靜電式振動電能轉換器之改良與測試

國 立 交 通 大 學

電機與控制工程研究所

碩士論文

靜電式振動電能轉換器之改良與測試

Improvement and Testing of an Electrostatic

Vibration-to-Electric Energy Converter

研究生 ：郭炯廷

指導教授：邱一 博士

靜電式振動電能轉換器之改良與測試

Improvement and Testing of an Electrostatic

Vibration-to-Electric Energy Converter

研 究 生: 郭炯廷 Student: Chiung-Ting Kuo

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

September 2006

Hsinchu, Taiwan, R.O. C

中華民國九十五年九月

中文摘要

微機電系統 MEMS 是以半導體產業中的平面製造觀念為基礎的一種整合 技術。微機電系統中的各種感測器或致動器的發展，均以和 IC 整合而形成智慧 型的模組或系統作為最終目標。當微系統的技術越來越成熟時，各種利用微感 測器或微傳感器所形成的智慧型網路或系統應用也隨之而生。在這些應用上， 每一個標器或節點的模組都可能有微型獨立電源的需求。拜先進的超大型積體 電路與 CMOS 技術所賜，現今這些微系統節點的電能需求已降至數十 µW 的程 度。因此，利用微機電技術將環境中的能源轉換成電能來取代傳統的電池會是 一個具有吸引力的方法。 靜電式振動電能轉換器可將生活中普遍存在的振動轉換為可用之電源，其 運作原理在於，利用由振動驅動的可變電容器的改變，搭配直流電壓源產生電 流輸出。轉換器的核心可變電容是利用 SOI 晶片搭配深蝕刻製程，製造梳齒狀 電極而成。本實驗室先前已完成此轉換器之設計與製造，然而，系統分析及模 擬並未考慮輸出端負載的效應，輸出電壓過高也造成無法與後端功率管理電路 相容，而製作完成的元件因為寄生電阻電容的存在影響了轉換器特性，因此， 根據先前的經驗和實驗結果，本篇論文的重點在於此轉換器之改良與測試。 系統分析及模擬平台已經修正，第二代元件的設計、製作流程及測試平台 亦完成改良。根據設計，轉換器在 3.3 V 的輸入電壓下，考慮 8 MΩ的輸出負載， 輸出功率能達到 200 µW (功率密度每立方公分 105 µW)，以及約 40 V 的輸出 電壓。元件成品大小約 0.8×1.4×1.7 cm3_{。雖然製程良率太低導致經過機械特性} 測試之後，沒有元件能夠進行輸出功率量測，但透過更完整的振動測試已得到 元件共振頻率與振幅。元件的電性量測也顯示，寄生電容和電阻並不存在。此 外，製程條件的影響和良率過低的原因也完成討論。

Abstract

Micro-Electro-Mechanical System (MEMS) is a technology platform based on the planar fabrication processes in the IC industry. The goal of MEMS actuators and sensors is the integration with circuits to form a smart module or system. Recent advances in the CMOS technology have reduced the power consumption of the micro system nodes to tens to hundreds of microwatts. Therefore, it is attractive to scavenge and transform the energy in the environment into electric energy.

An electrostatic vibration-to-electric energy converter can convert vibrations into electric energy. The device produces an current output from a DC voltage source. The core of the converter is a variable capacitor formed by comb fingers fabricated in a SOI wafer with DRIE processes. In our previous work, the effect of load on the output port was not considered in the device design. The output voltage was too high to be compatible to the power management circuit. Besides, parasitic conductance affected the characteristics of the fabricated device. Therefore, this thesis focuses on the improvement and testing of the electrostatic vibration-to-electric energy converter.

In this thesis, system analysis and simulation were improved for the design of the second generation device. The measurement setup and new fabrication processes were also developed. For the 3.3 V supply voltage and the optimal load of 8 MΩ, the output power was 200 µW with the output voltage of 40 V. The fabricated device had a size of 0.8×1.4×1.7 cm3. The low yield of device fabrication caused no device with fine electrical properties to survive, and thus the output power measurement could not be conducted. However, the complete mechanical characteristics were recorded, and the unwanted parasitic conductance was eliminated. Finally, explanations for the problems in the fabrication as well as proposed solutions are discussed.

致謝

轉眼間，兩年的碩士生涯即將邁入尾聲，能夠完成碩士學業和論文，首先我 要感謝的就是我的指導教授，邱一老師。老師對學生很用心，尤其是每個禮拜和 老師一對一的個人討論，讓我深刻感受到他做研究的仔細和追求完美的執著，無 形中激勵了我的做人處世態度，我覺得獲益良多。在我的論文中，老師也不厭其 煩的幫我校正和修改，寫英文論文雖然辛苦，但是唸學生的論文更需要耐心和毅 力，這也是我最佩服老師的地方，老師給我的感覺是亦師亦友，沒有距離，很慶 幸這兩年，我選對了指導教授。 我還要感謝我的口試委員：邱俊誠教授、邵家健教授、陳科宏教授，他們對 我的論文有諸多寶貴的建議和支援。當然還有學長們：林永峻、朱育杉、張文中、 莊志偉，多虧了他們給我的實驗經驗和幫忙，我才能一一度過難關。 在實驗室的兩年時間，有歡笑和汗水，這一切都有實驗室成員的陪伴，均宏、 建勳、忠衛、亦謙、繁果、煒智、子麟，你們讓我覺得不孤單，我很珍惜這段互 相打氣、支持，以及互相帶給對方歡樂的時光，如果沒有你們的笑容，這兩年我 的日子將會辛苦許多。 外系外校的同學，我也要獻上深深的感激，志柏和應崇，謝謝你們對我實驗 的協助，尤其是我面對不熟悉的儀器和環境時，你們的幫忙就如雪中送炭般令人 感動。 蕙誼，我也謝謝你，常常需要忍受我的牢騷但是永遠都會鼓勵我。 感謝我的父母，謝謝你們永遠支持我信賴我，多虧你們的養育、供應我學費 和生活費，我才能夠唸完碩士，希望我能不再讓你們操心，也希望我未來能讓你 們感受到一絲驕傲。 要感謝的人真的太多，實在無法一一列舉，但是今後我都會抱著感恩的心面 對週遭的每個人，謝謝！

Table of contents

中文摘要….………I Abstract... II 致謝………..III

Table of contents ...i

List of figures... iii

List of tables...v Chapter 1 Introduction………1 1.1 Motivation………1 1.2 Energy scavenging……….1 1.2.2 Light exposure…...………..2 1.2.2 Thermal gradients………..3 1.2.3 Human power…..………..4 1.2.4 Wind/air flow..………...………..4 1.2.5 Acoustic noise………...………..4 1.2.6 Vibration….………...………...5

1.2.7 Summary of power sources………...5

1.3 Vibration-to-electric energy conversion………....6

1.3.1 Electromagnetic energy conversion………..6

1.3.2 Piezoelectric energy conversion………....8

1.3.3 Electrostatic energy conversion………....9

1.3.4 Summary of vibration-to-electric conversion….………....10

1.4 Thesis objective and organization………..10

Chapter 2 Design………...………....10 2.1 Characteristics of vibration……….12 2.2 Operation priciple1………14 2.3 Device design……….18 2.3.1 Variable capacitor………..18 2.3.2 Static analysis………21 2.3.3 Dynamic analysis………..24 2.3.4 Spring design……….………....……29 2.3.5 Layout design...……….32

2.4 Circuits and energy storage………33

2.4.1 Measurement circuits………..33

2.4.2 Storage device……...………..35

Chapter 3 Fabrication process...37

3.1 Process flow………...……..37

3.2 Disccusion……….41

3.2.1 Overheating of wafers……….41

3.2.2 Residual stress of the oxide layer………46

3.3 Fabricated device………..47

3.4 Conclusion………50

Chapter 4 Measurement……….51

4.1 Mechanical measurement……….51

4.2 Electrical measurement...………….58

4.3 Output power measurement ...60

4.4 Conclusion………..60

Chapter 5 Conclusion………62

5.1 Summary………62

5.2 Future work………..63

List of Figures

Figure 1.1 Thermoelectric energy converter composed of two series thermocouples..3

Figure 1.2 Electromagnetic energy converter………....7

Figure 1.3 Piezoelectric bimorph beam………...…8

Figure 1.4 (a) Gap closing and (b) overlap in-plane variable capacitor……...……9

Figure 2.1 Vibration spectra by Roundy….……….………..…….13

Figure 2.2 Vibration spectrum of an air conditioner…………...………14

Figure 2.3 Vibration capacitor schematic...….….………14

Figure 2.4 (a) Operation of the electrostatic energy converter and (b) Output terminal voltage VL…...………15

Figure 2.5 Variable capacitor at Cmax position: (a) without coating, and (b) with dielectric coating………..………17

Figure 2.6 Equivalent Ctotal………..…17

Figure 2.7 Top view of the in-plane gap closing variable capacitor……….…...19

Figure 2.8 Output power (µW) for various RL and Cstor.……….……23

Figure 2.9 Output saturation voltage and power vs. initial finger gap (RL = 8 MΩ, Cstor = 20 nF)………23

Figure 2.10 Schematic of the conversion dynamic model………..………24

Figure 2.11 Dynamic simulation diagram………...………26

Figure 2.12 Maximum displacement and spring constant for various attached mass.27 Figure 2.13 Output voltage vs. time ………...………27

Figure 2.14 Schematic of a pair of finger gaps………...28

Figure 2.15 Spring structure top view……….30

Figure 2.16 Schematic of the current device………...………32

Figure 2.17 Schematic of the previous device……….………...33

Figure 2.18 Measurement circuit by Roundy……….33

Figure 2.19 Modified circuit schematic………...………34

Figure 2.20 AC output current……….35

Figure 2.21 Lithium-ion rechargeable battery……….………36

Figure 3.1 Processing steps……….40

Figure 3.2 Die and carrier wafer for DRIE…….………42

Figure 3.3 Sideways etched fingers: (a) illustration and (b) sideview…..…………42

Figure 3.4 Cross section of broken fingers………...………...43

Figure 3.5 RIE lag effect ………43

Figure 3.6 Burned photoresist due to poor cooling…...……… .45

Figure 3.7 Broken structures due to residual stress……….46 Figure 3.8 Overview of the device: (a) SEM photograph from frontside and (b)

optical microscope photograph from backside………..……….48

Figure 3.9 (a) Width, (b) perpendicularity of etched fingers……….…..49

Figure.3.10 Overview of mass attachment………50

Figure 4.1 (a) Schematic and (b) photograph of the mechanical measurement setup.52 Figure 4.2 Resonant frequency with various width of springs………53

Figure 4.3 Measured and simulated spring constants with feature size shrinkage considered………...53

Figure 4.4 Fingers under (a) 0 Hz and (b) 2160 Hz vibration………..54

Figure 4.5 Displacement of Y and Z………55

Figure 4.6 System response……….55

Figure 4.7 Device resonance at 156 Hz with maximum displacement………...56

Figure 4.8 Variable capacitor at (a) Cmin position and (b) Cmax position……….58

Figure 5.1 Improved device fabrication: (a) pit holes etched in a Pyrex wafer, (b) anodic bond and (c) structure defined by DRIE……….……62

List of tables

Table 1.1 Comparison of energy scavenging and power sources……...………...6 Table 2.1 Design parameters of the energy converter………..28 Table 2.2 Spring design and safety factor………31

Chapter 1 Introduction

1.1 Motivation

When portable microelectronic devices, such as biomedical, military, and environmental wireless micro-sensors continue to shrink and incorporate more functions, energy or power becomes insufficient. Furthermore, energy stored in the storage devices, such as batteries [1], micro-batteries [2], micro-fuel cells [3], ultra capacitors [4], micro-heat engines [5], and radioactive materials [6], is limited at small scales, resulting in short lifetime [7]. In order to lengthen the life of the portable devices, it is necessary to design the system with higher efficiency and minimize its power loss. Researchers also attempt to increase the energy density in those storage devices, but the solutions still have finite lifetime and high maintenance costs.

Advances in the low power CMOS technology along with the low duty cycles of wireless sensors have reduced power requirements to tens to hundreds of microwatts [8]. It becomes possible to power these sensor nodes by scavenging ambient energy from the environment. Therefore, it is attractive to design a self-renewable energy device that can replenish part or all of the consumed energy by utilizing the scavenged energy from the surrounding environment.

1.2 Energy scavenging

State-of-art scavengers and converters can extract energy from ambient natural sources, such as light exposure, thermal gradients, human power, air flow, acoustic noise, and vibration [9].

Energy scavenging means to convert ambient energy into usable electrical energy. Compared with the energy stored in common storage elements like fuel cells and batteries, the environment represents an inexhaustible energy source. As a result, energy scavenging methods introduced below are all characterized by their power density.

Various approaches to scavenge energy from the environment to power low power electronics are compared in this section. Finally, electrostatic vibration-to-electric energy conversion using the micro-electro-mechanical systems (MEMS) technology is chosen in this thesis because of its compatibility to IC processes and the characteristic of the power source.

1.2.1 Light exposure

The most commonly used and most mature method to scavenge energy is the photovoltaic cells or the solar cells. Photovoltaic cells convert incident light into electricity [10]. In direct sunlight at midday, photovoltaic cells offer an excellent and technically mature solution. Silicon photovoltaic cells have efficiencies ranging from 12% to 25% for single crystal silicon. Thin film polycrystalline and amorphous silicon photovoltaic cells are also commercially available. They cost less than single crystal silicon cells but have lower efficiency [11]. Overall, photovoltaic energy conversion offers high output power besides being a mature IC-compatible technology. Nevertheless, its power output depends heavily on environmental conditions and light intensities. For instance, if the target application is outdoors and needs to operate primarily during the daytime, solar cells offer adequate power density up to 15 mW/cm2. However, in normal office lighting, the same solar cell will only produce about 10 μW/cm2, which is hardly enough for most applications.

1.2.2 Thermal gradients

Environmental temperature variations can also serve as a power source. Thermal gradients in the environment are directly converted to electric energy through the Seebeck (thermoelectric) effect [12]. For these converters, the energy conversion is based on the electric potential difference between the cold end and hot end of a thermocouple as shown in Figure 1.1. Thermoelectric materials with large Seebeck coefficients and high electrical conductivity (low electrical resistance) can improve conversion efficiency and minimize power losses. Materials typically used for thermoelectric energy conversion include Sb2Te3, Bi2Te3, Bi-Sb, PbTe, Si-Ge,

polysilicon, BiSbTeSe compounds, and InSbTe, which are not completely compatible to the IC process [12]. Furthermore, although an output power of 40 μW/cm3 from a 5˚C temperature gradient has been demonstrated [13], temperature differences of this level (5˚C) are not common in a micro system [14]. Without large thermal gradients, the output voltage level is low and needs to be boosted. Connecting several thermocouple elements in a series configuration can be beneficial. However, large series resistance increases ohmic power losses and thus reduce the overall power efficiency.

1.2.3 Human power

A significant amount of work has been done on the possibility of scavenging power off the human body for use by wearable electronic devices [15,16]. The conclusion of studies undertaken at Massachusetts Institute of Technology suggested that the most energy rich and most easily exploitable source occurred at the foot during heel strike and in the bending of the ball of the foot. This research led to the development of the piezoelectric shoe inserts and the power density available from the shoe inserts was 330 μW/cm3. However, the problem of how to get the energy from the foot to other places on the body has not been satisfactorily solved. For an RFID tag or other wireless device worn on the shoe, the piezoelectric shoe inserts offer a good solution. Similar to temperature variation method, the application space for such devices is limited.

1.2.4 Wind/air flow

Wind power has been used as a power source for a long time. The potential available power from the moving air is related to the air velocity. About 5 mW/cm3 can be generated by a large windmill at a wind velocity around 8 m/s [9]. At lower air velocity, the conversion efficiency can be significantly lower and thus less power is generated (e. g. 380 μW/cm2 at 5 m/s air velocity) [9]. However, no effort on converting air flow to electric power at very small scale (on the order of a cubic centimeter or smaller) has been reported so far.

Another source is the acoustic noise. However, there is far too little power available form acoustic noise to be of use in the scenario being investigated, except for very rare environments with extremely high noise levels [17]. Therefore, it is not a feasible power source for most applications.

1.2.6 Vibration

Vibration-to-electricity conversion offers the potential for wireless sensor nodes to be self-sustaining in various environments. Most vibrations that can be utilized occur in environments such as automobiles, aircraft, ships, trains, large commercial buildings, industrial environments, and residential households. Theory and experiments show that more than 300 μW/cm3 could be generated [9]. In this thesis, vibrations were measured on some household appliances, and the resulting spectra were used to calculate the amount of power that could be generated. A more detailed discussion of this process presented in Chapter 2 shows that conversion of vibrations to electricity can provide sufficient power for applications in certain indoor environments.

1.2.7 Summary of power sources

Summary of power sources and energy storage devices is shown in Table 1.1 [9]. The top part of the table contains power sources; the bottom part of the table contains energy storage devices characterized by their energy density. Based on the survey above, vibration-to-electric energy conversion is the primary topic of the thesis due to its ubiquity and larger power density.

1.3 Vibration-to-electric energy conversion

Three approaches are typically used to convert vibration energy to electric energy. They are: electromagnetic (inductive), electrostatic (capacitive), and piezoelectric. In this section, these three approaches are discussed.

Table 1.1 Comparison of energy scavenging and power sources [9]

Power sources Power density

μW/cm3 _{or μW/cm}2

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 Yes Batteries (Lithium-ion) 34 Yes

Fuel cells 110 No

Ultracapacitors 1.6~3.2 Yes

Heat engine 105 No

Radioactive (63Ni) 52 No

1.3.1 Electromagnetic energy conversion

Electromagnetic energy conversion uses a magnetic field to convert mechanical energy to electricity based on Faraday’s law, which states that a voltage is produced as the magnetic flux linkage changes. In such a device, a coil is attached to the oscillating mass and moves through a magnetic field established by a permanent magnet as shown in Figure 1.2 [18,19]. The produced voltage by the electromagnetic

converter is proportional to the magnetic field and the number of turns of the coil. Shearwood and Yates [20] develop a device capable of producing 0.3 μW (power density of 10~15 μW/cm3) from a vibration source with displacement magnitude 500 nm at 4.4 kHz. The calculated AC output voltage of the 0.3 μW generator was 8 mV, which was too small to be rectified by a bridge rectifier that required a turn-on voltage of about 0.5 V.

More recently, Chandrakasa et al. have developed electromagnetic converters for vibrations with magnitude of about 2 cm at about 2 Hz generated by a walking person [21-23]. Their simulations showed a maximum output power of 400 µW could be achieved with the output voltage of 180 mV. The device size was 4 cm×4 cm×10 cm, and therefore the corresponding power density would be 2.5 µW/cm3.

The most common issue is that the induced voltage of the electromagnetic converters is inherently small. Methods to increase the induced voltage include using a transformer, increasing the number of the turns of the coil, and increasing the permanent magnetic field. However, all options are limited by the available space. Another issue is that it is difficult to fabricate large number of high quality coils with planer thin film processes. Thus the power density of electromagnet converter is

Figure 1.2 Electromagnetic energy converter [18]

Energy Harvesting

lower than other types of devices.

1.3.2 Piezoelectric energy conversion

Piezoelectric energy conversion converts mechanical energy to electricity by straining a piezoelectric material [9,14]. Strain in a piezoelectric material separates charge across the device and produce a voltage drop proportional to the applied stress.

Typically, the oscillating system is a cantilever beam with a mass attached at the free end (Figure 1.3). When vibrations drive the device, the converter provides an AC

voltage. However, in order to rectify and convert the extracted power to a stable supply, additional circuitry is needed.

Optimal power circuitry for piezoelectric generators driven by vibrations has been studied [25,26]. The maximum power output reported was 18 mW with a corresponding power density of 1.86 mW/cm3. The frequency of the driving vibrations was reported as 53.8 Hz. Prototypes of piezoelectric converters were also designed by another group [9,14,24]. The piezoelectric converter generated a power density of 200 µW/cm3 for the vibration input 2.25m/s2 at 120 Hz.

In the piezoelectric converter, high-piezoelectric-constant materials such as PZT are difficult to deposit and incompatible to the IC process. Most researches so far still utilize bulk materials, which is not suitable for the integrated microsystems.

1.3.3 Electrostatic energy conversion

The main part of an electrostatic converter is a initially charged variable capacitor formed by a comb structure (Figure 1.4). When the movable plate moves because of vibrations, mechanical energy is transformed into electricity.

Meninger et al. [23] designed an electrostatic converter using MEMS technology with a silicon on insulator (SOI) wafer. Simulation shows a power output of 8.6 μW for a device size of 1.5 cm× 0.5 cm×1 mm from a vibration source at 2.52 kHz. They did not present any actual test results. Another design was proposed by Roundy [14] with an output power density of 110 μW/cm3 (output voltage of 33 V) under vibration input 2.25 m/s2 at 120 Hz.

The most attractive feature of an electrostatic energy converter is its IC process compatibility. Typically, MEMS variable capacitors are fabricated through mature silicon micromachining process, such as deep reactive ion etching (DRIE). Therefore, it is suitable to power a microsystem or sensor nodes. The electrostatic energy converter also provides high output voltage levels and moderate power density. The drawback of the converter is that it needs an external voltage source Vin to initially

charge the variable capacitor. However, it is expected that besides powering the load, the output power can be fed back to the external voltage source and recharge it. If the output power from the energy converter exceeds the need of load terminals, the external supply voltage source has no energy loss, and the system becomes self-sustained.

1.3.4 Summary of vibration-to-electric energy conversion

According to the above literatures review, the electrostatic vibration-to-electric energy converter is studied in this thesis due to its compatibility to IC processes and the characteristic of the power source.

1.4 Thesis objective and organization

In our previous work [27], the system analysis and simulation of an electrostatic energy converter were accomplished. However, the effect of a resistive load on the output port was not considered. Besides, parasitic conductance led to the failure of the output power measurement. Therefore, the objectives of this thesis includes

(a) constructing a more detail conversion model with a resistive load taken into consideration;

(b) design a new electrostatic vibration-to-electric energy converter with higher output power and eliminate its parasitic conductance;

(c) fabricating the device based on optimal design form the simulation; (d) measuring the mechanical and electrical characteristics.

In order to design the vibration to electric energy converter, the nature of

(a) (b)

vibrations from potential sources must first be studied. Chapter 2 presents the characterization of several common occurring low level vibrations. A general conversion model and complete converter design are also presented in Chapter 2. The fabrication process, process issues and process results are described in Chapter 3. The measurement results and discussions are presented in Chapter 4. Future works is discussed in Chapter 5.

Chapter 2 Design

Electrostatic vibration-to-electricity conversion depends on the change of capacitance of a variable capacitor caused by vibration. The variable capacitor is initially charged, and as its movable electrode oscillates because of vibration, mechanical energy is converted into electrostatic energy. After the conversion process, the converted energy is then recurrently delivered to the output port, resulting in the output current through the load.

At first, characteristics of common low-level vibration is introduced in this chapter. The operation and device design, including static and dynamic analysis, are then discussed. Finally, circuitry including energy storage devices for this converter is presented.

2.1 Characteristics of vibration

The output power of a vibration driven converter depends on the nature of the vibration source, which must be known in order to estimate the generated power. There are various kinds of vibrations in the environment; however, it is desired to target those most common ones in homes, office buildings, cars, and factories to maximize the potential applicability of the device. In order to estimate how much power can be converted from vibration, the details of vibration characteristics must be considered.

Measurement of various vibration sources was conducted by Roundy [9], as shown in Figure 2.1. From the spectra of these measured low-level vibrations, two conclusions can be drawn. First, the assumption of steady vibration concentrated at

specific frequencies seems reasonable. Second, the high frequency vibration modes are lower in acceleration magnitude than the low frequency fundamental mode.

We have also measured the vibration spectrum of an air conditioner. As shown in Figure 2.2, The most energetic mode is the low-frequency one at about 120 Hz, as observed by Roundy. From Figure 2.2, it is noticed that the vibration of the air conditioner has a peak acceleration of about 2.25 m/s2 at about 120 Hz. These values are used in the following static and dynamic analysis of the energy converter to find out the optimal device design.

2.2 Operation principle

A variable capacitor Cv is the main component in the energy converter [19,30],

as shown in Figure 2.3. The energy stored in the capacitor is increased when the capacitance is changed from Cmax to Cmin by to the external vibration.

0 100 200 300 400 500 0.01 0.1 1 10 Frequency (Hz) A cc el era tion (m /s 2 )

Figure 2.2 Vibration spectrum of an air conditioner 2.25 m/s2 at 120 Hz y z Cmax Displacement due to vibration y z Cmin Displacement due to vibration

Figure 2.4 (a) shows a schematic circuit that can be used to extract the converted energy. The variable capacitor Cv is charged by an external voltage source Vin through

the switch SW1 when Cv is at its maximum Cmax. When Cv is charged to Vin, SW1 is

opened and then the capacitance is changed form Cmax to Cmin due to the electrode

displacement caused by vibration. In this process, the charge Q on the capacitor remains constant (SW1 and SW2 both open). Therefore, the terminal voltage across the capacitor is increased and the vibration energy is converted to the electriostatic energy stored in the capacitor. When the capacitance reaches Cmin (Vmax), SW2 is

closed and the charge is transferred to a storage capacitor Cstor. Let the conversion

cycle be Δt, the voltage variation of the n-th cycle before and after the charge transfer can be related by

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)

where Vmax is equal to VinCmax/Cmin , VL[n, t=tn] is the voltage after the charge transfer,

VL[n-1, t=tn-1+Δt] is the voltage before the charge transfer, and tn=tn-1+Δt, as shown in

Figure 2.4 (b).

Figure 2.4 (a) Operation of the electrostatic energy converter and (b) output terminal voltage VL Vin Cv Cstor RL VL SW1 SW2 (a) Time (b) 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

SW2 is then opened and Cv varies back to Cmax, completing one conversion cycle.

During this period Δt, the charge on Cstor is discharged by the load resistance RL with

time constant τ = CstorRL before it is charged again by Cv. Therefore, the voltage

across Cstor can be expressed as

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)

If the charge transferred to Cstor is more than that discharged through the load, the net

increment will result in the rises of VL step by step. In the steady state, the net

increment of charge on Cstor becomes zero. As shown in Figure 2.4(b), the initial and

final terminal voltages VL of the discharge process become constnat, VL[n, t=tn+Δt]=

VL[n-1, t=tn-1+Δt]= Vsat, Equation 2.2 is reduced to:

sat stor max min

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

From Equation 2.3, that the steady-state final terminal voltage Vsat in the

chrage-discharge cycle can be expressed as

max in stor sat min L stor stor C V C V = , (2.4) C (1+ ) exp( t/R C )-1 C × Δ

where Δt = conversion cycle time = 1/2f and f is the vibration frequency. When the voltage ripple of the charge-discharge process is small, as will be shown subsequently, the output power can be estimated by,

2 sat out L V P = . R (2.5)

For a more accurate calculation, integration of output terminal voltage is used to calculate the average power output as shown below,

L stor 2 -t/R C 2 0 L L L (V e ) V (t) P(t)= = , (2.6) R R

where V0=Vsat e t/R CL stor Cmax Δ

× ∝ is the voltage across Cstor before discharging in the

steady state (Figure 2.4 (b)). It can be observed that the output power is in general proportional to Cmax2. In the comb structure, Cmax is determined by the minimum

finger spacing. In a previous design [27], the minimum finger spacing is kept at 0.5 μm to prevent shortage of the uninsulated fingers (Figure 2.5(a)). If a dielectric coating can be applied to the side walls of the fingers for insulation (Figure 2.5(b)), the minimum spacing can be further reduced to increase Cmax and Pout. In this design,

the total capacitance becomes Cdielectric || Cair || Cdielectric (Figure 2.6). Silicon nitride

can be used as the dielectric material due to its process compatibility and high dielectric constant (εr = 7). With a 500-Å-thick nitride coating, Cmax can be increased

by a factor of four, compared to previous design. It should be noted that the dielectric coating barely increases Cmin. Therefore, the expected increase of output power will

not be affected by the change of Cmin.

Figure 2.5 Variable capacitor at Cmax position: (a) without coating, and (b) with

dielectric coating dielectric coating (a) (b) Cdielectric Cdielectric Cair Figure 2.6 Equivalent C 2 Δt stor 0 out ₀ L stor C V 1 P = P(t)dt= [1-exp(-2Δt/R C )], (2.7) Δt

∫

2Δt

2.3 Device design

To design the device, first the topology of the variable capacitor must be explored. Based on the previous study [27], the in-plane gap closing capacitor is chosen due to the large capacitance change and system stability. The static analysis of output power using Equation 2.4 and Equation 2.5 with dielectric coating taken into consideration is then performed. Numerical Simulink simulation are used for dynamic analysis to obtain the optimal design parameters.

From Equation 2.4, the output power strongly depends on Cmax. Thus the main

approach to increase output power is to maximize the value of the variable capacitance. Furthermore, it is desirable to target a fabrication process that can produce devices with large capacitances. A very thick device layer and a high aspect ratio are therefore necessary. This study takes advantage of the silicone-on-insulator (SOI) wafer in that it offers very thick structures (up to 200 μm or more ). As for high aspect ratio, the deep reactive ion etching (DRIE) process is used to fabricate the devices with aspect ratio up to 20:1.

2.3.1 Variable capacitor

The in-plane gap closing type variable capacitor is shown in Figure 2.7. The dark areas are structures anchored to the substrate, whereas the light areas are released structures that are free to move.

The symbols used in the following analysis are listed below. A0: top-view area of the movable plate,

d0 : initial gap between interdigitated fingers,

d0 : initial gap between the top plate and the substrate,

Lf : length of comb fingers,

h0 : thickness of comb fingers,

Ng: number of gaps in the interdigitated comb fingers,

z0 : displacement of the movable plate,

z0 : initial overlap length of interdigitated comb fingers,

W.: width of the plate, .L.: length of the plate.

As shown in Figure 2.7, the spring of the in-plane gap closing variable capacitor makes it easier to move perpendicular to the finger gaps. The motion is in the plane of the wafer and mechanical stops can be incorporated with standard fabrication processes. Therefore, the minimum dielectric gap and thus the maximum capacitance can be precisely controlled. The capacitance Cv without dielectric coating is

v g 0 f 2 2 2d C (z)=N ε L h( ),

d -z (2.8) Figure 2.7 Top view of the in-plane gap closing variable capacitor

d z Lf z0 W L

where ε is the permittivity of free space. The mechanical damping including the ₀ squeeze film damping force between interdigitated fingers and the lateral air drag force between the movable plate and substrate is given by [28, 29]

3 g f m 3 2 -1.5 0 μN L h μA 1 b (z)z= +α z, d d (1-ε ) ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠   (2.9)

where.α ≈ 1.74 is a coefficient related to the ratio of width and length of the movable plate,._{μ=1.82 10×} -5 _{Pa-sec is the viscosity of air at 1 atm, and ε=}z

d is the normalized displacement of the movable plate. Finally, the electrostitc force is given by _e 2 g 0 f -Q z b z= 2N dε L h, (2.10) where Q is the charge on the variable capacitor and the minus sign indicates an attraction force.

With dielectric coating of thickness t and the removal of the substrate beneath the movable plate by backside etching process (as will be explained in Chapter 3), Equation 2.8~2.10 should be corrected as:

r v g o f 2 2 r 2t 2( +d-2t) ε C (z)=N ε L h , 2t ( +d-2t) -z ε ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ .(2.11) 3 g f m 1.5 3 2 μN L h b (z)= α , z (d-2t) 1-( ) d-2t ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ _{⎡ ⎤} ⎟ ⎜ ⎟ ⎜ ⎢_⎣ ⎥_⎦ ⎟ ⎝ ⎠ (2.12) and 2 e g o f r -Q b z= z. 2t 2N ε L h( +d-2t) ε (2.13)

damping force between interdigitated fingers contributes to the mechanical damping force b (z) z_m ×  (Equation 2.12). Besides, according to Equation 2.13, the electrostatic force b_e× is proportional to the negative displacement of the movable z plate. Therefore, it acts more like a negative spring than a damper. In order to get enough change in the variable capacitance, the thickness h should be large and the displacement z should be close to the initial gap d. In our calculation, the variable capacitance can range from 44 pF to 6660 pF.

2.3.2 Static analysis

In Equation 2.4, RL and Cstor can be chosen so that the discharging time constant

τ = CstorRL is much larger than the conversion cycle time Δt. The output voltage ripple

in the steady state can therefore be neglected. In this case, Vsat can be approximated as

max in sat min L min L stor C V V , (2.14) t t C 1+ R C R C ≈ ⎛ Δ ₊ Δ ⎞ ⎜ ⎟ ⎝ ⎠

Usually Cmin is a small value (in the order of 100 pF). The other circuit components

in Equation 2.14 can be chosen so that Cstor >> Cmin and RLCmin << Δt and Equation

2.14 can be simplified as max in max in sat L min L min C V C V V = R , t _t C R C ≈ _Δ Δ (2.15)

The power output becomes

2 sat max in out 2 L L V C V P R , t R ⎛ ⎞ ≈ _{≈ ⎜ ⎟} Δ ⎝ ⎠ (2.16) For a typical low-power sensor node or module, the minimum output power requirement is about 200 μW. In addition, a power management circuit is needed to

convert the high output voltage to lower ones for various sensor and signal processing units. To be compatibile with the power management circuit, the maximum output voltage should be limited to about 40 V. Inserting these constraints into Equation 2.5, one can obtain the range of RL:

L

R ≤8 MΩ. (2.17) Even though a smaller RL can be used, this would require increasing Cmax in order to

satisfy the voltage and power requirement (Equation 2.15 and Equation 2.16), which in turn will have adverse effects in the dynamic behavior of the converter. Therefore, RL = 8 MΩ and hence the calculated Cmax of about 6.7 nF are used in the following

calculation.

Based on Equation 2.4 and Equation 2.5, the output power Pout for various Cstor

and RL is shown in Figure 2.8. For Cstor >> Cmin (44 pF), it can be seen that the output

power does not depend on the storage capacitor Cstor when it is relatively large.

Nevertheless, a large Cstor will result in long initial charge time when the converter

starts to work from a static status. Hence, a resonable Cstor of 20 nF is used.

From Equation 2.4 and with the values of Cstor and RL obtained from above,

input voltage Vin of 3.3 V, vibration frequency of 120 Hz, and chip area size of 1 cm2,

Figure 2.9 shows the calculated output saturation voltage and power as a function of the initial finger gap distance and the thickness of the silicon nitride layer. The finger thickness, length, and width are 200 μm, 1200 μm and 10 μm, repsectively [27]. The dimension of the fingers are based on the available deep etching process capability. The minimum gap distance is assumed to be 0.1 μm, which is controled by mechanical stops. It can be seen that with a 500-Å-thick nitride, the initial finger gap has an optimal value of 35 μm for a power output of 200 μW and output voltage of 40 V. Although a smaller initial finger gap can be also designed to generate enough power, the increased electrostatic force between interdigitated fingers (which causes

larger proof mass needed to initiate the vibration of the device) is not desirable in the dynamics of the microstructure. Therefore, only the optimal value of 35 μm is prefered.

Figure 2.8 Output power (μW) for various RL and Cstor

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 RL (MOhm) C st or (n F) 22 0 22 0 22_.0 44 .0 44 .0 44.0 66 .1 66 .1 66 1 88 .1 88 .1 88.1 110.1 11 0.1 110_.1 13 2.1 13 2.1 132.1 15 4.2 15 4.2 154.2 17 6.2 17 6.2 176.2 19 8.2 19 8.2 198_.2 22 0.2 22 0.2

Figure 2.9 Output saturation voltage and power vs. initial finger gap (RL =

8 MΩ, C = 20 nF) 5 10 15 20 25 30 35 40 45 50 0 100 200 300 400 500 Out put pow er P out (uW ) 5 10 15 20 25 30 35 40 45 500 20 30 40 50 60 5 10 15 20 25 30 35 40 45 500 20 30 40 50 60 5 10 15 20 25 30 35 40 45 500 20 30 40 50 60

Finger initial gap (um)

Out put s atu ra tion v olt age V sat ( V olts ) 0.05um-thick nitride 0.1um-thick nitride 0.2um-thick nitride Pout Vsat

2.3.3 Dynamic analysis

After the dimension of the variable capacitor is determined from the static analysis, the dynamics of the microstructure is analyzed so that the desired maximum displacement, and hence Cmax, can be achieved by the target vibration source. The

electro-mechanical dynamics of the converter can be modeled as a spring-damper- mass system, as shown in Figure 2.10.

The dynamic equation is

mz+b z+b (z)z+kz=-my, _{e m}   (2.18) where y is the displacement of the device frame caused by vibration, z is the displacement of the shuttle mass m with respect to the device frame, k is the spring coefficient, b (z)_m z.is the equivalent mechanical damping force representing energy loss caused mainly by the squeezed film effect, and bez is the electrostaitc force acting

on the MEMS structure discussed before in Section 2.3.1. Notice that the mechanical damping force,b (z) zm × , is a function of both the displacement z of the shuttle mass

and its velocity.z.[3].

In Equation 2.18,.b (z)m .and be are functions of z. Therefore the system is

m bm be k z(t) y(t)

nonlinear. In order to simplify the design, linear systems with fixed coefficients determined by the range of b (z)m .and be are used to approximate the original system.

Fourier transform is then applied to find the trend of system behavior. The vibration source is assumed to be sinusoidal with complex amplitude.Y.and frequency.ω. With the system operated in sinusoidal steady state, Equation 2.18 reduces to

2 2 m e

-mω Z+jωb Z+(k+b )Z=-mω Y, (2.19)    where Z is the complex amplitude of z. Solving Z :

2 2 2 2 2 e m mω Z = Y , (2.20) (k+b -mω ) +b ω   Notice that the denominator in Equation 2.20 is minimized if the term 2 2

e

(k+b -mω )

is set to zero, e.g. 2 e

k+b -mω = , and thus the displacement Z is maximized. In 0

other words, the resonant frequency of the spring mass system k+be

m must match the driving frequency. Nevertheless, because of the charging and discharging process on the variable capacitor, the charge Q carried on the variable capacitor is not a

constant, and neither is the resulting be (since be is equal to

2 g 0 f

-Q

2N dε L h). In fact, the calculation shows that be varies from -59 to -9124 μN/μm. Substituting 120×2π for

ω and solving

_ω= k+be

m , (2.21) a range for the relationship between optimal k and m is obtained:

k-567913m=59 ~ 9124 (μN/μm) . (2.22) This range is helpful for us to choose appropriate attached mass m and corresponding spring constant k later in this section.

(a) and Equation 2.18, as shown in Figure 2.11. The charge redistribution box calculates the charging and discharging events when Cv reaches Cmax or Cmin. This

process represents the power output. Due to the limited shuttle mass that can be achieved in a MEMS process using only silicon, an external attached mass m is considered in order to increase the displacement of the variable capacitor and the energy conversion efficiency.

According to Equation 2.22, various attached mass m and corresponding spring constant k are chosen to simulate the maximum achievable displacement. As shown in Figure 2.12, a mass of 7.2 gram is required to achieve the maximum 34.8 μm displacement according to the static design. The corresponding spring constant is 4300 μN/μm. With these values, the output voltage simulated by the Simulink model as a function of time is plotted in Figure 2.13. The charging-discharging cycles are evident and the saturation voltage Vsat is close to the expected value of 40 V. Table 2.1

summarizes the important device parameters according to both the static and dynamic analyses. The device thickness h, length of finger Lf, width of finger Wf, and initial

finger gap d are shown in Figure 2.14. acceleration charge redistribution pull-in detection .1/s velocity .1/s vibration source displacement contact detection

Figure 2.13 Output voltage vs. time 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35 40 45 Time (s) O utput v ol tage (V ol ts )

Figure 2.12 Maximum displacement and spring constant for various attached mass

2 3 4 5 6 7 8 9 15 20 25 30 35 40 2 3 4 5 6 7 8 91000 2000 3000 4000 5000 6000 7000 Mass (g) S pri ng c ons ta nt (uN /u m ) M ax di sp la ce m ent (um )

Table 2.1 Design parameters of the energy converter

Parameter Description

W Width of shuttle mass 10 mm L Length of shuttle mass 8 mm h Device thickness 200 μm L_f Length of finger 1200 μm W_f Width of finger 10 μm

m Shuttle mass 7.2 gram d Initial finger gap 35 μm dmin Minimum finger gap 0.1 μm

C_stor Storage capacitance 20 nF k Spring constant 4300 μN/μm

t Dielectric layer thickness 500 Å εr Dielectric constant 7 (SiN)

R_L Load resistance 8 MΩ

Vsat Output voltage ~ 40 V

P_out Output power ~ 200 μW

d d

Lf

Wf

h

The shuttle mass m and the spring constant k are determined from the dynamic analysis in the previous section. The 7.2-gram shuttle mass is huge in MEMS and can not be achieved even using SOI wafers. As a result, a high-density material such as tungsten (W) or steel should be attached to adjust the mass.

2.3.4 Spring design

Since the shuttle mass is extraordinary large, the out of plane elasticity can influence the reliability of the system. For the folded beam structure in Figure 2.15, the beams are anchored on the side of the device and the trusses allow expansion or contraction of the springs along the x-axis. Assuming rigid trusses, the spring constants in the three axes are [9,31]:

3 k z 3 k Eh W k =N 2L , (2.15) 3 k x 3 k EhW k =N 2L , (2.16) k x k EhW k =N 2L , (2.17) where N is the number of springs,

h is thickness of spring (=200 µm),

E is the young’s modulus of single crystal silicon (=169GPA), Lk and Wk are the length and width of beam, and

For a more extensive analysis of folded beams, including the effect of compliant trusses, the spring constants above must be multiplied by a coefficient λ , a function of beam and truss length and width [32]:

2 3 6 2 3 6

a +16as +44s

λ= , (2.18) 4a +34as +44s

where a is the truss length to beam length ratio (Lt/Lk) and.s is the truss width to beam

width ratio (Wt/Wk). In our spring design, Lt=50 µm, Lk=328 µm, Wt=25 µm and

Wk=10 µm. Hence, a and s are 0.1524 and 2.5, respectively. The calculated.λ.is equal

to 0.996, which implies the effect of compliant trusses can be ignored.

Several other issues should be considered. First, the vertical stiffness kz should

be at least 10 times lager than the lateral stiffness kx to reduce out-of-axis motion. The

static displacement under the weight of the proof mass, mg/kz, is also important.

Second, the yield stress for single crystal silicon is about 70 GPa. A safety factor Sf defined as the yield stress divided by the maximum stress on each axis will be helpful in checking the robustness of the spring. The maximum stress due to the lateral displacement and the static vertical loading of the proof mass are given

k max x 2 k 3EW x σ = 2L (2.19) Anchor Spring z y x Figure 2.15 Spring structure top view

Lk Wk Wt Lt Truss Beam

k z 2 k 3mgL σ = NW h , (2.20) where xmax is the maximum lateral displacement.

There are 8 springs, 4 on each side of the shuttle plate, and the resonant frequency is 123 Hz. The maximum lateral stress is 0.92 GPa when the maximum displacement is 34.8 μm. The vertical stress is 21.7 MPa with mass m=7.2 g. The resulting axial and vertical static safety factors are Sfx=76.08 and Sfz=3225.8,

respectively. The spring constant kx is 4300 μN/μm, which is far below the other two

spring constants. The final devices parameters of the springs are listed in Table 2.2. Table 2.2 Spring design and safety factor

Variable Description of variables

h Thickness of spring 200 μm

N Spring number 8

Wk Spring Width 10 μm

Lk Spring Length 328 μm

kz Vertical spring constant 1.72¥106 μN/μm

kx X-axis spring constant 4300 μN/μm

ky Y-axis spring constant 4.63¥106 μN/μm

kz / kx Vertical to lateral spring ratio 400

ky / kx Non-axial to axial spring ratio 1077

Sfx Safety factor –axial 76.08

Sfz Safety factor –vertical static 3225.8

Modal analysis is performed by Coventorware. The result shows that the first mode is the lateral mode with resonance frequency of 110 Hz. The second mode is the tilt mode with resonance frequency of 245 Hz. The second mode frequency is more

than twice of that of the first mode, which is quite safe in this application. The equivalent lateral spring constant (3704 μN/μm) is smaller than calculated. However, the shift in resonant frequency due to spring modeling can be compensated by adjusting the external load mass.

2.3.5 Layout design

Mechanical stops are designed on the anchor. The fixed fingers are electrically connected. The center hole on the movable plate is for the positioning of the attached mass (a steel ball or a battery cell). The size of the center hole is designed to keep the attached mass from touching the underneath substrate.

The overall layout schematic is shown in Figure 2.16. Compared to previous layout (Figure 2.17) [27], more fingers are inserted into the center plate to increase the variable capacitance by 50%.

Figure 2.16 Schematic of the current device

Comb Finger Spring

2.4 Circuits and energy storage

In this section, the circuit used to measure the power output and the devices used to store converted energy are discussed.

2.4.1 Measurement circuits

In the orginal design, the entire device including circuits should be test and measured according to the schematic shown in Figure 2.4(a). A similar prototype with a measurement circuit (Figure 2.18) was tested by Roundy [9].

Comb Finger Spring

Mechanical stops

Figure 2.17 Schematic of the previous device

D2 Vout Cv Cstor Vin D1 RL

However, the prototype fabricated by Roundy was not functional due to the reverse leakage current of diods. In fact, reverse leakage currents of commercially available diodes (range from about 1 µA to about 100 µA) are often to large. For a capacitor of about 100 pF (the order of Cmin), a 1 µA leakage current will result in a

10000 V/s voltage drop. In our design, the circuit is operating at 240 Hz (two times of the vibration frequency), which means each cycle lasts for 4.16 ms and the voltage drop will be 41.6 V, which is too large. Thus another circuit model with an AC current output as shown in Figure 2.19 is proposed [27]. For a DC voltage source Vin such as

battery, the serial variable capacitor will induce an AC current I(t) at the output port. Since DC current is blocked by the capacitor, there is no net power output from the voltage source. Thus the output power of this circuit is purely derived by the driving vibration.

Based on the modified circuit, the equations below can be derived:

in c L

V =V (t)+I(t) R , and× . (2.21) and _I(t)=dQ(t)₌d[C (t)V (t)]v c

dt dt . . (2.22) Equation 2.22 can be simulated by a Simulink model. Assuming the displacement Z(t)

Vin

CV(t)

RL

Figure 2.19 Modified circuit schematic I(t)

is sinusoid with an amplitude of 34.8 µm, the AC output current is about 15 µA (Figure 2.20) for a 3.3 V input voltage and 10 kΩ load resistance. Therefore, the output power is about 1.1 µW.

2.4.2 Storage device

When energy converters do not supply energy continuously for most of the time, a good solution is to store the converted energy, which means to convert energy in storage elements in order to provide power and energy more smoothly. Typical storage devices include capacitors, inductors, and batteries.

Capacitors and inductors have lower energy density. They often serve as intermediate and short-term energy storage cells because they are less sensitive to leakage. Batteries, such as NiZn, NiMH, NiCd, and Lithium-ion (Li-ion) store energy

Figure 2.20 AC output current

0 0.01 0.02 0.03 0.04 0.05 -20 -15 -10 -5 0 5 10 15 20 Time (s) A C out put c urrent (uA )

chemically and are rechargeable. Among these kinds of batteries, Li-ion batteries (Figure 2.21) offer best characteristics with higher energy density and discharge rate, higher cell voltage, longer cycle life, and nonexistent “memory” effects. The only drawback is Li-ion batteries are too sensitive to over charging and discharging. Charging them above 4.2 V or higher, or discharging them below 2.7 V will damage the batteries and make them vent or explode [33]. In this study, LIR1620 (3.6V, F16mm, H2.2mm, 1.2g) and LIR2016 (3.6V, F20mm, H1.8mm, 1.6g) Li-ion cells can be used to store converted energy. Moreover, the battery is able to contributes a part of mass needed if it is well bonded on the device.

2.5 Conclusion

A micro electrostatic vibration-to-electricity energy converter is designed in this chapter. For the 3.3 V supply voltage and 1cm2 chip area constraints, optimal device parameters were found from theoretical calculation and Simulink simulation. In the current design, the output power is 200 µW/cm2 for the optimal load of 8 MΩ. The device structures such as the variable capacitor and springs are also discussed.

Chapter 3 Fabrication Process

Processes to fabricate the variable capacitors described in Chapter 2 using MEMS fabrication technology are discussed. SOI wafers are used due to the large device thickness and therefore large capacitance. Additionally, deep reactive ion etching (DRIE) processes are used to fabricate devices with high aspect ratios to maximize capacitance. A further benefit of the thick device layer and high aspect ratio is that the resulting devices have a very large out-of-plane stiffness compared to the in-plane stiffness. This is important for the attachment of a significant amount of mass to the device after the fabrication process is completed. Finally, our previous work [27] showed that the substrate beneath the device was the major contribution to parasitic conductance and the stiction problem. Therefore, backside etching by DRIE is also included in the new process.

The proposed processes rely heavily on DRIE, which causes various problems. After the entire process flow, only a few devices survived. Explanations for some of the problems in the fabrication as well as proposed solutions will be discussed.

3.1 Process flow

Since the device is relatively large, the device layer should be highly conductive to reduce resistive losses. Thus the resistivity of the device layer is less than 0.02 Ω-cm. Parasitic capacitance caused by the substrate is reduced by removing the substrate under the center plate by backside etching. Though the backside etching does increase the processing complexity, the stiction in the releasing step can be prevented thereby. However, since the area of the etched substrate is very large, the

robustness of the wafer or die can be a problem. The width of the outer frame, which also serves as the electrode of the fixed finger, are extended to 2.5 mm to strengthen the support of the device and the attached mass.

Most of the fabrication was conducted in the Nano Facility Center at National Chiao-Tung University and the Nano Science and Technology Center at National Tsing-Hua University. The basic processing steps are illustrated in Figure 3.1 and discussed in the following.

(a) Start from a double-side polished P-type <100> SOI wafer with a device layer of 200.μm, oxide layer of 5.μm, and handle layer (substrate) of 400.µm. The resistivity of the device layer is less than 0.02 Ω-cm.

(b) Spin coat a thick photoresist AZ4620 of 6 μm on the wafer backside and pattern via photolithography.

(c) Coat and pattern the frontside photoresist AZ4620 of 6 μm using the double side aligner.

(d) Etch the device layer down to the oxide layer to form fingers, springs, and movable plates using DRIE.

(e) Etch the backside to form the outer frame and the dividing gap by DRIE.

(f) Remove photoresist and deposit silicon nitride on the finger side walls by low pressure chemical vapor deposition (LPCVD).

(g) Etch the top layer of silicon nitride on the frontside by reactive ion etching (RIE). (h) Etch the 5-μm-thick sacrificial oxide from backside by RIE to release the movable

parts.

(i) Coat aluminum of less than 5000 Å to form the pad contact and interconnection by thermal evaporation. After this step, the wafer is cleaved manually and wire bonding is conducted.

The DRIE etcher used in the fabrication process is an Alcatel AMS100 etcher using the standard Bosch process. Passivation is achieved by C4F8, and silicon etching

by SF6.

After the DRIE in step (g), the remaining photoresist are removed by oxygen plasma in the RIE chamber. The 5-µm-thick sacrificial oxide was then etched by CHF3 and SF6 for about 65~70 minutes. The oxide etching time should be controlled

carefully to avoid overetching and destroying the frontside devices.

In the dicing process (i), the cooling water often damaged fingers and caused a lot of broken pieces and shortage problems [27]. Therefore, wafer dicing was performed manually. A diamond scribe was used to cleave dies along the dividing gaps formed by DRIE.

Since the required mass is large, high density material such as tungsten or steel is used to reduce the size. In the final step of the fabrication process (step (j)), the mass needs to be placed precisely on the center of the device; otherwise the nonaxial motion will be induced. Therefore, the movable plate has a large hole in the center for a spherical ball to be fit into the position automatically. The resonant frequency can be adjusted by using balls with different diameter (and thus mass) to match the vibration frequency. The steel ball is bond to the center plate by a double stick tape.

(b) (a) (d) (e) (i) Si oxide nitride Al external mass P.R.

Figure 3.1 Processing steps: (a) start from a SOI wafer, (b) coat and pattern backside P.R., (c) coat and pattern frontside P.R., (d) etch the device layer by DRIE, (e) etch the backside by DRIE, (f) deposite silicon nitride on the finger side walls by LPCVD, (g) etch top silicon nitride layer on the frontside by RIE, (h) etch sacrificial oxide from backside by RIE, (i) apply Al by thermal coater, and (j) attach external mass

(f)

(g)

(h)

(j) (c)

3.2 Discussion

Problems and issues found in the fabrication process are discussed. Solutions are proposed and demonstrated in this section.

3.2.1 Overheating of the wafers

In the first run, the backside etching was done with KOH solution before defining frontside structures by DRIE. A 6000-Å-thick LPCVD silicon nitride was first deposited on both sides of the SOI wafer as the wet etching mask. After the etching window on the backside was opened, the full wafer was immersed in the 45.8 wt% KOH solution at 80˚C. The wet etching lasted for 10 hours and 45 minutes for an etching rate of 0.62 µm/min and stopped at the sacrificial oxide layer.

However, the long wet etching caused a problem for the subsequent DRIE process. Since the edge of wafer was not completely covered by the silicon nitride film in LPCVD, the wafer was attacked by KOH from its edge when fully immersed into the solution. Consequently, it became a smaller disk than a normal 4” wafer and could not be clamped well by the mechanical chuck in the DRIE etcher. One solution was to dice the wet-etched SOI wafer into dies and then bond them to a carrier wafer. As shown in Figure 3.2, photoresist was coated on the carrier wafer to provide adhesion for dies and a heat conducting path for the cooling gas (helium) to dissipate process heat. Unfortunately, the etching was not controlled well and structures were overetched. As a result, the fingers and springs were etched sideways (Figure 3.3) and disintegrated (Figure 3.4).

Figure 3.2 Die and carrier wafer for DRIE P.R.

Die

Carrier wafer

(a)

Bottom of fingers are etched

Finger Conneted to the fixed frame

(b)

~125 µm ~35 µm

Figure 3.5 RIE lag effect

Figure 3.4 Cross section of broken fingers Fingers

Overetched silicon Fixed frame

In the next try, the wet etching on the backside was replaced by DRIE. After the backside etching, the front device layer was also etched by DRIE. However, due to the RIE lag effect in dry etching, the narrow gaps between the fingers were etched more slowly than the wide hole in the center plate as shown in Figure 3.5. While the wider spaces was cleared in about 30 minutes, the narrower spaces need 10 more minutes or so. During this extra 10-minute period, the sacrificial oxide layer always broke due to its residual stress (this will be discussed later in this section). Once the oxide layer broke, helium escaped through the breach, leading to bad cooling of the wafer.

The other issue with this process is related to the heat conducting path of the suspended structures [34]. As the suspended structures were defined, all the process heat contained on the center plate must be dissipated through the thin springs. With a width of 10 , the springs were too thin to transfer enough heat outside. Combined with bad wafer cooling, it caused the temperature of the center plate, springs and movable fingers to rise dramatically. Thus, the photoresist on these sections was burned. Figure 3.6 shows burned photoresist on the suspended structures and photoresist in perfect condition on the anchor. The photoresist on the suspended springs, halfway in the thermal path between the center plate and the anchor, showed some signs of burning, but not as dramatic as that on the center plate. Once the photoresist was burned, springs were not protected and thus destroyed. Therefore, no working device was yielded in this run.

In the third run, several changes were made to provide better cooling and heat conduction in the DRIE process. Although the yield was still low, a few working devices were made. The device layer was etched first, followed by the backside through-etching as shown in Figure 3.1 (d) and (e). In the backside DRIE, the regions to be etched were large openings under the suspended structures and had a uniform size. Since the etching rate depended on the size of the opening, the etching time for each block were more uniform. After the first block was opened and helium started to escape through the breach in the oxide layer, very little extra time (about 2~3 minutes) was needed to clear the other regions. As a result, the leakage of helium would not last long. Besides, since the substrates had better heat conducting path to transfer enough heat outside, there was not so much heat accumulating on the wafer and thus the problem of overheating could be alleviated.

Figure 3.6 Burned photoresist due to poor cooling Anchor

(with unburned photoresist)

Center plate

(with burned photoresist) Spring

Fixed finger

Burned photoresist on the movable fingers

3.2.2 Residual stress of the oxide layer

After the bonding process of manufacturing the SOI wafer at a high temperature, the resulting sacrificial oxide layer became stressed due to the different thermal expansion coefficients of silicon and silicon dioxide [35]. In the third run, the residual stress caused most of the springs to break. After the structures in the device layer were defined, a large area under suspended structures was removed in the backside etching. Hence, no structure was left to hold the stressed oxide layer. The oxide layer started to buckle and bent the structures in the device layer. Therefore, the most fragile parts, the springs and fingers, were broken as shown in Figure 3.7. In the future, removing the oxide layer before etching the handle layer can be helpful to eliminate this issue. Even though this may cause helium leakage, it is usually not a serious problem in backside etching. Designing a new structure with more robust springs and less etched area may also alleviate the effect of residual stress.

Figure 3.7 Broken structures due to residual stress Cracked oxide film

3.3 Fabricated device

Figure 3.8 shows the SEM photograph of a fabricated device, with the springs, fingers, mechanical stops, and the center hole for mass attachment.

With the perpendicularity about 90°, the fabricated fingers are 200 µm deep, 1200 µm long and about 9.5 µm wide, as shown in Figure 3.9. In order to yield ideal finger width of 10 µm, the layout finger width is pre-enlarged to 12 µm to compensate for the feature size shrinkage during processing. The reasons for the shrunk feature size are the non-ideal photolithography and the rise of wafer temperature in DRIE process as mentioned above. First, the cross section of patterned thick photoresist is in a tapered shape, instead of a rectangular shape due to photolithography inaccuracy, such as over exposure, over development, or the characteristic of the photoresist itself.

Center hole Fingers Mechanical stop (a) Spring

Since the photoresist serves as the hard mask for DRIE, this deviation will influence the device feature size. To improve the feature size control, thermal or PECVD oxide can be used as the hard mask, since they provide higher selectivity in DRIE and can thus maintain the ideal feature size. Second, the DRIE process is a series of etching and passivation steps. The normal processing temperature is about 45˚C. When temperature increases, passivation effect is decreased. If the temperature is over 100˚C, the etching becomes isotropic and thus the structures are etched sideways. Increasing the flow rate of C4F8 (gas for passivation) or lengthening the time of the

passivation cycle can be a solution to this problem [36].

. Anchor Center plate Outer frame Fingers Spring (b)

Figure 3.8 Overview of the device: (a) SEM photograph from frontside and (b) optical microscope photograph from backside