整合機械式開關之微電容式振動-電能轉換器

國 立 交 通 大 學

電機與控制工程研究所

碩士論文

整合機械式開關之微電容式振動-電能轉換器

Micro Capacitive Vibration-to-Electric Energy

Converter with Integrated Mechanical Switches

研究生：曾繁果

指導教授：邱一 博士

整合機械式開關之微電容式振動-電能轉換器

Micro Capacitive Vibration-to-Electric Energy

Converter with Integrated Mechanical Switches

研 究 生: 曾繁果 Student: Victor F. G. Tseng

指導教授: 邱一 Advisor: Yi Chiu

國立交通大學 電機學院

電機與控制工程研究所

碩士論文

A Thesis

Submitted to Department of Electrical and Control Engineering

College of Electrical and Computer Engineering

National Chiao Tung University

In Partial Fulfillment of the Requirement

For the Degree of

Master

In

Electrical and Control Engineering

October 2007

Hsinchu, Taiwan, R.O. C

中華民國九十六年十月

中文摘要

微機電系統是一個微系統與電子電路整合的科技平台。在無線感測網路等應 用中，這些高度整合的可攜式元件都具有獨立電源的需求。拜先進的超大型積體 電路技術所賜，這些微系統節點的電能需求已降至數十μW 的程度。利用環境中 的能源轉換成電能來供給這些可攜式元件使用已經成為一個可行的方法。 此論文呈現一個電容式振動-電能轉換器的設計、製作以及量測。在 1 cm2 的元件面積以及 3.6 V 輔助電池電源的限制下，此元件的輸出功率可達 31 μW (輸出電壓約 40 V)。我們使用一個 4 克的外加質量塊來調整元件特性，使其在輸 入振動下共振。元件整合了機械式開關，以提供準確的充電-放電能量轉換控制。 元件是利用 SOI 晶圓並且搭配深蝕刻技術來製作，現階段已克服了所有的製程 問題。此能量轉換器已經過量測。元件在有無承載外加質量塊的不同情形下，其 共振頻率都符合設計值。元件的電容變化量比預期的還要小。利用背後基底部份 掏空的技術，元件的寄生電容已被最小化。元件在無外加質量塊、5 MΩ負載以 及1880 Hz 振動頻率的情形下，量測到的交流輸出功率為 1.2 μW。此情形的最 大輸出功率預計為 16 μW。有承載外加質量塊的元件之輸出功率量測仍在進行 中。

Abstract

Micro-Electro-Mechanical System (MEMS) is the technology platform that promotes the integration of various microsystems with circuit electronics on the same chip. When applied in fields such as wireless sensor networks, each one of these highly integrated portable devices needs an independent power supply. Due to recent advances in low power VLSI design technology, the power consumption is reduced to about a few tens of microwatts. Therefore, it becomes feasible to power the portable devices by scavenging the ambient energy.

The design, fabrication and measurement of a capacitive vibration-to-electric energy converter are presented in this thesis. With a device area constraint of 1 cm2 and an auxiliary battery supply of 3.6 V, the device was designed to generate an output power of 31 μW with an output saturation voltage of 40 V. An external mass of 4 grams was needed to adjust the device resonance to match the input vibration. Mechanical switches are integrated onto the device transducer unit to provide accurate charge-discharge energy conversion timing. The device was fabricated in SOI (silicon-on-insulator) wafers by deep silicon etching technology. By overcoming all processing issues, the device can be successfully fabricated by a modified fabrication process. Measurements on the energy converter were also conducted. Resonant frequencies of the device with and without the external mass agreed with the designed values. Capacitance change was smaller than expected. Parasitic capacitance was minimized by partial back side substrate removal. Without the external mass, the measured AC output power was 1.2 μW with a load of 5 MΩ at 1880 Hz. The maximum output power in this condition is expected to be 16 μW. AC output power measurement of the devices with external mass attached is still in progress.

致謝

伴隨著血淚以及汗水，碩士生涯在百感交集中結束了。這兩年的生活中，我 學會了很多、反省了很多，體會到了一絲成熟的智慧。感謝給我機會成長的大家。 首先，感謝我的指導教授邱一老師。老師在研究上的執著、堅持，帶給我非 常大的震撼以及啟發，激勵了我這個初試身手的新鮮人，使我在研究領域更能有 所成就。回想起最後那一段修改論文的日子，雖然天天熬夜，但老師依然天天與 我們一起拼命。老師同甘共苦的精神，實在令人動容。若非在碩士班生涯能遇上 老師的教誨，我便不能發現自己在微機電領域的興趣。希望在未來的日子裡，我 能夠以老師所給予我們的訓練作為基礎，不斷的擴張自己的專業能力。 感謝我的口試委員，邱俊誠主任、方維倫老師、陳科宏老師以及黃聖傑老師。 老師們能在繁忙之餘對我的研究提供指導和建議，我會懷著感激之情銘記在心。 感謝實驗室的學長，李企桓、郭炯廷、潘均宏、黃建勳、吳忠衛、溫亦謙。 若沒有你們的經驗傳承，我便不能順利得銜接上你們的研究步伐。同時也感謝其 他實驗室的學長，洪振均、黃信瑀、林志伯的支持。特別是洪振均學長，能與你 一起做實驗，讓我增廣不少見聞。非常感謝你一起外校做實驗時所給予我的協助。 感謝與我一起努力打拼的同學黃煒智。雖然你有些大條神經，但是能與你共 事，使我受益良多。如果沒有你的陪同，我恐怕早就支撐不住了。當然也感謝邱 俊誠實驗室的同學，林建賢、陳一帆、劉亞書、倪嘉宏，也感謝其他外系的同學 們。有了你們的資訊分享、專業協助、鼓勵打氣，使我避免了很多不必要的迷惘。 感謝帶給我歡樂時光的實驗室學弟，張子麟、陳弘諳、揚昇儒、吳昌修。從 你們每個人身上，我看到獨一無二的潛力，祝你們在未來研究的路上一帆風順。 最後，感謝我的父母以及家人的關懷。養教之恩，無從報答，但未來的我絕 不會令你們失望的。要感謝的人實在太多了，無法一一列舉，只盼望能將大家所 帶給我的成長發揚光大。誠摯得謝謝你們，謝謝培育我的交通大學，珍重再見。

Table of Content

中文摘要...i Abstract...ii 致謝... iii Table of Content...iv List of Figures...vi List of Tables...ix Chapter 1 Introduction...1 1.1 Motivation...1 1.2 Literature survey ...2

1.2.1 Photovoltaic light exposure...2

1.2.2 Thermal gradient potential...3

1.2.3 Human kinetic energy ...4

1.2.4 Aerodynamic air flow ...5

1.2.5 Acoustic noise power ...6

1.2.6 Ambient vibration ...6

1.2.7 Summary on energy sources ...6

1.3 Ambient vibration energy conversion...7

1.3.1 Electromagnetic energy conversion...8

1.3.2 Piezoelectric energy conversion ...9

1.3.3 Electrostatic capacitive energy conversion...10

1.3.4 Summary on vibration energy conversion technologies...12

1.3.5 Progress in previous generation devices ...12

1.4 Thesis objectives and organization ...12

Chapter 2 Principle and Design...14

2.1 Operation principle ...14

2.2 Preliminary study...16

2.2.1 Characteristics of vibration sources ...17

2.2.2 Auxiliary battery supply...18

2.3 Device design...19

2.3.1 Static analysis...20

2.3.2 Variable capacitor design ...21

2.3.3 Dynamic analysis ...26

2.3.4 Spring design ...32

2.3.5 Conversion efficiency ...36

2.4.1 SW1 design ...38

2.4.2 SW2 design ...39

2.5 Layout schematic ...44

2.6 Conclusion ...46

Chapter 3 Fabrication process...47

3.1 Fabrication process flow ...47

3.2 Processing issues...58

3.2.1 Non ideal effects of the ICP process ...58

3.2.2 Damaging in dicing process...64

3.2.3 Etching of silicon nitride during release ...65

3.2.4 Metal deposition issues ...66

3.3 Modified fabrication process ...67

3.4 Fabricated device ...70

3.5 Conclusion ...75

Chapter 4 Measurement and Experimental Results...76

4.1 Mechanical measurement...76

4.1.1 Mechanical characteristics without external mass...76

4.1.2 Mechanical characteristics with external mass ...81

4.2 Static electrical measurement...83

4.2.1 Measurement circuit...84

4.2.2 Variable capacitor measurement ...86

4.3 Dynamic electro-mechanical measurement ...92

4.3.1 AC output power measurement...92

4.3.2 DC output power measurement ...98

4.4 Switch measurement ...98

4.5 Conclusion ...99

Chapter 5 Conclusion and Future Work ...101

5.1 Conclusion ...101

5.2 Future work...102

References...104

List of Figures

Fig. 1.1 Typical operation schematic of photovoltaic energy conversion…….……..3

Fig. 1.2 Thermoelectric energy converter composed of two series thermocouple…..4

Fig. 1.3 Exploded view of the piezoelectric shoe inserts located underneath the heel and ball of the foot………...………..5

Fig. 1.4 Electromagnetic energy converter………..…9

Fig. 1.5 Bimorph cantilever beam piezoelectric energy converter………….…...10

Fig. 2.1 Operation of the electrostatic energy converter……….………..14

Fig. 2.2 Charge transfer process from Cv to output port……….………..15

Fig. 2.3 Vibration spectra by Roundy……….………...17

Fig. 2.4 Vibration spectrum of an air conditioner…………..………18

Fig. 2.5 Lithium-ion rechargeable battery……….………19

Fig. 2.6 Top view of the in-plane gap closing variable capacitor topology…..…....21

Fig. 2.7 (a) Close up view of fingers with silicon nitride sidewall coating, (b) equivalent capacitance model between fingers, (c) schematic view of one finger cell with the bump design………..………….……...23

Fig. 2.8 Output power and maximum be versus initial finger gap………...26

Fig. 2.9 Schematic of the conversion dynamic model……..……….26

Fig. 2.10 The needed k/be_max ratio versus maximum displacement………28

Fig. 2.11 Simulink model of device with ideal switch operation………...………….29

Fig. 2.12 Time response of the relative displacement xr……..………...30

Fig. 2.13 Time response of the charge Q on capacitor………...………...31

Fig. 2.14 Steady state displacement and charge operation………...………...…31

Fig. 2.15 Output voltage time response……….…...……….……..32

Fig. 2.16 Spring structure schematic view………...33

Fig. 2.17 CoventorWare simulation of the spring constant of a single spring element………...………..35

Fig. 2.18 CoventorWare modal analysis, (a) without external mass, (b) with external mass attached………..………..36

Fig. 2.19 Q-V plane (a) ideal operation, (b) operation with charge redistribution between Cv and Cstor………..…...37

Fig. 2.20 SW1 as a contact mechanical switch………39

Fig. 2.21 SW2 as a lateral pull-in contact switch………...40

Fig. 2.22 Simulink model of the device with switch operation…………...…………42

Fig. 2.23 Time response of SW2 gap and Vc………...…43

Fig. 2.25 Layout schematic view of the variable capacitor………...……..45

Fig. 2.26 Layout view of the variable capacitor and switches……….46

Fig. 3.1 Fabrication process flow of the SOI device……….…………....55

Fig. 3.2 (a) Notching and (b) etch rate lagging effect……….………..59

Fig. 3.3 Modified layout with guarding structures, (a) SW1, (b) SW2……….……60

Fig. 3.4 Experimental results of the notching effect, (a) (b) devices without guarding structures, (c) (d) devices with guarding structures…………...61

Fig. 3.5 ICP depth measurement after 80 minute etching, (a) fingers and spring trench, (b) SW1 trench, (c) SW2 trench………...…………61

Fig. 3.6 Schematic view of device with blocking structure………..……….63

Fig. 3.7 Device with photoresist protection coating, (a) current design with finger length of 425 μm, (b) previous design with finger length 1225 μm……....64

Fig. 3.8 Device after aluminum deposition……….………..67

Fig. 3.9 Modified fabrication process flow beginning from the release step……....68

Fig. 3.10 SEM overview of the fabricated device, (a) center, (b) corner…………....70

Fig. 3.11 SEM photograph of finger bumps, (a) over view, (b) close up view…...…71

Fig. 3.12 SEM of the fabricated SOI device, (a) finger width, (b) finger height, (c) SW1, (d) SW2……….………...………..73

Fig. 3.13 (a) Overview of the fabricated SOI device, (b) device with external tungsten mass attached………..………..74

Fig. 4.1 MMA system, (a) instrument setup, (b) device under static condition, (c) device driven by input vibration at 1.84 kHz………..………...…..77

Fig. 4.2 MMA measurement results of the device without external mass, (a) amplitude response, (b) phase response……….………..………78

Fig. 4.3 (a) Measurement system schematics, (b) photograph of the measurement system setup……….………80

Fig. 4.4 (a) Measured acceleration by the piezoelectric accelerometer at 1912 Hz, (b) device at resonance (relative displacement is about 9.5 μm)………..…...81

Fig. 4.5 MMA measurement of the device with external mass attached, (a) amplitude response, (b) phase response………...82

Fig. 4.6 (a) Device with the external mass attached at resonance, (b) measured acceleration at 120 Hz……….……….83

Fig. 4.7 (a) Circuit used to measure the voltage increasing effect, (b) circuit with additional resistance and switch……….…….………….84

Fig. 4.8 Circuitry used for capacitance variation measurement……….…………...86

Fig. 4.9 Parasitic resistance measurement circuit……….……….86

Fig. 4.10 RC discharge time constant measurement at different positions of the variable capacitor (original fabrication process)………..…..………..87

Fig. 4.11 Measured and theoretical RC discharge time constant versus displacement

(original fabrication process)………..………..…………89

Fig. 4.12 RC discharge time constant measurement at different positions of the variable capacitor (modified fabrication process)………..90

Fig. 4.13 Measured and theoretical capacitance versus displacement (modified fabrication process)………...………...91

Fig. 4.14 Circuitry used for AC power measurement………..………92

Fig. 4.15 AC output measurement without external mass………...…………93

Fig. 4.16 Modified circuitry used for AC power measurement…………...…………94

Fig. 4.17 Device during AC output power measurement, (a) static condition, (b) resonance at 1870 Hz……….………..94

Fig. 4.18 Measurement of AC output power for various RT………95

Fig. 4.19 Measured AC output power versus load resistance RT……….……...97

Fig. 4.20 Measurement circuit proposed by Roundy………...98

Fig. 4.21 (a) SW2 overview, (b) SW2 schematic circuit………...….….99

Fig. 4.22 SW2 with (a) no applied voltage, (b) 100 V applied voltage (pull-in)…...99

Fig. 5.1 Oblique metal deposition of the switch gaps……….………….102

List of Tables

Table 1.1 Comparison of energy scavenging and power sources…………...…...……7 Table 2.1 List of variable capacitor design parameters………25 Table 2.2 List of spring design parameters………...………...35 Table 2.3 SW2 parameters………...………42

Chapter 1 Introduction

1.1 Motivation

Micro-Electro-Mechanical System (MEMS) is the integration of mechanical elements, sensors, actuators, and electronics on a common substrate through micromachining processes compatible with conventional integrated circuit (IC) fabrication. By combining silicon based micro-machines with microelectronics, MEMS technology has revolutionary impact on all categories of applications, making possible the realization of the complete system on chip (SOC) concept. Current MEMS research and development has already been applied in fields such as micro optical systems, sensors and actuators, micro fluidic elements, and even biomedical applications, all with fruitful results.

Such continuous improvement of microsystem technology promotes the development of smart micro transducer networks, such as RFID (Radio Frequency Identification) and wireless sensor network [1]. These highly integrated portable devices have received increasing interest in recent years. Nevertheless, power consumption has become a severe limitation on the development due to the limited energy capacity of the small volume energy storage devices [2]. Traditional storage devices include batteries [3], micro batteries [4], micro fuel cells [5], ultra capacitors [6], micro heat engines [7], and radioactive materials [8]. Researchers attempt to increase the energy density in these storage devices, but the solutions still have finite lifetime and high maintenance costs.

Fortunately, the advance in low power VLSI (Very Large Scale Integrated circuit) technology, along with the low duty cycles of the wireless sensor networks, have reduced power requirements to tens to hundreds of microwatts [9]. It becomes

possible to power these portable devices by scavenging ambient energy from the environment, thus providing a self renewable or even self sustainable energy source which can replenish part or all of the consumed power. This concept has received attention along with the development of wireless sensor networks, and research on various ambient energy scavenging technologies are being conducted.

1.2 Literature survey

State-of-art ambient energy scavenging devices can extract energy from a range of ambient energy sources, such as light exposure, thermal gradients, human power, air flow, acoustic noise, and vibration [10]. Methods to harvest energy from various ambient energy forms are studied and compared in this section in order to decide the main energy conversion technology of concern in this thesis. Due to the inexhaustible energy providence from the environment, the performance of such harvesting devices is characterized by their power density, instead of energy density used for traditional storage devices.

1.2.1 Photovoltaic light exposure

Light exposure is converted into electrical power by photovoltaic cells, more popularly known as solar cells. Photovoltaic cells function by the photovoltaic effect [11], originated by the photo-generation of charge carriers in specially treated light absorbing semi-conductor material under light exposure. The charge carriers are then transmitted out by conductive contacts to form electricity. The operation schematic is shown in Fig. 1.1. Single crystal silicon photovoltaic cells possess conversion efficiency ranging from 12% to 25%. Thin film polycrystalline and amorphous silicon photovoltaic cells are also commercially available. They cost less but provide lower

conversion efficiency [12]. Overall, photovoltaic energy conversion offers sufficient output power for electronics. The fabrication is also compatible with conventional IC technology. Nevertheless, the output power of photovoltaic cells is dominated by environmental conditions. For instance, if the device is installed outdoors and operated primarily during daytime, the photovoltaic cell offers a sufficient power density up to 15 mW/cm2. However, under normal indoor office light exposure, the photovoltaic cell can only supply a power density below 5 μW/cm2. Due to this characteristic, the photovoltaic cell device is limited to specific applications.

Fig. 1.1 Typical operation schematic of photovoltaic energy conversion [11]

1.2.2 Thermal gradient potential

The thermal gradients in the environment can also serve as power sources through the Peltier–Seebeck effect, or the thermoelectric effect [13]. In this effect, a voltage difference, probably several microvolts per degree, will build up between two different metals or semiconductors in the presence of a temperature difference. If the two materials are connected in a closed loop, a continuous current will flow.

Materials with large Seebeck coefficients and high electrical conductivity can improve conversion efficiency and minimize power loss. However, typical materials

Back contact Front contact Light exposure Anti-reflective coating Specially treated semi-conductor material

used for thermoelectric energy conversion, such as Sb2Te3, Bi2Te3, Bi-Sb, PbTe, Si-Ge,

BiSbTeSe compounds, and InSbTe, are not completely compatible with the IC process. Furthermore, although an output power density of 40 μW/cm3 under a 5 ˚C temperature gradient has been demonstrated [14], temperature differences of this level (5 ˚C) are not common in typical micro system environment [15]. Without large thermal gradients, the output power is limited. Connecting several thermocouple elements in series can be used to generate larger output power, as shown in Fig. 1.2. However, the increased series resistance increases the ohmic power loss and thus reduces the overall power conversion efficiency.

Fig. 1.2 Thermoelectric energy converter composed of two series thermocouples [16]

1.2.3 Human kinetic energy

Another energy source with significant potential is the human body movement. Typical research on this subject use piezoelectric conversion to scavenge the kinetic energy produced by the human body, which has a pulse-like percussive energy form. Significant amount of work has been conducted to harvest energy off the human body by wearable devices [17, 18]. The studies by Massachusetts Institute of Technology

suggests that the human foot has the greatest potential as an energy source due to its high energy production rate at the heel and ball of the foot during walking. This research has led to the development of the piezoelectric shoe inserts, as shown in Fig. 1.3, with a power density of 330 μW/cm3. The application is however limited by the piezoelectric and IC integration issues as well as the power delivery issues. For specific requirements such as RFID tags and other wireless devices worn on the foot, the piezoelectric shoe inserts serves as a good solution.

Fig. 1.3 Exploded view of the piezoelectric shoe inserts located underneath the heel and ball of the foot [18]

1.2.4 Aerodynamic air flow

Traditional wind powered generators, such as wind mills, have existed for a long time. Current interest is to proceed into the centimeter scale. With the output power related to the air velocity, a 5 mW/cm3 power density can be achieved under an air velocity of 8 m/s [10]. Without sufficient air velocity, the output power significantly decreases (e. g. 380 μW/cm2 at 5 m/s air velocity) [10]. This eventually limits the application of such technology. Up to current date, no effort on converting air flow to electric power at centimeter scale has been reported.

1.2.5 Acoustic noise power

Another extraordinary power source is the acoustic noise power, which is usually considered as pollution. This perspective method should be especially useful in the urban environment or industrial environment, which is constantly contaminated by noise. Unfortunately, current research and development of this method has only been able to scavenge limited power from noise with extremely high decibel levels [1]. Therefore, it is not a feasible power source for common applications.

1.2.6 Ambient vibration

Similar but unlike human or acoustic vibration, the ambient vibration is another widely existing energy source. Typical ambient vibration sources are classified into two major categories. One is the steady low amplitude vibration with constant or small deviation of frequency. It is mainly observed in large commercial and office buildings, industrial environments, and residential household appliances. The other is the more randomly distributed vibration with varying frequency and intensive amplitude. It is often observed in automobiles, aircrafts, ships, trains and other machinery that produces intensive forces. Different conversion technologies are utilized for different types of vibration sources. Theory and experiments show that more than 300 μW/cm3 can be generated [10]. The potential of this method is greatly amplified when targeted on specific vibration sources. More discussion and detail will follow.

1.2.7 Summary on energy sources

Summary of the different ambient energy sources and energy storage devices is shown in Table 1.1 [10]. The upper portion shows the comparison of the ambient energy sources; the lower portion shows the comparison of the energy storage devices.

Based on the above survey, ambient vibration is chosen as the energy source for conversion due to its ubiquity and sufficient power density.

Table 1.1 Comparison of energy scavenging and power sources [10]

Power sources Power density

(μW/cm3 or μW/cm2)

Commercially available?

Solar (outdoors) 15, 000 μW/cm2 Yes

Solar (indoors) 10 μW/cm2 Yes

Temperature gradient 40 μW/cm3 at 5˚C gradient Soon

Human power 330 μW/cm3 No

Air flow 380 μW/cm3 at 5 m/s velocity No

Acoustic noise 0.96 μW/cm2 at 100 dB No

Vibration 375 μW/cm3 No

Storage devices Energy density

(μWyear/cm3)

Commercially available?

Batteries (Lithium) 90 μWyear/cm3

Yes

Batteries (Lithium-ion) 34 μWyear/cm3 Yes

Fuel cells 110 μWyear/cm3 No

Ultra capacitors 1.6~3.2 μWyear/cm3 Yes

Heat engine 105 μWyear/cm3 No

Radioactive (63Ni) 52 μWyear/cm3 No

1.3 Ambient vibration energy conversion

Based on the previous discussion, more details on the conversion of ambient vibration source energy into electrical power are discussed in this section. Typical

vibration-to-electric energy conversion technology is based on three methods. They are respectively electromagnetic inductive conversion, the electrostatic capacitive conversion, and the piezoelectric conversion.

1.3.1 Electromagnetic energy conversion

Electromagnetic energy conversion is based on the Faraday’s law of induction, which states that any change of the magnetic flux linkage in a coil will induce a voltage or electromotive force (EMF). This induced voltage is equal to the negative rate of change of magnetic flux times the number of turns in the coils. The operation of the electromagnetic energy converter is shown in Fig. 1.4 [16, 19]. The coil is attached to a vibration-driven oscillating mass and moves through a magnetic field established by a permanent magnet. The output AC power depends on the number of turns in the coil, the magnetic field intensity, and the vibration amplitude and frequency.

Shearwood and Yates [20] developed a device to produce a 0.3 μW output power (power density of 10~15 μW/cm3) from a vibration source with amplitude of 500 nm and frequency of 4.4 kHz. The output AC voltage was 8 mV, which was too small to be rectified by a bridge configuration that requires a turn-on voltage of about 0.5 V.

More recently, Chandrakasa et al. have developed an electromagnetic converter targeting the vibration with amplitude of 2 cm and frequency of 2 Hz of a walking person [21-23]. Their simulations showed that a maximum output power of 400 µW could be achieved with the output voltage of 180 mV. The device had a large size of 4 cm×4 cm×10 cm, and the corresponding power density was 2.5 µW/cm3_.

The most common drawback of electromagnetic energy conversion is the relatively low induced voltage, which can be foreseen from the scaling law on electromagnetic effect. Transformers or other solutions are inadequate due to the

limited device volume. Difficulty in fabricating high quality coils with large number of turns in the thin film process is also encountered. These drawbacks result in a large device volume, and thus a lower power density.

Fig. 1.4 Electromagnetic energy converter [16]

1.3.2 Piezoelectric energy conversion

Piezoelectric energy conversion relies on the piezoelectric effect of specific materials in the presence of an applied mechanical stress. When the electrical charge in the crystal lattice is separated by the stress, a voltage drop will be induced across the piezoelectric material. Typical piezoelectric conversion device consists of a bimorph piezoelectric cantilever beam with mass attached to the free end, as shown in Fig. 1.5. Piezoelectric energy conversion is more suitable for the frequency varying intensive amplitude vibration source mentioned before.

The output power due to vibration stimulation is in AC form, and further power management circuitry is needed to extract stable and thus usable output power. Optimal power circuitry for piezoelectric generators has been studied [24, 25]. The maximum reported output power was 18 mW with a power density of 1.86 mW/cm3 for a vibration frequency of 53.8 Hz. Other works on piezoelectric converters were

also conducted [10, 15, 26]. Power density of 200 µW/cm3 was achieved for the input vibration of 2.25m/s2 at 120 Hz.

In piezoelectric converters, high-piezoelectric-constant materials such as PZT are not compatible with conventional IC process. Most research so far use bulk fabricated materials to form the cantilever beam, which is not suitable for the integration with microsystem technology.

Fig. 1.5 Bimorph cantilever beam piezoelectric energy converter

1.3.3 Electrostatic capacitive energy conversion

Electrostatic capacitive energy conversion utilizes a variable capacitor to convert vibration energy into electric energy. The electrical energy W stored in a capacitor with capacitance C and voltage V is _W 1_CV2 1 Q2

2 2 C

= = . If the capacitance of a

pre-charged capacitor with constant charge Q is decreased due to vibration, the stored electrical energy in the capacitor will increase, thus converting the kinetic energy into electrical energy. The main concern of the capacitive energy conversion is how to extract the stored electrical energy in a properly controlled timing scheme. Capacitive energy conversion is more suitable for the steady frequency moderate amplitude

vibration source mentioned before. More detail on such charge-discharge conversion cycle operation is given in Chapter 2.

Design of the capacitive energy converter was carried out by Meninger et al. [23]. Comb structured variable capacitors were fabricated on silicon on insulator (SOI) wafers by MEMS technology. Simulation showed an output power of 8.6 μW with a device size of 1.5 cm × 0.5 cm × 1 mm from a 2.52 kHz vibration source. Another design was proposed by Roundy [15], which can achieve an output power density of 110 μW/cm3 from a vibration with amplitude of 2.25 m/s2 and frequency of 120 Hz.

MEMS variable capacitors can be fabricated through mature silicon-based micromachining process. Therefore, the capacitive energy converter is compatible with conventional IC process. It can also provide high output voltage and adequate power density. The drawback of the converter is that it needs an external voltage source Vin to charge the variable capacitor. Thus the life time of the external voltage

source must be considered. This issue can be alleviated by employing inductive flyback circuitry proposed by Bernard et al. [27], which constantly feeds back the temporary stored energy to the external voltage supply for further usage.

The extraction of the energy in capacitive energy conversion must be accurately timed in order to optimize the conversion efficiency. A prototype circuitry for capacitive energy conversion was proposed by Roundy [15], in which the two switches were realized by diodes. However, this model results in an excessive output power reduction due to the far from ideal operation of the diodes. Other researches [27-29] utilized gate clocked MOSFET switches or other circuit configuration. Problems such as power consumption by the electronics or parasitic capacitive and resistive coupling still exist in these designs, not to mention the non-synchronous operation of the circuitry with the input vibration. Therefore, improved switch design is critical for better energy conversion efficiency.

1.3.4 Summary on vibration energy conversion technologies

According to the above literature survey, electrostatic capacitive vibration-to-electric energy conversion is used to scavenge ambient vibration energy due to its compatibility to IC processes, ubiquity in the environment and sufficient output power density. A novel mechanical switch is proposed to address the timing switch issues in current technology as the focus of this thesis.

1.3.5 Progress in previous generation devices

Capacitive energy conversion by our team has been conducted in the past [30]. The achievements of the earlier generations of devices prior to this thesis include the preliminary modeling and optimization of the device, the fabrication process development (including backside substrate removal), and the measurement system setup. However, electrical power output has not been measured due to limited number of devices after final assembly. Therefore, this thesis will continue on the basis of the previous effort to improve the device in all aspects of interest, especially the power output measurement.

1.4 Thesis objectives and organization

Most of the works on capacitive vibration-to-electric energy conversion were focused on the backend power electronics. Literature survey and our previous effort [30] show that design optimization and fabrication processes of the MEMS variable capacitor itself can still be improved. New switches for charge-discharge control are also needed in order to eliminate the defects mentioned above. Therefore, the objectives of this thesis are:

steady operation and eliminate unwanted parasitic effects,

(b) Propose novel mechanical switches for charge-discharge conversion timing control,

(c) Construct the dynamic model of the converter including the capacitor unit and the mechanical switches,

(d) Fabricate and conduct preliminary measurement on the devices

The organization of this thesis is as the following. Design and analysis of the converter is given in Chapter 2. The fabrication process and technology are discussed in Chapter 3. Preliminary measurement results of the fabricated converter are presented in Chapter 4. Finally, conclusion and future work are discussed in Chapter 5.

Chapter 2 Principle and Design

The basic concept of the capacitive energy converter is the conversion of kinetic energy into electrical energy when a pre-charged variable capacitor is displaced by external vibration. Furthermore, the extraction of the electrical energy relies on a switching mechanism which is realized mechanically in this thesis. In order to achieve greater conversion efficiency, the variable capacitor, charge-discharge switches and output storage component must all be designed with care, as discussed in this chapter.

2.1 Operation principle

The converter is composed of an auxiliary battery supply Vin, a vibration driven

variable capacitor Cv and an output storage capacitor Cstor, which is connected to the

load RL, as shown in Fig. 2.1. Two switches, SW1 and SW2, are used to connect these

components and control the charge-discharge conversion timing [30]. The variable capacitor serves as the conversion transducer and the auxiliary battery supply is used to pre-charge the capacitor.

A basic operation cycle begins when the variable capacitor Cv is charged by the

auxiliary voltage supply Vin through SW1 at its maximum Cmax. After Cv is charged to

Vin, SW1 is opened and the capacitance changes from Cmax to Cmin due to vibration

Fig. 2.1 Operation of the electrostatic energy converter Vin Cv Cstor RL VL

driven displacement. In this process, the charge Q on the capacitor remains constant (SW1 and SW2 both open). Therefore, the terminal voltage on the capacitor is increased, converting the kinetic energy of vibration into electrical energy stored in Cv.

When the capacitance reaches Cmin and terminal voltage reaches Vmax, SW2 closes

and allows Cstor to be charged by Cv through charge redistribution, transfering the

energy to the output port. SW2 is then opened and Cv varies back to Cmax, preparing

for the next conversion cycle. During this period, the charge on Cstor is dissapated

through the load resistance RL with a time constant τ = RLCstor before it is charged

again by Cv, as shown in Fig. 2.2. The DC level of the output will increase with each

charging process. The output voltage VL will eventually reach the steady state when

the initial and final voltages of the charge-discharge process become equal.

Fig. 2.2 Charge transfer process from Cv to output port

Let the conversion cycle time be Δt, the output voltage variation of the n-th cycle before and after the charge transfer can be expressed as

L n-1 stor max min

L n stor min V [n-1,t = t + t]C +V C V [n, t = t ] = , C +C Δ (2.1) Cv Cstor RL VL SW2 Cv Cstor RL VL SW2 VL(t) SW2 open (discharging) SW2 close (charging) ‧‧‧ Vsat ‧‧‧ V0 VL[n, t=tn] VL[n-1, t=tn-1+Δt] tn tn-1 Δt

where Vmax is equal to VinCmax/Cmin, VL[n-1, t = tn-1+Δt] is the voltage before the

charge transfer, and VL[n, t = tn] is the voltage after the charge transfer. After SW2 is

opened, the output voltage in this charge dissiaption period is

L n stor max min

L n L stor stor min V [n-1, t = t + t]C +V C V [n, t = t + t] exp(- t/R C ). C +C Δ Δ = × Δ (2.2)

With relatively large time constant τ = RLCstor, the net charge transfer to Cstor is

positive, resulting in a rise of V_L cycle by cycle. In the steady state, the net increment of charge transfer to Cstor becomes zero and the initial and final values of

VL become the same (VL[n, t = tn-1+Δt] = VL[n-1, t = tn-1+Δt]). Defined as Vsat, the

final saturation voltage of the output terminal can be derived as

max in stor sat min L stor stor C V C V = , C (1+ ) exp( t/R C )-1 C × Δ (2.3)

where Δt = conversion cycle time = 1/2f and f is the vibration frequency. The average output power can be calculated as,

L stor -t/R C 2 2 0 L L L (V e ) V (t) P(t)= = , R R (2.4) 2 2 Δt _{stor 0 sat} out ₀ L stor L C V V 1 -2Δt P = P(t)dt= [1-exp( )] , Δt

∫

2Δt R C ≈ R (2.5) where V0 =Vs a t e t/R CL s to r Δ

× , as in Fig. 2.2. The approximation takes place when Δt << RLCstor, which also results in a small output voltage ripple.

2.2 Preliminary study

Before the design and analysis of the device and its components, the characteristics of various ambient vibration sources and battery supplies are studied to determine the targeted vibration source and the auxiliary battery supply.

2.2.1 Characteristics of vibration sources

In order to determine the achievable output power, the acceleration amplitude and frequency of the vibration source must be known beforehand. Measurement of different vibration sources was conducted by Roundy [10], as shown in Fig. 2.3. From the spectra of these low-level vibrations, a few points can be observed. First, a common low frequency fundamental peak (usually near 120 Hz) exists in a wide range of ambient vibration sources. Second, the acceleration amplitude is either constant or decreasing with frequency, in which no amplitude peaks appear in higher frequencies. This type of steady moderate vibration source is a suitable input for capacitive energy conversion. Designing the device dynamics to resonate with the input vibration will also greatly improve the conversion efficiency.

Fig. 2.3 Vibration spectra by Roundy [10]

Our own measurement of the vibration of an air conditioner is shown in Fig. 2.4. A fundamental vibration frequency similar to those acquired by Roundy can be

observed with an acceleration amplitude of about 2.25 m/s2. Therefore, the vibration source with a peak acceleration of 2.25 m/s2 and frequency of 120 Hz is chosen as our targeted input vibration source due to its common existence. It should be noticed that operating at such low frequency is not common for typical MEMS device, thus an external mass attachment is required.

Fig. 2.4 Vibration spectrum of an air conditioner

2.2.2 Auxiliary battery supply

The auxiliary battery supply is used to pre-charge the variable capacitor through SW1, similar to the charge pumping technique. When the ambient does not have vibration for the converter to provide enough power, the battery can also serve as the main voltage supply. The converted energy can also be restored back into the battery supply through an additional inductive flyback circuitry [27]. In this case, it functions as a general storage device and provides power more smoothly.

Typical storage devices include capacitors, inductors and batteries. Capacitors and inductors have lower energy density. They often serve as short-term energy

0 100 200 300 400 500 0.01 0.1 1 10 Frequency (Hz) A cc el erat io n (m/ s 2 ) 2.25 m/s2 at 120 Hz

storage cells. Batteries, such as NiZn, NiMH, NiCd, and Lithium-ion (Li-ion), store energy chemically and are rechargeable. Among these types, Li-ion batteries (Fig. 2.5) offer the best performance with high energy density, high discharge rate, high cell voltage, long life span, and no “memory” effects. The disadvantage is the higher sensitivity to over charging and discharging, which will damage the battery permanently [31]. In this study, LIR1620 (3.6 V, Φ 16 mm, H 2.2 mm, 1.2 g) and LIR2016 (3.6 V, Φ 20 mm, H 1.8 mm, 1.6 g) Li-ion cells can be used as the auxiliary battery supply. Moreover, the battery can act as part of the external mass if it is well bonded on the device.

Fig. 2.5 Lithium-ion rechargeable battery

2.3 Device design

The analysis of the device operation, structural design of the variable capacitor and, and simulation of the device dynamic behavior is discussed in this section. The design is focused on the modeling and optimization of the capacitive energy converter with two ideal switches. The mechanical design of the two switches is discussed in the next section. In the design flow, MEMS fabrication capability is considered in order to obtain feasible parameters.

The design is iterated between the static and dynamic analyses due to the influence of the maximum capacitance Cmax on the mechanical spring constant k,

known as the electrostatic spring softening effect. Design constraints on k and m sets a limit on Cmax (approximately below 2000 pF), and thus influencing the static design

on the variable capacitor. Under these limitations, the device is optimized to achieve maximum output power.

2.3.1 Static analysis

The static analysis is conducted to obtain mathematical guidelines for deciding overall parameters and output specifications. With the discharge time constant τ = CstorRL designed much larger than the conversion cycle time Δt to minimize the output

ripple, Eq. (2.3) can be simplified as

max in sat min L min L stor C V V . t t C 1+ R C R C ≈ ⎛ Δ ₊ Δ ⎞ ⎜ ⎟ ⎝ ⎠ (2.6)

Cmin is usually relatively small (about 100 pF). The other circuit components can be

chosen such that Cstor >> Cmin and RLCmin << Δt. Therefore, Eq. (2.6) can be further

simplified as max in max in sat L min L min C V C V V = R . t t C R C ≈ Δ Δ (2.7) The output power now becomes

2 2 sat max in out L L V C V P R . R t ⎛ ⎞ ≈ _{≈ ⎜ ⎟} Δ ⎝ ⎠ (2.8)

From Eq. (2.7) and Eq. (2.8), it can be seen that the output power is basically proportional to Cmax2 and RL.

A maximum device area of 1 cm2 was set as the device size constraint. The output should have a voltage below 40 V for further integration with power management circuits. With Vsat equal to 40 V for maximum output power, it is seen

from Eq. (2.7) that the load RL must increase due to limited Cmax. This increase of RL

will result in a decreased output power (Eq. (2.8)). With a limited value of Cmax =

1570 pF, RL is chosen as 50 MΩ, resulting in a corresponding output power of 31 μW.

Cstor generally does not influence the output power but has a tradeoff between the

output voltage ripple and the saturation time. For a output voltage ripple lower than 1 V, Cstor was chosen to be 5 nF.

2.3.2 Variable capacitor design

Deep silicon etching technology and SOI wafers with highly doped thick device layers were used to fabricate the devices. From [30], an in-plane gap-closing comb structure is used for the variable capacitor, as shown in Fig. 2.6. Compared with the in-plane overlap type comb structures, this topology has the advantage of larger capacitance change for smaller displacement. Compared with the out-of-plane capacitors, this topology has the advantage of lower mechanical damping loss and possibility to incorporate minimum gap control designs.

Fig. 2.6 Top view of the in-plane gap closing variable capacitor topology Relative motion Spring Fingers Proof mass Anchor Anchor

The symbols used in the following discussion are listed below: d: gap between comb fingers

dair: minimum air gap between fingers

Wf: comb finger width

Lf: overlap length of comb fingers

h: thickness of device layer

Ng: number of variable capacitor cells

xr: relative displacement between movable and still electrodes

t: thickness of silicon nitride sidewall dielectric coating

0

ε : permittivity of free space ( -12

0= 8.842 10

ε × F/m)

r

ε : relative permittivity of silicon nitride (ε _r = 7)

μ: viscosity of air at 1 atm (_{μ =1.82 10 ×} -5 _Pa-sec)

α: damping coefficient depending on effective region (α ≈ 1.74) Q: charge on the variable capacitor

Figure 2.7 (a) shows the comb finger design where silicon nitride is applied to the device sidewall for electrical insulation. Another purpose of the silicon nitride coating is to significantly increase Cmax without altering Cmin. As shown in the series

capacitance model in Fig. 2.7 (b), the equivalent air gap of the capacitor is

eq

r

2t d = d - 2t +

ε

with dielectric thickness t and relative permittivity ε . The r

equivalent capacitance is increased only when d is relatively small at the Cmax

position.

The finger width Wf is designed as 10 μm due to deep silicon etching limits on

high aspect ratio structures. The comb finger length must be limited to 425 μm with a overlap length Lf of 400 μm. The minimum air gap dair between the fingers is 0.5 μm.

(c) d Lf h Cdielectric Cdielectric Cair d t t (b) (a)

displacement due to vibration Bump Nitride coating Shuttle mass Anchor

Fig. 2.7 (a) Close up view of fingers with silicon nitride sidewall coating, (b) equivalent capacitance model between fingers, (c) schematic view of one finger cell with the bump design

There are two reasons to set these restrictions on the finger design. First, they are used to properly limit the maximum capacitance Cmax mentioned in p. 21. Second, it is used

to prevent the electrostatic pull-in between the fingers during the charging process at the Cmax position. The fingers are designed with special “bumps” on the sidewalls (Fig.

2.7 (a), (c)) to provide a more compliant minimum air gap control between electrodes. These bumps do not alter the capacitance due to their relatively small size.

With the sidewall dielectric coating and the removal of the substrate beneath the movable plate to eliminate parasitic capacitance, the total variable capacitance between comb fingers is [32]

r v r g o f 2 2 r r 2t 2( +d-2t) ε C (x )=N ε L h . 2t ( +d-2t) -x ε ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ (2.9)

The mechanical damping force for large displacement is [33, 34] 3 g f m m r r 1.5 r 3 r 2 μN L h F =b (x )x = α x , x (d-2t) 1-( ) d-2t ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ _{⎡ ⎤} ⎟ ⎜ ⎟ ⎜ ⎢_⎣ ⎥_⎦ ⎟ ⎝ ⎠   (2.10)

with b (x ) as the equivalent mechanical damping constant. Only squeeze film _{m r} damping between fingers is considered due to the backside substrate removal. Notice that b (x ) is a nonlinear function of x_{m r} r. It behaves as a normal damper for small

displacements, but causes a large damping force when device approaches the maximum displacement. The electrostatic force induced by the charge Q on Cv is [32]

2 e e r r g o f r -Q F =b x = x . 2t 2N ε L h( +d-2t) ε ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (2.11)

This force acts as a negative spring force with be as the electrostatic spring constant.

The electrostatic spring constant is determined by the charge Q on the variable capacitor, which varies in the charge-discharge process. The maximum value depends on Qmax = CmaxVin. This maximum electrostatic spring constant be_max will reduce the

mechanical spring constant of the device. Therefore it needs to be limited as low as possible. This addresses the need to limit the value of Cmax of the variable capacitor

mentioned before.

The output power versus variable capacitor parameters is calculated according to Eq. (2.5) and Eq. (2.9). Device thickness h is 200 μm to have large capacitance and robust structure. It is also a reasonable depth for fabrication. Output power increases with decreasing sidewall nitride thickness t. Therefore, a rather thin but reasonable thickness of 500 Å is used. With the above design parameters, the relationship of the output power Pout and maximum electrostatic spring constant be_max to the initial

the initial finger gap of 26 μm, and the corresponding value of be_max is 774 μN/μm.

With a maximum achievable number of variable capacitor finger cells Ng = 1126 by

compact layout design, the capacitance change is from 62 pF to 1570 pF. Design parameters of the variable capacitor are arranged in Table 2.1.

Table 2.1 List of variable capacitor design parameters

Variable Description of variables Designed value

h Device thickness 200 μm

Ng Number of variable capacitor cells 1126

Wf Finger width 10 μm

Lf Finger overlap length 400 μm

Lf_total Finger total length 425 μm

d Finger initial gap 26 μm

dair Minimum air gap 0.5 μm

t Silicon nitride sidewall thickness 500 Å

Cmax Maximum value of capacitance 1570 pF

Cmin Minimum value of capacitance 62 pF

be_max Maximum electrostatic spring const. 774 μN/μm

RL Driven load resistance 50 MΩ

Cstor Output temporary storage capacitor 5 nF

Vout Output voltage (steady state) 40 V

Fig. 2.8 Output power and maximum be versus initial finger gap

2.3.3 Dynamic analysis

The dynamic analysis is performed to decide the mechanical spring constant k and proof mass m in order to achieve the desired maximum displacement under the targeted input vibration. The electro-mechanical dynamics of the variable capacitor can be modeled as a spring–damper-mass system, as shown in Fig. 2.9.

Fig. 2.9 Schematic of the conversion dynamic model m bm be k xr(t) xi(t)

The dynamic equation is

r e r m r r r i

mx + b x + b (x )x + kx = -mx ,   (2.12) where x is the displacement of the device frame caused by the ambient vibration, _i

r

x is the relative displacement between movable and still electrodes, b (x )x is _{m r r} the mechanical damping force caused by the squeezed film damping effect (Eq. 2.10), and b x is the electrostatic force caused by the charge on the capacitor (Eq. 2.11). _{e r}

Equation (2.12) indicates a nonlinear system caused by the mechanical damping constant b (x ). In order to simplify the design, constant damping constant _{m r} determined from the range of b (x )_{m r} .is used to approximate the original system. For a sinusoidal vibration source with complex amplitude X and frequency _i ω, and relative displacement with complex amplitude X , Fourier transform is applied to _r solve the equation and yield

2 2 r m r e r i -mω X +jωb X +(k+b )X =-mω X ,    (2.13) 2 r _{2 2 2 2} i e m mω X = X . (k+b -mω ) +b ω   _(2.14)

The solution shows that the equivalent spring constant of the system is k’ = k + be,

which is “softened” by the negative electrostatic spring be. Thus, the resonant

frequency of the system is now

e n

k+b

ω = ,

m (2.15)

which indicates unsteady resonance due to the time varying electrostatic spring constant be. In order to maintain steady resonance, the mechanical spring constant k

should be relatively larger than the maximum value of be (be_max). Shown in Fig. 2.10

is the relationship of the needed k/be_max ratio in order to achieve the desired

2.5 3 3.5 4 4.5 5 5.5 6 6.5 25 30 35 40 45 50 55 60 65 Maximum displacement (μm) k/be _ma x

Fig. 2.10 The needed k/be_max ratio versus maximum displacement

The k/be_max ratio increases proportionally with the needed maximum

displacement in the displacement range of concern. This is due to the larger restoring force the spring has to offer in order to reach the larger maximum displacement. Therefore, the mechanical spring constant k can be decided directly from the knowledge of be_max and maximum displacement of x . The proof mass of the system _r

can then be obtained from

e n k b k m m + = ≈ ω (2.16) when the mechanical spring constant k is determined. The proof mass must be limited due to the device size constraints and the weight carrying ability of the device itself. For a conservative design, a spring constant k of 2425 N/m with a proof mass m of 4 grams is chosen to ensure maximum displacement during device resonance.

Dynamic response of the device was simulated by Simulink. The block diagram is shown in Fig. 2.11. The “MEMS_structure” block simulates the dynamics of the variable capacitor with constant charge, while the “Qcontrol” block decides the value of the charge during the charge-discharge process. The “SW1_Qmax” block determines

the operation of SW1 from the displacement, and the maximum value of charge on the capacitor. Similarly, the “SW2_Qmin_Output” block serves as the SW2 operation

control and generates the output power together with the output charge redistribution information. The operation of SW1 and SW2 is considered ideal. SW1 closes when maximum displacement is reached; SW2 closes when maximum voltage on capacitor is reached. A more realistic model considering switch timing will be constructed and discussed in next section. Detailed information on the model and function blocks can be seen in the appendix.

Fig. 2.11 Simulink model of device with ideal switch operation

Figure 2.12 shows the time response of the relative displacement x of the _r variable capacitor. Maximum displacement is reached after approximately 0.02 s, and

then the device undergoes steady vibration between -25.4 μm to 25.4 μm. When the maximum displacement is reached, charging to Cv begins. The time response of the

charge on Cv is shown in Fig. 2.13. The maximum charge is 5660 pC, while the lower

charge level increases by each cycle and saturates to a value of 2410 pC. Closer view of the displacement z and charge Q in steady state is shown in Fig. 2.14, which shows that the charge-discharge process operates at twice the frequency of the vibration.

The simulated time response of the output voltage is shown in Fig. 2.15. The saturation voltage is close to the expected 40 V. The saturation time is about 0.4 seconds. The close up view of the steady state response shows that output voltage ripple is indeed below 1 V.

Fig. 2.13 Time response of the charge Q on capacitor

Fig. 2.15 Output voltage time response

2.3.4 Spring design

In the variable capacitor design, the mechanical springs are arranged on the two sides of the shuttle mass. The primary deformation is along the direction of the relative displacement x . The springs have conventional folded serpentine structures, _r as shown in Fig. 2.16. Each spring consists of two beams connected by a truss. If the truss is assumed rigid, the spring constants in different directions are [35],

3 k z 3 k Eh W k =N , 2L (2.17) 3 k x 3 k EhW k =N , 2L (2.18) k y k EhW k =N . 2L (2.19) The number of springs N is 20 in the concentrated layout floor-planning. h is the thickness of the springs. E is the Young’s modulus of single crystal silicon. Lk and Wk

main spring constant used for device design.

Fig. 2.16 Spring structure schematic view

Typical Young’s modulus of single crystal silicon is 169 GPa in the <110>-type direction, 130 GPa in the <100>-type direction, and 190 GPa in the <111>-type direction. The SOI wafers in which the devices are fabricated have a heavily doped p-type device layer with <100> orientation. The device will be fabricated in the direction parallel to the flats of the wafer. Therefore, the <110>-type Young’s modulus will be utilized. Influence of heavy doping on the Young’s modulus is ignored.

If the effect of non-rigid truss is considered, the above spring constants should be multiplied by a coefficient λ [36], 2 3 6 2 3 6 a +16as +44s λ= , 4a +34as +44s (2.20) where a is the truss length to beam length ratio (L / L ) and_{t k} .s is the truss width to beam width ratio (W / W ). In our spring design, L_{t k} t = 53 μm, Lk = 574 μm, Wt = 40

μm and Wk = 11 μm. The calculated λ is equal to 0.998, which implies that the

effect of non-rigid trusses is small. Anchor Spring z y x Lk Wk Wt Lt Truss Beam Shuttle mass

Several issues must be considered when designing the spring structure. The z-axis stiffness kz and y-axis stiffness ky should be relatively larger than the lateral

x-axis stiffness kx to reduce the out-of-axis motion. Static displacement due to weight

mg of the external mass should be maintained small. The stress in the spring should be much smaller than the yield stress of single crystal silicon (7 GPa). The safety factor, defined as the yield stress divided by the maximum stress during deformation, is used to check the spring robustness. The maximum stress in the x and z directions for maximum displacement xmax and static weight loading mg are

k max x 2 k 3EW x σ = , 2L (2.21) k z 2 k 3mgL σ = , NW h (2.22) respectively.

For the device thickness of 200 μm, the vertical static load of 4 grams, the lateral maximum displacement of 25.4 μm, and the total number of 20 serpentine springs connected to the mass, Table 2.2 lists the spring dimensions, spring constants, the lateral and vertical stiffness ratio, and the safety factors. Fig. 2.17 shows the finite element method (FEM) simulation of a single spring element by CoventorWare. The total spring constant is designed to be 2425 N/m; thus a single spring element has a spring constant of 121.25 N/m. The simulation results agree well with the design value.

Fig. 2.18 shows the CoventorWare modal simulation of the device without the fingers. Simulation is performed with and without the external mass which is approximated by a cylinder with identical radius and mass to a 4 gram tungsten ball. Without the external mass, the first three modes are respectively the lateral mode, the vertical mode, and the torsional mode. With external mass attached, the second and third mode exchange orders due to the levitation of the center of mass. The first mode

Table 2.2 List of spring design parameters

Variable Description of variables Designed value

Wk Spring Width 11 μm

Lk Spring Length 574 μm

kz Vertical spring constant 8.01×105 μN/μm

kx X-axis spring constant 2425 μN/μm

ky Y-axis spring constant 6.6×106 μN/μm

kz / kx Vertical stiffness ratio 331

ky / kx Lateral stiffness ratio 2723

Sf_x Lateral safety factor 32.5

Sf_z Vertical safety factor 912.5

Fig. 2.17 CoventorWare simulation of the spring constant of a single spring element

frequency is 1.73 kHz without the external mass and 130 Hz with the external mass attached. The first mode frequency with the external mass differs from the desired value of 120 Hz. This is possibly due to the approximation of a ball by a cylinder

Spring constant ~ 121.6 N/m

structure. Other mode frequencies are at least 3.5 times higher than the primary mode in both situations. The separation is large enough to avoid stimulation of these unwanted modes by the input vibration.

Mode order

Mode frequency (without external mass)

1 1730 Hz

2 6110 Hz

3 7310 Hz

Fig. 2.18 CoventorWare modal analysis, (a) without external mass, (b) with external mass attached

2.3.5 Conversion efficiency

Figure 2.19 (a) shows the Q-V plane plot of the operation, which can be used to estimate the output power of such conversion process. The slopes of the lines are the capacitance in respective positions. The charge-discharge cycle starts from point A with no charge on Cv. The cycle proceeds to point B where Cv is charged to Qmax at

the Cmax position by Vin, and continues to point C where Cv changes to Cmin and the

voltage increases to Vmax. At last, the operation assumes total discharging of Cv at the

Cmin position and returns to point A. The converted energy of this ideal cycle is the

Mode order

Mode frequency (external mass attached)

1 130 Hz

2 463 Hz

3 810 Hz

area of the triangle ABC. Multiplying the area with the operation frequency yields ideal output power. The conversion efficiency is defined as the expected output power of the designed converter, which is 31 μW, divided by the ideal output power derived from Fig. 2.19 (a), which is 58.5 μW. The conversion efficiency is approximately 53 % in this case. Conversion efficiency is reduced by the incomplete discharging in the charge redistribution between Cv and Cstor. If this effect is considered, the Q-V plane

is modified into Fig. 2.18 (b). The discharging process stops at Qmin (point D), and

proceeds to point A’ for another charging process. In the steady state situation, where Qmax is 5660 pC and Qmin is 2410 pC, the output power derived from the Q-V plane is

47.7 μW. Conversion efficiency is now 65 %. The reason why the conversion efficiency is not close to 100 % in this case is probably due to the energy loss during charge transfer from Cv to Cstor. A more accurate modeling of the conversion

efficiency should be derived.

Fig. 2.19 Q-V plane (a) ideal operation, (b) operation with charge redistribution between Cv and Cstor

A B C Q V Vin Vmax Cmax Cmin Qmax (a) A’ B C Q V Vin Vmax Cmax Cmin Qmax Qmin D Vsat (b)

2.4 Mechanical switch

The switches SW1 and SW2 are realized as lateral contact mechanical switches. Conventional design of the charge-discharge timing control switches utilize diodes or clocked active switches [29-31]. In order to prevent charge leakage out of Cv and Cstor,

the switches must have a reverse leakage current lower than a few nA. This is not common in commercially available diodes and other switching circuitry. Capacitive coupling is another problem, in which the capacitance of the switch contributes to parasitic capacitance. Our design of SW1 and SW2 has barely zero charge leakage and very low capacitance coupling effect. Other advantages are the low energy consumption, the synchronous operation to the variable capacitor, and the monolithic integration with the whole device structure.

2.4.1 SW1 design

SW1 should ideally be closed when the variable capacitor is near the maximum displacement, and be opened immediately after charging is finished at the Cmax

position. In our design, SW1 is realized as a mechanical switch by a contact mechanism between nodes N1 and N2, as shown in Fig. 2.20. With one end connected to the movable proof mass of Cv and one end connected to the still charging electrode,

SW1 laterally contacts at the Cmax position when the comb fingers of the variable

capacitor touch.

Layout of SW1 is also shown in Fig. 2.20. Considering the extra displacement the elastic finger configuration can allow, SW1 is designed to contact simultaneously when or merely after the fingers have touched. The finger bump design mentioned before is used to maintain a constant Cmax during the SW1 charging process. SW1 is

provides enough contact force to reduce contact resistance during charging. In a previous research [37], a sputtered gold contact should have a contact force over several hundred μN to assure a reliable metallic contact resistance under about 100 mΩ. The restoring spring is designed to provide a 500 μN restoring force at an extra displacement of 0.2 μm to maintain small contact resistance during charging.

Fig. 2.20 SW1 as a contact mechanical switch

2.4.2 SW2 design

SW2 should ideally be closed when the variable capacitor moves to the middle position. At this position, the terminal voltage of Cv has a maximum value Vmax. This

high voltage is used to induce electrostatic pull-in between nodes N3 and N4 to actuate the switch, as shown in Fig. 2.21. When SW2 is about to close, the voltage on node N3 approaches to Vmax, and node N4 remains at an adjustable voltage Vadj. This

adjustable voltage is used to tune the pull-in timing of the switch to match the dynamics of the variable capacitor under fabrication uncertainties. When pull-in occurs, the movable node N3 is attracted by the electrostatic force to contact with node N5 before touching node N4. The layout of SW2 in Fig. 2.21 shows the suspended mass, springs, actuation electrodes, and output node N5.

RL

N1 N2

SW1 SW2

Vin Cv Cstor

Restoring spring structure Proof mass

N1 N2

Vin

Fig. 2.21 SW2 as a lateral pull-in contact switch

The pull-in voltage of a spring suspended parallel plate capacitor can be determined by the following equation

3 SW2 0 PI SW 2 k d 2 2 V , 3 3 hL = ε (2.23) where kSW2 is the spring constant, d0 is the initial gap between nodes N3 and N4, and

LSW2 is the total overlap length of nodes N3 and N4. The device thickness h is

identical to the variable capacitor. The maximum voltage Vmax of the variable

capacitor on N3 is max p max in min p C C V V , C C + = + (2.24) where Cp is the parasitic capacitance due to anchors. With Cp = 60 pF, Vmax drops

from the ideal 90 V to approximately 50 V. SW2 must be timed precisely to Vmax-Vadj

SW1 RL Vin N3 Cv Cstor SW2 N4 N5 Vadj N4 N4 N5 N3 Spring Suspended electrode Actuation

electrodes Output node

Anchor

d0 dc

to ensure maximum conversion efficiency. Therefore the pull-in voltage should be lower than 90 V and tuned to match Vmax by Vadj after Cp is determined by

measurement.

Another parameter is the release voltage in the hysteresis of the pull-in effect. Conventional pull-in systems have different in pull-in and release voltages. When the charge on Cv is transferred to Cstor and the voltage between node N3 and N4 drops

below the release voltage, SW2 will release and automatically open. In the current design, the output saturation voltage Vsat is about 40 V; therefore the release voltage VR should be higher than Vsat-Vadj. The release voltage is determined by

2 SW 2 c 0 c R SW2 2k d (d - d ) V hL = , ε (2.25) where dc is the initial gap between nodes N3 and N5. Due to design constraints, the

release voltage cannot be designed too high. The target of choice is about 50 V. For a parasitic capacitance of 60 pF as the worst case, Vmax and Vsat will drop to

50 V and 30 V, respectively, due to reduced capacitance variation in device operation. With VPI targeted at 70 V and VR targeted at 50 V, SW2 can still function with a Vadj =

-20 V under worst condition and a Vadj = 20 V under ideal condition.

SW2 can be modeled as a second order system considering the spring force, the squeeze film damping between nodes N3 and N4, the electrostatic force due to voltage Vc, and the inertial force of the proof mass. A Simulink model is constructed

to simulate the pull-in and release performance of SW2. Detailed information on the SW2 model is given in the appendix. Integrated Simulink model of the switch and the device is shown in Fig. 2.22. The “SW2” block determines the operation of SW2 by the voltage on the variable capacitor terminals. All device parameters were tuned until system response was identical to the case with ideal switches. The finely tuned parameters of SW2 are listed in Table 2.3, with the targeted voltages referred to the