design and fabrication of a convective 3-dof angular rate sensor

Design and Fabrication of a Convective 3-DOF Angular Rate Sensor Van Thanh Dau

Thien Xuan Dinh

Dzung Viet Dao

Otake Tomonori

Ritsumeikan Univ. Japan

Ritsumeikan Univ. Japan

Ritsumeikan Univ. Japan

Ritsumeikan Univ. Japan

good characteristics in terms of directivity or crosssensitivity because the alignment between hotwires and flow channel direction is now determined by photolithography.

Abstract— This paper reports the design, simulation and fabrication of a novel MEMS based convective gyroscope which can independently detect three components of angular rate at high sensitivity and low power consumption. The new sensor was designed to match the standard bulk MEMS technology. The highly 3D flow scheme in previous work was successfully integrated together with the in-plane hotwires by MEMS compatible laminated-structures. The cost of sensor will be significantly reduced while the sensitivity of the sensor is enhanced (up to 300% of that reported by the authors in [1]). In measurement application, the 3DOF gyro eliminates the sensor-to-sensor distance and has good characteristics in terms of directivity or cross-sensitivity because the alignment between hotwires and flow channel direction is now determined by photolithography. The sensor also has high shock resistance and prevents fatigue damage.

I.

II.

DESIGN AND WORKING PRINCIPLE

Figure 1 illustrates the configuration of the sensor; consists of a PZT pump, PMMA caps and hotwires located on the surface of a circular 0.5mm-thick silicon frame with the diameter of 30mm. The tungsten hotwire has dimension of 1000×40×0.4μm3, (L×W×T). The pump is oscillated to create a laminar jet flowing circularly. The plane of flow center is parallel and offset from the plane of hotwires a distance of 500μm. The inert neon gas, which was used in previous work, is filled inside at 1atm for simplicity in packaging process.

INTRODUCTION

This paper reports the design, simulation and fabrication of a novel MEMS based convective gyroscope which can independently detect three components of angular rate at high sensitivity and low power consumption.

PZT diaphragm

Cap

Hotwires Silicon frame

Recently, multi-axis gas gyroscopes utilizing the hotwire anemometry to measure the Coriolis-deflected flow was reported. However, the fabrication of the hotwires in threedimensional space is difficult and the circularly-flowing laminar jet in a confined space is not easy to integrated in MEMS gyros, therefore, in the previous gas gyroscope developed by the authors [1-4], the hotwires were fabricated independently and integrated into the sensor. This complicated process allows the sensor to sense dual axis of angular rate. Therefore the development of a three DOF gas gyro which can be mass-fabricated by MEMS is required. The proposed sensor utilizes in-plane hotwires, i.e. hotwires are in the plane parallels with flow axis, and the fabrication process is compatible with standard bulk MEMS technology. The size and the cost of sensor will be reduced while the sensitivity of the sensor is maintained (up to 300% of that reported in reference [1]). Compare with the first proposal design presented at Transducer’07 [5], this sensor provides better performance with lower power consumption since the laminar jet flow is easier to be maintained with small pump vibration. In measurement application, the 3DOF gyro eliminates the sensor-to-sensor distance and has

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Susumu Sugiyama Ritsumeikan Univ. Japan

Gas flow

Figure 1: Configuration of the 3DOF gas gyroscope. The blue arrows indicate the direction of the gas circulating inside the sensor

When angular rate is applied around Z-axis, the gas flow from nozzle is deflected due to Coriolis acceleration, causing the opposite cooling effects between the two opposite hotwires Rx (Fig. 2b). In case of X or Y-axis, because the flow center is offset from the plane of hotwires and the flows in 2 opposite sensing chambers reaching hotwires Rx in opposite directions, the opposite cooling effect again appears

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IEEE SENSORS 2007 Conference

at these two corresponding hotwires (Fig. 2c). Wheatstone bridge is used to convert these resistance changes to output voltage. Z Y gas flow

III.

C

∂ρ ∂ρ u + =0 ∂t ∂x

hotwire Rz

C

nozzle

(a)

i

∂ρ u ∂ρ u u ∂P ∂ + = −b − + ∂t ∂x ∂x ∂x

hotwire Ry

i

i

j

i

j

flow center

C-C

i

∂ρ H ∂ρ u H ∂p ∂ + = + ∂t ∂x ∂t ∂x

Ωz

(b)

Ωx

i

j

j

i

(5)

i

i

i

λ is the thermal conductivity. u and b are velocity and body

Z

X

j

⎛ ⎛ ∂u ∂u ⎞ ⎞ + ⎜ μ ⎜⎜ ⎟ ⎜ ∂x ∂x ⎟⎟ ⎟ ⎠⎠ ⎝ ⎝

⎛ ∂T ⎞ (6) ⎜λ ⎟ ⎝ ∂x ⎠ Here ρ is fluid density, μ is the molecular viscosity, and

nozzle

i

Y

(4)

i

hotwire Rx

X

SIMULATION - SENSITIVITY ANALYSIS

The solution of the flow is governed by a set of equations for mass, momentum, and energy. In index notation using a Cartesian coordinate system, the equations are written as follow [6]:

i

Y

i

force in the i th direction, respectively. T is the temperature of the fluid, t is the time and H is the total enthalpy.

(c)

Pump chamber with vibration PZT diaphragm

Figure 2: Configuration of the 3DOF gas gyroscope. The blue arrows indicate the direction of the gas circulating inside the sensor. Schematic view shows the sensor working principle (a). Deflections of flow velocity profile in sensing chambers in X-Y plane (b), Y-Z plane or X-Z plane (c) are used to detect applied Ωz, Ωx, and Ωy respectively.

Supposed that an angular rate is applied around Z axis, the gas flow is deflected due to Coriolis acceleration, which is expressed as

Symmetric conditions

Nozzle

G G G (1) aω z = 2ω z × Vz G G G where Vz , ω z , aω z are vectors of flow velocity from corresponding nozzle orifice to the hotwires RZ, applied angular rate around Z axis and corresponding Coriolis acceleration, respectively. The flow deflection δz is given by the double integration of Eq. (1)

L2 δ z = ωz z Vz

Figure 3: Simulation model of the sensor. Due to the symmetric, ¼ of the model was solved with suitable boundary conditions.

Because of the symmetry flow feature, only one-fourth of the gyro is considered. The computational domain is discreted into a structured mesh system generated by using commercial software of ANSYS Inc. The grids are clustered at high gradient place such as near the walls and near the pump diaphragm. Careful attention was paid to take into account the smallest length such as depth of the pump chamber. The minimum and maximum grid cells are 0.06mm and 1mm, respectively. The total number of the grids approximates to be 100,000. The FLUENT 6.2, ANSYS, Inc., which uses a control-volume-based technique to convert the governing equations to numerically solvable algebraic equations, is employed to obtain the values for the compressible flow variables. The discrete equations are advanced in time by a second-order time stepping method. The velocity-pressure coupling algorithm is SIMPLE scheme. The general version of Algebraic Multi-grid Method (General AMG) is used to solve Poisson equation.

(2)

where Lz is the distance from main nozzle to the hotwire Rz and Vz is mean velocity of the flow along distance Lz Similarly, when an angular rate

ωx , ω y

around X, Y axis is

applied to the gyro, the gas flow is deflected as

L2y L2x δ x = δ y = ωx = ω y Vx Vy

(3)

where Lx (Ly) and Vx (Vy) are the distance and mean flow velocity from nozzle to the corresponding hotwire Rx (or hotwire Ry) .

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The calculation was performed on a single CPU 4.0GHz computer in approximately 24hCPU time.

4

Lz= 4.5mm 3

Hotwire plane

Hotwires Rz 2

Flow velocity (m/s)

Flow velocity (m/s)

Vibration PZT diaphragm

Flow at hotwires

5

Ly=7mm

700 µm

2

1

0

-1 -4

The fluid properties of neon gas at reference temperature 298K are: the molecular weight W=20.179g/mol, viscosity

μ=3.156×10-5Pa.s, thermal conductivity λ=49.100×10-3K/m, specific heat cp=1031.0J/kgK. The estimated Knudsen number Kn = λF / L , where λ F = 124nm is mean free path of neon, is less than 10-3. Hence, the continuum hypothesis and non-slip condition at the walls are applicable. The boundary condition applied at the inlet is the vibration written in Eq. (7) 2

⎛ ⎛r⎞ ⎞ ∂θ (r , t ) (7) = 2π f Θ ⎜1 − ⎜ ⎟ ⎟ cos(2π ft ) ∂t ⎝ ⎝R⎠ ⎠ where Θ(t ) , R, r are the displacement of the membrane center, the radius of the membrane and the distance from the center respectively. Also, because Θ0 is small compared with the depth of the pump chamber, which is designed to be deeper than 500µm, it is not necessary to use deformation mesh in simulation. To utilize the convenience of previous process, the same PZT diaphragm is used [1-5]; therefore, the resonant frequency of the PZT diaphragm is known as 7 kHz. 2

-1 4

Figure 5: Flow velocity distributions along Y direction for Rz (at Lz=4.5mm, refer to Fig.2b), along X direction for Rx or Rx (Lx=Ly=7mm, refer to Fig.2c). L is the distance from the corresponding nozzle to the hotwires. Hotwires are placed in linear velocity region: distance between two opposite Rz is 700um, hotwire plane is offset from center of flow 500um.

Figure 4: Simulated result of the circular flow verifies the existence of laminar jet. The pump is oscillated at 7 KHz with maximum amplitude of 10µm. Transient simulation reveals the start-up time for the flow become stable is around 12milisecond.

u=

0.5

-2 0 2 Distance from symmetric center of the flow (mm)

The velocity distributions along the Z axis at the distances of Lx = Ly = 7mm is shown in Fig. 5. The distance from the hotwire plane to the flow axis is determined so that hotwire plane is at the center of linear region of this velocity distribution, i.e. the flow velocity is linearly proportional to the deflection δωx and δωy. Same requirement is applied for δωz with the velocity profile taken along X axis at Lz=4.5mm and at the decided hotwire plane. Therefore, the optimized offset distance from the hotwire plane to the center of flow will be 500um and the distance between two opposite hotwires Rz1,2 is 700um (Fig. 5). The sensitivity of the sensor is analyzed by applying the heat transfer phenomenon between the hotwire and the laminar jet flow. The relation between resistance change of hotwire and flow velocity change can be written as [1-5]:

0

ΔR =

− λπlαI 2 RTh 0

(λπlNu − I

2

RTh 0α

)

2

⋅

Nu n ⋅ ΔV V

(8)

where l is the length of thermistor. Since the flow deflection is small, and the thermistor is placed in the linear distribution of flow velocity, the velocity difference ΔV is proportional to the flow deflection δω and therefore, it is also linearly proportional with applied angular rate ω.

The pump working principle was successfully applied to the laminated model which is compatible to MEMS process. The dimensions of the model are strictly controlled so that the circulation of the laminar jet around the sensor can be realized. The pump will be activated at its resonant frequency and the required peak to peak amplitude is 20μm. (half of that previous design [5]). General view of the flow inside the simulated model is shown in Fig. 4. The profiles represent the direction and the amplitude of the flow velocity.

ΔV = K i δ ω i = K i

ωi L2i Vi

(9)

in which Ki is a constant, depends on the gradient of flow velocity distribution at the hotwire Ri. From figure 4, Kz is larger than Kx and Ky.

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1

silicon substrate

Z axis

Output voltage (mV)

X and Y axes

(a)

(b)

(c)

(d)

0.5

0

-100

-50

0

50

inserted pump

100

(e)

-0.5

Si

SiO2

PMMA -1 Applied angular rate (deg/sec)

Figure 6: Simulation for the sensitivity of the sensor. The scale factors of the sensor are SFx = 9.7μV/o /s, SFy = SFz = 3.6μV/o /s with power consumption of 5.4mW.

PZT suspended hotwire

(f)

Figure 7: Proposed fabrication process for gyroscope

Assembled PZT diaphragm

Figure 6 shows the simulated sensitivities of the gyro are SFz = 9.7μV/o /s, SFz = SFy = 3.6μV/o /s. The sensitivity of the 3DOF gas gyroscope is almost three times of that of a dual axis gas gyroscope presented in reference [1] if the same sensing element is used. IV.

W

Main chambers

Hotwires

PROPOSED FABRICATION PROCESS

The sensor can be fabricated by standard bulk micromachining process as illustrated in figure 7. First, a thermal oxide is deposited on both side of a 500 um thick silicon wafer as an insulation layer (Fig. 7a). A 0.3um layer of high TCR metal, such as tungsten/platinum is deposited onto the surface and is patterned by lift off technique (Fig. 7b). The flow path is aligned from the top side of the wafer by photolithography (Fig. 7c) and the etching process is carried on so as to release the suspended hotwire while not going through the silicon substrate (Fig. 7d). The caps of the gyro can be made by MEMS process with the same mask for flow path, or can be made by conventional fine machining (Figs. 7e). After the wafer is bonded with the cap, the chip is put onto the packaged base. Finally the PZT diaphragm is assembled from the top of the sealed cap and circuit is connected by wire bonding (Fig. 7f).

Figure 8: Packaged 3DOF gas gyroscope. The flow path is also created on both silicon frame and cap with different depths so that the hotwire plane is offset with the flow center along depth direction.

REFERENCES [1] Dzung Viet Dao, Van Thanh Dau, T. Shiozawa, H. Kumagai and S. Sugiyama, “A Dual Axis Gas Gyroscope Based On Convective and ThermoResistive Effects in Silicon with Low Thermal-Induced Stress Sensing Element”, Proceeding of the 19th IEEE MEMS (2006), pp.594-597. [2] Van Thanh Dau, Dzung Viet Dao, T. Shiozawa, H. Kumagai and S. Sugiyama, “A Dual axis gas gyroscope utilizing low doped silicon thermistor”, Proceeding of the 18th IEEE MEMS (2005), pp.626-629.

Figure 8 shows the preliminary fabricated sensor, the flow path is also created on the cap with different depth of the silicon patterns so that the hotwire plane is asymmetric with the flow along the depth direction. Experimental results of previous work show that the resistance and the TCR of hotwire will be around 6Ω and 2500ppm/oC respectively. To achieve the sensitivity analyzed on part III, the temperature of the hotwire should be 60oC and the corresponding power consumption is 5.4mW.

[3] Van Thanh Dau, Dzung Viet Dao, T. Shiozawa, H. Kumagai and S. Sugiyama,“Development of a Dual Axis Thermal Convective Gas Gyroscope”, J. Micromech. Microeng. 16 (2006) 1301-1306 [4] Van Thanh Dau, Dzung Viet Dao, Tatsuo Shiozawa and Susumu Sugiyama, “Convective gas gyroscope based on thermo-resistive effect in Si p-n junction”, Proc. of Transducer’07, pp2525-2528 [5] Dzung Viet Dao, Van Thanh Dau, Thien Xuan Dinh and Susumu Sugiyama,” A fully integrated MEMS-based convective 3-DOF gyroscope”, Proc. of Transducer’07, pp 1211-1214. [6] H. K. Versteeg and W. Malalasekera: An introduction to computational fluid dynamics – the finite volume method (Prentice Hall 1995) Chap. II.

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