In this chapter, the characterization of the fabricated energy converter is presented. Device displacement and resonance condition were observed in the mechanical measurement. Electrical measurements include static parasitic capacitance and resistance measurement. Mechanical switch measurement is presented in both the dynamic and static electrical measurement.
4.1 Mechanical measurement
The goal of mechanical measurement is to measure the mechanical frequency response of the device and determine its resonant frequency. Mechanical characteristics of the device are measured with input vibration acceleration generated by a shaker. The measurements were performed with the external mass attachment.
4.1.1 MEMS Motion Analyzer measurement
The dynamic response of the device was measured by the MEMS Motion Analyzer (MMA) as shown in Fig. 4.1. A piezoelectric-shaker mounted on the platform provided the input vibration. A function generator connected to the shaker applied the driving signal. The device was glued on the mini-shaker to ensure the stability during test. The MMA system utilizes image processing technique to determine dynamic characteristics. The MMA measures the periodic relative motion between the movable and the static structures of the device by captured images.
The device with and without the external mass were measured by the MMA system. The experiment results are shown in Fig. 4.2 and Fig. 4.3. From the amplitude and phase response, the resonant frequency is around 122 Hz and 1680Hz with and
Shaker
Device
Fig. 4.1 MMA system
Fig. 4.2 Frequency response with external mass
Fig. 4.3 Frequency without external mass
The amplitude and phase responses match a mass-damper-spring system characterized by the equation
2
2 2 2 2
Z = mω Y ,
(k-mω ) +b ωm (4.1) φ tan 1 ω 2,
ω
= − −
− bm
k m (4.2) where Y as the input displacement amplitude, Z as the output displacement amplitude, and φ is the phase difference. The response is zero at DC frequency and constant when frequency is over the resonant frequency. The amplitude response indicates a 3dB bandwidth of about Δω = 14 Hz with external mass, and 160Hz without external mass. The quality factor is 8.6 with external mass and 10.5 without external mass respectively. The low value does not match the expectation by the equation.
2
m
Q km
= b (4.3) From the Eq. 4.3, the device can operate in a low-damping environment to get a high quality factor. So the device packaging under vacuum environment is a proposed solution.
4.1.2 Vibration measurement by our shaker
Our test setup is shown in Fig. 4.4. The amplified sinusoidal signal was used to drive a LABWORK INC. ET-132 shaker. The sinusoidal vibration was measured by a piezoelectric accelerometer (PCB Piezotronics model 353B17) connected to an oscilloscope. The resonance of device was observed by an optical microscope and image of the relative displacement were captured.
Fig. 4.5(a) shows the device at rest. The vibration frequency was tuned from 100 Hz to 150 Hz to find the resonant frequency. From the images taken from the optical microscope, the resonant frequency was observed to be 118 Hz. For the accelerometer reading of 234.5mV, 2.27 m/s2 input acceleration was calculated with the sensor sensitivity of 103.2mV/m/s-2. The device has a displacement of 21 μm due to the large inertial force carried by the external mass, as shown in Fig. 4.5 (b). The input acceleration measured by the accelerometer module is shown in Fig. 4.5 (c)
Optical microscope
device
accelerometer
To power amplifier
To oscilloscope
(b)
Fig. 4.4 (a) Mechanical measurement schematic (b) measurement setup (a)
Shaker (LABWORK INC. ET 132)
Camera
Optical microscope
Power amplifier Function generator
Oscilloscope Accelerometer
Vibration
Device
(a) (b)
(c)
Fig. 4.5 (a) Device at rest (b) device at resonance of 118 Hz (c) input acceleration waveform.
4.2 Static electrical measurement
Parasitic resistance and variable capacitance of our devices were measured in static electrical measurement. In order to improve the insulation between fixed and movable fingers, LPCVD nitride layer was employed. The measurements were also compared with theoretic values and the difference between measurements and theoretical values are discussed in this section.
Tungsten ball Tungsten ball
Fingers Fingers
CA3140
4.2.1 Leakage resistance
In order to ensure good insulation, a measurement circuit was implemented to measure the leakage resistance of the LPCVD nitride insulation, as shown in Fig. 4.6.
The DC current through the device is zero if no leakage resistance Rp exists, resulting in a zero voltage drop across RT. The input bias current of the CA3140 CMOS operational amplifier is below 10 pA, and the output voltage offset caused by the buffer can be neglected. Using this measurement circuit with VT = 10 V and RT = 10 MΩ, the output voltage was 0.6 V, indicating a leakage resistance of about 156.7 MΩ.
The leakage resistance was also measured by an INSTEK-LCR-816 LCR meter. The results was 150 MΩ which agreed with the measurement from Fig. 4.6.
In our previous fabrication without using the high precision shadow mask, the parasitic resistance is below 1MΩ [43]. In the first device using shadow mask, the leakage resistance had been increased to 103MΩ [47]. Therefore, we had increase the value by 50% .
Fig. 4.6 Leakage resistance measurement circuit
Another circuit was used to measure the RC discharge time constant versus VDD
VT RT Vout
Cv
Rp
by a 5 V input Vtri. The relay SWr is initially closed by the control voltage Vtri. The variable capacitor is charged to Vin, and then the relay is opened so that the charge on Cv is discharged through RL. The pulse wave of Vtri is produced by a function generator to trigger the switch.
Fig. 4.7 Variable capacitor measurement circuit [43]
With a RL of 10 MΩ and a Vin of 10 V, the RC discharge time constant versus finger gap displacement is measured. Fig. 4.8 shows the RC discharge for different positions of the variable capacitor. The variable capacitor is moved by a microprobe and the static displacement is measured from the image captured by the optical microscope. The RC discharge time constant was calculated from the time span between 100% and 36.8% of Vin.
The discharge resistance is equal to the parallel connection of RT and the leakage resistance RP. The capacitance can then be calculated from the time constant. The calculated capacitance (Cactual) can be compared with the theoretical value (Cideal), as shown in Fig. 4.9. The calculated value of the minimum variable capacitor is 94 pF (theoretical value of 60 pF), indicating a parasitic capacitance of 34 pF in the device.
Trigger signal
Fixed Movable
Fixed Movable
Fixed Movable
Displacement = 0μm Time constant τ = 880μs
Displacement = 13μm Time constant τ = 1.06ms
Displacement = 17μm Time constant τ = 1.28ms
Fig. 4.8 RC discharge time constant measurement
Fixed Movable
Fixed Movable
0 5 10 15 20 25
300 200 400
100 500 600 700 800 900
Finger displacement (mm)
Variable capacitor (pF)
Displacement = 21μm Time constant τ = 1.88ms
Displacement = 25.5μm Time constant τ = 4.56ms Fig. 4.8 RC discharge time constant measurement (continued)
Fig. 4.9 Measured variable capacitor versus displacement
Moreover, the maximum capacitance of 485 pF is far lower than theoretical value Cideal of 1570 pF. Therefore, the oblique sidewall issues were considered. A non-parallel capacitance was defined by the non-vertical ICP etching [48]. The schematic of the non-parallel capacitance is shown in Fig. 4.10, where h is thickness of fingers, θ is the oblique angle of the finger sidewall, and d1 = 0.6μm and d2 = 51.4 μm are gap between the fingers. The non-parallel capacitance Cactual is expressed as follow [48] The ratio between the actual and the ideal capacitance (θ=0) is
actual 1 2 1 2
ideal 1 2 1 2
C d d (d +2hθ)(d +2hθ)
r = = ln( )
C 2hθ(d +d ) d d (4.5)
Fig. 4.10 Cross-section of non-parallel capacitor
The relationship between the oblique angle and ratio is plotted in Fig. 4.11. The ideal maximum capacitance of 1570 pF is shown in Fig. 4.9. Our measurement result of the maximum capacitance implies an oblique angle of 0.59D. Fig. 4.12(a) shows the oblique finger sidewalls. Furthermore, the rough sidewall surface also limits the gap between the fingers and thus produces the non-ideal maximum capacitance, as shown in Fig. 4.12(b). The issues are mentioned in Chapter 3. To improve this issue, a fine tuned recipe of ICP should be adopted.
θ
Fig. 4.11 Cactual/Cideal versus oblique angle
Fig. 4.12 SEM photo (a) Close-up of non-parallel capacitance (b) rough surface of finger sidewall [47].
4.2.2 Static measurement of SW1
Mechanical contact switches are designed to work in the DC mode, as shown in Fig. 4.13. SW1 should be turned on in the battery charging process. In static measurement, a microprobe was used to push the movable plate to turn SW1 on, as shown in Fig. 4.14. The gold wire was bonded to the PCB. The bias voltage Vin for
(a) (b) Rough surface
Vertical line
θ
Oblique angle for sidewall (degree) Cactual/Cideal
0 0.5 1 1.5 2 2.5
0 0.2 0.4 0.6 0.8 1
SW1 OFF
the variable capacitor is 3.6V. The output voltage was measured by an oscilloscope, as shown in Fig. 4.15. The result shows a voltage of 3.6V was measured on node B. That means the switch was turned on and charging process can work properly. The contact resistance of SW1 was also measured by a LCR meter to be 0.5 to 2Ω. This low contact resistance indicates that the SW1 can work successfully.
Fig. 4.13 DC model operation with mechanical switches
(a) (b)
B
GND C GND GND GND
B C Fig. 4.15 Charge Voltage
4.2.3 Static measurement of SW2
The pull-in voltage of SW2 was measured by applying a voltage between nodes B (SW2) and GND (pull-in electrode) while the displacement was observed through a microscope. The measurement shows that the pull-in voltage of SW2 is approximately 98V. The release voltage of 54V was also measured by reduce the voltage across the B and GND node. The pull-in voltage measurement is higher than the design value of 74V and the release voltage is also higher than the design value of 50V. The difference between measured and design value is also caused by non-vertical etching profile.
(a) (b)
Fig. 4.16 SW2 with (a) no applied voltage, (b) 98 V applied voltage (pull-in)
4.3 Dynamic electrical measurement
The voltage of the variable capacitor increases as the capacitance decreases.
SW1 are turned on when the fingers reaches the maximum relative displacement are reached. Thus the magnitude of mass movement should be large enough to make SW1 contact. The device without the mass attached was operated at the resonant frequency of 1739 Hz and the vibration acceleration of 25.2 m/s2. The voltage on the variable capacitor was also measured by the circuit shown in Fig. 4.13. The output signal is shown in Fig. 4.17. It shows the voltage of 3.6 V during the charging process. The maximum voltage Vmax of variable capacitor is 14.6 V which was smaller than the expected values of 91 V, indicating the change of variable capacitance is small. Fig.
4.18 shows the measurement of the voltage on the variable capacitor and the input acceleration.
Fig. 4.17 Voltage on the variable capacitor
Because the maximum voltage on variable capacitor is far lower than the design value, we tried to increase the voltage difference by applying a negative voltage of
Time (s) Voltage on Cv (V) Input vibration acceleration (m/s2 )
Vmax
SW1 on
However, as the SW2 closed, the minimum voltage of 87.6V across B and GND is still large than the release of 54V, causing SW2 to stick to the close position. We thus propose another method by applying a control signal to SW2 as shown in Fig. 4.20.
We first to use a full-wave rectifier to achieve synchronous, than we transfer a sinusoid wave into square wave, by controlling the delay signal, we may achieve a precise timing control of SW2. Finally, the precise control signal is amplified by a high voltage amplifier to reach pull-in and release voltage. Another method is to simply amplify the capacitor voltage by a high voltage amplifier as the pull-in control voltage. The measurement is still in progress.
Fig 4.18 Voltage on the variable capacitor and input acceleration
RL
Fig. 4.19 (a) SW2 overview, (b) SW2 schematic circuit
Fig. 4.20 Schematic of Switch2 control method
4.4 Summary
In this chapter, we demonstrated the results of mechanical and electrical measurement. The mechanical results included two parts, one is the MMA data which provide us with the mechanical characteristics of the energy converter. The other is the resonant frequency measured by our shaker and optical microscope. The variable capacitance and parasitic resistance was measured. The measured variable capacitance is less than the theoretical value due to the non-parallel vertical fingers effect caused by ICP etching. Finally the mechanical contact SW1 was tested. The contact
Power amplifier Function
was far lower than the voltage to trigger the SW2 to close due to non-parallel vertical comb. As a result, the DC power measurement is still in progress.