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
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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
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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
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List of Tables
2.1 Table to test captions and labels . . . . . . . . . . . . . . . . . . . . . . . . 10
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Acknowledgements
A lot of people are awesome. Probably your family, friends, advisor, and that one super
special high school teacher who believed in you.
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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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