加速度计设计.docx

MEMS Actuators and Sensors Coursework
Design of a Micromachined Accelerometer
CAO Zhuo ([e-mail])
PART1: Theoretical background
Micromachined Accelerometers
Mechanism
Piezoresistive
Capacitive
Principle
The suspension beams are fabricated by piezorisistive material. When the proof mass moves relative to the fixed frame, the deformation in the suspension beams will generate stress profile, hence change the resistivity of the embedded piezoresistors.
When external acceleration applied on the capacitive accelerometer, the relative displacement between the proof mass and the fixed conductive electrode frame will change, hence changing the capacitance.
Advantages
simply structure and readout circuit
They have high acceleration sensitivity, low temperature sensitivity, good noise performance and low power consumption.
Drawbacks
relatively large temperature sensitivity and small output signal
Must be properly packaged because of their high sensitivity to the electromagnetic interference (EMI).
Mechanism
Tunnelling
Resonant
Thermal
Principle
Using a constant tunnelling current between one tunnelling tip (attached to a movable microstructure) and its counterelectrode to sense displacement.
transferring the proof-mass inertial force to axial force on the resonant beams and hence shifting their frequency
The temperature flux from a heater to a heat-sink plate is inversely proportional to their separation. The change in separation between the plates can be measured by thermopiles.
Advantages
Very high resolution and sensitivity
direct digital output
Applied in the environment with large temperature gradient
Drawbacks
High supply voltage is required
Not clear
Not clear
Table.1 the main accelerometer mechanism and their characteristic
Although several types of MEMS accelerometers have been reported in the literature, the basic structure consists of a proof mass that is attached by a mechanical suspension system to a fixed frame. Theoretically, the mechanical transfer function of this system in Laplace domain is:
Hs=x(s)a(s)=1s2+DMs+KM=1s2+ωrQs+ωr2 (1)
In this equation, M refers to the proof mass. K refers to the effective spring constant of the suspension beams. D is the damping factor affecting the dynamic movement of the mass. ωr=KM is the natural resonance frequency, and the quality factor is Q=ωrMD=KMD. The static sensitivity of the accelerometer is defined by
S=xstatica=MK=1ωr2 (2)
According to equation 2, for all micromechined accelerometers, a position-measuring interface circuit is needed to measure the displacement of the mass due to the acceleration, and then it is converted to electrical signal. The different types of MEMS accelerometer mechanisms and their characteristics can be summarized in table 1. Nowadays, the main challenge of commercial accelerometers is development of low-cost, inertial-grade productions with sub-ug noise levels, good long-term stability, and low temperature sensitivity.
Micromachined Gyroscopes
All gyroscopes use vibration mechanical elements to sense rotation. When applied a rotation, Coriolis acceleration will generate the energy transfer between two vibration modes. Based on the performance, the gyroscopes can be classified into three categories: inertial-grade, tactical-grade, and rate-grade. Among these three different gyroscope types, rate-grade devices attracted most attention because of their application in automotive. Generally, the specifications of gyroscope include resolution, drift, zero-rate output (ZRO), and scale factor. The classic structure of gyroscopes is tuning fork, which consists of two tines connecting to a junction bar. When the device rotate, a differential sinusoidal force will developed on the individual tines, orthogonal to the main vibration. The main mechanisms used to drive the vibration structure into resonance are piezoelectric, electrostatic and electromagnetic. After that, piezoelectric, piezoresistive and capacitive are three main methods to detect the Coriolis-induced vibrations. The characteristics of each mechanism can be concluded in the following tables.
Vibration excitation mechanism
characteristics
piezoelectric
very high quality factors at atmospheric pressure with improved level of performance; batch processing is now compatible with IC fabrication technology
electrostatic
constant amplitude; maximum resolution is obtained when the outer gimbal is driven at the resonant frequency of the inner gimbal
electromagnetic
large amplitude of motion
Table.2 different excitation mechanisms of gyroscopes
Detection mechanism
characteristics
piezoresistive
easy to fabricate; only require a simpler electronic interface due to their lower output impedance; large temperature variation of offset; poor resolution
capacitive
Large zero-rate output; can be easily integrated; high sensitivity
Table.3 different detection mechanisms of gyroscopes
Similarly with accelerometers, the pick-off circuit of gyroscope can be either open loop or close loop. But this is still a trade-off between commercial cost and device performance.
PART2: capacitive accelerometer design
Micromachined fabrication
I. Brief process of proof mass fabrication
In order to form the proof mass and suspension beams system structure, unnecessary materials should be removed from the bulk substrates. Hence, bulk micromachining is applied in the fabrication process.
Firstly, etch away the material in the gap of figure 1(b). For micromachining etching, both wet etching and dry etching can be applied to the process. However, the etchant KOH used in wet etching lead to an anisotropic surface. Then the area in the top and the bottom of the proof mass will be different, which make the calculation of proof mass and other parameters more complicated. Hence, Deep Reactive Ion Etching (DRIE, one type of dry etching technologies) is applied in this process because of its very high aspect ratio and more vertical sidewall compared to other etching methods.
Secondly, etching the suspension beams area using DRIE from both front and back side. The reason of adopt DRIE is similar as the discussion above. At the last, the proof mass with a cube structure is obtained.

(a)
(b)

(c)
Fig.1 Schematic of proof mass fabrication process: (a) Silicon bulk material; (b) top view after etch through the gap; (3) diagonal cross-section view of the proof mass and suspension beams
The process of DRIE can be seen from the following figures:

(a)photoresistor spin on

(b) expose

(c) pattern develop

(d) DIRE process: use SF6 for isotropic etching and C4F8 for wall passivation in turns

(e) strip the photo resistor

(f) do the same process in the back side of the wafer
Fig.2 process flow of proof mass and connecting beams fabricaton
II Brief process of electrode fabrication
Because the electrode is thin, surface micromachining is used for top and bottom electrode fabrication.
Firstly, etch the central region of the bulk silicon to make the border district thicker than the centre. Secondly, deposited copper (Cu) as the electrode material in square, as well as the conducting wire. Schematics are shown in figure 3. And the detail of the Cu deposition flow is illustrated in figure 4
III. Wafer bonding
Wafer bonding is an assembly technique where two or more precisely aligned wafers are bonded together. By applying a high voltage to the stacked wafers that induce migration of ions form both wafer will be bonded, allowing a strong field assisted bond to form between silicon atoms. The final accelerometer cross-section schematic is illustrated in figure 5.

(a)

(b)

(c)
Fig.3 schematic of electrodes fabrication process: (a) silicon bulk material; (b) cross-section view of the bottom electrode; (c) top view of the bottom electrode

(a) Deposit and expose the photoresistor

(b) Develop the photoresistor

(c) Dry etch the silicon wafer by SF6

(d) strip the photo resistor

(e) deposit another photoresister layer

(f) expose

(g) develop

(h) Cu depositing

(i) Lift off the photoresistor and Cu on it
Fig.4 process flow of electrode fabrication

(a)
(b)
Fig.5 cross-section view of accelerometer bonding process: (a) before bonding; (b) after bonding
Parameter calculation
The specifications required for the accelerometer are:
· Bandwidth: BW=500 Hz=3141.6 rad/sec
· Sensitivity: 0.1 pF/g
· Dynamic range: +/- 10g
· Minimum detectable acceleration: 1mg
Some already know constants:
· Density of silicon: ρ=2300 kg/m3
· Young’s modulus for silicon: E=160*109 N/m2
· Permittivity of air: ε0=8.85*10-12 F/m
· Dynamic viscosity of air: m = 1.85´10-5 N/m2×s
Sensitivity
For the sensitivity defined in the text book [1] is S=M/K. Here the unit of sensitivity is pF/g. Based on the uniform of units, there is:
MK*ε*Ad02=0.1pFg (3)
And A=a2 is the area of the proof mass.
The differential capacitive sensing

Fig.6 Schematic of equivalent circuit for accelerometer
When there is a acceleration applied, the displacement of the capacitor gaps will lead to a change in the capacitance. They are C1=C0d0d0+x, C2=C0d0d0-x. Thus change the output voltage:
V0=-Vs+C1C1+C2*2Vs≈-xd0Vs (4)
The output voltage is proportional to the displacement x.
Assumptions and Limitations
From the equation 1, it is obvious that when critical damping, s2+ωrQs+ωr2=0 has only one solution. Then Q=1/2, which means the accelerometer is critical damped. Hence, three different cases can be distinguished:
Under damped system
Q>1/2
D<2KM
Critically damped system
Q=1/2
D=2KM
Over damped system
Q<1/2
D>2KM
Table.4 three different cases of damping
When the system is over damped, the bandwidth will be much smaller than the natural resonant frequency. Moreover, Higher Q factor indicates a lower rate of energy loss relative to the stored energy.So, under damper system is expected in this design. If the nature resonant frequency equals to the bandwidth required. And Making the quality factor equals to ½, 1, 2 respectively, the bode plot obtained is shown in the following figure.

Fig.7 Bode plot of ωr=500 Hz
Obviously, when Q=2, the BW=1820 rad/sec cannot satisfy the required bandwidth.
Hence, make an assumption that the natural resonant frequency is slight bigger than the required band width. In this design, make ωr equals to 5700 rad/sec = 907 Hz, and Q=5, the relevant bode plot is shown in figure 8.
From the plot it can be seen that the natural resonant frequency is not just the same with the peak value of the transfer function, but it is higher than the frequency relevant to the peak. When doing the optimization of wr and Q, it is observed that the higher the Q factor, the peak will be sharper. And the bandwidth will increase with the increasing of the natural resonant frequency wr.
The assumptions made here will be used to calculate the rest parameters of the capacitance accelerometer.

Fig.8 Bode plot of BW=500 Hz
Maximum detection situation
When applying a constant acceleration, it means that s=0 in equation 1, hence a=x*wr2. Suppose that the maximum measurable acceleration isamax, which equals to 10 g, then the maximum capacitance displacement is given by xmax=amaxωr2. So, xmax=3*10-7m.
From the text book [1], the gap of the capacitor d0 should be at least three times bigger than xmax. Thus, d0 should be at least 0.9 um.
Minimum detection situation
Suppose that the minimum measurable acceleration isamin, which equals to 1*10-3 g, then the minimum capacitance displacement is given by xmin=aminωr2. So, xmin=3*10-11m.
Noise
In the specification, the noise power spectral density of the front end amplifier is given to be 5nV/Hz. Thus, the voltage noise of the interface circuit Vn=5nVHz*500Hz=111nV≈0.1μV.
In the accelerometer system, in order to detect the minimum output voltage, the noise voltage of the amplifier circuit should be smaller than the output voltage of the capacitors.
Calculation
Supposed that the minimum output voltage is 0.2μV, which is higher than the voltage noise of the amplifier circuit. According to equation 4 and the source voltage is 5V,
d0=xminVomin*5V=7.5*10-4m
Furthermore, considering the following equation group:
KM=ωr2;
Q=MD*ωr;
0.1pFg=ε*ρ*aK*a2d02;
D=0.42μ*A2d03=0.42μ*1d0*a2d02;
In this equation group, the value of ωr and D were assumed. And the value of ε,ρ andμ are constants. Thus, it can be solved that:
Ÿ The width of cube mass: a=0.0013m=1.5 mm;
Ÿ The weight of proof mass: M=ρ*a3=7.0196*10-6 kg;
Ÿ The damping coefficient: D= 0.0080 N/m;
Ÿ The effective spring constant: K= 228.0661 N/m
When there is no accelerometer, the gap between the proof mass and the electrodes will not change. Hence
Ÿ The nominal capacitance C0=C1=C2=ϵ0*Ad0= 2.4828e-014 F.
Geometries of suspension beams
For the structure designed in this report has for suspension beams, hence, the effective spring constant K is given by
K=4E*w*t3L3
Here, w is the width of beam, t is the thickness of beam, L is the length of the beam. Giving any two values of these three parameters will get the rest one. Considering the limitation of the geometries, the final values of w, t, L are:
Ÿ Thickness: t=50 um;
Ÿ Length: L=4 mm;
Ÿ Weight: w=182 um
For present fabrication technology, these geometries can be achieved. However, in practical, the industry will optimize the geometries from a cost point of view.
Open-loop interface circuit design

Fig.9 Charge amplifier circuit for measuring the change in capacitance
Here is a simple pick-off circuit for the accelerometer designed in this report. C1 and C2 represent the variable capacitors of the sensing element. C3 is the parabolic capacitor between amplifier and sensor. R1 keeps the seismic mass at a defined potential and has to be sufficiently large. For the values of C3 and C4, it should be the same order with the value of C1 and C2. Hence, the value around pF should be suitable. And the gain of the amplifier is decided by R2.
To extent the open-loop interface design, an oscillator can be added to synchronize the system. An LPF in the end of the circuit can filter the high frequency noise generated by the circuit.

Fig. 10 block diagram of the open loop circuit
Closed loop force-feedback system

Fig.11 schematic of closed loop force feedback system
For close loop accelerometers, the output signal of the position measurement circuit can be used, together with a suitable controller, to steer an actuation mechanism that forces the proof mass back to its rest position. The electrical signal proportional to this feedback force provides a measure of the input acceleration. This process is simply shown is figure 11.
From the textbook [1], the feedback force F=2εAV0d02*Vf. It is clear that the feedback force