Corona-driven air propulsion for cooling of microelectronics

High voltage power supply HVPS provides required potential difference...10 Chapter Figure 2.6 Corona current-voltage relationship...11 Chapter Figure 2.7 Visual difference between positi

ByFumin Yang

A thesis submitted in partial fulfillment of the

requirements for the degree of

Master of Science in Electrical Engineering

University of Washington

2002

Program Authorized to Offer Degree: Electrical Engineering

Graduate School

This is to certify that I have examined this copy of a master’s thesis by

Fumin Yang

and have found that it is complete and satisfactory in all respects,

and that any and all revisions required by the final examining committee have been made

the University of Washington, I agree that the Library shall make its copies freelyavailable for inspection I further agree that extensive copying of this thesis is allowableonly for scholarly purposes, consistent with "fair use" as prescribed in the U.S CopyrightLaw Any other reproduction for any purposes or by any means shall not be allowedwithout my written permission.

Signature

Date

AbstractCorona-driven air propulsion for cooling of microelectronics

by Fumin YangChair of the Supervisory CommitteeAssistant Professor Alexander MamishevDepartment of Electrical Engineering

Rapid development of microelectronics has led to high component density thathas doubled every 12 months in the last decade Each semiconductor component emitsheat associated with its electrical resistance With higher density of electroniccomponents on a chip, heat sinks get denser and channels between them get narrower.Existing cooling devices are not efficient because gases become viscous in narrowchannels, which greatly hinders the air movement The problem of heat dissipation is one

of the most profound obstacles in the electronics industry today The object of this thesis

is to develop an electrostatic air pump that could be later incorporated into a chipstructure for heat withdrawal from microelectronics and MEMS devices

This thesis explores the possibility of building an electrostatic air pump used forcooling at chip level Numerical simulations are conducted for different devicegeometries and materials to achieve the optimal performance of air pumps Based on theresults of simulations, several prototypes of the electrostatic air pump were built.Measurements conducted to characterize this device included air velocity profile at theoutlet, voltage-air speed relationship, current-voltage relationship, and air resistance.Working efficiency of the device is calculated It is found that the efficiency of current airpump with single channel geometry has the same magnitude as that of traditionalcomputer cooling fans At the same time, it has more efficient airflow profile and severalother advantages compared to rotational computer fan

Analytical model of forces involved in the dehumidification process of air pumps is beingdeveloped Comparison of columbic and dielectrophoretic forces is provided The latter israrely discussed in framework of electrostatic devices, but may become a significantforce component under certain conditions Future direction of this research projecttowards miniaturization of existing devices is proposed

List of Figures 3

List of Tables 6

Acknowledgements 7

Chapter 1 Introduction 1

1.1 Background 1

1.2 Motivation 4

1.3 State of the art 6

1.3.1 Corona driven pump for air movement 6

1.3.2 Corona discharge 6

1.4 Thesis Outline 7

Chapter 2 Basic principles of electrostatic air pump operation 9

2.1 Operation of the electrostatic air pump 9

2.2 Ion generation in gases 10

2.2.1 Properties of gas in corona discharge 11

2.2.2 Ionization processes 12

2.2.3 Mathematical description of corona discharge 12

2.3 Positive and negative corona discharges 13

2.3.1 Positive corona 14

2.3.2 Negative corona 15

2.4 Theoretical current-voltage relationship 15

2.5 Electric field distribution 17

2.6 Enhancement of heat exchange through water evaporation 19

2.6.1 Charging process 20

2.6.2 Electric drag 22

2.6.3 Stability of a charged liquid droplet 23

2.7 Advantages of corona technology in micro-cooling 24

Chapter 3 Theoretical background 27

3.1 Comparison of forces acting on water droplets and particles in the air 27

3.2 Columbic force 27

3.3 Dielectrophoretic (polarization) forces 28

3.4 Biot-Savart force 35

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4.1 Simulation of a single pair electrodes air pump 36

4.1.1 Methodology 37

4.1.2 Results 37

4.2 Simulation on optimum air movement vs collection efficiency 44

4.3 Design and simulation of the air pump with channel geometry 46

4.3.1 Design of the air pump with channel geometry 46

4.3.2 Maxwell simulation of an air pump with single channel geometry 48

Chapter 5 Experimental setup, measurements, and results 53

5.1 Experimental setup 53

5.2 Air speed profile on the outlet of the air pump 56

5.3 Voltage-air speed relationship 58

5.4 Current-voltage relationship and air resistance 59

5.5 Energy efficiency 60

Chapter 6 Future research 62

6.1 Current problem 62

6.2 Future plans 63

Chapter 7 Conclusions 65

References 66

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Chapter Figure 1.1 Structural levels of a computer [1] 2

Chapter Figure 1.2 Microchannels on silicon chip [1] 3

Chapter Figure 1.3 Air-cooled multi-chip module used in IBM 4381 Processor [1] 4

Chapter Figure 1.4 Heat generation trend for Pentium microprocessors 5

Chapter Figure 2.5 Principle of operation of corona air pump High voltage power supply (HVPS) provides required potential difference 10

Chapter Figure 2.6 Corona current-voltage relationship 11

Chapter Figure 2.7 Visual difference between positive corona and negative corona [28] 14

Chapter Figure 2.8 Electrostatic dehumidification technology 20

Chapter Figure 2.9 Corona air pump can be used for cooling of computer chips 25

Chapter Figure 2.10 Contrast of air movement profile difference between a traditional fan and corona-driven pump 26

Chapter Figure 2.11 Dynamic airflow pattern can be controlled through varying voltage distribution 26

Chapter Figure 3.12 Columbic force distribution of an air pump 28

Chapter Figure 3.13 Dielectrophoretic force in an electric field of corona air pump 29

Chapter Figure 3.14 Columbic force and dielectrophoretic force along the radial position for a single water molecule with the 1e- net charge 31

Chapter Figure 3.15 Large water conglomerates in a strong electric field became polarized and elongated 31

Chapter Figure 3.16 Relationship between electric field gradient, dipole value, and the corresponding dielectrophoretic force produced 32

Chapter Figure 3.17 Calculated electric field intensity displayed as a function of dimensionless radial distance from corona electrode without space charge 33

Chapter Figure 3.18 Calculated electric field intensity displayed as a function of dimensionless radial distance from corona electrode with space charge 33

Chapter Figure 3.19 Calculated columbic force displayed as a function of dimensionless radial distance from corona electrode without space charge 33

Chapter Figure 3.20 Calculated columbic force displayed as a function of dimensionless radial distance from corona electrode with space charge 34

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dimensionless radial distance from corona electrode without space charge 34

Chapter Figure 3.22 Calculated dielectrophoretic force displayed as a function of dimensionless radial distance from corona electrode with space charge 34

Chapter Figure 4.23 Basic design concept of a corona air pump pair 36

Chapter Figure 4.24 Design I of ionic pump 38

Chapter Figure 4.25 Electric field and equipotential line plot of Design I 38

Chapter Figure 4.26 Force distribution between two electrodes in Design I 39

Chapter Figure 4.27 Design II of ionic pump 40

Chapter Figure 4.28 Electric field and equipotential line plot of Design II 40

Chapter Figure 4.29 Force distribution between two electrodes in Design II 41

Chapter Figure 4.30 Design III of ionic pump 42

Chapter Figure 4.31 Electric field and equipotential line plot of Design III 42

Chapter Figure 4.32 Force distribution between two electrodes in Design III 43

Chapter Figure 4.33 Geometry of a single pair of electrodes with possible non-linear voltage distribution at sidewalls 45

Chapter Figure 4.34 Field strength and voltage distribution of the electrode geometry for optimum air movement 45

Chapter Figure 4.35 Field strength and voltage distribution of the electrode geometry for optimum collecting efficiency 46

Chapter Figure 4.36 Corona electrodes are shielded with walls separating them 47

Chapter Figure 4.37 Channel geometry with film collector electrodes attached on sidewalls 48

Chapter Figure 4.38 Electric field and equipotential line distribution of Geometry I without space charge 50

Chapter Figure 4.39 Dielectrophoretic force distribution of Geometry I without space charge 50

Chapter Figure 4.40 Electric field and equipotential line distribution of Geometry I with constant space charge distribution 51

Chapter Figure 4.41 Dielectrophoretic force distribution of Geometry I with constant space charge distribution 51

Chapter Figure 4.42 Electric field and equip-potential line distribution of Geometry I with radially decreasing space charge distribution 52

Chapter Figure 4.43 Dielectrophoretic force distribution of Geometry I with radially decreasing space charge distribution 52

iv

Chapter Figure 5.45 The x-y-z translation stage to position the corona electrode 54

Chapter Figure 5.46 The corona electrode standing between collector electrodes 55

Chapter Figure 5.47 Semiconductive Kapton film attached to Teflon sheet forms the collector electrode 55

Chapter Figure 5.48 Zebra electrode: voltage gradient applied on insulating Kapton film through copper foil 56

Chapter Figure 5.49 Experimental setup with Zebra collector electrode 56

Chapter Figure 5.50 Air speed profile along the sidewall from the outlet 57

Chapter Figure 5.51 Air speed profile across the sidewall from the outlet 58

Chapter Figure 5.52 Measured corona voltage (Vc) vs air speed (lfm) on the outlet exhibits linear relationship 58

Chapter Figure 5.53 Measured corona voltage () vs current through collector electrode ( ) exhibits exponential dependence 59

Chapter Figure 5.54 Measured air resistance () as a function of corona voltage () 59

Chapter Figure 5.55 Energy efficiency as a function of input voltage 60

Chapter Figure 5.56 Fan efficiency in CFM/W as a function of input voltage 61

Chapter Figure 6.57 Contrast between the surface region without erosion and the region with erosion on a corona wire using SEM (Scanning Electron Microscopy) 63

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Chapter Table 4.1: Comparison of three designs 43

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I want to express gratitude to my research advisor, Prof Alexander Mamishev, for giving

me the opportunity to work on this research project I am especially grateful for his deepinsights, consistent guidance, and availability in each step of research process I am veryfortunate to have an advisor who has genuine caring, support, and patience for hisstudents in different situations His humor, optimistic attitude, and great leadership makethe entire SEAL lab’s working environment much more relaxed and cooperative Lasttwo years of working with him as his graduate student are invaluable to my professionaldevelopment and future career

I would like to thank my thesis committee members Prof Jiri Homola and Prof.Ann Mescher for taking their time to read my thesis and giving me instructive feedback

A significant portion of my research time was spent in the company of our industrialcollaboration partner, Kronos Air Technologies, Inc I am very grateful to Dr IgorKrichtafovitch, Chief Scientific Officer of the company, for providing resources and ideasfor the research I greatly appreciate his genuine advice and availability

This project is supported by the Royalty Research Fund of the University ofWashington and the United Engineering Foundation

I would like to express my sincere appreciation to an undergraduate student NelsJewell-Larsen for his enthusiastic participation from the beginning of this researchproject until now He made contributions in almost all aspects and phases of this project:introducing other talented undergraduate students to this project, setting up research plansfor each quarter, working on theoretical calculations, computer simulations, building thedevice, making posters, and giving thesis feedback His industriousness, integrity, grace,communication skills, and leadership served me as a role model of a young leader andgood researcher I would like to express my great thanks to the funding resources thatsupport his work: Mary Gates Scholarship, Washington State Space Grant and ElectricEnergy Industrial Consortium

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talented undergraduates under my supervision, as part of their undergraduate research at

UW I would like to acknowledge (in reverse chronological order) Kyle Pendergrass,John Burnette, Dan Brown, David Parker, Tram Kim Thai and Michelle Raymond, fortheir diligence and creativity

I also want to thank graduate students in SEAL lab: Min Wang, Bing Jiang, ShaneCantrell, and Xiaobei Li, for their genuine support, meaningful discussions, and sharing

of knowledge and skills

I want to thank my friends Lily Sun, Bryan and Shing Chen, Dorcas Wang,Xiaolin Sun, Ouyang Gong, Xiaoguang Zheng, Xiaohong Chen and Christine Qiu, whocheered me up when I needed it (usually) and helped me when I was in trouble (often)

Finally, I would like to thank my parents in China for their sacrificial love andencouragement I also want to thank my brother for his support all along

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1 Introduction

1.1 Background

Heat transfer has always been an essential research subject in microelectronics industry.With increasing density of transistors and other electronic components on silicon chips,the problem of high heat generation has been a significant bottleneck to furtheradvancements in the microelectronic revolution Micro chips are operating in all kinds ofelectronics and computers: refrigerators, electric rice cookers, CD players, digitalcameras, cell phones, robotics control boards, medical instruments, and a myriad of otherdevices They not only work under room temperature environment of homes, schools, andoffices, but also under stressful thermal environment like cars, ships, submarines, andsatellites As we know, the most abundant material in semiconductor chips is silicon,which requires a working environment below 100oC for its steady functioning [1].Therefore, it is essential to remove heat efficiently from electronics to reduce thermalstresses on silicon chips and other supporting components

Generally, 3D electronics packaging systems can be divided into three levels: thechip, the module, and the printed circuit board (PCB) [1], as shown in Figure 1 1 Chipsare the smallest components in the system; a module isolates the chip from the ambientatmosphere and at the same time provides the leads for transmission of signals and thesupply of power Printed circuit boards (PCB) integrate modules into a working network

To dissipate heat from the electronics system, cooling systems must be integrated on achip level and efficiently interact with board and system level thermal managementdevices

C h a p t e r

Figure 1.1 Structural levels of a computer [1].

Different modes of cooling include natural convection, forced convection,conduction, radiation, and phase-change heat transfer [1] Forced convection cooling hasbeen the most commonly used mode for heat removal purposes Natural convectioncooling reduces acoustic noise inherent in forced air-cooling of equipment It alsooperates at remote locations and extreme thermal environments, where normal air-moving mechanical devices can’t operate very long Conduction transfers heat from theunit through direct contact with outside components

Liquid cooling is a major alternative cooling technology, with main researchefforts concentrated around heat pipes [2] and micro-channels (see Figure 1 2) [1].Advantages offered by liquid coolants are related to their relative high specific heat,enabling large thermal transfers out of a system with corresponding small increase incoolant temperatures However, because of the need for electrical insulation, the liquidmust have high enough dielectric strength to have direct contact with the chips Since the1950s, major efforts have been waged to develop coolants of high dielectric strength andgood chemical stability, which include “FCs” (3M), “Coolanols” (Monsanto), “DCs”(Dow Corning), and “Freons” (Du Pont) [1] Liquids like water can not be utilized thisway due to their low dielectric strength In order to utilize low dielectric strength liquids

for cooling, insulation structures need to be built to shield the liquids Although liquidcooling generally gives higher cooling performance than air cooling, air is still apreferred coolant in electronics because it is cheap, stable, and easy to access.

Figure 1.2 Microchannels on silicon chip [1].

Blowing air toward heat generation units has been the most popular method ofcooling The mechanism is removing heat through blowing air with fan toward fin heatsinks, which connect to the heat generation unit and extend its surface With large surfacearea of heat dissipation, the heat is removed much easier with the impinging air Figure 1.3 [1] shows the impingement air-cooled fin structure used in IBM 4381 Processor.However, air cooling is reaching its technological limits because it requires largesurfaces, high air speeds, and, most significantly, heat conduction across several layers ofinterconnects before the heat flow reaches the heat exchanger [3] Furthermore, withhigher density of electronics components on a chip, heat sinks get denser and channelsget narrower According to the laws of fluid mechanics, gases become viscous in narrowchannels, which greatly hinders the air movement, and as a result, decreases the coolingefficiency To retain air as a coolant, micro-cooling systems that achieve high heattransfer coefficient and are close to the heat source should be developed

Figure 1.3 Air-cooled multi-chip module used in IBM 4381 Processor [1].

The purpose of this thesis is to enhance heat withdrawal from microelectronic andMEMS devices through developing an electrostatic air pump that could be incorporatedinto chip structure, which possesses better cooling ability and greater efficiency thanexisting devices while operating below audible level This technology has the potential toenable truly revolutionary advances in the microelectronics industry

1.2 Motivation

Rapid development of microelectronics led to immense component density that hasdoubled every 12 months in the last decade In 1971, the first computer microprocessor

4004 is made in at Intel There are about 2300 transistors on it In 2000, Pentium IV made

by Intel accommodates 42 millions transistors By the year 2005 microelectronicstechnology will begin bumping up against the point one barrier, i.e decreasing the size of

a single component to 0.1 micron Each semiconductor component emits heat associatedwith the electrical resistance The heat problem is one of the most profound obstacles inthe electronics industry today It can be seen from the heat generation trend of Pentiummicroprocessors in Figure 1 4

Pentium II 266-600 MHz

Pentium III 600-1000 MHz

Pentium IV 1.5 GHz

0 5 10 15 20 25 30 35 40 45

Pentium II 266-600 MHz

Pentium III 600-1000 MHz

Pentium IV 1.5 GHz

45

Desktop average heat flux

Pentium II 266-600 MHz

Pentium III 600-1000 MHz

Pentium IV 1.5 GHz

0 5 10 15 20 25 30 35 40 45

Pentium II 266-600 MHz

Pentium III 600-1000 MHz

Pentium IV 1.5 GHz

45

Desktop average heat flux

Figure 1.4 Heat generation trend for Pentium microprocessors.

In addition to common digital microelectronics, cooling has become a critical issuefor power electronics devices, such as IGBT and power diodes, where a very high powerdensity under normal operation conditions (up to 400 W/cm2) makes specific coolingsystems absolutely necessary for each device For high-speed MEMS applications, newissues are the introduction of combustion processes in micro-devices and mechanical heatgeneration due to friction In power electronics, high current applications require highoperating temperatures and dramatic improvements in heat dissipation Cooling ofmicroelectronics is becoming one of the most significant elements in a continuingprogress towards faster computers

The PC market drives the thermal management marketplace at this time but theneed for dissipation of heat from electronic devices is not limited to PCs All relatedproducts on the market today require some form of cooling technology The globalmarket for micro-cooling technology is expanding year by year While this industry hasbeen largely inhabited by traditional fans and heat sinks, the fastest growing segment isalternative cooling, showing an average growth rate of over 26% per year [4]

Why is this such a hot market? The prime mover in these markets is the problemfaced by integrated circuit manufacturers as they try to put more transistors in smallerspaces This results in more heat per unit volume to be dissipated AMD's top processorAnthlon contains 22 million transistors, nearly 20 times the 1.2 million found in the 486,

introduced in 1989, and with much denser interconnects According to the SemiconductorIndustry Association (SIA), in a report designed to map projections through the year

2005, the expected increase in need for thermal dissipation is the factor of four

Electrostatically assisted heat transfer on macro scale has been envisioned before[5], but until now it was not positioned to compete with traditional cooling Recentadvances in microfabrication and dramatically increased need for better cooling solutions

on device level are two main reasons for this technology to come to existence

1.3 State of the art

1.3.1 Corona driven pump for air movement

The principle of ionic air propulsion with corona-generated charged particles hasbeen known almost as long as electricity itself [6] One of the first references to movingair sensation near a charged tube appeared 300 years ago in a book by Francis Hauksbee[7] Many pioneers of electricity, including Newton, Faraday, and Maxwell, studied thisphenomenon [8-10] Studies continued to these days Extensive work was conducted onmodeling of charge and fluid dynamics [6;11;12] and heat transfer [13] in ionic pumps.Notably, most studies have been conducted with classic shapes of high-voltageelectrodes, such as needle-ring, needle-plane, and coaxial cylinders [14-18] Thefundamental aspects of electron wind technology have been compiled in severalauthoritative references [11-13;18] Since the 1960s, numerous studies addresseddifferent aspects of corona-driven wind, including effects of this phenomenon on airpollution [19;20], ozone generation, heat transfer, air propulsion, and bacteriasterilization Practical implementations of this approach appeared only in the last twodecades, driven by increased environmental awareness, advances in material science,microprocessor control, and market need

1.3.2 Corona discharge

Corona discharge is the phenomenon of discharge happening at the surface of aconductor, which is often accompanied by ionization of the surrounding atmosphere andoften by a power loss Gaugain [21] (1862) conducted one of the earliest research on

spark-breakdown voltages and fields for concentric-cylinder electrodes in air It wasfound that the breakdown field depends mostly on the diameter of the inner coronaelectrode wire and slightly on the diameter of the outer cylinder The result is represented

by the empirical equation

where E is the breakdown field at the surface of the inner electrode, 0 bis the radius of

the cylinder, A and C are experimental constants Rőntgen [22] (1878) started studies ofthe point-plane corona, where he found the existence of a critical voltage, corona onsetvoltage, below which no current is detected

The work of Peek [23] acted as the classic study of this subject, among the earlyinvestigations of high-voltage corona He determined the corona onset voltage as afunction of the wire diameter, air temperature and pressure, coating of the corona wireswith oil, water, and dirt films, and the material of wire-conductor Loeb [24;25]conducted outstanding research on the basic processes and properties of the coronadischarge, which covers the role of the first and second Townsend ionization coefficients,the essential part played by electron attachment in the negative corona, and theintermittent effects which are characteristic of the corona [26]

1.4 Thesis Outline

The thesis is focused on developing an electrostatic air pump that could be laterincorporated into a chip structure for heat withdrawal from microelectronics and MEMSdevices

The thesis starts with the basic principles of electrostatic air pump operation,followed by the theory of different forces in the discharge process After that, results ofnumerical simulations represent different device designs with the purpose of optimizingdevice’s performance Based on the simulations, the prototype of electrostatic air pump isbuilt and analyzed Finally, future development of this research project is discussed, withconclusions and summary at the end

In Chapter 2, first, the basic components and operation of corona air pump areintroduced The ionization process and physics of corona discharge are described,followed by the review of two important characteristics of corona discharge: current-voltage relationship and the distribution of electric field The advantage of thistechnology and its another major application in dehumidification are discussed in the end

of the chapter

Chapter 3 introduces three types of forces present in corona electric field toproduce motion of water droplets and other particles in air: columbic force,dielectrophoretic (polarization) force, and Biot-Savart force Dielectrophoretic force isthe focus of this chapter, since it is rarely discussed in framework of electrostatic devices,but it may be useful for further technology development

Based on the theory in the previous two chapters, Chapter 4 presents thenumerical simulations of electrostatic air pumps to find the optimal working geometry Itstarts with the geometry of a pairs of cylindrical corona electrode and collector electrode.Then it explores the channel geometry for collector electrode, which appears moresuitable for our device

Chapter 5 describes the experimental setup of the air pump prototype, with furthermeasurements of several important characteristics of air pump: voltage-air speedrelationship, current-voltage relationship, and air resistance variation in this process Thischapter also includes by calculations of the device efficiency and its comparison withtraditional computer cooling fan on the market

Chapter 6 discusses problems in the current design Future research direction ofthis research project towards miniaturization of existing devices is proposed Tentativeprocedures for prototype testing and evaluation are proposed in the same chapter

Chapter 7 draws the conclusions of the thesis

2 Basic principles of electrostatic air pump operation

2.1 Operation of the electrostatic air pump

Figure 2 5 shows the conceptual representation of the electrostatic air pumptechnology Electric potential difference applied between the corona electrode and thecollector electrode is sufficiently high to generate corona discharge in the fieldenhancement region (near the corona electrode), but below electric breakdown voltage.Ionized air particles are then accelerated by columbic force, which varies throughout thevolume of the device, but is directed mostly to the right, as shown in the diagram.Accelerated ions entrain air molecules in their movement and produce the same windeffect as a conventional fan

In addition to air movement, ions and electrons distributed in the volume of thedevice attach themselves to previously neutral molecules and particles Columbic forcesacting on these molecules and particles lead to their sedimentation on the electrodes ofopposite to their charge polarity Sometimes, this process is also accompanied by particleagglomeration

With appropriate electrode design and space charge control, it is possible to attractall generated ions on the electrodes with the opposite to the corona electrode polarity.Space charge leakage does not present problems at other devices with corona-inducedionization, such as photocopiers and printers

In terms of air movement, energy efficiency of electrostatic pumps is potentiallyhigher than that of conventional fans Main sources of energy losses in rotating fans areinduction motor core and copper losses as well as undesired air turbulence Since

C h a p t e r

electrostatic air movement of is based on electrostatic rather than magnetic field, energylosses could be much lower.

The required voltage difference is proportional to the distance between theelectrodes, on the order of 1 volt per micron Therefore, miniaturization of electrostaticpump technology can lead to important reduction of required voltage difference, which iscurrently on the order of thousands of volts

HVPS

Collector Electrode Gas molecules

Corona

Electrode

-+

Figure 2.5 Principle of operation of corona air pump High voltage power

supply (HVPS) provides required potential difference

2.2 Ion generation in gases

Ions are generated due to partial discharge activity present in the air near theelectrode This happens when the voltage applied between two electrodes exceeds thecritical voltage (called corona onset voltage) Below this voltage, no current between twoelectrodes can be detected After the voltage exceeds the critical value, current is present

in the air, as illustrated in Figure 2 .6 A further increase in voltage leads to adramatically increasing current until spark-over occurs, which marks the electricalbreakdown of the gas

Voltage Breakdown

Corona

Onset

Voltage

Figure 2.6 Corona current-voltage relationship.

2.2.1 Properties of gas in corona discharge

Gas differs fundamentally from solid and liquid in the way of conductingelectricity In solid and liquid conductors, electrons are moving in a certain range ofspace: either vibrate around its balance position or move through the conductor freely.Plus, solids and liquids have a much more compact and connected structure, whichallows charged particles travel easily across the material When an electric field is applied

on solid and liquid, it is much easier for charged particles to move through the medium,creating electric current, compared to gas For example, in metals like copper and silver,electrons are the free charge carriers moving through the crystal lattice with littleresistance

Gas, on the other hand, is composed of neutral molecules without free electronsand ions under normal conditions Its density, normally on the order of 1019 neutralmolecules per cm , is much lower compared to solid and liquid materials Gases are good3

electrical insulators However, when the potential between two electrodes is increasedsubstantially, a point is reached where ionization and the conductivity of the gas increasedramatically Electric current is conducted through the gas in this situation Because ofdifferent nature of ionization processes, there are different forms and characteristics ofcorona discharge such as sparks, arcs, coronas, and glow discharges [26]

2.2.2 Ionization processes

Once the voltage between two electrodes exceeds the corona onset voltage,molecules around corona electrode begin to ionize Electrons of these neutral moleculesgain enough energy from high electric field intensity and are peeled off from them tomove freely These electrons move fast toward one direction under the influence of theelectric field and the positive ions move in the opposite direction While moving, theycollide with other neutral molecules and may knock the electrons off them, too Electronsmoving with lower speed also could attach to certain gas molecules With high enoughvoltage, ionization is propagating dramatically, with the net result of a large amount ofelectrons and ions in the air Current flowing through these two electrodes can bemeasured and related to the density of moving charge carriers

2.2.3 Mathematical description of corona discharge

Townsend [27] investigated the ionization process and expressed the electronionization in a differential equation form as

where dn is the incremental increase in the number of electrons produced by n electrons

moving a distance dx in the electric field The coefficient α varies with the gas and is afunction of the electric field strength and gas density For a uniform electric field anddischarge conditions, α is also constant and (2.1) can be integrated to

0

x

where n is the number of free electrons at 0 x=0

In a more general case, where the field varies with x and α is also a function of x

0 0

strongly electronegative and act as effective electron traps in gas discharges [26].Electron attachment greatly reduces and counteracts electron ionization Electronattachment can be expressed as

0

x

where η is the coefficient of attachment, which depends on the gas and on the electric

field Combining (2.2) and (2.4), the value of n for uniform fields is:

( )

0

x

At low electric fields, η exceeds α , and the number of electrons declines with distance.

At the threshold value E , T η α= , and n remains constant At E E> T, α exceeds η, and

the number of electrons increases with distance [26]

2.3 Positive and negative corona discharges

There are two types of corona discharge: positive corona and negative corona.Polarity of corona discharge is determined by the sign of the voltage applied to the coronaelectrode Zeleny [28] described the striking difference in visual appearance between thepositive and negative corona The positive corona appears as a motionless, diffuse glowover the end of the point, while the negative corona appears as a localized brushoriginating from a tiny spot on the end of the point and spreading out into the gap infountain-shape form Fine wires exhibit the same general visual characteristics betweenthe positive and negative coronas For a given geometry, the corona onset voltage and theelectrical breakdown of the gas occur at higher voltages for negative corona than forpositive

Figure 2.7 Visual difference between positive corona and negative corona [28].

2.3.1 Positive corona

Positive corona has a very high positive voltage applied on the corona electrode, whichgenerates a strong electric field in its ambient atmosphere This field with high intensityionizes the air molecules into positive ion - electron pairs Electrons are drawn to thecorona electrode While moving, they bombard other neutral molecules and break them

into more positive ions and electrons All the positive ions are propelled toward thecollector electrode Positive corona is characterized by a smooth glow around the coronaelectrode

2.3.2 Negative corona

In the negative corona case, high intensity of electric field is also present around thecorona electrode, and the voltage applied to the electrode is negative Positive ion andelectron pairs are generated in the ambient atmosphere of corona wire, but this timepositive ions are attracted to the corona electrode and negative electrons are propelled tothe collector electrode Having much smaller mass, electrons move faster than ions Someelectrons attach to neutral air molecules and thus produce negative ions Negative coronashows as rapid dancing brushes It is characterized by intermittent Trichel pulses whichcan reach the frequency of 2 10× 5 cycles per second [29]

2.4 Theoretical current-voltage relationship

Current-voltage characteristics for the corona are functions of many variables whichinclude gas composition, gas temperature and pressure, electrode geometry, voltagepolarity, particles on the electrodes, and particle suspensions in the gas [26] Equationscan be derived for concentric cylinder electrodes, but for most other cases, therelationship can only be determined experimentally

The Poisson’s equation which governs all electrostatic phenomena is [30]:

2

4

where ρ is the space charge density and V is the electric potential

In cylindrical coordinates, assuming axial symmetry, θ and ϕ won’t affect the voltage

distribution, therefore, equation (2.6) reduces to

2 2

ρπ

where i is corona current, K is a constant, and

dV E

the corresponding radius is r Then 0 C can be expressed as

where a is the diameter of the corona wire, b is the diameter of the outer pipe, r is the0

outer radius of the plasma region around the wire and E is the corona initiation field0

strength at this point

According to Peek’s law, E is0

where

0 0

T P

T P

In equation (2.16), T is the absolute room temperature, 0 293K; P is the normal0

atmospheric pressure, 760 mmHg; T and P are the actual temperature and pressure of the air In (2.15), f is a roughness factor of the wire, which increases when the wire is rough, marred, or specked with dust The parameter f is usually between 0.5 and 0.7 for

dirty, scratched wire Corona initiation field strength E is also a function of gas density0

[26]

Corona initiation field strength is determined solely by the geometry of the coronaelectrode Corona onset voltage, on the other hand, is set by the design of both coronaand collector electrodes It can be calculated through (2.14) by setting i=0 and r0 =a

0 0logb 30 (1 0.30 / ) logb

2.5 Electric field distribution

Ions are generated in gas when the electric field exceeds the initiation field strength E 0

The electric field strength is determined by the geometric design and the operation of thedevice Eq (2.18) is a simple way to characterize the electric field

U E d

where U is the applied voltage on the corona electrode, and d is the distance betweenthe corona and collector electrodes The electric field is U s/ for plate-type and U r for/ 2

the tube-type designs, where r is the radius of the collecting tube This is an2

approximation since this equation only applies to electrodes with parallel plate geometry.The electric field is also affected by space charge distribution Therefore, a complicatediterative procedure to solve Poisson’s equation and the equation of space chargecontinuity is necessary To make the calculation easier, simpler approaches ignoring spacecharges or supposing a constant space charge distribution are utilized [31]

For tube-type electric field, the electric field strength for the coaxial geometrywithout considering space charge can be described as

( )

2 1

ln

U

E r

r r r

=

where U is the applied voltage, r is the corona wire radius, and 1 r is the radius of the2

collecting tube [31] Assuming a constant space charge distribution, Robison derived thedistribution as:

E is the corona initiation strength.

The electric field distribution can also be expressed in dimensionless form, which

is very helpful in comparing electric field strength with different electrode geometries.For the dimensionless electric field distribution without charge

( )

1

1' '

1' ln'

E r

r r

r r

= .For the dimensionless electric field distribution with charge

j

b U r

=

2.6 Enhancement of heat exchange through water

evaporation

In addition to cooling for electronics and MEMS through forced convection, it isalso possible to enhance heat exchange through the step of condensation in refrigerantcirculating system using electrostatic air pumps Evaporation of water droplets in theambient atmosphere of devices can enhance heat removal Like the compressor in therefrigerator, corona air pump can be used in the condensation process of the cooling cycle

to be used for cooling purpose Actually, dehumidification is also one major application

of corona air pumps

Currently available dehumidification equipment includes condensation-based ordesiccant based systems A condensation-based system chills the air below its dew point,causing moisture to form as condensation on the cold surface of the cooling coil and thusremoves water from the air The desiccant-based dehumidification system uses achemical to directly absorb moisture from the air while it is a vapor Both systems requiremultiple steps and significant additions to traditional HVAC systems Conventional solidand liquid desiccant systems generate heat when operating Besides, they require anadditional heat source to complete the collection and regeneration processes, whichresults in high energy consumption Moreover, current HVAC system in air conditionersrequires significant maintenance to prevent mechanical failure during operation Ahumidity control, air-cooling, air purification, and air movement all in one device wouldsave money, space, and energy The corona air pump is the alternative technology thathas the potential to fulfill all the above requirements

Neutral water vapor

Figure 2.8 Electrostatic dehumidification technology.

The mechanism of corona air pump is shown in Figure 2 8 Water vapor droplets

in the air are ionized as they pass through the high voltage plasma fan array, which iscomposed of corona electrodes and collector electrodes Then, ionized water vapor isdeflected by an electric field and forms larger droplets which fall out of the air Waterdroplets are then removed into a water collector Theoretical discussion on severalprocesses involved in this technology is given in the next few sections

2.6.1 Charging process

Analytical studies of the forces and the movement of water molecules in anelectrostatic field that exceeds the corona onset voltage have been conducted for manyyears and entered classical treatises [32] Several processes deserve attention becausethey are critical for application of electrostatic air pump in dehumidification Theseprocesses include field distortion due to space charge, dynamic force variation due toglobalization of aerosol particles, and interaction of ionic drag of non-polar gasmolecules and highly polar water molecules and droplets

The fundamental physics of the charging process of water droplets in corona field

has been studied extensively [26;33] Suppose that a water droplet is a sphere of radius a When the droplet is placed in a uniform electric field E 0 with an initially uniform unipolar

ion density n 0 , the potential distribution V is given by Poisson’s equation:

2

0

i

qn V

/ 4

E= −Ze πε a for Z charges ( Z >0 for positive charges and Z <0 for negative

charges) on the surface at any given time It is readily shown that at any point on thesphere,

where θ is the azimuthal angle in the spherical coordinate

The total electric flux ψ entering the molecular sphere is given by

E a Z

q

επε

where εr =ε ε/ 0, ε is the relative dielectric permittivity of water

The rate of charging is given by the charging current i ,

0

( )4

i

n qK d Ze i

dt

ψε

where K is the ion mobility Integration gives

a highly ionized gas They recognized that a sphere of radius a is negatively charged due

to greater mobility of electrons in comparison to ion mobility The electric drag force f q

is given by the following approximation to their numerical result [34]:

1/ 2 1

Here f is the total drag, f is the drag force of an uncharged sphere due to number Di

density n of ions or electrons; E is the ion kinetic energy relative to the sphere, i

The efficiency of the electrostatic pump in large part depends on the direction of

the forces acting on charged particles A figure of merit r proposed here is the integral

ratio of two orthogonal forces, with x-directed airflow:

x

mx lx mc

d

ly

E dx f

r r

This figure of merit can be estimated analytically only for the most primitiveelectrode arrangements, and is a strong function of space charge density In addition tocolumbic forces addressed in the previous equation, a more comprehensive figure ofmerit should include dielectrophoretic forces (connected to electric field gradient), andwith certain design, Biot-Savart forces (connected to magnetic field interaction withmoving charges).

2.6.3 Stability of a charged liquid droplet

Liquid droplets follow similar relations to those of a solid sphere except thatdeformation of a spherical droplet should be expected This phenomenon is particularlywell visualized in classic experiments with two transparent immiscible liquids, forexample, corn oil and water The surface tension of the water droplet acts against theforce of electrostatic repulsion of electric charges distributed over the surface of aconducting spheroid in an insulating fluid medium The ratio of the forces of electrostaticrepulsion over surface tension is usually denoted as the electrosurface number N , es

where σs is the surface tension

Rayleigh [35] found that a conducting spherical droplet is stable for N < 4 es

Aliam and Gallily [36] extended this stability criterion to cases of ellipsoids of

revolution Denote the principal axis along the axis of symmetry as c and the principal axis normal to the axis of symmetry as b If b > c, the droplet is an oblate ellipsoid, and when b < c, it is a prolate ellipsoid Suppose x = c/b, in which case the total energy can be called G1* in the oblate ellipsoid and G2* in the prolate ellipsoid For each

semi-es

N , there exists a minimum energy G1*min when x < 1 and G2*min when x > 1 Further

conclusion drawn by Soo [2] is that there might be a non-linear oscillation of a droplet

from a prolate to a spherical to an oblate form and back Also, normally G1*min > G2*min,which shows that prolate ellipsoid is more energy favorable as the steady droplet shape.Further, when the oscillation occurs, the charged droplet tends to shatter more oftenthrough stretching to prolate ellipsoid or rod shape, than to thin out to an oblate or disk

shape The form is very similar to a liquid filament As the droplet shatters, Nes of each

droplet is equal to the original Nes divided by the number of similar droplets produced by

2.7 Advantages of corona technology in micro-cooling

Although air velocity produced by the electrostatic air pump is incomparable to that

of conventional fans, the characteristics of generated airflow in the new device areadvantageous for heat sink cooling Two most significant positive aspects of thistechnology are (a) the ability to generate aerodynamic forces inside the narrow channelsand (b) the ability to remove the boundary layer at the interface of the heat sink and air

To understand the first property, visualize a conventional fan positioned above adense array of heat sink fins The pressure difference is generated at the fan blades, andthe flow stream tends to go around the closely positioned fins instead of penetratinginside and thus taking advantage of the increased total area of the heat sink On the otherhand, the forces that generate air movement are borne between the fins by coronaelectrodes The airflow in the narrow channels is much stronger and does not require highair speeds at the outer region of the heat sink, as it is shown in Figure 2 9 (The channelgeometry for computer chip cooling is discussed in Chapter 4.)

Corona electrode

Air/Ion flow trajectory

Collector electrodeCPU heat sink fin

High density electronicdevice with heat sink

Corona electrode

Air/Ion flow trajectory

Collector electrodeCPU heat sink fin

High density electronicdevice with heat sink

Figure 2.9 Corona air pump can be used for cooling of computer chips.

The distribution of electric potential around the shielding electrodes determinesthe exact pattern of air movement at the boundary layer When the corona electrode isinserted between the fins, with the collector electrode attached to the sidewall, the spacecharge is accelerated near the electrode surface The local columbic forces create local airmovement otherwise unobtainable with external to the channel air This can be seen inFigure 2 10 In traditional fan, a parabolic air velocity profile is formed due to viscouseffects, resulting in inefficient heat removal at the solid-fluid boundary Ionized airpropulsion counters much of the frictional losses because the local columbic forces tomove charged air molecules are applied inside the channel Thus, the corona driven pumphas much flatter flow profile, which greatly enhance the heat removal efficiency

Figure 2.10 Contrast of air movement profile difference between a

traditional fan and corona-driven pump

A very important advantage of the air pump is that it can be made into differentgeometry, shapes and sizes Corona electrodes can be made into tips, wires, edges ofrazors; collector electrodes can be made from films of different materials They can bebuilt in linear arrays to increase the airflow Also, corona driven pumps don’t havemoving parts This greatly reduces the noise that normal mechanical fan makes duringcomputer operation and thus provides a more quiet and relaxed working environment

A special feature of the corona air pump is that it can have very dynamic airflowprofile One way to change the airflow pattern is through changing the voltagedistribution applied on the device, which changes the ion moving trajectory andeventually the airflow pattern This can be seen from Figure 2 11

One of the promising approaches still subject to future exploration isagglomeration of water vapor into mist, in which case the proportional share ofdielectrophoretic forces grows For larger droplets, dielectrophoretic forces are moreeffective and may play a significant role in the dehumidification process The forcesshould be computed for typical electric field and electric field gradient values