Abstract

Circuit design for lab-on-a-chip diagnostic detection

Zachary A. Kobos

2018

Abstract goes here. Limit 750 words.

Circuit design for lab-on-a-chip diagnostic

detection

A DissertationPresented to the Faculty of the Graduate School

ofYale University

in Candidacy for the Degree ofDoctor of Philosophy

byZachary A. Kobos

Dissertation Director: Mark Reed

May, 2019

Copyright c© 2019 by Zachary A. Kobos

All rights reserved.

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Contents

Acknowledgements xiii

1 Introduction 1

1.1 Background and Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 What is a chip/integrated silicon electronics . . . . . . . . . . . . . . 1

1.1.2 What is diagnostic detection . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Methods of diagnostic detection . . . . . . . . . . . . . . . . . . . . . 3

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Economics of healthcare . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 Logistics of heath-care provision . . . . . . . . . . . . . . . . . . . . 5

1.2.3 Improvements in time-to-detection . . . . . . . . . . . . . . . . . . . 5

1.2.4 motivation for IC-compatible diagnostic detection . . . . . . . . . . 6

1.3 Outline and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Fundamentals of electrochemical impedance spectroscopy 8

2.1 Intro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 What is impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

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2.2.2 Circuit combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Impedance spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.4 Electrochemical impedance spectroscopy . . . . . . . . . . . . . . . . 12

2.2.5 Mathematics of EIS . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Physical phenomena and their discrete-element representations . . . . . . . 13

2.3.1 Key Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2 The metal-electrolyte interface/the Double Layer . . . . . . . . . . . 13

2.3.3 The Randles Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.4 The constant phase element . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 CIRCUIT MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.1 Nyquist and Bode Plots . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.2 The Randles Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4.3 Further variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Novel geometries for electrochemical impedance spectroscopy . . . . . . . . 24

3 Electrochemical impedance spectroscopy for biosensing applications 25

3.1 EIS for biosensing applications . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Silicon nanowires for EIS biosensing . . . . . . . . . . . . . . . . . . . . . . 26

3.2.1 what are silicon nanowires . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.2 The Debye Layer and ISFETs . . . . . . . . . . . . . . . . . . . . . . 29

3.3 The measurement of silicon nanowire EIS . . . . . . . . . . . . . . . . . . . 30

3.3.1 Fast Fourier Transform EIS . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Measurement apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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3.5.1 LBL on silicon nanowires . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5.2 DNA Hybridization . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.6 Forward guidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 Coulter Counter Fundamentals 46

4.1 Alternative applications of electrochemical impedance . . . . . . . . . . . . 46

4.2 The Coulter Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3 Design considerations for portable flow cytometry . . . . . . . . . . . . . . . 49

4.3.1 The fluidic constriction . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4 Design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4.1 Circuit architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4.2 Bridge component values . . . . . . . . . . . . . . . . . . . . . . . . 56

4.4.3 Operating frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4.4 Ramifications of planar electrode geometry . . . . . . . . . . . . . . 66

4.5 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.5.1 Microscope and stage mount . . . . . . . . . . . . . . . . . . . . . . 69

4.5.2 The electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.6 Calibration measurements - detection of polystyrene beads . . . . . . . . . . 75

5 Dielectrophoresis 76

5.1 Dielectrophoresis for lab-on-chip applications . . . . . . . . . . . . . . . . . 76

5.2 Derivation of the dielectrophoretic force . . . . . . . . . . . . . . . . . . . . 76

5.3 Realistic modeling of dielectrophoretic devices . . . . . . . . . . . . . . . . . 77

5.3.1 Developing the full circuit model . . . . . . . . . . . . . . . . . . . . 77

v

5.3.2 Ignored inductances . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.3.3 Ramifications for the capture force . . . . . . . . . . . . . . . . . . . 80

5.4 Experimental verification of the circuit model . . . . . . . . . . . . . . . . . 81

5.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.4.2 Lead-in width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.4.3 Finger length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.4.4 Channel width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.4.5 Number of fingers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5.2 Mitigating series resistances . . . . . . . . . . . . . . . . . . . . . . . 88

5.5.3 ramifications for Cox . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.5.4 Power transfer v. voltage . . . . . . . . . . . . . . . . . . . . . . . . 89

A Stuff 91

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List of Figures

2.1 a) b) c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Showing the difference between the physical structure of a) a MOSFET and

b) an ISFET. Passivation layers (orange) isolate the source and drain contacts

of the ISFET from the solution, and the gate electrode has been replaced with

a conductive solution with reference-electrode gating. . . . . . . . . . . . . . 27

3.2 A shift in the threshold voltage changes both the a) IDS−VGS characteristic

of the device b) the drain current at constant VGS . . . . . . . . . . . . . . . 29

3.3 Basic circuit model of the silicon nanowire operated as a biosensing ISFET.

Two DC voltage sources bias the gate (VGS) and drain (VDS). An AC stimu-

lus, VAC is superimposed upon the gate bias. The solution resistance, Rsoln is

in series with the parallel combination of the coating/membrane capacitance,

Cmem, the double-layer capacitance, CDL, and the charge-transfer resistance

of the coating, Rmem. Three additional capacitances (CGS , CGD, and Cox)

are included here. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 a) photograph showing the physical set-up for interfacing the silicon nanowire

devices. The gate electrode is shown inserted into the electrode tubing and

interfaced via alligator clip. The inlet tubing delivers solution to a microflu-

idic channel defined in PDMS and is surrounded by epoxy to prevent solution

leakage and passivate the source and drain contact pads of our ISFET, an

abstract schematic of which is shown in b) . . . . . . . . . . . . . . . . . . . 35

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3.5 The a) frequency sweep and b) DC gate bias are combined in c) a home-build

voltage adder to supply VGS to both d) silicon nanowire biosensing elements

(purple shaded regions). e) A DC sourcemeter supplies the constant VDS

while f) home-built voltage amplifiers (green shaded region) take the drain

current through each device and convert it to a voltage output recorded on

the g) four-channel oscilloscope. h) A user-written LabVIEW routine handles

measurement timing, data acquisition and digital signal processing. . . . . . 37

3.6 a) Abstract schematic of polyelectrolyte deposition on an ISFET in an mi-

crofluidic channel, and the resultant change in the b) real (solid) and imag-

inary (dashed) components of the device impedance model in response to

a change in Cmem. c) Imaginary component of the FFT-EIS spectra of a

single device being measured in buffer (magenta) to buffer with dissolved

PDDA (cyan). d) Plotting the center frequency of the peak in the imaginary

compononet of the FFT-EIS spectra for two devices (green, left y-axis and

lavender, right y-axis) for three alternating layers of polyelectrolyte. . . . . 40

3.7 a) DC LBL NW data. b) FFT-EIS LBL f0 over time from me, reproduced

from Fig. 3.6d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.8 a) Fluorescent microscope image showing enhanced brightness due to binding

of fluorescent DNA over two “active” devices (white circles). b) EIS spectra

for a control (blue) and active (brown) device both before (solid line) and

after (dashed line) flowing DNA in buffer. . . . . . . . . . . . . . . . . . . . 44

4.1 Abstract schematic of a three-electrode Coulter counter system in action

along with its signal response. a) A passing particle (purple sphere) nears

the sensing region within a fluidic channel before b) entering the sensing re-

gion between the left-most and middle electrode and subsequently c) passing

over the middle electrode before d) passing between the middle and right

electrodes and e) finally exiting the sensing region. f) The output signal

tracks this behavior as qualitatively shown. . . . . . . . . . . . . . . . . . . 47

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4.2 Conceptual schematic depicting the measurement circuitry . . . . . . . . . 49

4.3 a) Two resistors, R1 and R2, combine to form a voltage divider with an

output voltage Vout when driven by a voltage source VAC . b) An inverting

amplifier circuit. The operational-amplifier sources a voltage Vout such that

the inverting input (-) is also at circuit ground. The input voltage signal

drives a current to flow through R1, which must subsequently flow through

R2 due to the infinite input impedance of the op-amp. . . . . . . . . . . . . 54

4.4 a) Output differential signal (solid blue line) as a function of the ratio be-

tween the bridge (Rbr) and solution Rsoln impedances, assuming a 1% change

in impedance in one of the two sensing regions. Dashed red vertical lines indi-

cate where bridge resistor mismatch has decreased by a factor of 2. b) volume

displacement ratio as a function of particle diameter displacing solution in-

side a 20 µm x 20 µm x 17 µm fluidic constriction, the typical geometry of

our inter-electrode sensing region . . . . . . . . . . . . . . . . . . . . . . . . 58

4.5 Full circuit schematic of the measurement bridge circuit, incorporating the ca-

pacitance of the double-layer at the electrode-solution interface as well as two

additional parasitic capacitances: Csub, the capacitance between electrodes

through the substrate, and Cpara, the capacitance of the coaxial cabling used

for measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.6 Device impedance measurements taken without a chip connected, a dry chip,

and three concentrations of phosphate-buffered saline (PBS) to demonstrate

the effect of a) 2 µm of silicon dioxide versus b) an entirely-insulating glass

substrate for both low-frequency (LF) and high-frequency (HF) regimes. . . 64

4.7 a) computed impedance change for the b) sensing region circuit model in

response to a 1% change in solution resistance, demonstrating the signal

attenuation caused by the parasitic capacitance of the c) the silicon substrate

in contrast to d) devices fabricated on glass. Measurements for a 4.5 µm bead

in 0.01x PBS at 0.5 µL/min. for a 20 µm channel width and gap. . . . . . . 65

ix

4.8 a) top-down view of the lithographic definition pattern for two chips, each

of which contains several devices. b) PDMS (translucent grey) confines fluid

flow over our gold electrodes to a narrow width. Different devices on differ-

ent chips explored the ramifications of electrode transverse length, l, inter-

electrode gap distance, g, and the constriction width, width as indicated.

c) Optical micrograph of a freshly-fabricated electrode structure with a mi-

crofluidic channel aligned and bonded. . . . . . . . . . . . . . . . . . . . . . 66

4.9 a) conceptual illustration of the field lines emanating from the planar elec-

trode geometry, emphasizing how particle (purple spheres) vertical displace-

ment from the electrodes alters the density of field lines they will cross paths

with. b) COMSOL simulation of the electric field profile for a pair of planar

sensing electrodes generated by collaborators at the University of Alberta. . 67

4.10 a) simulation [?] of the impedance variation for an insulating sphere passing

over planar electrodes with a XX µm inter-electrode gap as a function of

vertical displacement from the electrodes and b) experimental data from a

bead transit event demonstrating the expected behavior. . . . . . . . . . . . 68

4.11 left) CAD schematic of the PCB stage-mount. The automated alignment

socket visible, recessed within the center groove. right) photograph of the

PCB stage-mount integrated with the microscope optics. The spring-loaded

pin array makes solid electrical contact with loaded chip. . . . . . . . . . . . 70

4.12 a) circuit diagram of the complete three-electrode structure, with all parasitic

capacitances made explicit. The middle electrode is driven by the sine wave

output of the b) function generator. The resulting voltage at the left and

right sensing electrodes is measured by the c) PCB-mounted instrumentation

amplifier before the signal is fed to the d) lock-in amplifier for demodulation.

The demodulated output signal from the lock-in amplifier is measured by e)

the oscilloscope which is programmatically controlled during acquisition by

f) MATLAB routines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

x

4.13 a) one of many consecutive data traces recorded during the course of an

experiment, containing many particle passage events. b) the transit time of

the bead is defined as the time elapsed between the two antisymmetric peaks

(crimson dots), and the peak height is the fitted height from baseline of both

peaks. The program aggregates this data from 102 − 104 fits and returns

a binned 2-D histogram, color-coded according to number of counts, shown

here for flowrates of c) 5.0 µL/min. and d) 1.0 µL/min. . . . . . . . . . . . 73

xi

List of Tables

2.1 Table to test captions and labels . . . . . . . . . . . . . . . . . . . . . . . . 10

xii

Acknowledgements

A lot of people are awesome. Probably your family, friends, advisor, and that one super

special high school teacher who believed in you.

xiii

Chapter 1

Introduction

Despite continued advances in the state of global healthcare, infectious disease remains

prevalent in the world today. These diseases are responsible for significant losses in quality-

adjusted life years, a measure of health outcomes that incorporates both mortality and

reductions in quality of life from less-than-perfect-health [?,?]. Reduction in infection rates

for the most prevalent diseases is a simple and effective method for improving the global

human condition. Reduction in total caseload depends on prevention of new infections,

recognition of infection within patients, and subsequently administering the necessary treat-

ment. Focusing on the need for disease recognition within the sick population, we want to

replace traditional methods of detecting infectious diseases within patients with measure-

ment techniques making use of integrated silicon electronics, colloquially referred to as a

lab on a chip.

1.1 Background and Context

1.1.1 What is a chip/integrated silicon electronics

Semiconductors are materials which fall between conventional insulators and metals in their

ability to conduct electricity. More importantly, the conductivity of semiconductor material

can be readily modified through the introduction of chemical impurities, allowing controlled

1

formation of electronic circuits. A chip is a flat piece of semiconductor material which can

have anywhere from several to hundreds and even thousands of such electronic circuits on it.

These circuits and the signals passing through them form the basis of modern electronics, the

backbone of which is the silicon wafer. Chips are designed and fabricated on silicon wafers.

Vastly complex circuits are built, layer-by-layer, through the deposition and patterning of

materials to form the circuit pattern. Doping, the aforementioned introduction of chemical

impurities, enables the creation of circuit elements. These elements are isolated from one

another through the deposition and growth of silicon dioxide as an insulator layer and

connected to one another through the deposition of metal. Photolithographic processing

creates the desired patterns. Masks selectively filter ultraviolet light onto the surface of

the wafer, creating a stencil pattern out of a protective chemical coating. Deposition then

proceeds through this stencil, which is subsequently chemically removed, leaving behind

the desired pattern of deposited material. The chips are then referred to as integrated

circuits, as the entire assembly is contained within one cohesive piece of material. In this

manner, highly complex circuits chips are created en masse on silicon wafers the size of

dinner plates. Chip sizes shrunk order of magnitudes over the decades, greatly enhancing

the per-wafer yield. Despite initial massive capital costs, great economies of scale are quite

possible. Depending on the complexity, integrated circuit chips can be had for anywhere

from a few pennies to a few dollars per chip (DEFINITE CITATION). Such a price point

would be quite competitive with healthcare administration costs [?,?].

The same forces behind the economies of scale yield high reproducibility from chip to

chip, trusting each integrated circuit to perform as expected. Once a tested design has

been packaged, the only real limits on portability are the power supply. Integrated circuits

designed to run off battery power can conceivably be taken anywhere. If the computing

power contained within a cell phone could be combined with integrated circuits capable of

performing diagnostic detection, it would significantly reduce the healthcare infrastructure

necessary to reach patients for some of the most prevalent diseases.

2

1.1.2 What is diagnostic detection

Diagnostic detection is the specific identification of the markers of an infectious disease

within the patient. The markers may be the pathogens (disease-causing agents) themselves,

or chemical signals or proteins produced by the body in response to the infection. The

presence of these markers enables specific detection, confirmation of the presence of a single

kind of infectious agent. EX: Tuberculosis test.

1.1.3 Methods of diagnostic detection

Pathogen detection has been accomplished traditionally via microscopy (CITATION or

culturing of bacterial cells (CITATION). Both pose their own obstacles. Microscope image

analysis by a trained professional remains the standard of care in much of the developing

world [?, ?]. In these environments, the demands on individual expertise and hardware

have already been targeted by engineers: microscopes obviated by smartphone cameras,

doctors in the field by remote transmission of acquired images, a.k.a. telemedicine [?].

Visual identification can confirm a suspected diagnosis but proves challenging when faced

with unknown pathogens given the genetic diversity of the microbial kingdom. Microbial

cultures, on the other hand, take a sample and amplify the population of infectious agent

over many cycles of reproduction. The significant scale in sample size allows small amounts

of sample to be tested against many different chemical recognition methods to elucidate

the identity of an unknown microbe [?]. However, culturing comes at a cost: the growth

time of the microbial culture [?, ?, ?]. Furthermore, not every pathogen of interest can be

cultured [?].

A new generation of diagnostic techniques emerged to overcome these limitations, no-

tably Polymerase Chain Reaction (PCR) and Enzyme-Linked ImmunoSorbent Assay (ELISA)

[?]. PCR extracts and rapidly amplifies specific genetic material within the sample [?,?,?].

The amplified material is then tested against a range of genetic recognition elements for

pathogen identification. For pathogens which cannot be cultured or require long cultivation

times, PCR is a significant upgrade on microbial cultures [?]. ELISA techniques dispense

3

the sample over an array of differing recognition elements [?]. Each region binds a spe-

cific analyte, if present in the sample. The first binding event enables binding of a second

recognition element, modified to include a fluorescent tag. After a final wash step, the user

measures a fluorescence intensity signal proportional to the initial concentration of target

analyte in the sample.

1.2 Motivation

Examining the trajectory of healthcare in the 21st century reveals a past laden with progress

in terms of our ability to diagnose and treat diseases. Nevertheless, the future remains ripe

with opportunity for further improvements. Particularly in the realm of pathogen detection,

there are three fundamental realms where device engineers stand to make significant contri-

butions: reduction in required infrastructure [?], reduction in procedural cost(CITATION?),

and reduction in time to diagnosis [?]. Strides made in any of the aforementioned target

areas produce significant benefits in terms of global healthcare access and outcomes [?]

(CITATION WHO preferably).

1.2.1 Economics of healthcare

Procedural cost and prerequisite infrastructure are commensurate, but not completely in-

terchangeable, aspects of healthcare provision. Healthcare services exist on a market across

many schemes for provider reimbursement (CITATION?). Provision is therefore sensitive to

the cost of services weighed against the impact on patient outcomes (CITATION). Reduc-

tion in cost lowers the threshold for marginal utility required to render a given procedure

the rational choice on a traditional supply and demand curve. This analysis treats health-

care services as a normal good a dangerous assumption. Demand is largely decoupled from

price on the supply curves of inelastic goods (CITE KENNETH ARROW). Reduction of

cost for services leading to improved outcomes directly benefits the consumer who able to

pay either cost. The consumer for whom only the reduced cost is within his ability to pay

benefits tremendously: the choice to seek treatment is no longer a priori made for them by

4

market forces.

1.2.2 Logistics of heath-care provision

Another significant determinant of healthcare outcomes is access to infrastructure. While

the new techniques eliminate the need for human visual expertise to achieve specific detec-

tion and enhanced performance compared to microbial culturing, the need for a fully-staffed

wetlab remains a significant barrier to access in underserved communities globally [?]. In

regions where providers are few and far-between, due to low density of population or capital,

patients face either long transportation times or the prospect of limited available services, if

not both. Reductions in the facilities required for diagnosis and treatment increase the ca-

pacity for providing care. TALK ABOUT BILL GATES FOUNDATION HERE. ZAMBIA

AFRICA PAPER AS WELL.

1.2.3 Improvements in time-to-detection

Pathogen-based diseases run similar courses through infected human hosts. Symptoms and

outcomes may vary wildly from disease to disease, patient to patient, yet in an abstract

sense the life-cycle of the illness remains the same (CITATION). Detecting pathogens prior

to the disease becoming fully-developed affords healthcare providers more time to inter-

vene [?]. Improvements in detection rapidity generally come about in one of two man-

ners(CITATION): either a new method is capable of detection at lower levels of signal (the

limit-of-detection, LOD) or the new method delivers results more quickly at the same sig-

nal level. Clinically, both pathways result in a faster diagnosis and thus a better prognosis.

Engineering procedures for resource efficiency reduces barriers in terms of cost and infras-

tructure; engineering new procedures for enhanced sensitivity should lead to reductions in

the time to diagnosis.

5

1.2.4 motivation for IC-compatible diagnostic detection

Integrated silicon electronics have persistently driven down the cost of computing power

since the onset of the silicon age. Integrated circuits deliver chips with excellent reliability

and scalability while reducing per-device cost on an absolute basis. The advent of portable

electronics has furthered the ubiquity and availability of processing power in our daily lives.

Developing biosensing modalities with electrical read-out and the capability of interfacing

with chip-based electronics bears a resoundingly clear impetus: structurally challenging cost

and infrastructure as barriers to healthcare access for millions worldwide [?].

This clarion call has been heard by researchers worldwide. Antibody-based detec-

tion [?,?,?] schemes have found multiple embodiments for electrical read-out. The blood-

glucose sensor for diabetes monitoring is the most iconic example [?]. Researchers have

also developed chip-level analogues of ELISA(CITATION) and PCR [?,?]. As long as the

impetus to improve healthcare provision remain, efforts to transduce biological interactions

into electrical signals will continue in the field.

Big idea: no need to pretreat blood sample *cell/biomarker separation : get it out of

particular environment and isolate it. Move sample of interest to another region/solution

that is easier to measure in

*concentration: perform a pseudo-culture by artificially boosting the density of a small

sample by aggregating all the cells of one DEP w/PCR to make life easier [?]

*people have been working on specific detection but its tricky and always room in the

inn for more specific detection as we seek

The application of electric fields in microfluidics is also significant because it led to

continuous cell separation systems capable to trapping bacteria or discriminating between

dead and live yeast [131-133]. [?]

6

1.3 Outline and scope

This dissertation presents work done to improve different electrochemical sensing modalities

in anticipation of their combination for true lab-on-a-chip device functionality, aiming to

combine cell sorting and counting with specific detection of target pathogens from whole

blood environments. I extend the research of this lab and biosensing researchers worldwide.

Counting and sorting are performed with gold electrodes. The initial proposed sensor for

detection is silicon nanowires; the optimal specific embodiment remains an open question.

The thesis is structured as follows:

Chapter 2 introduces the basic concepts of electrochemical circuits and discusses efforts at

specific detection.

Chapter 3 discusses the development of the cell counting circuitry used throughout the

work.

Chapter 4 elucidates the working principles for cell capture circuitry.

Chapter 5 presents the ramifications of capture circuitry parameters on capture perfor-

mance.

Chapter 6 demonstrates the combined application of counting and capture circuitry for

biosensing in high-salinity environs.

Chapter 7 summarizes the work presented in this thesis, revisiting specific detection progress

necessary to realize single-stream diagnostic potential.

7

Chapter 2

Fundamentals of electrochemical

impedance spectroscopy

(CITE: Lasia, Electrochemical Impedance Spectroscopy and its Applications)

2.1 Intro

We aim to develop biological sensing devices capable of being integrated with silicon elec-

tronics, reducing both the cost and infrastructure required for diagnostics. Therefore, we

must transduce biological recognition events into electrical signals for measurement. Biol-

ogy exists and happens within ionic solutions. Monitoring the electrochemical properties

of these solutions is the most direct avenue towards our desired sensing modality. Electro-

chemical impedance spectroscopy analyzes the response of ionic solutions to applied voltage

signals in order to measure the properties of interest.

8

2.2 Impedance

2.2.1 What is impedance

Impedance is opposition to current flow in response to voltage stimulus. Impedance is

an intrinsic property of electrical circuit components and is comprised of resistance and

reactance. Resistance is the simpler concept, a constant of proportionality describing the

components ability to resist charge passing through it in response to an applied voltage:

V = IR (2.1)

Reactance is the component of impedance which responds to time-varying voltages or

currents. The canonical reactances are capacitance and inductance. Capacitance refers to

the capacity to store charge. Consider the case of two parallel metal plates. In response

to a step input voltage applied across the plates, equal and opposite charges accumulate

on the adjacent plates until the voltage across the two plates is equal to the input voltage.

The process of charge build-up stores energy in the electric field between the two plates of

the capacitor, energy which can be dissipated in response to changes in the voltage across

the two plates. The current flowing in response is proportional to storage capacity of the

plates and the rate of change of the voltage signal:

I = CdV

dt(2.2)

where I is the current flowing through the capacitor, C is the capacitance, and dVdt the

time rate-of-change of the voltage across the capacitor. It can be seen from Eqn. 2.2 that

the more rapidly the voltage changes, the more current passes through the capacitor as

the electric field charges and discharges to react to the new equilibrium imposed by the

instantaneous values of the applied voltage. Thus is can be seen that the reactance (and

thus impedance) of an ideal capacitor decreases with increasing signal frequency.

Inductors are circuit elements which oppose any changes in the current flowing through

9

Circuit element Impedance Physical explanation

Resistor R AFGCapacitor 1

jωC ALA

Inductor jωL ALB

Table 2.1: Table to test captions and labels

them. As current passes through an inductor, energy is stored in a magnetic field in the

element. Changes in the amount of current flowing through an inductor generate a voltage

across the element that opposes the change in current flow:

V = Ldi

dt(2.3)

where L is the inductance, and didt the derivative of current with respect to time. The

voltage generated across the inductive element increases with more rapid current swings

as the energy in the magnetic field releases or accumulates to counter-act the changes in

current. Inductors therefore exhibit increasing impedance with increasing frequency.

2.1 lists the frequency-dependent impedances of the three basic circuit elements de-

scribed thus far. These relations are generated by inserting sinusoidal input signals into

the behavior-governing equations ??. The reactive elements impedance explicitly depends

upon the angular frequency of the excitation signal, ω, and j is the imaginary unit.

2.2.2 Circuit combinations

We have thus far considered the impedance of individual circuit elements and implicitly

acknowledged the existence of equipment capable of sourcing voltages and currents. Inter-

esting behavior emerges with the combination of circuit elements. Depending on the circuit

arrangement, all manners of frequency-dependent behavior can be constructed. In example,

circuits may permit signals only above or below a certain frequency to pass, or they may

reject all frequencies within or outside of a given frequency range.

INSERT FIGURE HERE: two impedance elements in series and two impedance elements

in parallel, with the equivalent impedances?

10

This frequency-dependent behavior occurs due to the differing frequency dependence

of the impedances in 2.1. Broadly speaking, circuit elements (and their commensurate

impedances) may be combined in one of two ways. If current must flow through one element

in order to then flow through another, those two elements are said to be inseries. If current

could, conceivably, go through either one of two elements as it passes through the circuit,

those two elements are inparallel. The impedance of elements in series add together:

Zseries = Z1 + Z2 (2.4)

The impedances of two elements in parallel add inversely: that is, the reciprocal of the

combined impedance is equal to the sum to the reciprocals of the two parallel elements

impedances:

1

Zparallel=

1

Z1+

1

Z2(2.5)

2.2.3 Impedance spectroscopy

Working back through a circuit, these impedances can be combined again and again until

the entirety of the circuits impedance has been captured in a single, frequency-dependent

equivalent impedance. This single equivalent impedance contains all the information nec-

essary to compute the circuits response to a given input current or voltage signal.

This procedure is well and good for analysis of a known system. Often, however, the

internal workings of the system of interest are not known apriori. For linear systems

INSERT RELEVANT DEFINITION OF LINEARITY we can construct an equivalent

circuit model that effectively captures the circuit behavior, even if the precise internal

workings are unknown [?]. We measure the unknown circuits impedance at a given frequency

by monitoring the output voltage in response to an input current signal at a that frequency.

Repeating this procedure over a range of frequencies maps the impedance as a function of

frequency, a process broadly known as impedancespectroscopy.

11

The researcher then proposes a circuit model which should qualitatively reproduce the

observed impedance behavior. Treating the individual component values as fit parameters,

the circuit model is then fit to empirical data. If a reliably good fit is achieved, the researcher

can use this model to predict circuit response within the range of mapped frequencies.

2.2.4 Electrochemical impedance spectroscopy

Performing impedance spectroscopy on metal electrodes in ionic solutions is known as elec-

trochemical impedance spectroscopy (EIS). EIS is a widely-used technique for characterizing

material systems such as: [?] protective organic coatings on metal electrodes [?,?], recharge-

able batteries (CITATIONS), and fuel cells(CITATIONS). The substrate electrodes, coating

materials, and other chemical treatments all impact the observed electrochemical behavior.

Structural properties such as coating adhesion and defects, interface reactivity, and solution

permeability are then inferred from changes in the EIS results.

2.2.5 Mathematics of EIS

EIS characterizes an electrochemical system by measuring the current, i (t), flowing in re-

sponse to a small-amplitude linear voltage perturbation, v (t) over a wide range of signal

frequencies. Successive application of sinusoidal frequencies(CITATIONS) or Fourier trans-

formation(CITATIONS) of the time-domain excitation and response yields the frequency-

dependent impedance, Z (ω) = v (ω) /i (ω) governing the electrochemical system. The

researcher then proposes a circuit model to explain the electrochemical behavior, following

two principles [?]. First, each element in the proposed model must be grounded in the

physical principles underlying the system. Second, the model must be as simple as possible

within acceptably small error. Physical properties of the electrode-solution interface are

then extracted [?] from the proposed circuit model used to interpret these results.

Circuit models generated without any reference to the system producing the data serve

as nothing more than heuristics for describing a response. If the researcher desires to extract

truly meaningful information about the system under examination, each discrete element

12

within the circuit model must serve to represent some phenomenon or subcomponent of

the device under test. To develop the intuition for these attributions, we must understand

the physical processes which take place at the metal-electrolyte interface and elaborate the

surface science contained within.

2.3 Physical phenomena and their discrete-element repre-

sentations

2.3.1 Key Parts

Electrodes

Insert section on electrodes: working, reference, pseudoreference counter Electrodes are

indispensable in the performance of EIS measurements. An electrode is a material which

(GET DEF AND CITE). The working electrode is the metal electrode whose electrode-

solution surface is being probed (CITE). Reference electrodes establish in the solution a

potential with respect to a known thermodynamic equilibrium (CITE). Quasi- or pseudo-

reference electrodes function similarly in establishing a steady potential but do not provide a

true equilibrium, and instead must be referenced back to some known equilibrium indirectly

(create ref: https : //doi.org/10.1007/978 − 3 − 642 − 36188 − 314). Counter electrodes,

occasionally encountered in the literature, are large-area pseudoreference electrodes capable

of sinking large amounts of current if those current magnitudes are necessary to establish a

stable solution voltage (CITE DUH).

2.3.2 The metal-electrolyte interface/the Double Layer

FIGURE: METAL INTERFACE, IHP, OHP, with PSI(X) OVERLAIN

When a metal electrode is immersed in an electrolytic solution, an electrical double

layer forms at the metal-electrolytic solution interface: mobile charge carriers gather near

the surface of the metal electrode, and an ionic distribution within solution which coun-

13

terbalances that charge [?]. Our understanding of the nature of this ionic distribution has

evolved [?, ?, ?, ?] with continued study of the surface science involved. The ionic distri-

bution includes ions adsorbed on the metal surface, a diffuse region incorporating solvated

ions of both polarities, and neutral molecules which influence the interface interactions [?].

For an ideal metal electrode, no charge crosses the interface while establishing equilibrium

independent of the potential applied across the solution and electrode [?]. One consequence

of this, arising from the thermodynamics of the interface, is the notion of a differential

capacitance:

−dqdE

= C (2.6)

where q is the surface charge density of the metal, and E the potential difference between

the electrode and solution. This differential capacitance is highly nonlinear in the applied

potential and reflects changes in the structure of the ionic distribution.

The Helmholtz Planes

Helmholtz proposed a model for the solution side of the interface comprised of two distinct

planes of ions, henceforth the inner and outer Helmholtz planes (CITATION). The inner

Helmholtz plane is comprised of the adsorbed ions, whether due to covalent bonding or

van der Waals forces [?]. Solvated and hydrated ions in contact with, but not adsorbed

to, the mercury surface form the outer of the two Helmholtz planes [?]. The differential

capacitance is dominated by the contribution of the inner plane, typically 32-34 µF/cm2

for a wide range of sodium chloride under conditions of minimal ion adsorption.

Guoy-Chapman-Stern Layer

Electrostatic and thermodynamic interactions govern the behavior of the diffuse double

layer outside of the Helmholtz planes. The diffuse double layer consists of ions, mobile

in solution, which gather with sufficient charge density to counterbalance the portion of

14

the metal electrodes surface charge not neutralized by the Helmholtz planes [?]. Mathe-

matical description of the diffuse double layer is constructed through the combination of

electrostatics, Poissons equation:

d2Ψ(x)

dx2=−ρ

4πεrε0(2.7)

and Boltzmanns equation:

ni = n0ie−qziεrε0Ψ/kT (2.8)

where ψ(x) is the potential at a distance x from the metal-solution interface taken

relative to the bulk of the solution, ρ the charge density of the ions in solution, and ni

the density of ions per unit volume for all points with potential ψ. This model neglects

the work necessary to for an ion to displace the solvation shell of another ion as it closely

approaches the metal electrode. The model therefore cannot be applied at distances closer

than the outer Helmholtz plane. The ion density and charge density are intimately related.

Substituting 2.8 into 2.7 and introducing a summation over ion species:

d2ψ(x)

dx2=−qεrε0

∑i

n0izie−ziqψ/kT (2.9)

from whence

(dψ

dx

)2

=

(nd

εrε0

)2

=−2kT

εrε0

∑i

n0izie−qziψ/kT (2.10)

And thus we find nd, the surface charge density of the electrical double layer, the total

charge per unit area in the column of liquid extending from the metal-electrode interface

to the bulk solution:

nd =

√2kTεrε0

∑i

n0izie−qziψ/kT (2.11)

15

And in the case of a simple monovalent system:

nd = −4kTεrε0n0i sinh qziψ/2kT (2.12)

The integral capacitance of the diffuse layer is simply ?? divided by the potential at the

outer Helmholtz plane. The differential capacitance is then:

Cd = −2qεrε0n0i cosh qziψ/2kT (2.13)

These capacitances are quite large and in series with the capacitances between the metal

surface and the outer Helmholtz plane. Therefore, the capacitance between the OHP and

the metal surface dominates contributions.

The Debye Layer

It remains to be seen how the potential decays as one moves into solution from the metal-

electrode interface. The previous derivation of the diffuse layer differential capacitance

considers the potential to be a known independent variable. We must return to that deriva-

tion to obtain an expression for the position dependence of the potential within solution.

Combining 2.10 and 2.12, we find:

dx = −√

εrε08kTn0i

csch

(qzψ

2kT

)dψ (2.14)

We can thus solve for the potential as a function of distance from the electrode-solution

interface, introducing the constant x∞, the distance from the interface at which the hyper-

bolic tangent would become unity and therefore ψ(x) is infinite, assuming the differential

equation were valid for all x.

x− x∞ = x = −√

εrε02kTn0iz2

ln

(tanh|| qzψ

4kT

)(2.15)

16

For large values of x− x∞, the potential takes the form:

ψ (x) = ±4kT

zqe−κx (2.16)

Which has not yet been subjected to any boundary-matching conditions at the interface.

The constant Debye-Hckel length, κ, has been introduced, which dictates the decay length

of the electrostatic field due the space charge of the ionic layer, and depends upon both the

valence and concentration of mobile ions:

κ =

√2n0iz2q2

εrε0kT= 3.28z

√cinm

−1 (2.17)

At 25 C, where ci is the molar concentration of the solvent ion. At distances beyond

the Debye length from the outer Helmholtz plane, charges are effectively entirely screened

by the mobile ion distribution.

2.3.3 The Randles Circuit

The Randles circuit is the fundamental circuit model employed for analysis of electrochemi-

cal circuits. Alternative models encountered in the literature are variations on /the Randles

model with increasing amounts of complexity as dictated by the physical realities of the

system. To better understand how these physical parameters are extracted from fitting to

circuit models, let us now consider the theory expounded by J.E.B. Randles in 1947 [?].

Randles originally investigated the consequence of applying a small alternating potential

to a liquid mercury electrode in an aqueous solution [?]. Consider a small concentration of

metal ions in solution, which can react:

Mn+ + ne←→M (2.18)

with a low concentration, C, of metal ions dispersed in the aqueous solution, and

identically-low (for simplicity) concentration of metal atoms in the liquid mercury electrode.

17

An additional ionic species, which does not participate in the metal ionization reaction, is

present to prevent migration of ionized species along a potential gradient.

Biasing the mercury electrode until ionization reaction is at equilibrium, we apply a small

sinusoidal voltage perturbation, v = V cos (ωt) between the mercury electrode and ionic

solution with radial frequency ω. A small current flows, i = I cos (ωt+ φ) at some phase φ

with respect to the voltage signal. The harmonic current oscillation establishes sinusoidal

variations in the concentration of the metal in the mercury, δC1 = ∆C1 cos (ωt+ θ) where

∆C1 is the amplitude of the concentration oscillation at the metal-solution interface and θ

the phase of the oscillations with respect to the applied potential.

Solving the drift-diffusion equation subject to the boundary condition at the interface

gives rise to decaying waves in the metal species conductivity for increasing distances from

the metal-solution interface, x:

δC1,x,t = ∆C1e−√

ω2D1

xcos

(ωt−

√ω

2D1x+ θ

)(2.19)

where D1 is the diffusion constant of metal ions in the mercury electrode. Differentiating

2.19 with respect to displacement from the electrode-solution interface gives the velocity of

metal atoms within the waves, and thereby the current:

i = nFAD1∆C1

√ωD1

2cos(ωt+ θ +

π

4

)(2.20)

wherein n is the number of electrons per ionization reaction, F is Faradays constant,

and A the area of the mercury electrode. Compare this with the prediction of the Butler-

Volmer equation(CITATION), assuming the potential drops evenly across the metal-solution

interface:

i = nFAk(

[C1 − δC1] evnF2RT − [C1 + δC1] e

−vnF2RT

)(2.21)

where T is the temperature and R the ideal gas constant. The prior assumption of small

18

amplitude for the modulation voltage, v, permits linear approximation for the exponential

terms. Differentiating both 2.20 and 2.21 with respect to time, both expressions may be

expanded into sums of cosωt and sinωt. A sequence of algebraic manipulations leads to

ratio between the amplitudes of the sinusoidal current and voltage signals:

I

V=n2F 2AC

√ωD/2

RTsinφ (2.22)

where

cotφ = 1 +1

k

√ωD

2(2.23)

Thus, the current response due to the redox reaction occurring at the solution-electrode

interface leads the voltage perturbation applied to the system. Thus, Randles proposed

modelling the circuit as a series resistance and capacitance, from which one could compute

the presence of the redox reaction:

RRandles =RT

n2F 2AC

(√2

ωD+

1

k

)(2.24)

and

CRandles =n2F 2AC

RT

(√D

2ω

)(2.25)

Notice that both the first term in the series resistance (2.24) and the series capacitance

(2.25) bear a magnitude dependence proportional to the square root of the perturbation

frequency. This is quite unlike their macroscopic circuit element counterparts and arises

from the solution of the diffusion equation, as ionic diffusion is the proposed mechanism of

charge transport in Randles model. Further observation reveals striking similarities in the

structure of the two terms, and we may rewrite the total impedance of the electrochemical

system as:

19

RRandles +1

jωCRandles=

RT

n2F 2AC

1

k+

RT

n2F 2AC

√2

ωD(1− j) = Rct +

ZW√ω

(2.26)

where the impedance contributions have now been explicitly separated into terms with

and without frequency dependence, and j is the imaginary unit. The first term in 2.26 is

the charge-transfer resistance, Rct, which is dictated by the kinetics of the reaction occur-

ring at the metal-electrode surface. The second term is the frequency-dependent Warburg

impedance, ZW , arising from the diffusion of ions over a semi-infinite length from the metal-

solution interface.

DISCUSS consequence of changes in A, D, C for signal

2.3.4 The constant phase element

Figure: circuit diagrams of the Randles and variants

The model of the double layer and diffuse ion regions predict differential capacitances

to arise at the metal-electrolyte interface, with impedances inversely proportional to the

excitation frequency. Empirical reality has stubbornly refused to comply with theory, ne-

cessitating the concept of the constant phase element (CPE) in EIS analysis [?, ?]. The

impedance of the constant phase element may be expressed:

ZCPE =1

Q0 (iω)n(2.27)

Where n is a frequency-independent constant ranging from 0 to 1, and Q0 is the pseu-

docapacitance and also independent of frequency. The impedance of the CPE recovers

resistive (capacitive) behavior in the limit n goes to 0 (1) but typically ranges from 0.8-0.9

in experimental conditions. It is an explicit decision to invoke pseudocapacitance in naming

this constant. The constant phase element phenomenon is thought to arise from physical

inhomogeneities at the electrode surface, giving rise to a local dimensionality interpolant

between 2- and 3-D [?,?]. Conway [?] first demonstrated remarkably large electrochemical

20

capacitance with porous electrode structures, enabled by rapidly reversible redox reactions

and anomalous dimensionality thereof. Conway referred to these structures as pseudoca-

pacitors for their atypical mechanism of action [?].

2.4 CIRCUIT MODELS

Equipped with an understanding of how different physical processes produce different elec-

trochemical behavior, researchers can then extract meaningful information with sound in-

tuition and parsimonious choice of equivalent-circuit models. In the following section, I will

outline how the impedance data is conventionally represented and discuss commonly-used

circuits for modelling the empirical data.

2.4.1 Nyquist and Bode Plots

Nyquist and Bode plots have their origins in system control theory [?], conveying the output

response of a linear, dynamic system to a time-varying input signal of a given frequency [?].

The complex-valued ratio of the system output to system input is referred to as the transfer

function. For the purposes of EIS, the complex-valued impedance is the transfer function

describing the output current in response to an excitation voltage.

Rsoln

RmemCmem

a) b)

Figure 2.1: a) b) c)

21

Nyquist plots present the real and imaginary portion on the x- and y-axes. Because

electrochemical impedance spectroscopy involves with capacitive loads almost to exclusion,

the imaginary impedance is traditionally inverted when presenting the data. Each data-

point is the response at a single frequency frequency varies along the curve of a Nyquist

plot. An ideal resistor results in a single dot along the x-axis, whereas a lone capacitor

produces a vertical line approaching the x-axis as frequenchy increases in contrast to the

Warburg element, which produces a line of unity slope. In control theory, Nyquist plots

are a convenient means of visualizing the stability of the system response [?]. In the realm

of electrochemical impedance spectroscopy, charge transfer processes manifest as semicir-

cular arcs modeled as a parallel combination of a resistor and a capacitor. The radius and

x-intercepts of these arcs contain valuable information about the reaction process itself.

2.4.2 The Randles Circuit

The Randles circuit is the fundamental circuit model employed for analysis of electrochem-

ical circuits. Alternative models encountered in the literature are variations on the Randles

model with increasing amounts of complexity as dictated by the physical realities of the

system. The Warburg impedance, ZW and the charge-transfer resistance, Rct, as derived

by Randles [?] are placed in parallel with the interfacial capacitance of the ionic double layer

(a conductive electrolyte is an assumed prerequisite for EIS). These impedance elements,

representing the surface phenomena of the system, are then placed in series with a solution

resistance, Rs, governed by the bulk conductivity of the electrolyte solution.

FIG: RANDLES CIRCUIT WITH ZW INCLUDED, NYQUIST SHOWING BEHAV-

IOR FOR ZW AND ALSO ILLUSTRATING WHAT HAPPENS IF YOU SET IT TO

ZERO

One of the most common assumptions in the literature [?] is that of the rapidly-reversible

reaction. If the kinetics are rapid enough, the coefficient of the Warburg element is assumed

to be negligible with respect to the charge transfer resistance, further simplifying the circuit

behavior. This assumption may be justified for a given system provided the excitation signal

22

does not extend to arbitrarily low frequencies. ??a illustrates the Randles circuit model

with the Warburg impedance incorporated, and ??b demonstrates the ramifications of this

assumption for the Nyquist plot.

2.4.3 Further variations

Embedded Randles’ Circuits

FIG: Circuit model for embedded v sequential Randles’ circuits

Particularly in the study of multi-layered coatings, multiple redox reactions will appear

between the solution and the working electrode []. Depending on the nature of the system,

these may appear as either sequential [?] or embedded [] copies of the single Randles’ circuit

when modeling the device performance data.

Redox-less EIS

In the absence of redox reactions at the electrode-solution interface, the charge-transfer

impedance (Rct) of the Randles’ model becomes effectively infinite under normal operating

conditions. When this condition is satisfied, such as in the absence of redox-active species []

or in the presence of a protective insulating layer such as a high-quality oxide [], the circuit

model for the interface simplifies greatly. The double-layer impedance in series with the

solution resistance comprises the entirety of the model.

Alterations of the double layer

Sample fabrication procedures also alter the circuit models necessary to effectively capture

sample behavior. The double-layer capacitance term in the Randles’ model may need to be

replaced with a constant-phase element, as previously discussed, depending on the geometry

of the working electrode.

23

2.5 Novel geometries for electrochemical impedance spec-

troscopy

The conventional schema for electrochemical impedance spectroscopy is the reference elec-

trode as the source of the voltage signal and current flow through the working electrode the

measured output. Counter electrodes provided a necessary current source/sink to maintain

the established solution potential. This protocol produces a vertical, layered hierarchy:

current flows from an external electrode, through solution, through the electrode/solution

interface, to the working electrode. Such an approach is well-suited to the study of coatings

and macroscopic phenomenon.

A different paradigm is required for studying microscopic phenomena with EIS [?,?,?].

Researchers turned to interdigitated electrodes (IDEs), fabricated with gaps as narrow as

a few microns [?] to provide a new impedance sensing element. The small gap sizes greatly

mitigates the influence of ion diffusion time for redox reactions at either surface [?]. The

interdigitated, planar electrode geometry greatly enhances the surface-area-to-volume ratio

of the sensor, while the reduced overall dimension greatly improves the sensitivity to small

changes at the electrode-solution interface [].

FIG: top-down v. IDE EIS and circuit models.

The transition to IDE-based impedance sensing does not alter the fundamental physics

behind the surface phenomena being studied. Due to the symmetry of the electrode struc-

tures, the circuit models themselves remain almost entirely unchanged: the additional copy

of the metal/electrode interface model is indistinguishable from multiplying all fit parame-

ters by a factor of two. There is one exception. A self-capacitance of the electrodes coupled

to themselves through the substrate material must also be introduced [?].

24

Chapter 3

Electrochemical impedance

spectroscopy for biosensing

applications

3.1 EIS for biosensing applications

After decades monitoring surface properties for industrial applications, electrochemical

impedance spectroscopy expanded to the realm of biological detection [?,?]. Surface coat-

ings for industrial applications were replaced with biological recognition elements. Biological

recognition elements are chemical modifications bound to the electrode surface which are

capable of binding to a specific biological target. The binding event should then produce

some change in the metal-electrode interface, altering the measured impedance spectra.

Common recognition elements (and their biological targets) include antibodies (anti-

gens) [?, ?, ?, ?, ?, ?, ?, ?, ?], single-stranded DNA (DNA strands, genetic markers) [?, ?, ?,

?, ?, ?, ?, ?, ?, ?, ?, ?, ?], aptamers (molecules) [?, ?, ?, ?, ?, ?, ?], peptides () [?, ?, ?, ?, ?, ?],

and enzymes (substrates) [?, ?, ?]. Researchers made use of both conventional top-down

EIS in bulk solution [?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?] and microfabricated electrode struc-

tures [?,?,?,?,?,?] as well as some more exotic sensing element designs [?,?,?,?] depending

25

on the specific needs of the system. LOD, sample volume, chemistry concerns

The vast majority of the literature makes use of so-called Faradaic EIS, in which re-

dox reactions proceed at the electode-solution interface. Changes in the reaction rate are

monitored through the EIS measurement and used to infer changes in the electrode coating

coverage. Biological systems do not inherently lend themselves to Faradaic EIS, and there-

fore researchers resort to introducing redox-active ionic species, known as redox markers,

to introduce this signal into their data [?,?,?,?,?], even in so-called label-free approaches.

The necessity of the addition of the redox marker to the sample introduces an extra ad-

ditional step for diagnosis, hindering adoption in portable systems. Potassium ferrocyanate,

or Prussian blue, is the canonical redox marker. Some researchers [?] have found that the

introduction of potassium ferrocyanate interferes with DNA/protein binding interactions,

interfering with the very kinetics they aim to measure. For others, the dissociated metal

ions of the redox agent leads to aggregation of the biomarkers, yielding the same deleterious

effect [?]. Overcoming these limitations requires a different approach, non-Faraidaic EIS:

electrochemical impedance spectroscopy without the use of redox markers [?].

3.2 Silicon nanowires for EIS biosensing

3.2.1 what are silicon nanowires

Silicon nanowires are field-effect transistors with nanometer-scale dimensions. A transistor

is a three-terminal device where the current flowing between two terminals is controlled

by an electrical signal at the third. Silicon nanowires are a type of transistor known as

a metal-oxide-semiconductor field-effect transistor (MOSFET). The effect of the electric

field produced by the third terminal generates the transistor behavior. This third terminal,

known as the gate, is typically a metal electrode which is electrically isolated from the semi-

conductor material underneath by a passivating oxide layer. The semiconducting material,

for our applications silicon, forms a channel between two other terminals, the source and

drain.

26

source gate drain

substrate

channel

source

gate

drain

substrate

channel

b)a)

MOSFET ISFET

Figure 3.1: Showing the difference between the physical structure of a) a MOSFET and b)

an ISFET. Passivation layers (orange) isolate the source and drain contacts of the ISFET

from the solution, and the gate electrode has been replaced with a conductive solution with

reference-electrode gating.

Silicon nanowires, used for biosensing, are designed as ion-sensitive field-effect transistors

(ISFETs) [?]. ISFETs are MOSFETs sans a metal gate electrode. The metal gate electrode

has been replaced by a reference electrode in a conductive solution which controls the

potential at the solution-oxide interface. Silicon nanowires offer particular appeal as ISFET

biosensors due to their large surface-to-volume ratio and ease of fabrication compared to

traditional, bulk ISFETs [?].

In the operating regime of our silicon nanowire biosensors, the current between the

source and drain terminals may be expressed as:

IDS = µCoxW

L(VGSVT )VDS (3.1)

where IDS is the current between the source and drain terminals, µ the mobility of the

charge carriers in the silicon, Cox the capacitance of the oxide per unit area, W and L

the width and length of the nanowire channel, VGS the electric potential at the gate with

respect to the source and VDS the electric potential at the drain with respect to the source.

VT is the threshold voltage, the voltage necessary for conduction between the two terminals

to occur, and is given by:

27

VT =ΦEl − ΦSi

q−ΨEl −Ψ0 + χsoln − σox

Cox(3.2)

where ΦEl,Si is the work function of the reference electrode in solution and the silicon,

respectively, ΨEl the potential drop at the solution-reference electrode interface (constant

for a true reference electrode) and χsoln the surface dipole moment of the solution. The last

remaining term, Ψ0, is the potential drop at the oxide-solution interface and is a function

of the bare surface charge. Psi0 is the only variable term within the threshold voltage for a

fixed VDS [?]. Thus we see via Eqn. 3.1 that by monitoring the source-drain current flowing

through an ISFET, we can measure changes in the bare surface charge on the oxide due to

changing pH or the binding of small molecules to the surface.

Differentiating Eqn. 3.1 with respect to the applied gate voltage, we obtain the transcon-

ductance, gm of our device:

gm =δIDSδVGS

= µCoxW

LVDS (3.3)

Provided a stable drain-source voltage, the transconductance of a silicon nanowire IS-

FET is a constant depending on the details of its fabrication. If VGS is held fixed at the

reference electrode, changes in the drain current are solely due to shifts in the threshold

voltage, and therefore:

∆Ψ0 =∆IDSgm

(3.4)

Changes in the bare surface charge change the y-intercept of the IDS-VGS curves of the

device, as can be seen in Fig. 3.2.

28

a) b)

∆IDS∆VT

Figure 3.2: A shift in the threshold voltage changes both the a) IDS − VGS characteristic

of the device b) the drain current at constant VGS .

3.2.2 The Debye Layer and ISFETs

Detection of binding events proves more challenging in physiological saline concentrations.

In solution, an electrical double layer forms at the oxide-solution interface, as previously

discussed in section (TRACK DOWN). The width of the Debye layer depends on the con-

centration of mobile ions in solution, per Eqn. ??(FROMCHAP2). In physiological saline,

this width is less than one nanometer. Thus, binding events of small and highly charged

molecules are feasible [?]. However, detection of larger charged molecules such as protein

antigens is strongly precluded by the screening of the double layer. To overcome this limi-

tation, researchers have resorted to sample dilution or chemical desalinization [?,?,?]. The

function and therefore sensitivity of antigen-binding interactions can be compromised in

lowered-salinity environments [?]. Additionally, such approaches significantly complicate

detection procedure at point-of-care or device construction or both, a significant drawback

to adoption for widespread commercial use.

Past approaches to overcome Debye layer screening for ISFET sensors in physiological

salinities attempted to modify the ratio of the sensing element to the Debye length, either

through the use of protons [] (pH sensing), engineering smaller antigens [], or more recently

29

by engineering surface treatments to extend the effective Debye length [?].

Borrowing concepts from EIS, researchers [?, ?] abandoned the concept of a constant

excitation signal. Exploiting the finite mobility of dissolved ions in solution, they stim-

ulated nanowire sensors with high-frequency signals. At elevated frequencies, the mobile

ions forming the double layer are not able to fully adjust their spatial distribution to screen

out the electric field, allowing the electrical signal to (partially) penetrate the double layer.

Biosensing via electrochemical impedance spectroscopy of silicon nanowires presented the

possibility of simultaneously avoiding the inherent drawbacks from redox markers in con-

ventional biosensing EIS while simultaneously overcoming Debye layer screening limitations

from DC approaches to nanowire biosensing.

3.3 The measurement of silicon nanowire EIS

Following previously-reported results utilizing nanowire ISFETs as impedimetric biosen-

sors [?,?,?], we imposed an AC modulation atop a fixed DC bias applied to the reference

electrode in solution. Oscillations in the solution gate voltage would be mirrored in oscil-

lations in the drain current through a frequency-dependent transfer function of the silicon

nanowire (SiNW) transconductance, provided a constant bias is maintained between the

source and drain electrodes. The high quality of the gate oxide on the nanowires obviates

the need for a counter electrode, as very little current flows through solution [?].

30

+

-VAC

VGS

Rsoln

Rct CDLCmembCGS CGD

VDS

Figure 3.3: Basic circuit model of the silicon nanowire operated as a biosensing ISFET.

Two DC voltage sources bias the gate (VGS) and drain (VDS). An AC stimulus, VAC is

superimposed upon the gate bias. The solution resistance, Rsoln is in series with the parallel

combination of the coating/membrane capacitance, Cmem, the double-layer capacitance,

CDL, and the charge-transfer resistance of the coating, Rmem. Three additional capacitances

(CGS , CGD, and Cox) are included here.

The circuit model presented in Fig. 3.3 is predicated upon extant models for interpreting

silicon nanowire ISFET data in the literature [?, ?, ?, ?, ?]. The presence of chloride ions

in solution allows the Ag/AgCl reference electrode to establish thermodynamic equilibrium

at the interface. The acqueous solution volume between the reference electrode and the

nanowire interface presents a finite solution resistance, Rsoln. The silicon nanowire ISFET

is coated in a biological recognition element, presenting a finite charge-transfer resistance

Rmem and capacitance Cmem of the membrane coating, in parallel with with double-layer

capacitance CDL of mobile ions near the solution-oxide interface.

The remaining circuit elements presented in Fig. ?? are three coupling capacitances

common to MOSFET models. CGD and CGS reflect the capacitance between the solution

gate and the ISFET source or drain, respectively. Lastly, there’s the capacitance of the

high-quality dielectric forming the gate oxide of our silicon nanowire biosensors, Cox.

31

3.3.1 Fast Fourier Transform EIS

Electrochemical impedance spectroscopy evaluates the complex impedance of the device

under test as a function of frequency. Conventionally, this is done by application of a sin-

gle, small-amplitude sine wave perturbation at a given frequency. The response is recorded

and the frequency is subsequently changed to the next measurement point. This approach,

single-sine EIS, is adequate for measurements where the system can reasonably be expected

to remain (quasi-)static over the course of the measurement and duration of the measure-

ment is not a significant concern. Depending on the sensitivity required of the system and

the number of data-points to be acquired, these measurements can require times of 2-30

minutes to acquire.

Systems that do not satisfy the quasi-static requirement (or whose dynamics are of

interest require reduced measurement times. Researchers thus experimented with multi-

sine approaches [?, ?], wherein the device was simultaneously excited with sine waves of

several frequencies simultaneously. With this approach, electrochemical impedance spectra

can be recorded across a range of frequencies fairly quickly. However, the measurement

apparatus constrains the number of frequencies that can be interrogated.

Fast Fourier Transform EIS (FFT-EIS) overcomes these limitations [?]. Simultaneously

measuring the input signal and system response for excitations with a broad spectrum of

frequency components, researchers can probe the frequency response over a wide range of

frequencies at once. Conceptually an extension of the multi-sine approach, three broad

categories of excitation signals are used: white noise, step functions, and frequency sweeps.

Generated from a random or pseudo-random voltage source, white noise has a flat power

density it contains an equal signal amplitude at all frequencies. It provides a uniform input

signal upon which the system impresses its output response. White noise excitation has

two significant limitations. Excitation power provided at frequencies outside the range of

measurement frequency or frequencies of interest is effectively wasted. Furthermore, the

Johnson noise of a resistor, such as an unterminated voltmeter input or a low transcon-

ductance nanowire also has a white-noise spectrum. Selection of an AC excitation with a

32

distinct qualitative shape serves as a straightforward control to validate signal input/output

during measurement operation.

Measuring the complex impedance maps the output response, typically a current, as

a function of the input stimulus, typically a voltage signal. This frequency-dependence

response the transfer function of the system. In principal, the entirety of the transfer

function can be mapped from monitoring the system response to an impulse function, an

infinitely narrow peak of finite amplitude. An impulse function, like white noise, contains

components at all frequencies. While impulse functions are difficult to realize empirically,

excellent sources of step functions abound. A step function is the time-domain integral of

an impulse function. Conversely, therefore, differentiating the time-domain signal from step

function recovers the system impulse response. While this approach has been used with

some success [] the differentiation process heightens the measurement sensitivity to noise.

Swept-sine signals are an interesting solution for measuring system impulse responses

adopted from the realm of audio engineering [?] performance analysis. Swept-sine signals

modulate the input with a sine wave whose frequency is an explicit function of time. Con-

ventionally, the frequency is either a linear:

f (t) = fstart + (fstop − fstart)t

T(3.5)

or exponential:

f (t) = fstart

(fstopfstart

) tT

(3.6)

function of time, wherein fstart and fstop are the start and stop frequencies of the

sweep, respectively, and T the duration of the measurement. A linear sweep also has a flat

power spectrum, akin to a white noise excitation, however this condition only exists within

the range of frequencies dictated by the sweep parameters. The exponential sweep has a

constant power density per decade of frequency.

Conventional EIS sweeps are performed with a fixed number of datapoints per decade

33

of frequency, whereas computed FFT amplitudes are linear in frequency. For cleanliness of

visualization and to enable direct comparison to conventional EIS approaches, we binned

our FFT amplitudes into bins with exponentially-increasing widths. We thereby obtained

an output spectrum with a fixed number of datapoints per decade, as desired. Thus we chose

an exponential sweep profile for our stimulus, as each binned datapoint would correspond

to the same amount of input signal power across the measurement range.

The frequency limits of the measurement are bounded by the signal-recording appa-

ratus. The sampling interval determines the maximum frequency component permissible

per the Nyquist criterion. The lower bound is conversely determined by the measurement

interval, with longer acquisition durations extending the lower frequency limit. Broadband

signal components in the mHz regime are therefore computationally prohibitive in a single

measurement with kHz regime frequencies.

Nevertheless, over our region of interest (10 Hz 100 kHz), we were able to acquire spectra

in 0.2 1.0 s, improving upon our single-sine comparison by roughly three orders of magni-

tude. Due to this measurement duration, traditional single-sine approaches are restricted

to either dichotomous before-after measurements or evaluation of processes over hundreds

of hours. We can therefore use our FFT-EIS infrastructure to measure real-time binding

kinetics of different receptor-target interactions in physiological ionic concentrations.

Differential measurement

The FFT-EIS measurement routine was designed to simultaneously acquire EIS spectra

of two devices, allowing for real-time monitoring of both active detection elements and

control devices. This measurement architecture provides robustness against false positives

for detecting small changes in the biosensor response.

34

3.4 Measurement apparatus

drainsource

gatea) b)

gate

PDMS

epoxy

Figure 3.4: a) photograph showing the physical set-up for interfacing the silicon nanowire

devices. The gate electrode is shown inserted into the electrode tubing and interfaced via

alligator clip. The inlet tubing delivers solution to a microfluidic channel defined in PDMS

and is surrounded by epoxy to prevent solution leakage and passivate the source and drain

contact pads of our ISFET, an abstract schematic of which is shown in b)

The devices

Over the past three years, my thesis research has been conducted with the support of a

biological diagnostics company, QuantuMDx, who provided us with the silicon nanowire

devices used for many of our lab’s biosensing experiments. The QuantuMDx devices were

fabricated in state-of-the-art cleanroom facilities, resulting in excellent performance. A more

thorough description of the fabrication protocol, not relevant to discussion here, is provided

in my colleague’s thesis [?]. Eliminating the demand to provide my own devices allowed me

to focus strictly on development of the measurement apparatus for silicon nanowire EIS.

Fig. 3.4 illustrates the standard protocol for interfacing our devices for measurement,

directly adapted from the implementation of DC, amperometric (current-based) nanowire

sensing. We attach the silicon nanowire chip to a 28-pin ceramic chip carrier package,

wirebonding a number of the silicon nanowires to the package leads. The package is then

35

loaded into a zero-insertion-force (ZIF) socket (Fig. 3.4a, green). Each pin of the package

is thereby connected to a BNC coaxial connector mounted on the metal box, as can be seen

in the lower-left. All 28 coaxial connectors share a common ground which is isolated from

the metal housing to allow for construction of a Faraday cage to shield the wiring from

electromagnetic interference.

Rather than being immersed in a fluidic reservoir for sample delivery, we actively flow

solution over the silicon nanowire surface during our sensing experiments. Polydimethyl-

siloxane (PDMS) is a malleable and inert polymer compound commonly used in biological

experiments. The blocks are cast with a mold whose imprint defines the geometry of the

microfluidic channel. The PDMS microchannels allow continuous, controlled delivery of

sample while inhibiting changes in sample conductivity over long time-scales due to evapo-

ration, a common problem in previous reservoir-based experiments.

Semiconductor Parameter Analyzer

Prior to FFT-EIS measurement, the IDS − VGS characteristic of each device was measured

with an HP4156B semiconductor parameter analyzer at a constant VDS of 0.5 V. Mea-

surements were taken both before and after introduction of buffer solution into the fluidic

channel.

36

OUT

TRIG

YOKOGAWA 7651

KEITHLEY 2400

+-

+-

CH1

CH2

CH3

USB

++

RctRct

Rsoln Rsoln

Rf Rf

Cf

Ctot

a)

b)

c)

CfCtot

d)

f)

e)

g)

h)

Figure 3.5: The a) frequency sweep and b) DC gate bias are combined in c) a home-

build voltage adder to supply VGS to both d) silicon nanowire biosensing elements (purple

shaded regions). e) A DC sourcemeter supplies the constant VDS while f) home-built voltage

amplifiers (green shaded region) take the drain current through each device and convert it to

a voltage output recorded on the g) four-channel oscilloscope. h) A user-written LabVIEW

routine handles measurement timing, data acquisition and digital signal processing.

Voltage sources

The DC gate voltage and AC stimulus were sourced from a Yokogawa 7651 DC generator

and Agilent 33120A function generator, respectively. The two signals were combined in a

PCB-mounted home-built voltage adder circuit designed by a former undergraduate stu-

dent in the group. This signal was delivered via alligator-clip connection to an Ag/AgCl

pseudo-reference electrode contained within the microfluidic inlet tubing. A Keithley 2400

sourcemeter provided a constant VDS of 0.5 V to both active devices at once.

Voltage read-out

The drain terminal of both devices under test was connected to the inverting input terminal

of two nominally-identical PCB-mounted inverting amplifiers with a 100 kΩ feedback resis-

37

tor, followed by a unity-gain inversion stage to rotate the signal 180. The analog output

signal from each channel was simultaneously recorded by a Tektronix DPO4104 oscilloscope,

along with the input voltage stimulus.

Programmatic control

Programmatic control of the measurement process was handled in user-written LabVIEW

code. Instruments were interfaced via GPIB or USB serial interfaces. TTL triggering

synchronized excitation and acquisition timing to ensure that the full stimulus response

and only the full stimulus response were recorded.

Time-stamped acquisitions were performed every 10s, with both active devices excited

and recorded simultaneously. Data transfer of recorded traces occurred during the down-

time between measurements. The sampling rate-duration product to achieve the desired

frequency range produced data arrays which would quickly overwhelm system working mem-

ory and consume all available storage space over the course of a measurement time-series.

Multiple levels of digital signal processing occuring in real-time greatly reduced memory

demands. The first stage computed the FFT-EIS spectra and performed the exponential

binning, reducing the array sizes to a few hundred integers apiece. The second stage per-

formed complex non-linear least-squares fitting of the computed FFT-EIS spectra to extract

fit parameters for the ISFET circuit model. The acquisition routine could be conducted

with none, the first, or both of the analysis stages depending on measurement and user

demands.

3.5 Experimental results

Establishing FFT-EIS as a superior methodology to amperometric DC measurement of sil-

icon nanowire biosensing requires extensive validation through carefully-conducted control

experiments. Throughout the development process, we made comparisons to both conven-

tional EIS and DC nanowire sensing measurements to assess viability of the technique.

38

3.5.1 LBL on silicon nanowires

Biological recognition elements should produce alterations in the surface charge at the oxide-

solution interface upon target binding. A conventional simulacrum is layered deposition of

highly-charged molecules onto the device. Polyelectrolytes are polymer compounds which

become highly charged in aqueous solution. The sign of the charge depends upon the

chemical structure of the molecule which in turn dictates the direction of the expected

threshold voltage shift for a silicon nanowire sensor. The high charge density and large

fractional surface area coating produces clear, reversible response as alternatingly-charged

layers are deposited onto the device. This process is refered to as layer-by-layer (LBL)

deposition.

39

Rsoln

RmemCmem

PSS

MES

PDDA

a) b)

d)

flow

c)

Figure 3.6: a) Abstract schematic of polyelectrolyte deposition on an ISFET in an mi-

crofluidic channel, and the resultant change in the b) real (solid) and imaginary (dashed)

components of the device impedance model in response to a change in Cmem. c) Imaginary

component of the FFT-EIS spectra of a single device being measured in buffer (magenta)

to buffer with dissolved PDDA (cyan). d) Plotting the center frequency of the peak in

the imaginary compononet of the FFT-EIS spectra for two devices (green, left y-axis and

lavender, right y-axis) for three alternating layers of polyelectrolyte.

Two oppositely-charged electrolytes, polystyrenesulfonate [?] (PSS) and poly(diallyldimethylammonium

chloride) [?] (PDDA) were diluted at 1 mg/mL into buffer solution containing 140 mM

sodium chloride and 10 mM 2-ethanesulfonic acid (MES) buffer. We performed continu-

ous sample flow in a microfluidic channel to match experimental conditions undertaken by

40

another member of the group, Luye Mu.

The Ag/AgCl reference electrode was inserted into the inlet tubing of the channel to

establish the global gate voltage. The choice of gate voltage was determined from measure-

ment of the IDS − VGS characteristic at a constant VDS of 0.5 V. Previous members of the

group found that maximal sensitivity to surface charge variation occurs in the subthreshold

regime of the drain current response [?]. This measurement is therefore essential in selecting

the proper operating conditions prior to introduction of the polyelectrolytes.

An alternating sequence of buffer-PSS-buffer-PDDA-buffer was repeated multiple times.

Stokes’ law [?] predicts that settling rate of particles in aqueous solution is proportional to

the fourth power of the radius. The large size of the polyelectrolyte compounds minimizes

their settling time, even in the presence of steady laminar flow within the channel. At the

oxide-solution interface, coulombic interactions between the charged polyelectrolytes and

surface charge on the oxide promotes adhesion, illustrated in Fig. 3.6a.

A change in the electrical properties of the oxide-solution interface alters the impedance

spectrum. Fig. 3.6b demonstrates this principle for a change in the interfacial capacitance

of the inset circuit model. The real component of the impedance transitions from the

sum of the membrane (Rmem) and solution (Rsoln) resistances at low frequencies to simply

the solution resistance at high frequencies where the membrane capacitance (Cmem) has

effectively shorted the membrane resistance. The interpolant region, the impedance of the

circuit is dominated by the parallel combination of the membrane resistance. The reactance

of the circuit has a maximum in this regime which shifts from f0 to f1 with the change in

Cmem.

The shift in peak frequency is observed during polyelectrolyte solution on our silicon

nanowires. Fig. 3.6c demonstrates this process occuring for the device in buffer (thick

magenta trace) until PDDA in solution passes over and is deposited on the surface (cyan).

FFT-EIS spectra were acquired once every ten seconds. The first and last traces are high-

lighted to emphasis the transition, and the remaining traces fairly tightly overlap into two

groupings. Only a single intermediary spectra is observed, highlighting the rapidity of the

41

transition. In contrast to simple example shown in Fig. 3.6b, the amplitude and frequency

of the reactance peak changes, indicative of changes in Rct.

Another important feature to note in Fig. 3.6c is the presence of significant spikes in

the low-frequency regime of the spectrum. These spikes occur at frequencies of 60, 120, and

180 Hz and originate due to interference from harmonics of the power mains. The multiple

layers of shielding implemented in Fig. 3.4a were constructed in response to this signature.

The main determinant of this noise signature was physical proximity of the microfluidic

pump to the device itself. The power supply of the pump was not designed with respect

to electromagnetic interference, radiating noise at 60 Hz into the environment. For the DC

amperometric sensing apparatus, the deleterious effect of the microfluidic power supply was

markedly attenuated both low corner frequency (1.6 Hz) of the low-pass filter signal con-

ditioning and time-domain averaging of the voltage signal during measurement acquisition

which further suppresses periodic noise and random noise.

Beyond observing a single transition of poly-electrolyte binding, Fig. 3.6d contains

simultaneously-recorded data from two devices for a repeated LBL deposition spanning the

course of three hours. The device was initially measured in buffer. The fluidic condition was

alternated every 600 seconds in order PSS-buffer-PDDA-buffer for three full cycles. The

roughly thirty minutes delay between the start of the experiment and the arrival of the first

buffer solution reflects the long length of inlet tubing necessary to isolate the device from

the power supply of the microfluidic pump.

Device 1, in green, exhibits a clear alternating response. The peak frequency increases

as PSS (solid blue line) accumulates on the surface, decreases as some PSS washes away

in buffer (dashed black line) flow, decreasing again as PDDA (solid red line) flows over the

surface and then increasing again as some PDDA is washed away in buffer. Device two, in

lavender, exhibits a much sharper step response to the first and third PSS conditions but

an over-all noisier response.

42

a)PSS

MES

PDDA

b)

Figure 3.7: a) DC LBL NW data. b) FFT-EIS LBL f0 over time from me, reproduced from

Fig. 3.6d.

Fig. 3.7 contrasts the performance of b) FFT-EIS vs. a) traditional amperometric silicon

nanowire sensing measurements. Both datasets have been linearly detrended to correct for

long-term drift typically seen in silicon nanowire ISFET measurements [?].

The frequency responses of device 1 and device 2 are plotted on separate y-axes (left

and right, respectively). Closer inspection of Fig. 3.7b reveals two common problems

which beset silicon nanowire FFT-EIS. Device one’s response to the alternating solutions

is synchronous with recorded solution exchanges initially. Solution exchange inevitably

introduces a small air bubble, the presence of which is used to track the initial time delay

between the first solution exchange and the solution arriving in the channel. Subsequent

exchanges result in multiple small bubbles in the tubing due to the length of the inlet,

rendering this approach impractical for their timing.

A small time-delay can be observed between the expected arrival of the second PSS

condition and the observed device response, propagating along to all subsequent conditions.

The surface tension of bubbles in the microfluidic channel would often cause them to become

temporarily stuck, disrupting the linear flow rate in the tubing and introducing the observed

delay in the experimental data. The coincident response of both devices to the third PSS

condition exemplifies the nature of this delay.

43

Of far greater concern is the distinction between the qualitative behavior of the two

devices. While the silicon nanowires exhibited great uniformity when measuring their IDS−

VGS behavior in solution, devices exhibited peak frequencies ranging from a few hundred

Hz to nearly ten kHz. The origin of this dispersion was not resolved but typically devices

with peak frequencies in excess of 3 kHz, such as device two, exhibited markedly poorer

response characteristics, as can be observed.

The signal-to-noise of the layer-by-layer response is much higher for the DC method

as opposed to the FFT-EIS response. Polyelectrolyte deposition brings the highly-charged

molecules directly in contact with the oxide interface. The extracted signal for ampero-

metric sensing is the DC current flowing through the device, rather than a superimposed

perturbation over a broad range of frequencies as for FFT-EIS. Therefore, it is not neces-

sarily expected that FFT-EIS would outperform in these contexts.

3.5.2 DNA Hybridization

a) b)

Figure 3.8: a) Fluorescent microscope image showing enhanced brightness due to binding

of fluorescent DNA over two “active” devices (white circles). b) EIS spectra for a control

(blue) and active (brown) device both before (solid line) and after (dashed line) flowing

DNA in buffer.

44

During the construction and testing of the FFT-EIS infrastructure, a single-sine approach

utilizing lock-in amplifiers was also implemented for more direct comparison to our collab-

orators’ results. Fig. 3.8 contains preliminary data illustrating successful detection of DNA

binding with the single-sine EIS approach in our lab, confirmed with optical detection of

fluorescence signatures. The DNA, with a stock concentration of µM , was diluted XXX-

fold in 1.0x SSC buffer and flown over the device for ZZZ minutes. Device performance was

measured before and after exposure to DNA in the 1.0x SSC buffer.

The EIS spectra acquired via single-sine techniques exhibit no shift in peak frequency

for the control device (blue) before (solid line) and after (dashed line) flowing buffer solu-

tion with target DNA. Compare this to the active device (brown) demonstrating a clear

shift in peak frequency of 100 Hz. At this time, our collaborators had not been able

to demonstrate this with DC approaches, motivating the aforementioned development of

the FFT-EIS infrastructure for real-time detection of the binding kinetics to cement the

technique.

Failure to reproduce

3.6 Forward guidance

* FFTEIS dies here - 1 MHz to lock ions? / compute Debye screening frequency - PEG

layer instead -reliability, reproducibility - attempt nonfaradaic EIS w/gold IDEs to overcome

redox issue * EIS dead and buried, still move on towards other electrochemical

45

Chapter 4

Coulter Counter Fundamentals

4.1 Alternative applications of electrochemical impedance

Electrochemical impedance spectroscopy (EIS) has been used successfully to probe the elec-

trical properties of electrode-solution interfaces. Circuit models for EIS examined changes

over time in the circuit elements modeling the surface properties over the system. The

solution resistance remained static throughout the analysis.

Inverting this paradigm on its head leads to an entirely new sensing modality, wherein

changes in the solution resistance between electrodes informs the researcher of physical

changes occurring in the sensing region. This idea underpins the Coulter principle [?,?], in

which the sensing element is the solution resistance of a narrow fluidic constriction between

two electrodes. Particles passing through the constriction red blood cells were the initial

target alter the volume of conductive fluid within the constriction. The significant disparity

in particle and solution conductivities produces a change in the channel impedance for each

passage event, proportional to the displaced volume of solution. Monitoring the impedance

of the channel in real-time results in brief pulses containing constriction-dependent infor-

mation about the number, size, and velocity of particles involved.

46

a) b) c)

d) e)

a

b

c

b

e

Figure 4.1: Abstract schematic of a three-electrode Coulter counter system in action along

with its signal response. a) A passing particle (purple sphere) nears the sensing region

within a fluidic channel before b) entering the sensing region between the left-most and

middle electrode and subsequently c) passing over the middle electrode before d) passing

between the middle and right electrodes and e) finally exiting the sensing region. f) The

output signal tracks this behavior as qualitatively shown.

Fig. 4.1 depicts the process by which a typical Coulter counter signal is generated in

a three-electrode geometry. The left- and right-most electrodes serve as sensing elements,

monitoring the impedance between them and the middle electrode at which an external

voltage is applied. As the particle approaches and enters the sensing region formed between

the left-most and middle electrodes, the solution resistance is increased due to the volume

displaced by the particle. As the particle passes back over the middle electrode, the solution

resistance returns to its normal operating state. The same process happens as the particle

flows between the middle and right-most electrodes before finally exiting the sensing region.

The output of this configuration is a voltage signal proportional to the difference in resis-

tance between the left and right sensing regions, whose time-domain behavior during such

a transit event is shown.

47

4.2 The Coulter Principle

Wallace H. Coulters initial paper [?] described a benchtop instrument capable of obtaining

cell size distributions on a half-milliliter sample in a matter of minutes. Orders of magnitude

increases to the sample size and elimination of human error from visual counts greatly

improved test-retest validity for obtaining red blood cell counts. The principle of size-based

discrimination to differentiate between cell species was also outlined: the mixture of sheep

or goats blood to a human blood sample produced a separate identifiable peak in the cell

size distribution, as well as tumor cells floating in the bloodstream.

The first Coulter counter was not without its limitations. The desire to improve per-

formance has driven efforts to reduce the aperture size of the fluidic constriction and with

it the minimum particle diameter that can be detected [?, ?]. Approaches to reduce the

frequency of clogging [?, ?, ?] and identify multi-particle passage scenarios [?] have been

necessary to improve throughput.

The past decade has seen an expansion of interest [?,?,?,?,?,?,?,?,?,?,?,?] in developing

Coulter counter-based devices no longer confined to the laboratory benchtop.

*Electrode geometries []

*Elevated frequency for discriminating based upon cell properties [?,?,?,?,?,?]

*Use of EIS for monitoring cell health/population size/bulk enumeration [?,?,?,?,?,?]

4.2.1 Principle of operation

Our particle counter device also employs the Coulter principle. Impedance-based cytometry,

the use of electrical signals to count cells, remains a promising candidate for portable, lab-

on-a-chip form factors. The advantages that Wallace Coulters method held over visual

or photoelectric approaches have been amplified by the revolution in integrated circuits

that has taken place over the past six decades. Component reliability has increased, cost

decreased, and computational power for sizing has expanded exponentially.

Desire to build a low-cost and portable flow cytometer has driven myriad design choices

48

throughout the development of our device. In the following sections, I will discuss the

operating principle of our device and elaborate on the logic underpinning the aforementioned

choices. The terms particle and cell will be used interchangeably throughout this discussion.

The small capacitance of cell membranes gives the appearance of an insulating particle in

the measurement signal for sufficiently low operating frequencies, typically below 1 MHz.

4.3 Design considerations for portable flow cytometry

The measurement circuit

RsolnRsoln

V1

RbrCbr VACRbr

V2

V1

V2

+

-IN

X

Y

0000 0000

a)

b)

c)

Figure 4.2: Conceptual schematic depicting the measurement circuitry

Our impedance-based flow cytometer adopts a three-electrode design, conceptually modeled

after the cytometer presented by N.N. Watkins, et al., among others [?,?]. The circuit, as

depicted in Fig. 4.2, operates as an impedance bridge. A time-varying excitation signal

(VAC) at the middle electrode drives current flow through solution to the left and right

sensing electrodes. Each of the sensing electrodes is connected to circuit ground by a resistor,

henceforth referred to as the bridge resistor (Rbr). The potential that forms at each sensing

electrode (V1, V2) is governed by the ratio of the bridge resistor to the solution impedance

(Rsoln) between the excitation and sensing electrodes. Under ideal operating conditions,

the solution impedances and bridge resistors are perfectly symmetric and thus both sensing

49

electrodes are at identical potentials. When a non-conductive particle passes between the

excitation and one of the sensing electrodes, the solution impedance is temporarily increased,

changing the voltage measured at the sensing electrode. The process repeats as the particle

subsequently passes between the excitation electrode and the second sensing electrode. In

this manner, a passing particle generates a characteristic voltage signal encoding information

about both its velocity and its size.

The AC approach

Employing a time varying voltage signal simplifies measurement logistics compared to direct

current (DC) approaches. Reference (or pseudo-reference) electrodes are necessary to estab-

lish stable DC potentials in solution [?,?] and therefore present a trade-off between simplicity

of design and measurement capabilities. A drifting DC potential will complicate measure-

ment attempts, presenting a constantly-moving baseline for event recognition. Steady-state

sensing approaches typically employ potential magnitudes which are prohibitively large from

a supply power standpoint in portable systems.

As previously discussed, at sufficiently low frequencies the cell membrane capacitance

renders cells electrically indistinguishable from insulating particles. However, researchers

have also begun to use elevated frequencies in the MHz regime as part of their excitation

signal. At elevated frequencies, the impedance of the membrane capacitance is significantly

reduced, allowing researchers to probe the inner conductivity of the cell. In this manner,

cell populations of comparable size but differing in physiology may be discriminated from

one another, enhancing the counters capabilities.

Microelectrode design

The implementation of planar microelectrodes for impedance-based sensing confers multiple

advantages over more complicated geometries. The electrode definition requires only a few

steps, metal deposition, pattern definition, and a subsequent chemical etch. This simplicity

compared to alternative electrode geometries significantly reduces per-device fabrication

50

cost. The ease of fabrication conceptually simplifies challenges inherent in combining the

impedance sensor with additional sensing modalities (e.g., target capture, target recogni-

tion) into a single microfluidic sensing platform, a highly desirable functionality [?].

The extended emphasis on design simplicity suggests that elimination of the third elec-

trode in favor of a two-electrode approach is preferable. Indeed, such implementation is

observed in much of the early Coulter counter work [?, ?, ?]. The third electrode offers

significant improvements to the sensor functionality that should not be understated. The

additional resistive sensing element formed by the third electrode transforms the char-

acteristic output signal from a single voltage peak to an antisymmetric peak structure.

The elapsed time between the local maxima and minima of the antisymmetric structure

reduces uncertainty in transit time measurements during flow conditions, compared to ex-

tracting particle velocity information from the full-width at half-maximum (FWHM) of a

two-electrode configuration.

The anti-symmetric nature of the output signal lowers the systems detection threshold,

enabling enumeration of smaller targets under fixed channel geometries and flow conditions

than a simple two-electrode structure. The antisymmetry of the expected waveform for

particle detection allows for coincidence-based detection, rejecting single spikes in either

direction arising due to measurement noise, device handling, or changes in fluid flow rate.

The addition of a third electrode also allows for differential measurement, a well-established

technique for reducing measurement noise. The two solution impedance elements formed

between the middle and the left and right electrodes, respectively, are nominally iden-

tical under all flow conditions. Monitoring changes in the difference between these two

impedances greatly enhances sensitivity by reducing the background signal upon which the

transitory resistive pulse of a passing bead is imposed.

51

4.3.1 The fluidic constriction

Constriction diameter and signal magnitude

Design of the fluidic constriction is an integral aspect of the microfabricated Coulter counter

performance. The Coulter principle depends upon the displaced volume of conductive

solution by a passing particle. Therefore, the ratio of the volume of the sensing region to

the target analyte strongly determines sensor performance. To estimate the magnitude of

this effect, consider a spherical particle passing through a cylindrical volume of conductive

solution. The effective change in solution resistance of the cylinder is given by [?,?]:

Eqngoeshere (4.1)

where . The choice of cylindrical geometry is a simplifying assumption, but nevertheless

Eqn. 4.1 illustrates the strength of the dependence. We immediately see why we desire to

confine the conducting volume between our sensing electrodes. With solely this constraint

in mind, the constriction diameter should be roughly in equal to the diameter of the largest

analyte body in the envisioned end-user sample.

Matching the diameter of the constriction to the largest target analyte maximizes sen-

sitivity for a given heterogenous sample. It assumes that no debris larger than the largest

analyte exists in the solution, or else the debris must be filtered out upstream of the con-

striction region to prevent it from blocking the channel.

Constriction diameter and clogging probability

A blocked channel effectively halts the device′s ability to count particles until the block

is removed, rendering the device ineffective. It also presents a biohazard for devices with

actively-driven fluid flow. Large hydraulic pressures build up in the channel as fluid con-

tinues to be pumped. The resultant pressures can cause catastrophic containment failure

of the fluidic channel. When dealing with samples in sterile buffer, this is merely a failed

device. Containment failures represent a significant biohazard to the end user when dealing

52

with biological samples, however.

FIGURE: Show conceptually one bead then three beads trapped in a counter, as well

as an image of a full-on jam from microscope capture.

Large debris in the sample is not the only culprit for clogged microfluidic constrictions.

During normal operation, there is a finite probability that an incident particle will adhere to

the side-wall of the channel. As the fluidic channel narrows down to the constriction diam-

eter, wall-particle interactions become increasingly likely. A common failure mode observed

in our fluidic channels is one such event failing to become unstuck before a subsequent par-

ticle enters and adheres to the first. An aggregate quickly forms in the constriction region,

driving jam formation and rapid onset of clogging.

Researchers have investigated [?] the factors influencing the mean-time-to-failure (MTF)

for clog formation in fluidic constrictions. Particle number density, flow rate, constriction

cross-section, and constriction length all influence this failure mode, as do particle rigidity

and the geometry of the narrowing region approaching the constriction [?,?]. In the process

of sensor development, we may manipulate all of these parameters to minimize clogging

probability during measurement. Ultimately, the particle number density, rigidity, and flow

rate are dictated by the end-user application. At that point, engineering of the constriction

region becomes the main option to extend the MTF, a full investigation of which is outside

the scope of this dissertation.

4.4 Design considerations

4.4.1 Circuit architecture

Voltage Dividers

Recent literature in impedance-based flow cytometry has been split between two measure-

ment approaches, broadly categorized as voltage dividers and voltage amplifiers. Voltage

dividers apply a voltage signal across two circuit elements in series. Monitoring the voltage

53

at the node between the two elements provides information about the relative impedances

of both elements. When one or both of these impedance elements is the conductive solution

between two sensor electrodes, this configuration can be used to measure the changes in

solution impedance expected to occur as particles pass between the electrodes.

Voltage amplifiers

a) b)

Vout

R2

Vin +

-

R1

Vout

VAC

R1

R2

+

+

-

-

iloop

𝑖𝑙𝑜𝑜𝑝 =𝑉𝐴𝐶

𝑅1 + 𝑅2

𝑉𝑜𝑢𝑡 = 𝑖𝑙𝑜𝑜𝑝𝑅2

iin

0 V

𝑖𝑖𝑛 =𝑉𝐼𝑁 − 0

𝑅1

𝑉𝑜𝑢𝑡 = 0 − 𝑖𝑖𝑛𝑅2

= −𝑉𝐼𝑁𝑅1

𝑅2

Figure 4.3: a) Two resistors, R1 and R2, combine to form a voltage divider with an output

voltage Vout when driven by a voltage source VAC . b) An inverting amplifier circuit. The

operational-amplifier sources a voltage Vout such that the inverting input (-) is also at

circuit ground. The input voltage signal drives a current to flow through R1, which must

subsequently flow through R2 due to the infinite input impedance of the op-amp.

Voltage amplifier approaches employ circuit elements known as operational amplifiers (op-

amps) to generate a voltage signal proportional to the solution impedance between the two

sensors. Ideal op-amps will attempt to source whatever voltage is necessary to achieve

zero voltage difference between their input terminals, and draw no current at either input

terminal. The voltage amplifier configuration shown in Fig.4.3 b) is known as an invert-

ing amplifier. Analysis of the circuit is based upon the two rules governing ideal op-amp

behavior. Assuming that the inverting input of the amplifier is being driven to ground to

match the non-inverting input, the current flowing through the solution impedance (Zsoln)

is Vin−0Zsoln

. This current must then continue to flow across resistor (Rgain) according to Kir-

choffs current law. Thus the output voltage from the op-amp must be 0−VoutRgain

. Setting these

two currents equal, we observe that the output voltage of the circuit is given by:

54

Vout = −RgainZsoln

Vin (4.2)

By monitoring changes in the magnitude of the output voltage, we can infer changes in

the magnitude of the solution impedance. The inverting amplifier configuration can also be

thought of as a voltage divider, wherein the voltage across the input resistor, here Zsoln,

programs the voltage drop across the second resistor in the divider, Rgain.

Contrasting approaches: divider vs. amplifier

For both the two- and three-electrode configurations, the bridge circuit approach eliminates

the need for an operational amplifier to drive the output voltage. This reduces per-device

component costs and power consumption. Furthermore, the bridge circuit approach is

inherently designed for differential measurement.

A particularly pernicious problem in voltage amplifier design instabilities caused by the

loop gain of the feedback network. The gain derived in 4.2 assumed an ideal op-amp. In

fact, the physical internal workings of an op-amp integrated circuit limit the possible gain

at a given signal frequency. This is known as the gain-bandwidth product (GBW) of the

op-amp. The internally-generated phase shift of the gain observed in a physical op-amp

can turn the negative feedback employed in Fig. 4.3 positive. This results in peak in the

gain response near the corner frequency of the voltage amplifiers feedback circuit. The issue

becomes more pronounced in the presence of capacitive loads (i.e., appreciably long coaxial

cabling). This problem is typically addressed through the introduction of a compensation

capacitor, which introduces a frequency-dependent roll-off in the circuit gain such that this

instability is not encountered during operation. This solution improves stability at the cost

of bandwidth, the range of frequencies over which the amplifier response is flat.

Successfully juggling the demands of compensation for stability and bandwidth for mea-

surement is difficult. This problem is exacerbated by the reasonably large impedances dealt

with in our feedback circuit. Even small parasitic capacitances appearing between compo-

nents can result in appreciable differences in performance near the cut-off frequency of the

55

flat-band response region. Small differences in gain in this region increases the background

difference output by the differential measurement, obscuring measurement of particle tran-

sits.

4.4.2 Bridge component values

Determination of the bridge resistance

Component values of bridge circuit elements plays a strong role in determining the perfor-

mance of the Coulter counter measurement system. The equilibrium voltage, Veq, for each

branch of the bridge circuit is determined by the ratio of the solution resistance (Rsoln) to

the value of the resistor forming the bottom half of the bridge, Rbr, and the magnitude of

the driving voltage (VAC):

Veq =Rbr

Rbr +RsolnVAC (4.3)

Eqn. 4.3 assumes the impedance of the double-layer capacitance is negligible with

respect to Rsoln at the operating frequency. The differential voltage forming across the two

sides of the bridge circuit is thus:

Vdiff =Rbr

Rbr +RsolnVAC −

RbrRbr +Rsoln + δRsoln

VAC (4.4)

Where we have introduced the term δRsoln to denote a small deviation in the observed

solution resistance in the latter branch, as would occur during a cell passage event. We

divide by the drive voltage, VAC , to render both sides dimensionless, and solve:

VdiffVAC

=RbrδRsoln

(Rsoln +Rbr) (Rsoln + δRsoln +Rbr)(4.5)

To find the sensitivity maximum, we differentiate with respect to Rbr. Setting the

resultant expression to zero, we obtain:

56

0 = R2soln +RsolnδRsoln −R2

br (4.6)

Operating under the assumption that the perturbation in the solution resistance is small

with respect to the overall resistance, the middle term may be ignored. This condition is

satisfied when the volunme of the analyte is small with respect to that of the sensing region,

which our devices satisfy. Thus, the maximal sensitivity occurs for the case that Rbr equals

Rsoln, yielding:

VdiffVAC

=1

4

δRsolnRsoln

(4.7)

corresponding to a signal amplitude of 2.5 mV per percent displaced volume per volt

of excitation signal. This figure of merit is the upper performance limit for our device,

contingent upon a perfectly-matched bridge circuit. The calculated response of the bridge

circuit from Eqn. 4.7 is shown in the Fig. 4.4 as the ratio of the solution to bridge resistanceis

varied, illustrating the sensitivity loss arising due to imperfect matching of impedances.

While maximal sensitivity occurs for perfect matching, signal attenuation is less than a

factor of two for bridge resistor mismatches up to a factor of 5.3x, indicating reasonable

tolerance for slight variations in component values selected. In subsequent sections we will

discuss other physical considerations which attenuate the sensor response to values below

this theoretical maximum.

57

a) b)

Figure 4.4: a) Output differential signal (solid blue line) as a function of the ratio between

the bridge (Rbr) and solution Rsoln impedances, assuming a 1% change in impedance in

one of the two sensing regions. Dashed red vertical lines indicate where bridge resistor

mismatch has decreased by a factor of 2. b) volume displacement ratio as a function of

particle diameter displacing solution inside a 20 µm x 20 µm x 17 µm fluidic constriction,

the typical geometry of our inter-electrode sensing region

Influence of the bridge capacitance

The bridge capacitor connects the two output terminals of the Wheatstone bridge config-

uration used to generate the sensing signal. The effect of this capacitor is to introduce

a low-pass filter, attenuating high-frequency noise in the sensing environment. Potential

sources of high-frequency noise include monitor flicker, higher harmonics of the modulating

frequency from the function generator, or power sources. The choice of the value of the

bridge capacitor must be made after establishing the operating solution impedance and

bridge resistance of your device. The bridge capacitor must be chosen such that there is

minimal, if any, attenuation at the signal frequency.

The ultimate aim of the impedance-based cell counter is integration with additional

biosensing modalities on a single chip. One such modality employed in our lab is dielec-

trophoresis, used for the selective capture of bacteria from conductive solution. For many

applications, this will involve driving electrodes near our sensor with signal amplitudes up-

58

wards of 10-20 VPP at frequencies in the regime of 1-10 MHz. Any coupling between the

dielectrophoresis drive signal and our impedance-based sensors will be common to both

branches of the bridge circuit due to the relatively low impedance of the capacitor at those

frequencies, and subtracted out via the differential measurement.

Influence of parasitic capacitances

Parasitic capacitances are capacitances arising between conductive elements within a circuit

that are not an intentional portion of the circuit design. Parasitic capacitances are an

unavoidable fact of life in circuit construction as a direct consequence of placing conductors

in close physical proximity, arising in parallel with the circuit elements. With care, the

impact of these parasitic capacitances can be thoroughly mitigated.

Rsoln Rsoln

CDLCDL CDL CDL

Cpara Cpara

CsubCsub

Rbr RbrCbr

Figure 4.5: Full circuit schematic of the measurement bridge circuit, incorporating the

capacitance of the double-layer at the electrode-solution interface as well as two additional

parasitic capacitances: Csub, the capacitance between electrodes through the substrate, and

Cpara, the capacitance of the coaxial cabling used for measurement.

Three key stray capacitances arise in construction of the Coulter counter measurement

circuitry, in parallel with the bridge capacitor, solution impedance, and bridge resistor. A

parasitic capacitance in parallel with the intentionally-placed bridge capacitor will effec-

tively increase the value of the bridge capacitor, decreasing the cut-off frequency of the

59

low-pass filter formed. Operating at frequencies above the cut-off frequency will result in

significant attenuation of the measured voltage.

A parasitic capacitance in parallel with the solution resistance replaces the solution

resistance with an equivalent impedance in the bridge circuit. Parallel impedances combine

reciprocally, and therefore the smaller term dominates the equivalent impedance of the

two elements. Even if the two impedances are comparable in magnitude, combining the

static impedance of the parasitic capacitance with the dynamic impedance of the solution

resistance obfuscates changes in the solution resistance caused by the passage of particles.

As discussed previously, the maximum bridge circuit response to a particle passage

event occurs for the case that the solution impedance is equal to the bridge resistance. If a

parasitic capacitance forms in parallel with the bridge resistance, this can have significantly

deleterious effects. The solution resistance is typically on the orders of hundreds of kilo-

ohms, and thus the bridge resistance as well. A small parasitic capacitance in parallel

with this bridge resistance will cause the effective impedance to fall off dramatically with

increasing frequency, and thus the sensitivity.

During my investigations, two particular origins of stray capacitances were identified,

arising from coupling between contact pads as well as coupling between PCB traces. The

contact pads for interfacing the device were fabricated with areas of 1.5 mm2 atop of 2 µm

of silicon dioxide insulation isolating the electrodes from the doped silicon substrate.

The thick insulator provides excellent isolation of the electrode pads for DC signals. We

would expect to observe the same behavior at signal frequencies, owing to the macroscopic

separation between pads. However, the doping of the substrate is sufficient to render it fairly

conductive. Regarding it as a short, we can consider two neighboring pads to be capacitvely-

coupled plates with only 4 µm of dielectric between them. We may then compute a crude

estimate of this capacitance as:

C =κε0A

d(4.8)

60

where κ is the relative permittivity of our insulator, 3.9 for silicon dioxide, ε0 is the

relative permittivity of free space, and A is the area of the plates, and d the separation

between them. Conductance measurements, such as those shown in Fig. 4.6, found a net

parasitic capacitance of 15 pF between pads, in excellent agreement with this estimate when

accounting for additional sources of parasitic capacitance in parallel with the pad-to-pad

mechanism.

Similarly, small parasitics between pads arose due to the metal wiring layout on the

printed circuit board design. The macroscopic separation between traces, 0.06 ′′, limits

the magnitude of this effect, but from Eqn. 4.8 it contributes roughly 1.1 pF of parallel

capacitance per inch of wiring at this minimum separation. This additional contribution

likely accounts for most of the discrepancy between the calculated 12.9 pF and 15 pF for

the pad-to-pad capacitance.

Far more deleterious is the effect of coaxial cabling, used to make electrical connection

to BNC jacks mounted on the printed circuit board. Coaxial cable acts as a distributed

circuit element, offering a capacitance per unit length of (ISBN 0-201-50418-9) [?]:

C

l=

2πεrε0ln (D/d)

(4.9)

where D is the inside diameter of the coaxial shield and d the outside diameter of the

inner conductor. For commercially-available coaxial cabling, this produces capacitances

of 50-100 pF/m depending upon the particular design. When interfacing directly with the

bridge circuit for measurements, this places a sizeable capacitance in parallel with the bridge

resistor even for reasonable cabling lengths.

4.4.3 Operating frequency

During solution flow, researchers measure the passing particles size from the voltage sig-

nal formed across the bridge circuit in the simplest model of the Coulter counter behav-

ior. This analysis is predicated on the assumption that the particle possesses a uniform

61

and frequency-independent conductivity. The picture becomes more nuanced for biologi-

cal mediums. Cell samples of interest typically possess one of two outer layers: either a

cell membrane (semi-permeable) or cell wall (impermeable) [?]. These outer layers sur-

round a somewhat-conductive inner medium [?]. By configuring the Coulter to record both

magnitude and phase information, or simultaneously monitor at multiple frequencies, re-

searchers can also measure the electrical properties of these outer layers, allowing further

discrimination amongst similarly-sized species of bacteria [?].

Frequency Constraints

Physical considerations of the measurement circuitry itself form the first independent con-

straint on frequency of operation. The capacitive double-layer that forms at the counter

electrode-solution interface presents an additional impedance in the bridge circuitry. Since

the operating principle of the counter relies on detecting changes in the net impedance

between two counter electrodes, and the double-layer impedance would not be modified

appreciably by passage of a particle overhead, the counter should be operated at frequen-

cies where the impedance of the ionic double layer is negligible in order to maximize the

signal-to-noise ratio.

Physical considerations of the analyte present a second, deterministic constraint in choice

of operating frequency. Monitoring the magnitude and phase of the circuit response at a

fixed frequency requires a choice of frequency such that the membrane is semi-transparent

(DEFINE SEMITRANSPARENT) [?]. Multi-frequency approaches instead employ two

frequencies: a low frequency, for which the membrane impedance is very high, and a high

frequency, for which the membrane impedance is small compared to the internal impedance

of the cell [?]. The low-frequency signature encapsulates the relevant size information,

whereas the high-frequency signature conveys information about the outer layer of the cell.

The upper cutoff for the operating frequency is determined by the physical embodiment

of the counter itself. Parasitic capacitances are capacitances which form between two adja-

cent metal electrodes by virtue of their proximity, rather than being intentionally designed

62

to occur. The substrate on which the counter electrodes are deposited can present a parasitic

capacitance between the two electrodes, operating in parallel with the solution impedance

particularly between neighboring pads used to contact the electrodes in laboratory settings.

Parasitic capacitances also form between adjacent wiring, components in the bridge circuit,

and instrumentation cabling. All of these capacitances present an impedance in parallel

with the solution resistance. As the operating frequency increases, the impedance of this

parallel pathway falls off. At sufficiently high frequencies, it becomes the sole determinant

of the impedance of the parallel combination, effectively suppressing all observed changes

in the solution resistance due to passing particles and cells.

Extending the frequency range

Parasitic capacitances are an unavoidable fact of life. Researchers aiming to operate their

counter circuitry at frequencies in the megahertz regime can take several steps to mitigate

their impact. Choice of substrate matters. The dominant parasitic capacitance we have

observed occurs between contact pads as defined by the metallization masks. These are

lain down atop 2 µm of silicon dioxide, a good insulator. However, the oxide sits atop a

conductive silicon handle,

COMMENT HERE ON THE CONDUCTIVITY OF THE HANDLE PER EMAIL

WITH SHARI

permitting the flow of current from one contact pad to another. Reducing the size of

the contact pads or replacing the substrate with a better insulator such as glass reduces the

magnitude of this source of parasitic capacitance.

63

a) b)

Figure 4.6: Device impedance measurements taken without a chip connected, a dry chip,

and three concentrations of phosphate-buffered saline (PBS) to demonstrate the effect of a)

2 µm of silicon dioxide versus b) an entirely-insulating glass substrate for both low-frequency

(LF) and high-frequency (HF) regimes.

Fig. 4.6 shows the significant influence of the choice of substrate on the device impedance.

A voltage signal was applied to the middle electrode of the counter structure, and one of the

adjacent sensing electrodes was connected to the inverting input of a voltage amplifier with

a 100 Ω feedback resistor. In this manner, an inverting amplifier as depicted in Fig. 4.3

b is constructed, wherein R1 is replaced by the impedance between the source and sensing

electrodes.

Several significant changes can be observed. Improvements to the printed circuit board

design increase the measured impedance two-fold in the absence of a chip (blue lines). The

influence of switching from 2 µm of silicon dioxide to a glass substrate increases the measured

impedance of a dry device by an order of magnitude, to the upper bound of measureable

impedance established by the measurement circuitry itself. The resultant improvement in

SNR can be observed in Fig. 4.7. The impact of the substrate is markedly more dramatic

at lower solution conductivities (wherein the solution resistance is higher). While less

consequential in the high-salinity of whole-blood environments, we desire lower conductivity

64

for other applications for which fabrication on glass becomes essential.

Rsoln

CDLCDL

Csub

a) b)

c)

d)4.5um in 0.01x @ 0.5uL on glass

Figure 4.7: a) computed impedance change for the b) sensing region circuit model in re-

sponse to a 1% change in solution resistance, demonstrating the signal attenuation caused

by the parasitic capacitance of the c) the silicon substrate in contrast to d) devices fabri-

cated on glass. Measurements for a 4.5 µm bead in 0.01x PBS at 0.5 µL/min. for a 20 µm

channel width and gap.

Improvements beyond substrate-based solutions are also possible. Integration of the

bridge circuit onto a printed circuit board (PCB) minimizes stray capacitances between

components. Furthermore, locating the bridge circuit components spatially adjacent to

the PCB-chip interface to minimize stray capacitance picked up by wiring length. If these

efforts alone do not suffice to achieve the desired measurement bandwidth, consider imple-

menting an on-board differential amplifier. The differential amplifier will output a voltage

proportional to the difference between the two arms of the bridge circuit. This function

is typically performed by the lock-in amplifier itself but creating the differential circuitry

on-board will eliminate capacitances from the cabling and lock-in amplifier input terminals

being introduced prior to the evaluation of the differential signal.

65

4.4.4 Ramifications of planar electrode geometry

b)

a)

l g c)

QUALITY OPTICAL IMAGE OF COUNTER WITH PDMS ON IT

Figure 4.8: a) top-down view of the lithographic definition pattern for two chips, each of

which contains several devices. b) PDMS (translucent grey) confines fluid flow over our gold

electrodes to a narrow width. Different devices on different chips explored the ramifications

of electrode transverse length, l, inter-electrode gap distance, g, and the constriction width,

width as indicated. c) Optical micrograph of a freshly-fabricated electrode structure with

a microfluidic channel aligned and bonded.

The planar electrode geometry adapted in our sensing set-up greatly simplifies the device

fabrication process. A single mask and a single metallization layer is all that is required

for both the Coulter counter sensing electrodes and capture fingers for dielectrophoretic

capture, greatly reducing the complexity and cost per sensing device.

66

a) b)

Figure 4.9: a) conceptual illustration of the field lines emanating from the planar electrode

geometry, emphasizing how particle (purple spheres) vertical displacement from the elec-

trodes alters the density of field lines they will cross paths with. b) COMSOL simulation

of the electric field profile for a pair of planar sensing electrodes generated by collaborators

at the University of Alberta.

There is an inherent trade-off for this ease of fabrication. During device operation, the

solution volume passes over the planar sensing electrodes. An electric field forms when an

electric potential is applied across the two electrodes. The electric field that forms is non-

homogenous as shown in Fig. 4.9. While the solution conductivity might remain uniform

over the entirety of the sensing volume, different regions of the solution have nonidentical

contributions to the impedance between the two electrodes.

As a direct consequence of this non-uniformity, the magnitude of the impedance-based

signal acquires a significant vertical dependence [?,?,?] which might be conflated for large

dispersion in particle sizes, as can be seen in Fig. 4.10.

67

a) b)

Figure 4.10: a) simulation [?] of the impedance variation for an insulating sphere passing

over planar electrodes with a XX µm inter-electrode gap as a function of vertical displace-

ment from the electrodes and b) experimental data from a bead transit event demonstrating

the expected behavior.

Solutions to the vertical dependence take two possible forms: either manipulation of

the incoming particle stream or an overhaul of the electrode design. The laminar flow pro-

file in microfluidic channels lends itself to particle-focusing. Researchers have implemented

solutions based on pressure waves (DOI: 10.1039/c4lc00982g, SAW FOCUSING), sheath

flows, and negative dielectrophoresis [?]. Alternatively, structuring the electrodes in three

dimensions can greatly simplify(CITE ME) the electric field profile at the cost of complicat-

ing device fabrication. Understanding the clinical demands of the end user is critical when

evaluating the benefits of implementing these corrective measures in the particle counter

system.

68

4.5 Experimental Apparatus

4.5.1 Microscope and stage mount

Microscope

Optical imaging for performance verification is highly desirable during the development

of electrical impedance-based cell counters. To this end, all of our sensing experiments

are conducted on the viewing stage of our laboratorys microscope. The microscope is an

Olympus BX51 microscope equipped with 5x, 10x, and 40x objectives as well as multiple

filter lenses for fluorescence imaging. An Olympus DP70 camera system allows for image

and video capture for later analysis, such as correlation with time-stamped impedance

mesaurements. An Xcite Series 120Q laser source provides an intense source for fluorescence-

mode viewing of particles such as 1.77 µm beads and fluorescently-tagged bacteria.

Stage mount and Printed Circuit Board

Robust transmission of signals without attenuation is critical for measurement fidelity and

maximizing the signal-to-noise ratio. Prior home-made cabling solutions, necessary to elec-

trically interface devices contemporaneously with microscope observation, introduced sig-

nificant noise by functioning as antenna for electromagnetic interference and were prone to

mechanical failure modes at solder joints or points of contact with the device itself.

69

Figure 4.11: left) CAD schematic of the PCB stage-mount. The automated alignment

socket visible, recessed within the center groove. right) photograph of the PCB stage-

mount integrated with the microscope optics. The spring-loaded pin array makes solid

electrical contact with loaded chip.

To this end, I designed a printed circuit board (PCB) which permitted electrical contact

to individual pins on the device through coaxial connectors mounted on the board, while

leaving a sufficient unused footprint to allow room for microscope objective lenses as desired.

The PCB made contact to the device via spring-loaded connectors projecting from the

underside of the board.

I then designed a metal sample mount to mate with the PCB. A groove milled out of the

sample mount, as shown in 4.11, allows devices to easily be loaded underneath the spring-

loaded connector from the side. A slot recessed in the center of the milled-out groove has

been machined with lateral displacement tolerances much smaller than the contact pads.

In this manner, alignment in-plane is automatically handled mechanically by the sample

mount. Vertical alignment with the spring-loaded pins is likewise mechanically determine

by the vertical displacement between the bottom of the slot and the height of the PCB.

Thus, the combination of the PCB and sample mount provides a secure and robust con-

nection between the device and the coaxial connections on the PCB. Alignment in all three

dimensions is completely addressed by the physical structure, removing a significant barrier

70

to reliability and ease-of-use. Furthermore, the metal sample mount and the ground plane

of the PCB form a Faraday cage around the device to shield the device from electromagnetic

interference.

4.5.2 The electronics

Rsoln Rsoln

CDL CDL CDL CDL

Cpara Cpara

CsubCsub

Rbr Rbr

Cbr

+

-X

Y

0000 0000IN

REFSINE

TRIG

CH1 CH2

a)

b)c)

d)

e)

f)

USB

Figure 4.12: a) circuit diagram of the complete three-electrode structure, with all parasitic

capacitances made explicit. The middle electrode is driven by the sine wave output of

the b) function generator. The resulting voltage at the left and right sensing electrodes

is measured by the c) PCB-mounted instrumentation amplifier before the signal is fed to

the d) lock-in amplifier for demodulation. The demodulated output signal from the lock-in

amplifier is measured by e) the oscilloscope which is programmatically controlled during

acquisition by f) MATLAB routines.

Function generators

Two different function generators provide the AC excitation signal throughout the course

of these experiments. Both the Tektronix AFG 3252 and the Agilent 33120A demonstrated

lower noise floors and higher spectral purity than the sine wave generator of our SR830

lock-in amplifier, as measured on a network analyzer. During the evaluation of sources of

system noise, it was discovered that either benchtop function generator reduced background

noise levels on the measured waveforms. Background noise was a significant challenge for

71

early iterations of our microfabricated Coulter counter. In the absence of a compelling

reason to alter a known good working configuration, the function generators remain.

Only one sinusoidal voltage is required for our three-electrode bridge circuit. Two func-

tion generators are redundant from this perspective. Development of the measurement

system was conducted in the same environment in which future measurements would take

place. Benchtop space adjacent to the Olympus microscope was at a premium. Initial

work on the Coulter counter was conducted with the Tektronix function generator which

had been configured for experiments with dielectrophoresis (manipulation of particles in

solution via radio-frequency signals) conducted by other members of our lab. The Tekronix

funciton generator has dual output channels with programmable phase offsets, highly desir-

able for application of bipolar RF signals for dielectrophoresis. We brought in the Agilent

function generator to source the excitation voltage for our Coulter counter as soon as we

began experimenting with integrating the two techniques on a single chip.

Lock-in amplifier

We monitor the output signal from the bridge circuit during experiments with a Stan-

ford Research Systems SR830 lock-in amplifier. Conceptually, lock-in amplifiers exploit

the orthogonality of sine and cosine functions to measure the amplitude of a very specific

frequency component of the input signal. This enables detection of the small changes in

the bridge resistance during particle transit events expected due to our channel geometry,

despite the presence of significant environmental noise from both 60 Hz power supplies as

well as large-amplitude radio-frequency signals integrated in future design iterations.

The SR830 imposes some additional limitations on experimental parameters. The max-

imum permissible operating frequency is 100 kHz [?], constraining our choice of frequency.

As can be observed in Fig. 4.6, the magnitude of our solution impedance remains flat over

the range of 50 - 100 kHz, implying that such frequencies are sufficiently high to overcome

Debye layer screening at the electrode-solution interface. Therefore, this limitation is in-

significant for enumeration applications but prohibits measurement at frequencies typically

72

used to probe cytoplasm contents.

a) b)

c) d)

Figure 4.13: a) one of many consecutive data traces recorded during the course of an

experiment, containing many particle passage events. b) the transit time of the bead is

defined as the time elapsed between the two antisymmetric peaks (crimson dots), and the

peak height is the fitted height from baseline of both peaks. The program aggregates this

data from 102 − 104 fits and returns a binned 2-D histogram, color-coded according to

number of counts, shown here for flowrates of c) 5.0 µL/min. and d) 1.0 µL/min.

THIS FIGURE AND DISCUSSION GOES AFTER HEATMAP CONVERSATION.

The signal arising due to a particle of a given volume passing through the sensing region

should be independent of flow velocity. Instead, we observe that the signal magnitude

decreases with decreasing transit time below some critical threshold. The output response

time of the SR830 is dictated by the steepness of its bandpass filter as well as the integration

constant chosen. For maximal signal-to-noise ratio during measurements at our targeted

73

volumetric flow rate, a 30 µs time constant and 24 dB./decade roll-off were chosen. Per

the SR830 datasheet, this generates a 99% response time of 300 µs. Furthermore, the rear

outputs at which we monitor the lock-in measurement have an output bandwidth of 100 kHz

[?], setting the maximum allowable frequency-domain response possible by manipulation of

time constants and roll-off.

An additional lock-in amplifier, the Stanford Research Systems 844, was used to charac-

terize the impedance of of our devices in the 25 kHz - 1 MHz regime. The additional order

of magnitude in frequency range over which we took measurements provided additional

information about circuit electrical characteristics.

Oscilloscope

Individual reading queries via serial communication with the lock-in amplifier is prohibitively

slow on account of the data transfer rate, drastically limiting the ability to detect the pas-

sage of particles. From the perspective of the Nyquist criterion, the minimum sampling

frequency is 2δt , where δt is the transit time of a particle passage. Researchers typically

aim for a minimum of 20 datapoints per event, requiring sampling rates of 10-1000 kHz

depending upon desired flowrate and constriction geometry. To satisfy this condition, we

employ a Tektronix DPO4104 to record the time domain analog voltage signal from the

rear panel of the lock-in amplifier.

The measurement circuit

The printed circuit board comes equipped with the ability to interface with up to six

counter structures at a single time. Each counter structure has a single Texas Instruments

OPA-2227 operational amplifier configured as a dual-channel unity-gain voltage follower. A

gain-bandwith product [?] of 8 MHz more than exceeds the necessary operating frequency of

our Coulter counters. For a balanced bridge being driven by the typical 1 Vrms amplitude,

the equivalent peak-to-peak voltage occuring at either node is 1.415 Vpp. Given the specified

slew-rate of 2.3 V/µs, operation up to 1.6 MHz is possible. A dual-channel op-amp is chosen

74

for this application to eliminate the effects of variance among individual integrated circuits

which would appear as a differnetial signal between the two terminals.

In addition to the dual-channel voltage follower, we also introduced a precision instru-

mentation amplifier for each Coulter counter measurement channel. An instrumentation

amplifier provides a unity-gain follower for each of the two input signals, which provides a

buffer to isolate the device being measured from the internal feedback circuitry. The instru-

mentation amplifier produces a signal proportional to the difference between the two input

terminals. Signals common to both terminals are subtracted out. The efficacy to which

signals common to both inputs are suppressed is referred to as the common-mode rejection

ratio. Furthermore, it can be configured to provide additional gain of the differential signal,

elevating the signal of interest further over the suppressed background signal (and shared

noise!) between the two amplifiers.

A criticial figure of merit for measurement circuitry performance is the background

differential signal arising from slight imbalances in the bridge circuit measurement pathway.

Even for the case of a perfectly symmetric sensor device, this signal can persist due to small

discrepancies in the bridge resistor component values. At higher frequencies, differences in

wiring trace length between the bridge resistor and the buffer amplifier for either branch

can introduce small differences in parasitic capacitances to ground, also contributing to

a constant differential background. For our constriction geometry and typical analytes,

we expect our Coulter counter to produce signals on the order of mV. Therefore, even

small background signals and their concomitant noise can contribute to obfuscating the

measurement of passing patricles.

The syringe pump

4.6 Calibration measurements - detection of polystyrene beads

* bead size, conductivity data -T.B.D. once narrative is more established.

velocity v flowrate

75

Chapter 5

Dielectrophoresis

5.1 Dielectrophoresis for lab-on-chip applications

Introduction: what is dielectrophoresis? Why do we want to use DEP? * one possibility

for obviating cell cultures is DEP artificially preconcentrating the target bacteria sample

out of blood. Also reduce need for time-consuming wash steps, etc.? * DEP relies not

on impedance but polariziablity for the force * impedance still matters to reduce power

consumption on circuit for IC apps

5.2 Derivation of the dielectrophoretic force

* paper I sent Ayaska which derives FDEP for an infinitesimal volume - go over the deriva-

tion of the DEP Force * theoretical underpinning of DEP: start with voltage across cubic

volume of solution, use the paper that I sent to Ayaska to explain. - discussion over the

meaning and use of Clausius-Mossatti factor for this section 3 Fabrication of finger elec-

trodes * Fab process, why oxide Talk PDMS channels Demonstrate the ability to capture

beads * demonstrate the ability to capture beads, bacteria

76

5.3 Realistic modeling of dielectrophoretic devices

Theoretical investigations analyzing the influence of electrode geometry on the magnitude

of the DEP force (and therefore device performance) contain an inherent assumption that

blinds them to fundamental consequences of the physical nature of the electrodes themselves.

The simplest derivation of the dielectrophoretic force consider the polarizable particle ex-

periencing an AC potential gradient between two parallel plate electrodes [?]. Variations in

the electrode design geometry alter the spatial profile of the potential gradient which alters

device performance, an effect which physics-based simulations effectively capture [?].

Trouble arises when these computations cast the DEP force term as a function of the

potential at the electrode-solution interface [?]. Theorists and experimentalists alike have

equated [?] this potential with the externally-applied potential when optimizing device de-

sign. They experience significant deviations [?] from expected performance in the operating

regimes where this assumption breaks down. We must incorporate a fuller understanding

of electrochemical impedance and real-world limitations to understand where this occurs.

5.3.1 Developing the full circuit model

Consider the infinitesimal of solution volume used in computing the DEP force experienced

by a particle. The potential appearing at the boundaries of this solution volume generate

the potential gradient which establishes the magnitude of the DEP force. As we expand the

boundaries of the solution volume into consideration, the infinitesimal solution resistance

element becomes approximated by the familiar solution resistance element invoked during

discussions of electrochemical impedance spectroscopy.

FIGURE: ELECTRODES IN SOLUTION WITH DL IONS AND CELL MADE READ-

ILY APPARENT

77

The electrode-solution interface

As the volume expands to its logical limit, the boundaries of the volume approach the

electrode-solution interface. The impedance of the diffused double-layer and the potential

drop which forms is the first term not taken into consideration when modeling the behavior

of DEP structures. For solution saline concentrations exceeding 1 mM, the length scale of

the diffused layer is less than 10 nm. Comparing this to the typical size scale of cells being

manipulated via DEP, on the order of microns, we can conclude that the potential gradient

dropping across the double-layer itself will only exert on an incredibly small volume fraction

of the cell, if at all. Therefore, the true potential determining the magnitude of the DEP

force for device capture is the proportion of the applied voltage signal that forms across the

solution resistance, between the double-layers of the two electrodes.

The electrodes

FIGURE: TOP-DOWN VIEW OF IDEs, DISTRIBUTED ELEMENT MADE CLEAR

WITH ARROWS FOR CURRENT

As previously discussed (Section N.N.n), the impedance between two electrodes in solu-

tion contains two parallel conduction pathways: the capacitance between the two electrodes

through the substrate in parallel with the electrode-solution-electrode circuit. Parameters

governing the inter-electrode capacitance include the length and width of the electrodes as

well as the gap between them [?].

The deposited electrodes are not perfect conductors and do not transmit the externally-

applied voltage signal without attenuation. Consider first the interdigitated electrodes

themselves, as shown in Fig. ??. As fabricated, the electrodes present a series resistance

of XXX Ω per YYY length. The applied voltage causes a net current to flow along and

between the electrodes, a small amount flowing from one electrode to the other per unit

length of the interdigitated structure. Current flow along a resistance induces a voltage

drop from Ohmic losses in the electrode. Therefore, application of a voltage signal to the

interdigitated electrode structure induces a voltage gradient along the planar electrodes as

78

well as the intended gradient across it.

Invoking resistivity and current flow per unit length naturally leads to treating the

impedance of the interdigitated electrode as a distributed impedance network as opposed

to a discrete element in the circuit analysis. The antisymmetric nature of the infinitesimal

model renders common [?] methods for simplifying the infinite component network inappli-

cable. The present work is motivated to find design heuristics to improve the performance of

the IDEs for DEP capture, and for this purpose treating the IDEs as lumped-sum/discrete

elements suffices. A complete analysis of the distributed-element network would be worth

future investigation: the qualitative description proposes a voltage gradient along the elec-

trode which would explain the puzzling phenomenological observation of motion along the

electrodes of captured particles.

Moving beyond the interdigitated electrode region, deposited electrode leads enable

connection to macroscopic circuit elements (e.g., coaxial cabling) with fabricated contact

pads. The lead-ins themselves also possess a finite resistance per unit length which will

induce ohmic losses as a potential drop between the contact pad and the IDE region. The

transmission line formed by the cabling connection to the voltage source instrumentation

introduces an additional impedance, as does the output impedance of the voltage source

itself (typically, 50 Ω).

The substrate capacitance

Even in the absence of solution conduction, the large footprint of the interdigitated electrode

structures and close physical proximity produces a capacitance between the two electrodes

which may be measured directly in the dry state. This capacitance is a strong function of

the electrode geometry and choice of substrate. Whether or not it may be safely ignored

hinges upon the solution conductivity and area of the electrodes.

79

5.3.2 Ignored inductances

A complete analysis of the dielectrophoresis circuit model cannot be achieved without con-

sideration of the inductances formed by sharp bends in the electrode structure, occuring in

the IDE structure and potentially in the electrode leads themselves.

ESTIMATE OF INDUCTANCE FOR QUARTER-TURN WITH TURNING RADIUS

10um

The operating frequencies for this work ranged between 500 kHz 10 MHz and would

require inductances on the order of 10-1000s of µH to pose a significant contribution to the

overall device impedance. Therefore, the influence of such sources of inductances has been

neglected in this work.

The full circuit model

FIGURE: FULL CIRCUIT MODEL WITH INSTRUMENTATION AND DISCRETE EL-

EMENTS SHOWN. CONTRAST IT WITH THE CIRCUIT MODEL OF THE THEO-

RISTS. Figure: Wrap up with circuit model of our set-up overlain on abstract schematic

(gold electrodes, oxide, individual salt ions, etc.)

Integrating these different circuit elements into a single model, we arrive at the circuit

of Fig. ??. We have assumed no charge-transfer at the electrode-solution interface which

motivates our selection of gold for the electrode material. The resistance of the interdigitated

electrodes, RIDE , and structure of the leads, Rlead, is here depicted to be symmetric but this

need not be the case. The elements shaded in Fig. ?? are those not considered in theoretical

investigations of the DEP force, wherein the DEP electrodes and generated gradient are

assumed to be isopotential with the external function generator.

5.3.3 Ramifications for the capture force

From visual inspection, multiple impedance elements exist in series between the solution

resistance and the voltage generator. Since we equate VDEP in Eqn. ?? with Vsoln in the

80

circuit model, to find the transfer function of the externally-applied voltage to the voltage

experienced by particles in solution, we write:

Eqngoeshere (5.1)

wherein Rout is the output impedance of the function generator, typically 50 Ω, Csub is

the capacitance of the electrode structures coupled through the substrate, and ZCPE the

constant-phase element representing the double-layer capacitance of the planar electrode

structures.

There exist three separate frequency regimes embodied within Eqn. ??. In the highest

range of applied frequencies, both the double layer and the substrate capacitances are

virtual shorts, at which point the voltage across the solution resistance drops precipitously,

eliminating the ability to manipulate particles via dielectrophoresis.

In the intermediary regime, the impedance of the substrate capacitance is comparable to

or much greater than the solution resistance, whereas the double-layer capacitance remains

virtually shorted. In this regime, the maximal applied voltage drops across the solution

resistance for a fixed electrode geometry and this therefore presents the desired regime of

operation.

At frequencies below this intermediary regime, the impedance of the double-layer ca-

pacitance is no longer negligible. With decreasing frequency, larger and larger proportions

of the voltage appearing at the metal-solution interface drop across the double-layer capac-

itance, effectively screening out the bulk of the DEP signal from particles in solution. This

prediction is consistant with empirical reports [?] of decreased DEP capture efficiency at

lower frequencies despite the Clausius-Mossatti factor being predicted to remain constant.

5.4 Experimental verification of the circuit model

Transitioning from a theoretical hypothesis to electrode design guidelines requires exper-

imental verification of the predicted behavior for our electrode structures. We therefore

81

fabricated electrodes as described in Section N.N.n with carefully chosen design manipula-

tions to illustrate the role each element in Fig. ?? plays in device performance.

5.4.1 Methodology

The solution

In order to measure the effect of design conditions on the DEP force, we needed a target

particle that could be readily-tracked optically and captured by our device. Fluorescent

polystyrene beads, 1.77 µm in diameter, were purchased from SOURCE (ID No.: NNN).

These particles were diluted 20,000x from their stock concentration in a buffer solution of

0.1x PBS. The buffer concentration was chosen so as to maximize solution conductivity

while retaining the ability to exert a positive DEP force on the polystyrene beads. As can

be seen from inspection of Eqn. ??, the largest influence of electrode design is expected to

be seen when the solution resistance is comparable to the electrode resistances.

Operating conditions

Solution was flown through the microfluidic channels at rates between 0.2 1.0 µL/min.,

depending on the width of the microfluidic channel under investigating. The linear flow

speed, and thus the viscous drag force, varies inversely with channel width. The effect of

the dielectrophoretic force is in opposition to this drag force. The flow rates were chosen

such that the magnitude of the two forces would be comparable to improve detection. For

all capture experiments, a voltage magnitude of 1.2 VPP (CHECK THIS) at 1 MHz was

sourced from the function generator to a power amplifier, which amplified the signal ten-

fold before transmission to the device through coaxial cabling. The choice of amplitude was

governed by dielectric breakdown atop the sample and the choice of frequency by known

good frequency ranges for performing positive DEP on polystyrene beads in the buffer

solution.

82

The measurement

FIG: HALF IDE, HALF NOT, VELOCITY ONE, VELOCITY TWO, FORCE DIAGRAM,

X VERSUS TIME PLOT TO ILLUSTRATE

Particles flowing in solution quickly reach an equilibrium velocity, determined by the

competition between the viscous force (inertial drag) and the constant transfer of momentum

from solution colliding with the rear of the bead as it the solution is pumped forward. When

passing over the interdigitated electrode arrays, the particles experiencing pDEP experience

an additional force opposing their direction of motion, reducing their equilibrium velocity.

For full pDEP capture, the equilibrium velocity is reduced to zero.

This process is illustrated in Fig. ??, depicting the position as a function of time as a

particle passes over the interdigitated electrode array, located at x0. The change in slope

represents the shift in equilibrium velocities of the particle as it passes over the array, a shift

which is proportional to the magnitude of the DEP force. In generating the position-time

traces for the hundreds of particles passing over the IDE region, we perform sequential image

analysis to track and trace the position of particles frame-by-frame from recorded videos.

The beads are fluorescently-tagged, and therefore we employ fluorescence imaging with a

laser excitation source and optical filter to maximize the particle-background contrast.

We monitor this shift in velocity as a measure of the time-averaged strength of the DEP

force. Multiple difficulties arise in extracting the precise force dieletrophoresis exerts on the

passing particles. Force, proportional to acceleration, is related to the second derivative

of position. Optical approaches measure the position as a function of time, and therefore

extracting the acceleration requires differentiating twice with respect to time. Evaluating

multiple orders of numerical derivatives inherently amplifies measurement noise, here gen-

erated both by uncertainty in the position as well as uncertainties in frame-to-frame timing

interval.

Furthermore, the instantaneous forces experienced by the particles are rapidly changing.

The dielecrophoretic force varies not only as the particles pass over the electrodes, between

the gap, but also depends on their height within the channel. The laminar flow profile of a

83

microfluidic channel is fastest in the center, thereby introducing variance in the drag force

arising from vertical height as well as the lateral position within the channel. And lastly,

the microfluidic pump used to drive fluid flow is not perfectly continuous but rather is cyclic

in nature.

These factors combine to render evaluation of the dielectrophoretic force magnitude

challenging to put in their appropriate context. The desired end functionality of dielec-

trophoretic capture is a change from the initial equilibrium velocity to nil in the electrode

region.

Naively, one would expect that monitoring the fraction of captured to incident particles a

more suitable metric. However, capture is an unbounded threshold condition a bead cannot

be more captured by DEP forces far exceeding those necessary to reduce the equilibrium

velocity. For a given input voltage, there will be a range of electrode geometries for which the

voltage across the solution resistance is sufficient for high capture and a range of geometries

for which the voltage is insufficient for any capture. The only nuance in the measurement

lies in the interpolant regime in which some, but not all, incident particles are captured.

This regime is not apriori guaranteed to span a wide range of geometries, nor include any

of the extant devices for a given set of operating conditions.

Measuring changes in the equilibrium velocity, however, avoids the pitfalls of capture-

efficiency based performance evaluation. Sensitivity lost due to excessive capture force

is avoided entirely by eschewing capture altogether, operating the experiment below that

threshold. Evaluating differing equilibrium velocities allows us to then make comparisons

between a range of electrode geometries, all of which achieve no capture for the initial

conditions chosen.

5.4.2 Lead-in width

FIGURE: Abstract of Experiment 1 chip showing electrode width varied, still from DEP

capture video, show a few particle y v. t traces on a graph, net change in velocity as a

function of series resistance for the three widths. Device impedances plot.

84

In the first set of experiments, we varied the width of the electrode leads on the devices

to evaluate the role of the electrode resistance on the performance. All other aspects of

device geometry were held constant. The lead-in resistance scales inversely with the width,

which can be estimated for our structures as:

EQN: electrode resistivity eqn

Where R = , ρ is the , A is the cross-sectional area, and L is the length of the electrodes,

XXX microns in our design. For electrode thicknesses of 10, 25, and 100 µm this corresponds

to lead resistances of XX, YY, and ZZ Ω, respectively. The variation in device impedance

with electrode width can be see in Fig. ??. We also introduced additional series resistances

in line with each of the devices to simulate the effect of increasing electrode resistances, or,

equivalently, operating at even higher solution conductivities with fixed electrode resistance.

As we can see from Fig. ??, the change in equilibrium velocity increases with increasing

width under identical operating conditions, illustrating the effect of the reduction in the

series resistance of the leads. Furthermore, we can also see a clear and pronounced decrease

in the change in velocity with an increase in series resitance, as to be expected. The three

curves in Fig. ?? are offset by roughly XX and YY Ω, respectively, in accordance with our

rough estimates from Eqn. ?? This suggests that lead width

5.4.3 Finger length

FIGURE: Abstract of Experiment 2 chip showing electrode finger length varied, still from

DEP capture video, show a few particle y v. t traces on a graph, then show the net change

in velocity for the three finger lengths. Device impedances plot.

In the second set of experiments, we varied the length of the interdigitated electrode

fingers at a constant solution channel width. The resistance of the interdigitated fingers

should increase with increasing finger length, reducing the potential seen across the solution

element.

As we can see from Fig. ??, the change in equilibrium velocity increases with increasing

velocity under identical operating conditions, illustrating the effect of the reduction on the

85

finger length in the leads.

This suggests that finger length presenting a trade-off between the difficult of microflu-

idic alignment and optimal device performance. The effect is much less pronounced in

comparison to the influence of the electrode width as observed in the previous electrode

width experiment.

5.4.4 Channel width

FIGURE: Abstract of Experiment 3 chip showing channel width varied, still from DEP

capture video, show a few particle y v. t traces on a graph, then show the net change in

velocity for the three finger lengths. Device impedances plot.

In the third set of experiments, we varied the width of the microfluidic channel over the

interdigitated electrode fingers between 0.5, 1.0 and 2.0 mm. The planar electrode geometry

was nominally identical for all three experimental conditions, and the finger length chosen

was such that it could fully span all three channel widths without issue. Operating at a

frequency where the impedance of the capacitive double-layer is negligible, this experiment

manipulates the value of the lumped-sum impedance As we can see from Fig. ??, the change

in equilibrium velocity decreases with increasing channel width, illustrating the effect of the

ratio of the solution resistance to the external series resistances on the performance of the

device.

GO BACK AND COMMENT DO WE SHOW COMPARISON WITH IDENTICAL

FLOW RATE OR IDENTICAL VELOCITY

This suggests that finger length presenting a trade-off between the difficult of microflu-

idic alignment and optimal device performance. The effect is much less pronounced in

comparison to the influence of the electrode width as observed in the previous electrode

width experiment.

86

5.4.5 Number of fingers

FIGURE: NFingers Simulation

Building off the result wherein the channel width is varied, we varied the number of inter-

digitated electrode finger pairs while keeping the exterior electrode and channel geometries

constant. Numerical COMSOL simulations performed by my colleague, Shari Yosinski,

suggest that capture efficiency should increase monotonically with the number of electrode

finger pairs, each pair presenting an additional opportunity to capture target particles that

would have otherwise escape, as can be seen in Fig. ??.

As a consequence, then, it was posited that the only upper bound on capture electrode

area was the maximal permissible footprint of the device. By observing the change in the

equilibrium velocity as a function of the number of fingers, we see that instead there exists a

crossover regime wherein the increasing capture probability is offset by the decrease in DEP

voltage, thereby constraining the number of fingers to a geometry- and conductivity-specific

optimum.

FIGURE: Abstract of Experiment 4 chip showing number of fingers varied, still from

DEP capture video, show a few particle y v. t traces on a graph, then show the net change

in velocity for the different number of fingers. Conceptual roll-off between capture efficiency

and n-fingers with increase and decrease. Device impedances plot.

5.5 Conclusions

5.5.1 Motivation

The ramifications of the design recommendations of this study cannot be understated. First

and foremost, the principles of electrode design for dielectrophoretic capture are empirically

investigated in order to maximize capture efficiency for a given source voltage, reducing

the operational demands (voltage, power) of the high-frequency signal generators used for

DEP. This lowers the barrier to implementation for portable lab-on-chip applications. Fur-

87

thermore, the insights gained from the investigation of the dielectrophoretic force directly

inform efforts to utilize the technology successfully in physiological saline concentrations,

which have been plagued by weak force magnitude [?] and sample/device destruction from

Joule heating [?].

5.5.2 Mitigating series resistances

For mitigating the negative impacts of the series resistance, the electrode width should be

increased and lead-in length minimized. Researchers should be aware that there are dimin-

ishing returns to these increases for the electrode leads as the series resistance contribution

approaches a few Ω at most.

Finger resistance should be primarily address through minimizing the excess finger

length. Further study into the interplay of the electrode width/gap on the DEP force, but

such design changes also alter the gradient profile driving the DEP capture and therefore

require a more nuance and target-specific view but remains an active area of investigating

for performance engineering.

The series resistance of the solution, however, should be maximized. This is most readily

done by adjusting the conductivity of the sample solution used and helps to explain the

prevalence of DEP in the literature conducted at lower conductivity: with low conductiv-

ity/large resistance, other design considerations are unlikely to have a significant deleterious

impact on performance.

5.5.3 ramifications for Cox

Another active area of research has been insulator-DEP, or iDEP. iDEP has been primarily

motivated by the desire to coat the electrodes with a passivating oxide which discourages

adhesion at the electrode surface. Adhesion is undesirable as it prevents the subsequent

release of captured particles, either to prepare for another sample or for some additional

downstream processing. While successfully addressing adhesion concerns, iDEP is quite

undesirable in that it typically requires quite large [?] DC field strengths (order hundreds

88

of volts) to achieve the desired capture. The circuit model contained within provides a

framework for introducing the effect of a protective coating on interdigitated structures.

Introducing a series capacitance between the finger resistance and the double-layer ca-

pacitance into the circuit model of Fig. ??, we combine the two capacitors into a single,

equivalent capacitor. Capacitors in series combine like resistors in parallel, and therefore

the smaller of the two capacitances dominates. Due to the atomically-thin nature of the

ionic double-layer, the deposited coating is the determining factor. Provided the impedance

of the coating capacitance is small compared to the solution resistance at the desired op-

erational frequency, the coating will not significantly impair device performance under the

proposed circuit model. Thereby researchers may obtain the benefit of iDEP without the

marked drawbacks usually associated.

Permitting insulating protective layers has an added benefit of no longer limiting the

choice of metal to noble metals such as gold or platinum. Contained with an insulated

coating, aluminum works perfectly well as an electrode material of choice (and has the

advantage of a high-quality native oxide to act as a thin protective layer), thereby signifi-

cantly reducing fabrication costs per device, clearing one additional hurdle for commercial

adoption.

5.5.4 Power transfer v. voltage

A common point of confusion should also briefly be discussed. Intuition suggests that load

and output impedances should be matched, particularly when dealing with high-frequency

signals. Satisfying this criterion maximizes power transfer to the load, and minimizes sig-

nal reflection to the voltage source, which may not be capable of handling the incoming

power. This intuition fails in three respects in the context of dielectrophoresis: total input

power to the device is not the relevant figure of merit, the spatial gradient driving the

dielectrophoretic force can be designed for improved performance at identical power deliv-

eries across the solution resistance, and efforts to minimize the solution resistance itself will

increase the influence of parasitics and lead to rampant Joule heating.

89

As can be seen from Eqn. ??, the dielectrophoretic force scales with the gradient of the

potential squared. When a voltage is applied across a resistor, it also dissipates a power

proportional to the square of the applied potential. Efforts to maximize the total power

dissipated in the device on a macroscopic level neglect the critical role of the potential

gradient across solution in determining the performance of a dielectrophoretic device.

For this same reason, efforts to improve power delivery by reducing the solution resis-

tance (increasing the cross-sectional area at a fixed conductivity, for instance) fail to consider

the parasitic effects of the physical electrodes themselves. Maximizing power dissipated

outside the microfluidic solution region only serves to increase device power consumption

without improving performance.

Lastly, designers must be aware of the deleterious effects of maximizing power transfer

in its own right. Capture via dielectrophoresis, as previously discussed, is a very binary

result: either the particle is held near the electrode or it is not. Excess capture force

(and therefore excess voltage) induces additional power dissipation in the fluidic region

without added benefit to performance. This power dissipation induces Joule heating in

the local region of the fluidic constriction. This is a common problem when performing

dielectrophoretic capture in high-conductivity (i.e., physiological salinity) oslutions, wherein

the heating causes solution to rapidly boil off, destroying the electrodes and sample alike.

Solutions must either minimize the excess applied voltage to reduce the aggregate power

or address the localized heating by increasing thermal dissipation or spreading the thermal

load across a larger region of the device.

Lastly, at a fixed magnitude potential across solution it remains possible to optimize the

design of the electrode pattern to maximize the gradient of the electric field lines between

the two electrodes. Designs which present equivalent solution impedances yet have differing

spatial profiles would exert different dielectrophoretic forces on nearby particles. Electrode

patterning for dielectrophoresis remains an active area of research both in the literature

and in this lab.

90

Appendix A

Stuff

If you need an appendix, it will go here.

91

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