pilani (Rajasthan) 333 031, India; c Image Processing Systems Institute of the Russian Academy of Sciences, Samara, Russia; * E-mail:
[email protected] ABSTRACT This paper presents the design and simulation of a 3-DOF (degree-of-freedom) MEMS gyroscope structure with 1-DOF drive mode and anchored 2-DOF sense mode, based on UV-LIGA technology. The 3-DOF system has the drive resonance located in the flat zone between the two sense resonances. It is an inherently robust structure and offers a high sense frequency band width and high gain without much scaling down the mass on which the sensing comb fingers are attached and it is also immune to process imperfections and environmental conditions. The design is optimized to be compatible with the UV-LIGA process, having 9 μm thick nickel as structural layer. The electrostatic gap between the drive comb fingers is 4 µm and sense comb fingers gap are 4 µm/12 µm. The damping effect is considered by assuming the flexures and the proof mass suspended about 6 µm over the substrate. Accordingly, mask is designed in L-Edit software. Keywords: MEMS, Gyroscope, UV-LIGA, MATLAB®, CoventorWare®
INTRODUCTION MEMS technology, as one of the most promising technologies in the present technological scenario, has attracted researchers from all parts of the globe and the advancements are taking place at a very fast pace. Some of the most common areas that have been targeted are pressure sensing and inertial sensing, which form a major proportion of the MEMS market apart from Optical-mems, Bio-mems etc. There has been an exponential rise in the development of Inertial sensors due to the wide range of applications, including automotive industry, robots and position control devices [1, 2], inertial navigation and guiding [3], basic daily activities analysis [4], human body motion monitoring systems used in e-health solutions such as gait and posture analysis [5, 6], fall detection [7] and motion tracking [8]. Gyroscope and accelerometer are two major categories of inertial sensors. These sensors can be configured to form an Inertial Measurement Unit for measurement of both angular rate and acceleration. One of the major challenges in realization of IMU is the design of gyroscope which is usually associated with the problem of frequency variation due to environmental and fabrication variations. It is well known that conventional gyroscope structure consists of two orthogonal components of accelerometers with a single common proof mass or multi-masses. These gyroscopes are based on the principle of transfer of energy form the drive mode to the sense mode in the event of an input angular rate. The mechanical interference between the modes and mode coupling are the critical issues in conventional gyroscope devices. These issues related to mode matching and temperature dependence have been addressed to some extent in conventional resonant gyroscopes by introducing designs with resonator systems [9] and symmetric suspensions [10]. However, in the presence of the above mentioned perturbations, none of these symmetric designs could provide the required degree of mode-matching without active tuning and feedback control [11]. The mechanical interference between the modes and mode coupling are other drawbacks. So for the last several years research has been carried out to enhance the robustness and reduce the mechanical interference of the micro gyroscope [12]. In order to improve the robustness, some multi-DOF vibratory gyroscopes structures have been presented by increasing the number of DOF in either drive or sense-mode [13, 14], among which Optical Technologies for Telecommunications 2015, edited by Vladimir A. Andreev, Anton V. Bourdine, Vladimir A. Burdin, Oleg G. Morozov, Albert H. Sultanov, Proc. of SPIE Vol. 9807, 98070D © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2231372 Proc. of SPIE Vol. 9807 98070D-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/31/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
one of the implemented design is 1-DOF drive mode and 2-DOF sense mode structure [15, 16]. This design showed wide bandwidth of sense mode. But this design has the limitation of structural design space and the trade-off between die size and detection capacitance. To overcome the limitation of this design, centrally anchored 2-DOF sense mass structure with two masses and three springs has been used along with two sets of electrostatic tuning fingers [17]. Another important aspect of micro fabricated devices is the selection of fabrication technology. Fabrication process adaptability, processing cost, time and ease of fabrication are some of the main points of concern for process selection. Fabrication of gyroscope has been demonstrated using various techniques such as bulk micromachining, surface micromachining or a combination of both. But these techniques require expensive equipments like DRIE, wafer bonder, LPCVD Furnaces etc. On the other hand, UV-LIGA is an economical alternative to its expensive counterparts as it involves cost-effective processes, UV lithographic patterning of thick photoresist and electroforming of structural materials into the patterned photoresist mold [18]. The device design presented in this paper is designed as per process compatibility based on UV-LIGA fabrication technology.
MECHANICAL DESIGN AND DYNAMICS The gyroscope structure presented in this paper consists of 1-DOF drive and fully coupled 2-DOF sense mode oscillators with center anchoring. The sense masses and interconnected by spring are suspended inside the drive outer frame mass to ensure that they are mechanically decoupled. The decoupling frame masses , and the two sense masses and move together in unanimity and form a resonant 1-DOF oscillator in the drive direction, while the sense mass acts as a passive mass and dynamic vibration absorber of mass resulting thereby in a 2-DOF oscillator in the sense direction. The additional third suspension element , in -direction, and a second, inner decoupling frame, connects the sense mass to a central anchor as shown in Fig. 1. With the inclusion of the suspension element and the inner decoupling frame , the centrally anchored 2-DOF sense mode is realized without the need for bidirectional flexures. In the event of an angular rate, both the sense masses and are influenced by Coriolis force in the sense direction.
4-kir: Inner decoupling frame (m p)
Sense mass (m1)
Fd
x1 _
1
Outer decoupling frame (m fo)
Lx (a)
(b)
Figure 1. (a) Physical layout schematic; (b) mass-spring-damper lumped configuration of a 1-DOF drive and anchored 2-DOF sense modes gyroscope.
The dynamic equations of the gyroscope are presented based on the lumped configuration shown in the schematic in Fig. 1(b). By using vector analysis [16, 18], the simplified differential equation associated with each degree of freedom can be represented as: ̈
̇
(
)
( )
Proc. of SPIE Vol. 9807 98070D-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/31/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
(1)
̈
̇ ̈
where, ( ( ) axis. The terms, ̇ The notations, , in Fig. 1.
̇
(
)
(
)
̇
(2)
̇
(3)
) is the total drive mass, is the time invariant input angular rate about the z, is the electrical force applied to drive the active mass system with the driving frequency . and ̇ are the Coriolis forces that excite respective masses, and in sense direction. and are the damping constants and , , , and are the spring constants as shown
To facilitate the analysis of frequency response, the Laplace transform of (1)-(3) are taken, and solve for corresponding displacements, transfer function which are written as; ( ) ( ) ( )
(
(4)
)
( )( (
)
)(
)
( )( (
(
)
(
)
)
)(
)
(5)
(6)
where, is the Laplace parameter. Other notations are defined as, (
)
(
)
(
) }
The drive mode equation (4) consists of inner and outer decoupling frame and both sense masses and moving in unison in drive direction due to harmonic electrical force. This is identical to drive displacement represented by conventional device with exception of additional sense masses. Equation (5) is represents the active sense mass, , amplitude arisen due to Coriolis action in the event of angular motion. This expression also has the anti-resonance at frequency, ( ) that is evident from its numerator. The denominator of this factor causes two resonances at which the amplitude peaks. In between these two resonances there is flat region where said anti-resonance exists. Similarly passive sense mass, , equation (6) also reveals the resonances at the same frequencies. But anti-resonance frequency, ( ), is well beyond the flat region of the amplitude. The denominator of the sense mode equation (6) reveals that, the coupling between the masses can be controlled by the suspension element, , without changing the structural frequencies, as the denominator is a strong function of the ( ).
ANALYTICAL RESULTS DISCUSSION The sense amplitude of the passive mass, is maximum, with respect to that of larger mass, , at anti-resonance, hence it amplifies the passive mass amplitude. In order to achieve the robust sense performance and maximum amplification of passive mass system, the operating frequencies must be designed to satisfy ( ) condition, so as to reject the influence of the damping despite its presence during the device operation. The following figures have been plotted using the results obtained from MATLAB ® under such operating conditions of the system unless it is specified.
Proc. of SPIE Vol. 9807 98070D-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/31/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
Figure 2 show the respective drive mode amplitude of mass, , and corresponding phase variations with frequency. Figure 2 has been calculated by making use of Eq. (4) considering ambient damping as a parameter. The plot shows resonance at frequency, , i.e. drive operating frequency where amplitude is the maximum. From this figure it is also clear that the maximum effect of the damping in the amplitude occurs at resonances, which is obvious. The results of phase associated to drive amplitude as illustrated in the figure. The phase plot reveals almost insignificant impact of damping at discontinuity point, whereas, at the other region of the frequency curve the damping does affect. The phase values at these discontinuity points lead to 90o.
0
Q -160 -170 -180 -180 4 0
4.5
5.0
5.5
60
Frequency (kHz)
Figure 2. Drive mode amplitude and phase spectral responses for different values of damping parameters.
Figure 3 shows the results of passive mass, amplitude and phase variations with frequency for different values of damping. This figure has been calculated by using the Eq. (5) for respective amplitude and associated phase related to mass, . As depicted in Fig. 3 the amplitude shows two resonances ( ) at which it peaks. The damping effect is apparent at resonances. The phase curves show its variation with frequency from 90 o to -270o revealing abrupt transitions at resonances and anti-resonance points. The damping effect is obviously pronounced at the vicinities of these discontinuity points.
-140
Ê -160 m
a
-180
-a
0«.
' -200 E
Q
-220 -240
40
Figure 3. Active sense mass ( parameters.
4.5
5.0
Frequency (kHz)
5.5
60
) amplitude and phase variations with frequency for different values of damping
Figure 4 corresponds to sense amplitude and phase spectral responses considering damping as a parameter. The amplitude, calculated with the help of Eq. (6), exhibits three resonances at which it is the maximum and anti-resonance beyond the flat region at which amplitude is the minimum. The damping effect is dominant on all the peaks and the other portion of the amplitude plots remains almost invariant. The phase varies from 90 o to -450o within the entire calculated range of frequency. The phase shows four abrupt transition points corresponding to each of three resonances and an antiresonance. The damping is obviously effective beside these discontinuity points of the phase.
Proc. of SPIE Vol. 9807 98070D-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/31/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
Figure 5 shows the effect of the suspension element, , on the amplitude of the sense passive mass and the phases in the frequency domain. This figure has been plotted by considering Eq. (6). It is evident from the figure that the amplitude of the sense oscillator increases by decreasing the suspension element, , and reduction in bandwidth is also achieved. This suspension parameter is also found to have an effect on the anti-resonance frequency, which decreases with decreasing coupling parameter as shown in Fig. 5 even then it occurs beyond the flat region at which amplitude is the minimum. So this allows a wide sense bandwidth and high gain without much scaling down the mass on which the sensing comb fingers are attached. The use of the additional anchoring beam in the sense direction, also causes the enhancement in the coupling strength of sense mode resonance frequencies. -100
180
-120 -
2'11x
90
=50s -100si -0
"i-140 -160
4-180 1-200
2'h= 2'2,,
=150s --90 ó --180`:: -
-270
Q -220 -240
a
-360
- -450
-260
40
4.5
5.0
5.5
6.0
75
7.0
6.5
Frequency (kHz)
) amplitude and phase variations with frequency for different values of damping
Figure 4. Passive sense mass ( parameters.
360
-120 -140
ñ,Ix= %1 _ X2v
50 s
- 270
180
-160 MI-180-
90
k2,
a)
0
4 -200
-90
=a -220 -
-180 ÿ
Q
-240 -
-270
-260 -280 -
-360
3
Figure 5. Passive sense mass (
-450 4
5
Frequency (kHz)
6
7
) amplitude and phase spectral responses for different values of the stiffness,
.
PROTOTYPE DESIGN AND FEM SIMULATION RESULT Based on the analytical formulation and calculation of the damping effect, the design parameters are finalized. The structural features are designed for fabrication compatibility using UV-LIGA process. The minimum feature size was designed based on the feasibility of pattern definition using SU-8 2010 negative photoresist and the perforations size and spacing was decided keeping in view the sacrificial release of the structure. Accordingly, the proof mass values used for prototype design are 274.1 x 10-9 kg, 17.13 x 10-9 kg, outer frame mass 36.214 x 10-9 kg, and the -9 inner frame mass is 5.45 x 10 kg. Structural frequencies, and are designed to be equal according to our theoretical analysis at 5.0 kHz and = 4.933 kHz respectively; yielding a mass ratio of 0.0625. The values of spring constants are 320.94 N/m, 263.4 N/m, 7.184 N/m, 9.29 N/m and 7.22 N/m. Table 1 provides the details of others design parameters.
Proc. of SPIE Vol. 9807 98070D-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/31/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
Table 1: Parameter values used for prototype.
Parameters Sense Resonance frequencies: ω2 and ω1 Number of drive comb fingers (Nx) Number of sense comb fingers (Ny) Drive finger overlap length Sense finger overlap length Drive comb finger gap Sense comb finger gap (narrow/wide) Beam width Beam length, ( L1x ) Beam length, ( L1y ) Beam length, ( L2y ) Beam length, ( La ) Beam length, ( Lb ) Perforation size Young’s Modulus Density Sacrificial layer Modal Displacement Mag. i1.1E+00
(a)
3.2E-01 um
Values 4.69 kHz and 5.22 kHz 260 144 10 µm 20 µm 4 µm 4 µm/12 µm 4 µm 92.5 µm 98.5 µm 260.5 µm 301 µm 260 µm 8 µm x 8 µm 220.5 GPa 8910 kg/m3 6 µm Modal Dbplacement Mag.
(b)
1.1E+00 8.2E-01 5.5E-01 2.7E-01 n,0E+00
5.5E -01 2.7E -01
0.0E+00
