Electrolyte-Gated Graphene Field-Effect Transistors: ARCHIVES
Modeling and Applications
ASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
By
MAR 19 2015
Charles Edward Mackin
LIBRARIES
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
0 Massachusetts Institute of Technology 2014. All rights reserved.
Signature redacted
Signature of Author:
Department of Electrical Engineering & Computer Science
December 11, 2014
Signature redacted
Certified by:
Tomis Palacios
Professor of Electrical Engineering and Computer Science
Thesis supervisor
Accepted by:
Signature redacted
Le~ i'e. IKolodziejski
Chair, Departmental Commi tee on Graduate students
2
Graphene Electrolyte-Gated Field-Effect Transistors: Modeling and
Applications
By
Charles Mackin
Submitted to the Department of Electrical Engineering & Computer Science
on August 29, 2014 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in Electrical Engineering and
Computer Science
ABSTRACT
This work presents a model for electrolyte-gated graphene field-effect transistors
(EGFETs) that incorporates the effects of the double layer capacitance and the
quantum capacitance of graphene. The model is validated through experimental
graphene EGFETs, which were fabricated and measured to provide experimental
data and extract graphene EGFET parameters such as mobility, minimum carrier
concentration, interface capacitance, contact resistance, and effective charged
impurity concentration.
The proposed graphene EGFET model accurately
determines a number of properties necessary for circuit design such as currentvoltage characteristics, transconductance, output resistance, and intrinsic gain. The
model can also be used to optimize the design of EGFETs. For example, simulated
and experimental results show that avoiding the practice of partial channel
passivation enhances the transconductance of graphene EGFETs.
Graphene EGFETs are fabricated for pH sensing. The location of the Dirac point is
measured for pH concentrations varying from 4 to 10. In this range, graphene
EGFETs are shown to produce -50.8 mV/pH sensitivity. Graphene EGFETs are also
fabricated for use in a real-time polymerase chain reaction (RTPCR) system. RTPCR
is run successfully to identify DNA segments thought responsible for the metabolism
of clopidogrel, a widely prescribed antiplatelet medication. The graphene EGFETs,
however, failed to sense an increase in DNA concentration. Further optimization of
the PCR mix is required to ensure that increased DNA concentration lowers the PCR
mix pH without rendering the DNA polymerase ineffective. Lastly, graphene
EGFETs fabricated for electrogenic cell sensing using the optimized parameters
from the newly developed graphene EGFET current-voltage model. Hippocampal
mouse neurons were cultured on top of the graphene EGFETs in attempt record
action potentials.
Thesis Supervisor: Tomis Palacios
Title: Professor of Electrical Engineering and Computer Science
3
Contents
Chapter 1- Introduction
1- Introduction to Graphene
2- Introduction Graphene Electrolyte-Gated Field-Effect Transistors
(EGFETs)
3- Graphene EGFET Operation Principles
4- Relevant Principles in Electrochemistry
Chapter 2 - Graphene EGFET Fabrication & Setup
1234-
Graphene Synthesis
Graphene Transfer Process
Graphene EGFET Fabrication
Measurement Setup
Chapter 3 - Monolayer Graphene EGFET Characterization
1- Graphene-Electrolyte Interface Capacitance Modeling
2- Fundamental Current-Voltage Model for Graphene EGFETs
3- Current-Voltage Model for Graphene EGFETs with Heterogeneous TopGate Capacitances
4- Minimum Conduction Point
5- Fitting the Current-Voltage Model to Experimental Data
6- Passivation Scheme Comparison
7- Performance Optimization for Electrogenic Cell Sensing
Chapter 4 - Graphene EGFET Applications
1- pH Sensing
2- Monitoring Real-time Polymerase Chain Reaction
3- Electrogenic Cell Sensing
Chapter 5 - Summary & Conclusions
4
Chapter 1 - Introduction
1. Introduction to Graphene
Graphene consists of an atomically-thin planar sheet of sp 2 -bonded carbon atoms
arranged in a hexagonal lattice [1]-[5]. Graphene is one of three low-dimensional
carbon allotropes depicted in Fig. 1.1. As a zero band gap and all-surface material,
graphene's electrical properties are affected by its surrounding environment. This
serves as the chief motivation for graphene's use in sensing applications. Graphene
also possesses a combination of electrical, mechanical and chemical properties that
make it promising for use in chemical and biological sensors. These properties
include room temperature mobilities in excess of 50,000 cm 2 /Vs [6], high surfaceto-weight ratio of 2630 m 2 /g [7], [8], flexibility [9]-[12], high Young's modulus of 1
TPa and breaking strength of 42 N/in [13], a wide electrochemical potential window
of 2.5 V in phosphate buffered saline [14], and relatively inert electrochemistry
[15]-[18].
a)
b)
19MW--_C)
Fig. 1.1: New carbon allotropes a) spherical Buckminster fullerene b) 1D carbon nanotube c) 2D
graphene [19].
Graphene may be synthesized using a number of methods. Monolayer and few layer
graphene were initially isolated by repeated mechanical exfoliation of highly
oriented pyrolytic graphite (HOPG) [20]. Graphene may also be grown by thermal
decomposition of silicon carbide [21]. In this process, silicon carbide is annealed at
high temperature-typically above 1000*C-in an inert gas. This causes silicon
atoms to desorb from the silicon carbide lattice leaving behind a layer of carbon
atoms at the surface, which rearrange and bond to form epitaxial graphene. Lower
quality and multilayered graphene films are also commonly synthesized by reducing
graphene oxide [7]. Lastly, graphene may be synthesized using chemical vapor
deposition (CVD). In this process, methane is flowed over a metal foil-usually
nickel or copper-at around 1000*C resulting in graphene formation on the metal
surface. CVD graphene synthesis is capable of producing large sheets of graphene at
relatively low cost [22]-[24].
5
2. Introduction to Graphene Electrolyte-Gated FieldEffect Transistors (EGFETs)
A number of graphene-based chemical and biological sensing devices have been
developed in recent years. The vast majority of these graphene chemical and
biological sensors may be categorized as optical, electrochemical, or FET-based.
Optical-based graphene sensors offer analyte detection without the risk of adversely
altering the analyte environment [25]. These sensors, however, often require light
sources, mirrors, and filters making low-cost and miniaturization difficult.
Electrochemical graphene sensors not only provide analyte detection but a wealth
of information regarding analyte reaction kinetics. These sensors, however,
typically require bulky and expensive potentiostats as well as a trained professional
to run a number of measurements and to interpret the complex data. FET-based
approaches, on the other hand, offer the ability to make cheap, stand-alone, and
small (e.g. implantable) sensors with greatly simplified readout systems. Equally
important, FET-based graphene sensors are promising in terms of performance. For
instance, reported detection limits for FET-based graphene dopamine sensors are
on par or better than their electrochemical counterparts [26]-[37].
Graphene's inertness enables a direct interface with many chemical and biological
environments. This is particularly beneficial for the electrolytic environments
present in a variety of biological and chemical sensing applications because
graphene can exploit the electrical double layer phenomenon and resulting ultrahigh interface capacitance [38]. This large capacitance coupled with graphene's
high mobility enables high-transconductance field-effect transistor (FET) sensors,
which have been shown capable of less than 10pV RMS gate noise [39]-[43].
Graphene electrolyte-gated field-effect transistors (EGFETs) consist of a graphene
channel between two conductive source-drain contacts, which are typically metals.
Some portion of the graphene channel is exposed to the electrolytic environment;
either directly or via some selectively permeable membrane. This allows changes in
the electrolytic environment to alter the graphene channel's electrical properties.
Some form of read out circuitry is then used to identify these changes in electrical
properties. No material constraints are imposed on the substrate, which can vary
from glass to silicon to polymer. Fig. 1.2 depicts the layout and measurement setup
of a typical graphene EGFET.
6
VGS
-- VDS
-
Vs
Si LjSiO2
=
Ti/Au/Pt E2Graphene
Polyimide IZ
LI SU-8
=j
Electrolyte
Fig. 1.2: Graphene EGFET with heterogeneous top-gate
capacitance due to non-self-aligned completely passivated
source and drain regions. VS, VDS, and VGs represent the
voltages applied to the source, drain, and gate, respectively.
3. Graphene EGFET Operation Principles
Graphene electrolyte-gated field-effect transistor (EGFET) sensors rely on one of two
operation principles: Dirac point shifts or VGS modulation. In the Dirac point shift
approach, a change in the electrolytic environment alters the graphene Fermi level. In
other words, the graphene become more p-type or n-type. For certain applications such
as electrogenic cell sensing, graphene EGFETs can be thought of as operating based on
VGS modulation. For instance, when a neuron produces an action potential near the
graphene surface, it alters the distribution of ions found at the graphene surface. Even
though VGS is held constant, this process can be thought of as a slight modulation in the
effective Vcs voltage. The change in the effective VGS then results in a detectable change
in IDS current. Figs. 1.3, 1.4 depict how Dirac point shifts and VGs modulation impacts
the measured current-voltage characteristic.
IDS
IDS
AIDS{
'----1~
I'
Ii
Ii
I
AVDRAC
VGS
0
Fig. 1.3: Change in electrolyte composition alters
graphene doping and the location of the Dirac
point.
ll
A-r.
~
VGS
0
Fig. 1.4: Change in ionic composition near the
graphene surface due to electrogenic cell activation
modulates the applied Vcs voltage.
7
4. Relevant Principles in Electrochemistry
Understanding graphene electrolyte-gate field-effect transistor operation requires
an introduction to a couple fundamental principles of electrochemistry: electric
double layer formation and electrochemical potential windows.
An electric double layer is formed whenever an electrode is interfaced with an
electrolyte of a different electrochemical potential. This causes either the cations or
anions of the electrolyte to preferentially migrate to the surface of the electrode. In
equilibrium, the ionic charge is screened by an equal and opposite amount of charge
within the electrode so that net charge neutrality is maintained. The charge
separation occurs primarily over a few nanometers. As a result, electric double
layer capacitances are quite large and typically range from a few pF/cm 2 to tens of
pF/cm 2 . Several models have been developed to describe the electric double layer
phenomenon. The most common are the Helmholtz model, Gouy-Chapman model,
and the Gouy-Chapman-Stern model.
Helmholtz, who credited with discovery the electric double layers, assumed all ions
were specifically adsorbed onto the electrode surface and therefore modeled the
electric double layer using a simple parallel plate capacitor. The Gouy-Chapman
model is a diffuse electric double layer model, which takes into account the fact that
the ions are subject to diffusive and electrostatic forces within the electrolyte.
Lastly, the Gouy-Chapman-Stern model combines the previous two models to allow
for layer of specifically adsorbed ions as well as a diffusive region. Fig. 1.5 depicts
the three different electric double layer models.
diffuse layer
diffuse layer
a O solvent
%
0
(a) Helmholtz modcl
Stern layer
(b) Gouy-Chapman model
moIlcuIl
anion
(c) Gouy -Chapman-Stern modcl
Fig. 1.5: The three most common models used to describe electric double layers a) Helmholtz model
b) Gouy-Chapman model c) Gouy-Chapman-Stern model [44].
The drawback with these models is that they model ions as point charges. In
actuality, ions occupy a certain amount of volume and have a limited packing
8
density. In general, this means the Helmholtz, Gouy-Chapman, and Gouy-ChapmanStern models only accurately model electric double layers at low ionic
concentrations and low potentials. More accurate models such as the modified
Poisson-Boltzmann (MPB) account for steric effects and are described by the
following equations [45].
21p
_zqN
c0
2 sinh(q z 0
)
1+2sinh~qkBT)
1+2vinh
where ip is the potential, c, represents the ion species bulk concentration, z is the
corresponding ion valency, NA is Avogadro's number, kB is the Boltzmann constant,
E is the permittivity, q is the elementary charge, and T is temperature. Steric effects
are included via the denominator term in the summation and are governed by the
packing parameter v. The packing parameter represents the maximum density to
which ions may accumulate at the graphene-electrolyte interface and is given by the
following equation.
v = 2a 3cO
where a is the effective diameter of the ion species and c, again represents the bulk
ion species concentration.
Solutions to the modified Poisson-Boltzmann equation play an important role in
building intuition on how a number of factors might influence the grapheneelectrolyte interface (Figs. 1.6 - 1.9). The effects of bulk electrolyte composition,
permittivity, and effective ion sizes have been determined for the potential, ion
concentration, total electrical double layer charge, and capacitance. Analytic
solutions to the modified Poisson-Boltzmann equation become difficult or
impossible for many scenarios applicable to graphene EGFETs. Because of this,
solutions to the modified Poisson-Boltzmann equation are obtained numerically
from a custom built simulation.
9
Ion Concentration v. Distance from Interface (MPB)
(z = 1, CO = 0.15 M, P0 = 25 mV, ion size = 1 nm)
Total Charge per Area v. Applied Voltage (P0)
(z = 1, er = 78.3, ion size = 1 nm)
45,
-er
0.35
-er
= 78.3 (z = +1)
-- er=78.3(z=-1)
er = 100 (z =+1)
er =100 (z =-1)
-er = 120 (z =+1)
er = 120 (z =-1)
0.3
0.25
0.2
-
= 30 (z = +1)
er = 30 (z = -1)
---- er = 50 (z = +1)
- -er = 50 (z = -1)
0.4
-CO =0.01 M(PB)
CO = 0.01 M (MPB)
CO = 0.05 M (PB)
-CO = 0.05 M(MPB)
_-_ CO = 0.10 M (PB)
-- CO = 0.10 M (MPB)
CO = 0.15 M (PB)
C = 0.15 M(MPB)
--CO = 0.30 M (PB)
L--C0 = 0.30 M (MPB)
0.6
0.8
1
-10
105
>
0.15
< 10
0.1
.- 0
0.2
0. 8
0.4
0.6
Distance(m)
108
1
x 108
E"f
-- Et.
-Eff.
-Eff.
E 150
'-Eff.
0.2
0.4
P0 (V)
Fig. 1.7: Electric double layer charge density as a
function of electrode potential for various
electrolyte concentrations. Solid lines represent are
MPB solutions that include steric effects. Dashed
lines are Poisson-Boltzmann solutions, which
neglect steric effects.
Fig. 1.6: Cation and anion concentrations as a
function of distance from the electrode surface for
varying electrolyte permittivity.
200
0
-Concentration =10 mM
10
Ion Size = 5 A
Ion Size = 1 nm
Ion Size = 2 nm
Ion Size =3 nm
Ion Size = 4 nm
-Concentration
-Concentration
50 mM
= 100 mM
=
Concentration = 150 mM
- Concentration = 200 sM
E
S60 L
100-
.0 40
c-
C- 50
co 20-
0~
-
-1.5
-
-05
0
Potential (V)
05
1
15
Fig. 1.8: Electric double layer capacitance versus
applied potential for various effective ion sizes.
The simulated data includes steric effects and is
for 100 mM symmetric aqueous electrolyte with
relative permittivity 78.3.
2
-
:2-15
-1
-0.5
0
Potential (V)
05
1
1.5
Fig. 1.9: Electric double layer capacitance versus
applied potential for various ion concentrations.
The simulated data includes steric effects and is
for an aqueous symmetric electrolyte with a 1
nm effective ion size and relative permittivity of
78.3.
Electrochemical potential windows are another important concept to understanding
graphene EGFET operation. The basic layout for a graphene EGFET is re-illustrated
in Fig. 1.10 for convenience. Note that the graphene is directly interfaced with the
electrolyte. Both the graphene and electrolyte are conductive so the pertinent
question becomes: what prevents current from flowing from the gate through
electrolyte and into the graphene channel towards the source terminal?
2
10
vGS
Si
II
SiO2 l
Polyimide K
Graphene LI
TI/Au/Pt n
SU-8
=l
Electrolyte
Fig. 1.10: Graphene EGFET with heterogeneous top-gate
capacitance due to non-self-aligned completely passivated
source and drain regions. Vs, VDS, and VGs represent the
voltages applied to the source, drain, and gate, respectively.
In order for a DC current to flow at the graphene electrolyte interface, there must be
a sustained reduction or oxidation of one of the chemical species. In the case of
aqueous NaCl electrolyte, either Na+ must be reduced, Cl- must be oxidized, or water
molecules must be split in order to create oxygen and hydrogen gases. These
processes all require some activation barrier to be overcome. Fortunately, these
activation barriers are quite high for many graphene-electrolyte reactions including
aqueous NaCl and phosphate buffered saline (PBS) [14].
The current density due to the oxidation and reduction of chemical species at an
electrode is described by the Butler-Volmer equation (Eq. 1.1).
j
= jo[eaanFi/RT
-
e-acnFl/RT1
(1.1)
Where j is the current density, jo is the exchange current density, aa is the anodic
charge transfer coefficient, a, is the cathodic charge transfer coefficient, n is the
number of electrons involved in the reaction, R is the universal gas constant, T is the
The graphene-electrolyte
absolute temperature, and -q is the overpotential.
interface possesses a low exchange current density. This results in a large potential
range where negligible DC current exists across the graphene-electrolyte interface.
Fig. 1.11 depicts the wide electrochemical potential window of graphene in 1M
aqueous NaCl.
I1
1.5
1 --
0.50-0.5-1--
5
-0.5
0
0.5
1
1.5
Voltage (V)
Fig. 1.11: Graphene electrode current versus potential in 1M
aqueous NaCl using an Ag/AgCl reference electrode and 1 mm
diameter platinum button counter electrode. The grapheneelectrolyte interface has dimensions W/L = 40 pm/20um.
The graphene channel may be biased anywhere from -1 to +1 volts without bringing
on any oxidation or reduction currents. Thus, the gate leakage current can be kept
at negligible levels without requiring graphene passivation by some oxide material.
This wide electrochemical potential window enables graphene EGFETs to be
directly interfaced with electrolytic environments and take full advantage of the
high electric double layer capacitance. It is also important to note that the total
oxidation-reduction currents are directly proportional to the exposed electrode area.
Simply decreasing the area of the graphene channel can therefore be employed to
further reduce the oxidation-reduction currents.
References
[1]
A. K. Geim and K. S. Novoselov, "The Rise of Graphene," Nat. Mater., vol. 6, no.
3, pp. 183-91, Mar. 2007.
[2]
Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, "Graphene
and Graphene Oxide: Synthesis, Properties, and Applications," Adv. Mater., vol.
22, no. 35, pp. 3906-24, Sep. 2010.
[3]
A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim,
"The Electronic Properties of Graphene," Rev. Mod. Phys., vol. 81, no. 1, pp.
109-162, Jan. 2009.
[4]
K. Tahy, T. Fang, P. Zhao, A. Konar, C. Lian, H. G. Xing, M. Kelly, and D. Jena,
"Graphene Transistors," 2008.
[5]
C. Soldano, A. Mahmood, and E. Dujardin, "Production, Properties and
Potential of Graphene," Carbon N. Y, vol. 48, no. 8, pp. 2127-2150, Jul. 2010.
12
[6]
N. Petrone, C. R. Dean, I. Meric, A. M. van der Zande, P. Y. Huang, L. Wang, D.
Muller, K. L. Shepard, and J. Hone, "Chemical Vapor Deposition-Derived
Graphene with Electrical Performance of Exfoliated Graphene," Nano Lett., vol.
12, no. 6, pp. 2751-6, Jun. 2012.
[7]
S. Park and R. S. Ruoff, "Chemical Methods for the Production of Graphenes,"
Nat. Nanotechnol., vol. 4, no. 4, pp. 217-24, Apr. 2009.
[8]
M. D. Stoller, S. Park, Y. Zhu, J. An, and R. S. Ruoff, "Graphene-Based
Ultracapacitors," Nano Lett., vol. 8, no. 10, pp. 3498-502, Oct. 2008.
[9]
S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R.
Kim, Y. I Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S.
lijima, "Roll-to-roll production of 30-inch graphene films for transparent
electrodes.," Nat. Nanotechnol., vol. 5, no. 8, pp. 574-8, Aug. 2010.
[10]
U. St6berl, U. Wurstbauer, W. Wegscheider, D. Weiss, and J. Eroms,
"Morphology and Flexibility of Graphene and Few-Layer Graphene on Various
Substrates," AppL. Phys. Lett., vol. 93, no. 5, p. 051906, 2008.
[11]
Y. Xu, Y. Wang, J. Liang, Y. Huang, Y. Ma, X. Wan, and Y. Chen, "A Hybrid
Material of Graphene and Poly (3,4-ethyldioxythiophene) with High
Conductivity, Flexibility, and Transparency," Nano Res., vol. 2, no. 4, pp. 343348, Apr. 2009.
[12]
K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y.
Choi, and B. H. Hong, "Large-Scale Pattern Growth of Graphene Films for
Stretchable Transparent Electrodes," Nature, vol. 457, no. 7230, pp. 706-10,
Mar. 2009.
[13]
C. Lee, X. Wei, J. W. Kysar, and J. Hone, "Measurement of the Elastic Properties
and Intrinsic Strength of Monolayer Graphene," Science (80-.)., vol. 321, no.
July, pp. 385-388, 2008.
[14]
M. Zhou, Y. Zhai, and S. Dong, "Electrochemical Sensing and Biosensing
Platform Based on Chemically Reduced Graphene Oxide," Anal. Chem., vol. 81,
no. 14, pp. 5603-13, Jul. 2009.
[15] D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V Morozov, P. Blake, M. P. Halsall, A.
C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov,
"Control of Graphene's Properties by Reversible Hydrogenation: Evidence for
Graphane,"Science, vol. 323, no. 5914, pp. 610-3, Jan. 2009.
[16]
Y. Shao, J. Wang, H. Wu, J. Liu, I. A. Aksay, and Y. Lin, "Graphene Based
Electrochemical Sensors and Biosensors: A Review," Electroanalysis,vol. 22,
no. 10, pp. 1027-1036, May 2010.
13
[17]
D. A. C. Brownson, D. K. Kampouris, and C. E. Banks, Graphene
Electrochemistry:FundamentalConcepts Through to ProminentApplications,
vol. 41, no. 21. 2012, pp. 6944-76.
[18]
D. Chen, L. Tang, and J. Li, "Graphene-Based Materials in Electrochemistry,"
Chem. Soc. Rev., vol. 39, no. 8, pp. 3157-80, Aug. 2010.
[19]
M. Scarselli, P. Castrucci, and M. De Crescenzi, "Electronic and Optoelectronic
Nano-Devices Based on Carbon Nanotubes,"J. Phys. Condens. Matter, vol. 24,
no. 31, p. 313202, Aug. 2012.
[20]
K. S. Novoselov, a K. Geim, S. V Morozov, D. Jiang, Y. Zhang, S. V Dubonos, I. V
Grigorieva, and a a Firsov, "Electric Field Effect in Atomically Thin Carbon
Films," Science, vol. 306, no. 5696, pp. 666-9, Oct. 2004.
[21]
H. Hibino, S. Tanabe, S. Mizuno, and H. Kageshima, "Growth and Electronic
Transport Properties of Epitaxial Graphene on SiC," J. Phys. D. Appl. Phys., vol.
45, no. 15, p. 154008, Apr. 2012.
[22]
X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, 1. Jung, E.
Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, "Large-Area Synthesis of
High-Quality and Uniform Graphene Films on Copper Foils," Science, vol. 324,
no. 5932, pp. 1312-4, Jun. 2009.
[23]
A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J.
Kong, "Large Area, Few-Layer Graphene Films on Arbitrary Substrates by
Chemical Vapor Deposition," Nano Lett., vol. 9, no. 1, pp. 30-5, Jan. 2009.
[24]
Y. Huang, X. Dong, Y. Shi, C. M. Li, L.-J. Li, and P. Chen, "Nanoelectronic
Biosensors Based on CVD Grown Graphene," Nanoscale, vol. 2, no. 8, pp. 14858, Aug. 2010.
[25]
G. L. C. Paulus, K. Y. Lee, N. F. Reuel, Q. H. Wang, and R. Brittany, "A GrapheneBased Physiometer Array for the Analysis of Single Biological Cells," in
American Institute of Chemical Engineers, 2013.
[26]
Y. Wang, Y. Li, L. Tang, J. Lu, and J. Li, "Application of Graphene-Modified
Electrode for Selective Detection of Dopamine," Electrochem. commun., vol. 11,
no. 4, pp. 889-892, Apr. 2009.
[27]
M. Zhang, C. Liao, Y. Yao, Z. Liu, F. Gong, and F. Yan, "High-Performance
Dopamine Sensors Based on Whole-Graphene Solution-Gated Transistors,"
Adv. Funct. Mater., vol. 24, no. 7, pp. 978-985, Feb. 2014.
[28]
Y.-R. Kim, S. Bong, Y.-J. Kang, Y. Yang, R. K. Mahajan, J. S. Kim, and H. Kim,
"Electrochemical Detection of Dopamine in the Presence of Ascorbic Acid
14
using Graphene Modified Electrodes," Biosens. Bioelectron., vol. 25, no. 10, pp.
2366-9, Jun. 2010.
[29]
C.-L. Sun, H.-H. Lee, J.-M. Yang, and C.-C. Wu, "The Simultaneous
Electrochemical Detection of Ascorbic Acid, Dopamine, and Uric Acid using
Graphene/Size-Selected Pt Nanocomposites.," Biosens. Bioelectron., vol. 26, no.
8, pp. 3450-5, Apr. 2011.
[30]
S. Hou, M. L. Kasner, S. Su, K. Patel, and R. Cuellari, "Highly Sensitive and
Selective Dopamine Biosensor Fabricated with Silanized Graphene,"J. Phys.
Chem. C, vol. 114, no. 35, pp. 14915-14921, Sep. 2010.
[31]
L. Wu, L. Feng, J. Ren, and X. Qu, "Electrochemical Detection of Dopamine
using Porphyrin-Functionalized Graphene," Biosens. Bioelectron., vol. 34, no. 1,
pp. 57-62, Apr. 2012.
[32]
Y. Zeng, Y. Zhou, L. Kong, T. Zhou, and G. Shi, "A Novel Composite of Si02Coated Graphene Oxide and Molecularly Imprinted Polymers for
Electrochemical Sensing Dopamine," Biosens. Bioelectron., vol. 45, pp. 25-33,
Jul. 2013.
[33]
L. Tan, K.-G. Zhou, Y.-H. Zhang, H.-X. Wang, X.-D. Wang, Y.-F. Guo, and H.-L.
Zhang, "Nanomolar Detection of Dopamine in the Presence of Ascorbic Acid at
P-Cyclodextrin/Graphene Nanocomposite Platform," Electrochem. commun.,
vol. 12, no. 4, pp. 557-560, Apr. 2010.
[34]
Y. Mao, Y. Bao, S. Gan, F. Li, and L. Niu, "Electrochemical Sensor for Dopamine
Based on a Novel Graphene-Molecular Imprinted Polymers Composite
Recognition Element," Biosens. Bioelectron., vol. 28, no. 1, pp. 291-7, Oct. 2011.
[35]
J. Du, R. Yue, F. Ren, Z. Yao, F. Jiang, P. Yang, and Y. Du, "Novel Graphene
Flowers Modified Carbon Fibers for Simultaneous Determination of Ascorbic
Acid, Dopamine and Uric Acid," Biosens. Bioelectron., vol. 53, pp. 220-4, Mar.
2014.
[36]
L. Yang, D. Liu, J. Huang, and T. You, "Simultaneous Determination of
Dopamine, Ascorbic Acid and Uric Acid at Electrochemically Reduced
Graphene Oxide Modified Electrode," Sensors Actuators B Chem., vol. 193, pp.
166-172, Mar. 2014.
[37]
T. Qian, C. Yu, X. Zhou, S. Wu, and J. Shen, "Au Nanoparticles Decorated
Polypyrrole/Reduced Graphene Oxide Hybrid Sheets for Ultrasensitive
Dopamine Detection," Sensors Actuators B Chem., vol. 193, pp. 759-763, Mar.
2014.
15
[38]
M. D. Stoller, C. W. Magnuson, Y. Zhu, S. Murali, J. W. Suk, R. Piner, and R. S.
Ruoff, "Interfacial Capacitance of Single Layer Graphene," Energy Environ. Sci.,
vol. 4, no. 11, p. 4685, 2011.
[39]
L. H. Hess, M. V. Hauf, M. Seifert, F. Speck, T. Seyller, M. Stutzmann, I. D. Sharp,
and J. A. Garrido, "High-Transconductance Graphene Solution-Gated Field
Effect Transistors," AppL. Phys. Lett., vol. 99, no. 3, p. 033503, 2011.
[40]
L. H. Hess, M. Seifert, and J. a. Garrido, "Graphene Transistors for
Bioelectronics," Proc. IEEE, vol. 101, no. 7, pp. 1780-1792, 2013.
[41] M. Dankerl, M. V. Hauf, A. Lippert, L. H. Hess, S. Birner, I. D. Sharp, A. Mahmood,
P. Mallet, J.-Y. Veuillen, M. Stutzmann, and J. a. Garrido, "Graphene SolutionGated Field-Effect Transistor Array for Sensing Applications," Adv. Funct.
Mater., vol. 20, no. 18, pp. 3117-3124, Sep. 2010.
[42]
Z. Cheng, Q. Li, Z. Li, Q. Zhou, and Y. Fang, "Suspended Graphene Sensors with
Improved Signal and Reduced Noise," Nano Lett., vol. 10, no. 5, pp. 1864-8,
May 2010.
[43]
L. H. Hess, M. Jansen, V. Maybeck, M. V Hauf, M. Seifert, M. Stutzmann, I. D.
Sharp, A. Offenhausser, and J. a Garrido, "Graphene Transistor Arrays for
Recording Action Potentials from Electrogenic Cells," Adv. Mater., vol. 23, no.
43, pp. 5045-9, Nov. 2011.
[44]
H. Wang and L. Pilon, "Accurate Simulations of Electric Double Layer
Capacitance of Ultramicroelectrodes,"]. Phys. Chem. C, vol. 115, no. 33, pp.
16711-16719, Aug. 2011.
[45]
M. Kilic, M. Bazant, and A. Ajdari, "Steric Effects in the Dynamics of
Electrolytes at Large Applied Voltages. I. Double-layer Charging," Phys. Rev. E,
vol. 75, no. 2, p. 021502, Feb. 2007.
16
Chapter 2 - Graphene EGFET
Fabrication & Setup
1. Chemical Vapor Deposition Graphene Synthesis
Chemical vapor deposition (CVD) graphene synthesis has been demonstrated by
flowing methane over a number of transition metals including cobalt, ruthenium,
nickel, and copper [1]-[4]. In this process, the metal substrate serves as a catalyst
for methane decomposition as given by the following chemical reaction (Eq. 2.1).
CH 4 -+ C + 2H 2
(2.1)
The transition metal substrate also provides nucleation sites for graphene growth
[5]. Copper, however, has become dominant substrate for CVD graphene synthesis
because the graphene growth process self-terminates after the formation of
monolayer graphene. This phenomenon is attributed to the low carbon solubility in
copper, which prevents additional layers of graphene from forming via the out
diffusion of carbon from the copper substrate.
The CVD graphene used for this work was grown by first loading copper foils inside
a quartz tube furnace and heating the copper substrate to 1000'C for thirty minutes
in a mixture of argon and hydrogen gas. This step removes the oxide from the
copper surface and helps reduce the number of surface impurities. A mixture of
methane and hydrogen gas is then flown over the copper substrate at 1000*C for
forty minutes during the graphene synthesis stage (Fig. 2.1). Finally, the copper
substrate is cooled to room temperature while flowing a mixture of hydrogen and
methane. The resulting graphene film is depicted in Fig. 2.2.
~H2
CH 4
Bl
1Boundary layer
6
H* + C*+.3
CH
Surface
Fig. 2.1: CVD graphene synthesis depicting
formation from methane decomposition and
carbon nucleation at the copper substrate [5].
Fig. 2.3: Optical microscope image of a large-area
intact and clean CVD graphene on a Si/SiO 2 wafer
substrate.
17
2. Graphene Transfer Process
A well-developed graphene transfer process is essential for well-functioning
EGFETs with reasonably consistent electrical properties. Poor graphene transfer
processes may result in discontinuous graphene, large amounts of wrinkling, and a
great deal of unwanted photoresist residue at the graphene-electrolyte interface.
The following illustration provides an overview of the most essential graphene
transfer processes [3]. A more detailed description of the transfer process is given
thereafter.
Graphene
Cu Foil
Wax Paper
PET
PMMA
-
Target Substrate
1. Graphene Growth on Cu Foil
2. Transfer Graphene/Cu Foil to Wax
Paper & PET
3. Spin Coat PIMMA
4. Cut Off Wax Paper and PET
5. Back Etch Graphene
6. Dissolve Cu Substrate
7. Transfer Graphene/PMMA to Target
Substrate
8. Remove PMMA
Graphene is first grown on both sides of a copper foil using the previously described
method of chemical vapor deposition. The graphene/copper foil is then placed on
top of a slightly larger piece of wax paper. The graphene/copper foil and wax paper
and then taped down around the edges to a slightly larger piece of polyethylene
18
terephthalate (PET). PMMA A9 is then diluted with anisole in a 1:1 ratio and spin
coated on top of the entire structure at 2500 rpm for 60 seconds. This results in
structures such as those depicted in Fig. 2.4.
PET
Wax Paper
Graphene/Cu Foil
Fig. 2.4: Graphene/copper foils on top of wax paper and PET. The entire structure
has been spin coated with PMMA.
The graphene/copper foil with coated in PMMA is then released by cutting just
inside the edges of the tape. The graphene/copper foil then has exposed graphene
on one side and PMMA-covered graphene on the other side. The exposed graphene
is then removed using reactive ion etching for 30 seconds in 02 and He plasma.
The copper foil/graphene/PMMA structure is then floated on top of copper etchant
(Transene CE-100) in a Petri dish. After 30 minutes, the copper foil is completely
etched away leaving only the graphene/PMMA film floating on the surface of the
copper etchant. The graphene/PMMA film is then scooped out using a silicon wafer
piece or glass slide and transferred into a new Petri dish containing deionized (DI)
water. This dilutes any copper etchant solution that may have remained on the
graphene/PMMA film. The graphene/PMMA film is transferred twice more to Petri
dishes containing DI water. This further dilutes any copper etchant contamination
and helps ensure that the graphene surface is clean. Next, the graphene/PMMA film
is transferred to HCl/DI H 20 (1:2) mixture for 30 minutes. This process helps to
remove metal ion contaminants and reduce the level of graphene doping. The
graphene is then transferred three times to Petri dishes containing DI water to
further clean the graphene surface. Finally, the graphene/PMMA film is transferred
to the target substrate.
Once on the target substrate, the graphene/PMMA film is gently blow-dried using a
nitrogen gun. The nitrogen gas is aimed at the center of the graphene/PMMA film
causing any water trapped between the graphene and the substrate to be pushed
out towards the edges. This also helps to reduce wrinkles in the graphene/PMMA
film. The graphene/PMMA film is blow-dried until the film is as smooth as possible
and the majority of the water is removed from underneath the film.
19
The target substrate with the graphene/PMMA film is then baked at 80*C for 5
minutes and 130*C for 30 minutes. This allows the PMMA to reflow, which allows
for better adhesion between the graphene and the target substrate. This process
also aids in evaporating any remaining water. The target substrate with the
graphene/PMMA film is then immersed in acetone for two hours to remove the
PMMA film. Any remaining PMMA residue is then further removed by annealing the
sample at 350*C for three hours in 400 sccm of argon and 700 sccm of hydrogen.
The following optical microscope images depict both failed and successful graphene
transfers for Van der Pauw structures. The graphene area is approximately 100 ptm
x 100 ptm. The fabrication of such large-area graphene structures without tears,
excessive wrinkles, and other defects requires consistent implementation of a welldeveloped transfer process. For a detailed description of the entire graphene
EGFET fabrication process, see the subsequent section.
SU-8
Si02
Fig. 2.5: Optical microscope image of poor
graphene transfer for a Van der Pauw structure.
SU-8
S'02
Fig. 2.6: Optical microscope image of a successful
graphene transfer for a Van der Pauw structure.
3. Graphene EGFET Fabrication
Graphene EGFETs were fabricated using a clean 4" silicon wafer coated with Spm of
spin-on polyimide (HD-8820). The polyimide film was annealed at 375*C in 700
sccm argon to prevent outgassing in subsequent high-temperature annealing steps.
Source and drain Ti/Au/Pt (10nm/100nm/20nm) contacts were patterned using
optical lift-off photolithography. Monolayer graphene was then grown on copper
foils using chemical vapor deposition (CVD) and transferred over the entire
substrate using polymethyl methacrylate (PMMA) [6]. PMMA was removed by
immersion in acetone and devices were rinsed with isopropanol. PMMA residue
was further reduced by annealing at 350 0 C in 400 sccm argon and 700 sccm
hydrogen for three hours. The graphene channel regions were defined using
20
MMA/OCG825 photoresist stacks and helium and oxygen plasma, 16 sccm and 8
sccm, respectively. The graphene channel dimensions are W/L = 40 pim / 30 pim.
The MMA/0CG825 photoresist stacks were removed using acetone and isopropanol.
The samples were annealed once more at 350*C in 400 sccm argon and 700 sccm
hydrogen for three hours to further remove MMA residue. The entire wafer was
passivated with 2.4 im of SU-8 2002 and windows were photo defined to provide
electrolyte access to the graphene EGFET channel regions. The SU-8 was hard-baked
at 150*C for five minutes to remove cracks and pinholes. Similar devices were
fabricated on 300 nm SiO 2 to facilitate better wire bonding, which was required for
the interface capacitance measurement [7].
Polyimide
SU-8
Fig. 2.7: Optical microscope image of a graphene
EGFET on a polyimide substrate with SU-8
passivation extending into the graphene channel
region.
20 pm
Fig. 2.8: Optical microscope image of a graphene
EGFET with recessed SU-8 passivation leaving
portions of the source drain contact metal
exposed to the electrolyte.
Similar graphene EGFETs were fabricated on SiO 2 with W/L = 10 pim / 5 Im.
Hardbaking SU-8 photoresist was found to effectively remove cracks. The following
optical microscope images show SU-8 before and after hardbaking.
Fig. 2.9: Optical microscope image of a graphene
EGFET on SiO 2 substrate with recessed SU-8
passivation. The SU-8 has cracks near the
corners before hardbaking.
Fig. 2.10: Optical microscope image of a
graphene EGFET on SiO 2 substrate with recessed
SU-8 passivation. Hardbaking removes cracks in
the SU-8 near the corners.
21
Raman spectroscopy data of was acquired from every graphene EGFET device on a
single die. The Raman data is offset in the y-direction to prevent the data from
overlapping and allow for easy comparison. The G peak mean and standard
deviation are 1596.8 cm-1 and 2.8 cm-1, respectively. The 2D peak mean and
standard deviation are 2693.4 cm-1 and 4.5 cm-1, respectively. These values are in
agreement with previously reported G and 2D peak values [6], [8]. The consistency
of the Raman spectroscopy data indicates that consistency in the graphene quality
across the sample.
600
A
, 500
-CU
C')
T
400
300
C
k,
AA1V
200
O&A
1 00
A
100
1400
1600
1800
2000 2200 2400
Shift (cm-1)
2600
2800
3000
Fig. 2.11: Raman spectroscopy data from eleven graphene EGFET channel regions all from the same
die. Raman spectroscopy data was acquired using a 532 nm laser.
4. Measurement Setup
Graphene EGFETs possess three terminals: source, drain, and gate. The source
terminal is typically ground. The drain terminal is biased at a positive voltage to
create positive current flow through the graphene channel, IDS. The gate voltage is
applied to the electrolyte and is used to modulate the current in the graphene
channel, IDS. Because the graphene EGFET is a symmetric device, the source and
drain terminals can be switched and the measured current-voltage characteristics
will remain the same. The following illustration shows a graphene EGFET and the
location of each terminal in the measurement setup.
22
VGS
Si
SiO2
=
Polyimide =
Ti/Au/Pt EMGraphene
=
SU-8
=
Electrolyte
Fig. 2.12: Graphene EGFET with heterogeneous top-gate
capacitance due to non-self-aligned and completely
passivated source and drain regions. Vs,
VDS,
and
VGS
represent the voltages applied to the source, drain, and gate,
respectively.
Graphene EGFET current-voltage characteristics may be measured directly from the
die (without packaging) by using a standard DC probe station. The only special
setup requirement is that the die be large enough for an electrolyte droplet to cover
the graphene gate region without providing a conductive path between the source
and drain terminals. The DC probe station tips connecting to the source and drain
are kept out of the electrolyte to ensure that the measured IDS current stems solely
from conduction through the graphene EGFET channel region. The probes of the DC
probe station are typically made of tungsten. The probe inserted into the electrolyte
for the gate terminal is substituted for a platinum wire, which is known to be inert
and serve well as an electrode material.
Most potentiostat measurements either apply a voltage and measure a resulting
current or apply a current and measure the resulting voltage. Ideally, such
measurements only require two terminals. Potentiostats, however, possess three
terminals: a working electrode, reference electrode, and counter electrode. This is
because in a two terminal setup, supplying current through an electrode can also
alter its potential and lead to erroneous results. Therefore, potentiostats make use
of a reference electrode, which passes virtually no current and maintains a very
stable reference potential. The counter electrode then supplies whatever current is
necessary in order for the working electrode to have the desired potential with
respect to the reference electrode.
Many types of reference electrodes exist, but the most common for aqueous-based
electrochemical experiments are the Ag/AgCl and saturated calomel reference
electrodes. Because saturated calomel reference electrodes contain mercury,
Ag/AgCl have become the most popular. Reference electrodes are designed to act as
ideal non-polarizable electrodes. This means that the interface potential between
the reference electrode and the electrolyte is very stable (Fig. 2.13). This is in stark
contrast to graphene, which has a large electrochemical potential window and is
closer to an ideal polarizable electrode. Recall, that graphene was biased from -1 to
+1 volts in 1M aqueous NaCl while producing minimal DC current (Fig. 2.14).
23
Graphene accommodates this changing potential by storing charge like a capacitor
in the electric double layer.
V
V
Fig. 2.13: Electrode current versus electrode
potential for an almost ideal non-polarizable
electrode.
Fig. 2.14: Electrode current versus electrode
potential for an almost ideal polarizable
electrode.
Graphene EGFET characterization also required measurement of the grapheneelectrolyte interface capacitance. This capacitance was measured using a Gamry
Reference 600 potentiostat in conjunction with the Mott-Schottky experiment
within the electrochemical impedance spectroscopy software suite. In the MottSchottky experiment setup, the source and drain terminals are connected together.
The source and drain terminals are then connected to the potentiostat such that the
graphene channel becomes the working electrode. A platinum wire is used as the
counter electrode and an Ag/AgCI electrode is used as the reference electrode. The
Ag/AgCl reference electrode, however, is too large to fit into an electrolyte droplet
pipetted on the 8 mm x 8 mm die. Therefore, the graphene EGFETs were packaged
by wire-bonding the die to a chip carrier, passivating the wire bonds with medicalgrade epoxy, and mounting a glass cylinder around the devices with epoxy.
Fig. 2.15: Graphene EGFETs packaged in a chip
carrier with glass cylinder on top for electrolyte
storage.
Fig. 2.16: Bird's eye view of graphene EGFETs
packaged in a chip carrier with glass cylinder on
top for electrolyte storage.
24
The Mott-Schottky experiment determines the graphene-electrolyte interface
capacitance by applying a small sinusoidal voltage signal (typically 10 mV) to the
gate and recording the resulting sinusoidal current from the gate to source/drain
terminals. Magnitude and phase relationship between the voltage and current
signals determine the complex impedance of the interface.
Z = V sin(wt)
1 sin(wt+O)
(2.2)
This procedure is repeated for frequencies ranging from 1 Hz to 1 MHz. Now that
the graphene-electrolyte interface impedance is known as a function of frequency, it
can be represented as either as either a Bode plot or a Nyquist plot. The majority of
electrolyte-electrode interfaces can be modeled using the Randles circuit. By fitting
the experimental data to the Randles circuit model, the interface capacitance is
extracted [9]. Note that the interface capacitance is due to the electric double layer
capacitance, CEDL.
RCT
Img(Z)
Rs
Re(Z)
CEDL
Zw
Fig. 2.17: Randles circuit model for the grapheneelectrolyte interface.
Rs
RS+RCT
Fig. 2.18: Typical Nyquist plot of the electrodeelectrolyte interface impedance.
References
[1]
H. Ago, Y. Ito, N. Mizuta, K. Yoshida, B. Hu, C. M. Orofeo, M. Tsuji, K. Ikeda, and
S. Mizuno, "Epitaxial Chemical Vapor Deposition Growth of Single-Layer
Graphene over Cobalt Film Crystallized on Sapphire," ACS Nano, vol. 4, no. 12,
pp. 7407-14, Dec. 2010.
[2]
P. W. Sutter, J.-I. Flege, and E. a Sutter, "Epitaxial Graphene on Ruthenium,"
Nat. Mater., vol. 7, no. 5, pp. 406-11, May 2008.
[3]
A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J.
Kong, "Large Area, Few-Layer Graphene Films on Arbitrary Substrates by
Chemical Vapor Deposition," Nano Lett., vol. 9, no. 1, pp. 30-35, 2009.
[4]
X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E.
Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, "Large-Area Synthesis of
25
High-Quality and Uniform Graphene Films on Copper Foils," Science, vol. 324,
no. 5932, pp. 1312-4, Jun. 2009.
[5]
S. Bhaviripudi, X. Jia, M. S. Dresselhaus, and J. Kong, "Role of Kinetic Factors in
Chemical Vapor Deposition Synthesis of Uniform Large Area Graphene using
Copper Catalyst," Nano Lett., vol. 10, no. 10, pp. 4128-33, Oct. 2010.
[6]
J. W.
[7]
E. F. Transistors, C. Mackin, L. H. Hess, A. Hsu, Y. Song, J. Kong, J. A. Garrido,
and T. Palacios, "A Current-Voltage Model for Graphene Electrolyte-Gated
Field-Effect Transistors," IEEE Trans. Electron Devices, vol. 61, no. 12, pp.
3971-3977, 2014.
[8]
Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, "Graphene
and Graphene Oxide: Synthesis, Properties, and Applications," Adv Mater., vol.
22, no. 35, pp. 3906-24, Sep. 2010.
[9]
A. J. Bard, L. R. Faulkner, E. Swain, and C. Robey, ElectrochemicalMethods:
FundamentalsandApplications. 2001.
Suk, A. Kitt, C. W. Magnuson, Y. Hao, S. Ahmed, J. An, A. K. Swan, B. B.
Goldberg, and R. S. Ruoff, "Transfer of CVD-Grown Monolayer Graphene onto
Arbitrary Substrates," ACS Nano, vol. 5, no. 9, pp. 6916-24, Sep. 2011.
26
Chapter 3 - Monolayer Graphene EGFET
Characterization
1. Graphene-Electrolyte
Modeling
Interface
Capacitance
Immersion of graphene in an electrolyte results in the accumulation of ions at the
graphene surface due to differences in electrochemical potentials. This phenomenon
is termed an electric double layer. The capacitance of the electric double layer is
large enough that accurately modeling the graphene-electrolyte interface
capacitance requires inclusion of the graphene quantum capacitance. Quantum
capacitance is proportional to the density of states and can serve as the limiting
capacitive component for two-dimensional materials such as graphene. The
graphene quantum capacitance is given by the Eqs. 3.1, 3.2 [1].
(InGI+ In*1)1/2
CQ=
nG
=
(qVc2
(3.1)
(3.2)
where h is the reduce Planck constant, VF is the Fermi velocity, nG is the carrier
concentration induced by the gate voltage, n* is the effective charged impurity
concentration, and Ve is the electric potential of the graphene channel.
Experimental data shows that the graphene-electrolyte interface capacitance,
CTOP,EXP, may be modeled using a parallel plate capacitor, CEDL,EFF, in series with the
graphene quantum capacitance, CQ. As a hydrophobic material, graphene repels
aqueous electrolytes resulting in what may be modeled as an angstrom-scale gap
between the electrolyte and graphene surface. This forms a parallel plate capacitor,
which reduces the complex voltage-dependence capacitance typical of electric
double layers. This effect was previously measured and modeled and is reproduced
for this work [2]-[4].
Experimental data also includes a parallel capacitive component due to device leads,
Co. The interface capacitance is measured at 100 Hz with an Ag/AgCl reference
electrode using a Gamry Reference 600 potentiostat. The measurement was taken in
1M aqueous NaCl. The measured data is fit to the capacitive model using the
Levenberg-Marquardt algorithm from the MATLAB optimization toolbox (Fig. 3.2).
The data confirms the applicability of the interface capacitance model in the
current-voltage graphene EGFET model.
27
10k
C
C0
-
IU
4-
CU
C
0
CQ
-
Q
CEDLEFF
--
2-2
TOPSIM
CoPx
TOP,EXPEDL,EFF
C
-1.5
-1
0.5
0
-0.5
1
1.5
2
VG - VIRAC (V)
Fig. 3.1: Capacitive components comprising
the overall graphene-electrolyte interface
capacitance.
Fig. 3.2: Simulated versus experimental top-gate
capacitance for a graphene SGFET on Si02. The device
has W/L = 40Vm/40im where the center 20im is
unpassivated. CEDL,EFF = 8.8RF/cm 2, n* = 1.0x1011
.
/cm 2 , Co = 11.3 pF/cm2
2- Fundamental Current-Voltage
Graphene EGFETs
Model
for
A number of models have been developed to study and predict the behavior of
metal-oxide-gated graphene FETs [5]-[10]. Little work, however, has been reported
for graphene electrolyte-gated FET models [11]. Electrolyte-gated graphene FET
models represent an increase in complexity over metal-oxide-gated graphene FETs
because the top-gate capacitance cannot be considered constant. The top-gate
capacitance of graphene EGFETs, which is comprised of the electrical double layer
capacitance and graphene quantum capacitance, varies as a function of ionic species,
ionic concentration, and also spatially along the graphene channel [1], [12].
The current at any given position along the channel is determined by the product of
the carrier concentration and the carrier drift velocity, which is scaled appropriately
by the elementary charge and channel width. This principle combined with current
continuity enables calculation of the graphene EGFET current and the
corresponding channel potential profile. Fig. 3.3 depicts a typical layout for a
graphene EGFET.
Substrate
Passivation
Graphene
S/D Contact
Fig. 3.3: Graphene SGFET structure with mostly passivated
source and drain regions.
28
The channel current is given by the following equation.
IDS =
(3.3)
q W n Vdrift
where q is the elementary charge, W is the channel width, n is the carrier
concentration, and Vdrift is the carrier drift velocity. The drift velocity may be
rewritten.
vdrift =
(3.4)
dV
where y is the carrier mobility, and V is the channel potential which is a function of
position. This model assumes carrier mobility is equal for holes and electrons and
independent of the carrier concentration. The carrier concentration is a function of
potential and is given by the following equation.
n(V) ~ no + [CTop(V)[VGS,TOP - V - Vo]/q] 2
(3.5)
where no is the minimum carrier concentration [13], [14], CTOP is the top-gate
capacitance, VGS,TOP is the applied top gate voltage, and V is the potential along the
channel. V, represents the potential at the Dirac point.
VO = VGOS,TOP +
COCP(VvS,BACK -
VGS,BACK)
(3.6)
are the locations of the Dirac point as experimentally
determined from top gating and back gating, respectively. CBACK is the back-gate
capacitance. The majority of graphene EGFETs - including the ones examined in
this work - are fabricated on thick insulating substrates to provide structural
support and ensure the measured source-drain current stems solely from the
graphene channel. As a result, the back gate capacitance is far less the than top gate
capacitance, which is typically several pF/cm 2 . The equation for threshold voltage
can then be simplified to the following.
VGOS,TOP and VGOS,BACK
VO = VGOS,TOP
(3.7)
Including the effects of saturation velocity and contact resistance produces the
following equation describing the channel current. Contact resistances are assumed
symmetric. It is also important to note that chemical and biological sensors
employing graphene EGFETs are typically be biased at low voltages to avoid the
undesirable reduction of chemical species in the solution. Because of this, carrier
drift velocity is typically well below the saturation velocity. Saturation velocity is
included nonetheless for completeness.
29
W VDS-IDSRC
qp
I
2 ri~~
*o+[CTOP(V)LVGS,TOP-V-V]/q)
dV
(3.8)
-
IDS
DSDSRC
1+I
Lv sa
c)
Because the top-gate capacitance is a function of potential, this equation cannot
readily be integrated. As a result, a numerical equation describing the channel
potential profile is employed where h represents the step width.
h-IDS [1I(VDQS-2QDSRC)j]
I
(LVsat
0O-x <L
+
V(x + h) = V(x)
q iW n+[CTOP (VGS,TOP--V(x)-Vo )VGS,TOP -V(x)-VO]/q)2
(3.9)
The graphene EGFET channel current problem may be reformulated as a root
finding problem and solved using the bisection method. This is a robust method
with guaranteed convergence provided that the initial bounds span the solution and
that the solution is unique. The following pseudocode describes the bisection
method and its adaptation to the EGFET current and channel potential problem.
Bisection Method Pseudocode
Graphene EGFET Problem Pseudocode
XLOW < XROOT < XHIGH
'DS,LOW < 'DS < 'DS,HIGH
XMID =
0.5
IDSMID
(XLOW + XHIGH)
while(f(XMID) > Error Tolerance)
if(f (XLOW) *f(XMID) < 0)
=
0.5 (IDS,LOW +
while(VDS,ERROR (DS,MID)
(XMID)
-f
(XHIGH)
IDS,HIGH
<0
0.5
(XLOW
+
XHIGH)
(DS,MID)
'DS,LOW
IDSMID
=
<0)
'DSMID
if(VDS,ERROR(IDS,MID) 'VDS,ERROR(LDS,HIGH)
XLOW = XMID
XMID =
> Error Tolerance)
if(VDSERROR (lDS,LOW) -VDS,ERROR
XHIGH = XMID
Wf
IDS,HIGH)
=
<0)
'DS,MID
0-5 (IDS,LOW +
IDS,HIGH)
is initialized to zero. IDS,HIGH is initialized to the maximum possible channel
current value. IDS,MID is then calculated and employed as the initial guess for IDS.
Based on the IDS guess, the channel potential profile may be calculated. The first and
last points of the profile are used to calculate VDS. If the calculated VDS is greater than
the VDS input parameter, the IDS guess was too large and must be revised to a smaller
value. Similarly, if the VDS value is smaller than the VDS input parameter, then the IDS
guess was too small and must be revised to a larger value.
IDS,LOW
Application of the bisection method algorithm causes the simulation to converge
towards the unique solution where channel current IDS and channel potential profile
V(x) are in agreement. The solution obtained possesses some VDS and IDS error less
30
than the user-specified maximum tolerable errors. The IDS error tolerance exit
condition is omitted from the pseudocode for simplicity and ease of illustration.
3- Current-Voltage Model for Graphene EGFETs
with Heterogeneous Top-gate Capacitance
The ability to model heterogeneous top-gate capacitances is important for cases
where source/drain region passivation extends into the channel region. This
common practice is used to ensure complete passivation of the source/drain regions
and minimize leakage current (Fig. 3.4).
The importance of modeling heterogeneous top-gate capacitances is not limited to
the study of passivation schemes. This model also applies to the study of
electrogenic cells, which due to their uncontrolled positioning may cover only a
portion of the graphene channel. These cells act to modulate the top-gate
capacitance over a limited region of the channel. From a modeling standpoint, this
is equivalent to applying a thick layer of passivation in the regions unmodulated by
the electrogenic cell.
VGS
Vs
VDS
IIDS
RC
I
R,
0
Si
SiO2
=
Polyimide
x1
L
R
RG(X)
x2
:
RC
L
Ti/Au/Pt L JGraphene =J
SU-8
=l
Electrolyte
Fig. 3.4: Graphene EGFET with heterogeneous top-gate
capacitance due to non-self-aligned completely passivated
source and drain regions.
Splitting the channel into regions corresponding to the different top-gate
capacitances yields the following piecewise numerical channel potential equation:
31
h-IDS j1
V(x) +
P(VDS-21DSRC~j
0 < X< X
12
IILvsat,p
qppW no p+[CTOP,PASS(V)[VGS,TOP -V(x)-Vo]/q
2
h-IDS 14 R(VDS-21DSRC~j
V(x + h) =
V(x) +
'I+I
vDsa
)
x1
x
x
2
qpwjno+[CTOP(V)[VGS,TOP-V(x)-Vo]/q)
h-IDS 1+I
V(x) +
(VDS-21DSRC
Lvsat,p
0 S,TO P - V(x) - VO]/q)
q p~ np[TP,P AS S(V) [VG
X2 < X<
L
(3.10)
where ptp is the graphene mobility in the passivated regions, no,p is the minimum
carrier concentration in the passivated regions, and CTop,PAss(V) is the top-gate
capacitance in the passivated regions.
Alternatively, one can realize that the passivated graphene regions may be modeled
as an additional series resistance described by the following equation.
R1
(3.11)
-
qlpp jn,p+[CTOP,PASS(V)[VGS,TOP-V(x)-Vo]/q
2
W
For the typical case where the passivation regions possess a very small capacitance
of nF/cm 2 , the equation for the passivation series resistance can be simplified to a
constant.
Rp ~
q
I
pp no,p
(3.12)
W
This produces the following revised form of the graphene EGFET channel current
equation. It now becomes evident that introducing passivation into the graphene
channel regions acts to increase the overall series resistance.
1+
V(x + h) = V(x) +
h-IDS
VDS-2IDS(RC+Rp)1
Lvsat
1
x,
x 5 x2
(3.13)
qpwjnf+[cTOP(V)[VGS,TOP-V(x)-Vo]/q
4- Minimum Conduction Point
The location of the minimum conduction point, also known as the Dirac point, is a
key parameter in the current-voltage characteristic. It marks the transition from
negative to positive transconductance and approximates VGS,TOP, which provides a
32
measure of graphene doping. With this in mind, it is important to develop an
understanding of what value of VGS produces the minimum value of IDS. This
particular value of VGS is defined as VDIRAC. To analytically arrive at an equation for
VDIRAC and gain an understanding of the parameters that determine the location of
VDIRAC, a simplified EGFET equation is employed where series resistance and
velocity saturation are neglected.
IDS--
q -'0 WfVS
n01+ [CTOP(V)[VGS,Top
-
V - Vo]/q] 2 dV
(3.14)
The following derivation of VDIRAC stems from the realization that the integral is
minimized when the minimum of n(V) falls precisely in the center of the integration
bounds. In other words, IDS is minimized when min(n(V)) = n(VDs/ 2 ).
n(V)
0
Vos/2
VDS
Fig. 3.5: IDS integral geometry to
illustrate
IDS
minimization when
the n(V) minimum occurs at the
center of the integration bounds.
The minimum of n(V) occurs when V = VGS,ToP - V0 . For the simplest case where
VDS is very small and Vo = 0, if V = VGS,TOP the graphene potential is equivalent to
the applied potential VGS,TOP. Thus no voltage bias is applied to the graphene and the
total carrier concentration is equal to the minimum graphene carrier concentration.
Alternatively, the location of the n(V) minimum can be obtained by setting the
derivative of n(V) with respect to V equal to zero.
dn
_
CTOP(VDIRAC-v-Vo)/q
d
jno+[CToP(VDIRAC-V-Vo)/q]
VDIRAC - V - Vo = 0
=
0
(3.15)
(3.16)
Recall that IDS is minimized when the minimum of n(V) is located in the center of the
integration bounds. Thus V = VDs/2.
VDIRAC =
Vo +
2
(3.17)
33
The slope between the VDIRAC and VDS should be roughly equal to . In addition, VO
may be extrapolated by tracing the minimum conduction point to VDS = 0 V.
5- Fitting the Model to Experimental Data
The graphene EGFET model is fit to experimental data obtained from a device with
dimensions W/L = 40pim/30pm and recessed passivation. The device was measured
using Pt wire pseudo-reference electrode. An aqueous electrolyte consisting of 100
mM NaCl was selected because of its symmetry and similarity to physiological
osmolarity. The data is fit using bounded simulated annealing from MATLAB's
optimization toolbox as shown in Figs. 3.6-3.9. The extracted device parameters and
sensitivity analysis are provided in Tables I and II, respectively. The data is
acquired by sweeping VGS from -0.2 to 1.2 V and VDS from 10 mV to 300 mV. The
experimental and simulation step size is 10 mV for both VGs and VDS. The VGS step
rate was 500 ms per 10 mV. In addition, a ten second hold time was allotted when
resetting VGS from 1.2 V to -0.2 V and incrementing VDS by 10 mV. Further
increasing the hold time and decreasing the sweep rate had little effect on the
measured IV curves meaning sufficient time was given for the ions to redistribute
and for the electric double layer to reach steady state. The mean percent error for
the entire data set is 2%. Transconductance, output impedance, and intrinsic gain
may be computed from the current-voltage characteristic using finite differences
(Figs. 3.10-3.15).
TABLE
Parameters
VGS,ToP
no
I: SIMULATED
ANNEALING EXTRACTED PARAMETERS
Extracted
Reported
560 mV
N/A
2.4x10 12 /cm
2
2x1011 - 4x10 12 /cm
2
/cm
11.5kn m
2.1xlO1
2
[5], [14]
[15]
[1], [2], [16]
300 cm /V.s
> 3 pF/cm 2
451 cm /Vs
9.6 [iF/cm 2
CEDLEFF
n*
Rc
2
2
2
p
References
2x10 1 1 - 4x10 12 /cm
2
[5], [14]
--
--
TABLE 1I: SENSITIVITY ANALYSIS
Extracted Values
Parameters
560 mV
2.4x101 /cm 2
451 cm 2/Vs
9.6 iF/cm 2
VGS,TOP
no
CEDLEFF
2.1x1012 /cm 2
n*
R
1
11.5 kQ pm
Mean Errorfor
Mean Error for
1.O*Parameter
0.9*Parameter
1.22pA
1.22pA
1.22ptA
1.224A
1.22pA
1.22piA
(2.06%)
(2.06%)
(2.06%)
(2.06%)
(2.06%)
(2.06%)
10.1 pA
1.48pA
5.58pA
2.84pA
1.26ptA
5.03pA
(12.3%)
(2.23%)
(6.11%)
(3.27%)
(2.12%)
(4.96%)
Mean Errorfor
1.1*Parameter
9.84pA
1.53 jA
5.45pA
2.76 pA
1.21 pA
4.30ptA
(13.6%)
(3.00%)
(6.78%)
(3.3 1%)
(2.07%)
(4.14%)
34
1300
300
200
200
0
0
--- VGS exp = mV
---VGS sim = mV
-VGS
= 200 mV
VGS Sim = 200 mV
--VS
240m
VGS sxm = 400 mV
VG x
mV
exp
00
-VG
VG
i 00 MV-00
x=
mV
- --VGS sim = 1400 mV-- VGS
=8100 mV
00
0
exp
100
0
0.2
0.4
0.6
0.8
VGS (V)
0
1 2
.
-0.2
03
0.25
0.2
0.15
VDS (V)
0.1
0.05
Fig. 3.7: Experimental (solid) and simulated
(dashed) current versus VDs data. VGs varies from 0
mV to 1000 mV in increments of 200 mV.
Fig. 3.6: Experimental (solid) and simulated
(dashed) current versus VGs data. VDS varies from
50 mV to 300 mV in increments of 50 mV.
350
0.3
300
0.25
250
3 50
mal
3 50
2' 50
0.2
S0.1E
1' 50
150
0.1
100
0
0.2
0.6
0.4
VGS (V)
0.8
1
-0.2
1.2
g5 0
0.2
0
1.2
1
0.8
0.6
0.4
VGS (V)
Fig. 3.9: Simulated data for current as a function
VDs and VGs.
Fig. 3.8: Experimental data for current as a function
of VDs and VGS.
0.
00
0.05
50
-0.2
10
5
0.
I5
E
-5
0.
J;.
02
0.
0
AW15 0
0
1
-5
-10
-0.2
0
0.2
0.4
0.6
VGS (V)
0.8
1
of
10
0.251
0.2
0.1
0
2
200
00j
0 i
-10
-0.2
1.2
0.2
0
1
0.8
0.6
0.4
VGS (V)
1.2
Fig. 3.10: Experimental transconductance data as a
Fig. 3.11: Simulated transconductance as a function
function of VDs and
of VDs and VGS-
VGS-
0.3
250
0.
0.2
150cc
100
50
0
0.2
0.4
0.6
VGS (V)
0.8
1
1.2
Fig. 3.12: Experimental output impedance data as a
function of VDs and VGS.
150
>
E
-0.2
200
0.25411U
200
0
00
m
m
U)0.15
100
0.1
0.05
-0.2
E
50
5
A
0
0.2
0.6
0.4
VGS (V)
0.8
1
1.2
Fig. 3.13: Simulated output impedance as a function
Of VDS and VGS.
35
0.3
0.25
2.5
0.2
1.5
0.
0.25
2
C)0.15
0.5
0
0.05
-0.5
-0.2
0
0.2
0.4
0.6
VGS (V)
0.8
1
1.5
0.2
>
0.1
2
1.2
Fig. 3.14: Experimental intrinsic gain data as a
function of VDs and VGS.
u)2
0.15
-0.5
00.1.
0
0.05
-0.2
-0.5
0
0.2
0.4
0.6
VGS (V)
0.8
1
1.2
Fig. 3.15: Simulated intrinsic gain as a function of
VDS and VGs.
6- Passivation Scheme Comparison
The graphene EGFET model (Eq. 3.13) shows that increasing the degree of channel
passivation increases the total series resistance. Large series resistance translates
into diminished transconductance and decreased sensitivity. Optimal graphene
EGFET designs should therefore eliminate the need for passivation in the channel
region. Recessed channel passivation, however, directly exposes source and drain
contacts to the electrolyte, which may result in large leakage currents. Excessive
leakage current may be avoided by minimizing the exposed area and using a sourcedrain metal such as platinum, which possesses wide electrochemical potential
window in aqueous NaCl electrolytes (Figs. 3.16, 3.17). Platinum's high chemical
stability and biocompatibility also make it well suited for chemical and biological
sensing applications.
Devices with and without partial channel passivation were fabricated on the same
die and compared (Figs. 3.18 - 3.21). The electrolyte is 100 mM aqueous NaCl and
the graphene EGFET channel dimensions are W/L = 40pum/30ptm. Graphene
EGFETs with recessed channel passivation were found to produce roughly four
times higher transconductance (Figs. 3.22 - 3.25). Experimental data shows devices
with recessed passivation also may be biased over a wider range of VGS values while
still producing near-optimal transconductance. Output impedance data is provided
in Figs. 3.26, 3.27. Devices with recessed channel passivation also produce higher
intrinsic gain (Figs. 3.28, 3.29). This stems from the reduced series resistance of
devices with recessed passivation. The effect of series resistance on intrinsic gain is
examined in detail in the subsequent section. As expected, gate leakage current
increases in devices with recessed channel passivation, but remains negligible in
comparison to the channel current. Lastly, the dependence of VDIRC on VDS
described by Eq. 3.17 is verified (Figs. 3.30, 3.31).
36
0.3
0.
2
20
3
15
0.2
2
0.1
0.1w
0.05
0
0.2
0.4
0.6
VGS (V)
U.0
40
0.6
0.4
VGS (V)
1.2
1
0.8
Fig. 3.17: Gate leakage current as a function of
and VDS for a device with recessed passivation.
120
60
0.2
0
-0.2
1.2
I
Fig. 3.16: Gate leakage current as a function of VGS
and VDS for a device with partial channel
passivation.
80
5
0
-0.2
100
10C
U0.15
) 0.15
-VDS
-VDS
300-
VGS
= 50 mV
= 100 mV
-VDS = 150 mV
VDS =200 mV
250
-VDS
= 50 mV
= 100 mV
-VDS
= 150 mV
-VDS
-VDS=200mV
-VDS = 250 mV
VDS = 300 mV
0
-VDS
= 250 mV
_VDS =300 mV
200
150
100
50
20
0
-0.2
0.2
1
0.8
0.6
0.4
VGS (V)
1.2
0.2
0.6
0.4
VGS (V)
1.2
1
0.8
Fig. 3.19: Current-voltage data for a device with
recessed passivation.
Fig. 3.18: Current-voltage data for a device with
partial channel passivation.
0.:
120
0.2!
0
-0.2
100
0.3
350
0.25
300
250
0.2
200<
80
=L
0.15
60
l0. 15
0.1
40
0.1
0.05
20
0.05
-0.2
0
0.2
0.4
0.6
VGS (V)
0.8
Fig. 3.20: Channel current as a function of VGS and
VDS for a device with partial channel passivation.
100
50
0.2
0
-0.2
1.2
1
150
0.6
0.4
VGS (V)
0.8
1
1.2
Fig. 3.21: Channel current as a function of VGs and
for a device with recessed passivation.
VDS
100
400
50
: 200-
ca
= 50 mV
= 100 mV
= 150 mV
= 200 mV
-VDS = 250 mV
m
8
50
-VDS
-VDS
-- VDS
- VDS
E
--100L
-0.2
C
E
- -2 0
-VDS =510m
V D S =50 m V
-VDS =100 mV
=1250 mV
-VDS =2300 mV
0-
-00-VDS
VDS =300 mV l
0
0.2
0.6
0.4
VGS (V)
0.8
1
1.2
Fig. 3.22: Transconductance versus VGs for a device
with partial channel passivation.
-602
0
0.2
0.4
0.6
VGS (V)
0.8
1
1.2
Fig. 3.23: Transconductance versus VGS for a device
with recessed passivation.
37
0.3i
I
2
10
0.25 :
5
0.2:
0.
0
0. 11
0.051
-0.2
0
0.2
0.4
0.6
VGS (V)
E
0
0.1
C
C/)
-1
0.
-5
-2
0.0
-10
0
VGS (V)
Fig. 3.24: Transconductance as a function of VGS
and VDS for a device with partial channel
passivation.
Fig. 3.25: Transconductance as a function of
and
VDS
VGS
for a device with recessed passivation.
0.
140
250
0.
0.2,'
130
200
120 E
a
110
0.1
100
100
0.0
-0.2
150
90
0
0.2
0.4
0.6
VGS (V)
0.8
1
50
-0.2
1.2
Fig. 3.26: Output impedance as a function of VGS
and VDS for a device with partial channel
passivation.
0
0.2
1.2
1
0.8
0.4
0.6
VGS (V)
Fig. 3.27: Output impedance as a function of
and VDS for a device with recessed passivation.
VGS
2.5
0.2
0.
0.
2
1.5
(I)
>
0:
'
0.1
0.5
-0.1
0
-0.2
|1
2
-0.5
-0.2
VGS (V)
Fig. 3.28: Intrinsic gain as a function of VGS and
VDS for a device with partial channel passivation.
-VDIRAC
0.2
1.2
1
0.8
0.6
0.4
VGS (V)
Fig. 3.29: Intrinsic gain as a function of VGS and
VDS for a device with recessed passivation.
0.75
0.75
0
0
-VDMR AC = 0.53771*'VDS +
= 0.50968*VDS + 0.57733
0.54632
0.7-
0.7-
0.65
C-)
0.655
S0.6-
0.5 5-
0. 5 '
00.05
0.1
0.1
0.2
VDS (V)
- -0 25
-
0.6
0.3
0.35
Fig. 3.30: Dirac point as a function of VDS for a
device with partial channel passivation.
0
00
.5
02
VDS (V)
02
Fig. 3.31: Dirac point as a function of
device with recessed passivation.
0.35
VDS
for a
38
7- Performance Optimization for Electrogenic Cell
Sensing
EGFET performance trends are investigated using the parameters extracted for our
polyimide substrate process. Electrogenic cell sensing and more specifically
neuronal action potential sensing is chosen as a specific application for device
optimization. This sets the maximum channel width to 10 im, which is roughly the
diameter of a mouse hippocampal neuron. Channel widths greater than the neuron
diameter result in only partial channel modulation and sub-optimal sensitivity.
Channel current is then computed as a function of VGS and VDS while varying the
channel length by several orders of magnitude. Given a maximum VDS of 1 V and VGS
range from -0.2 to 1.2 V, the graphene EGFETs are shown capable of intrinsic gains
of 9 V/V.
10'
10
8
10
10
10
10,
101
10010
4
10
/
2
10
100
10
2
)
10
103
1
103
1
0
14J
01
10
Fig. 3.32: Simulated maximum intrinsic gain and
current consumption versus channel length.
10'
0
100
10
L (pm)
102
103
Fig. 3.33: Simulated transconductance
output impedance versus channel length.
10
and
The gain versus channel length plot depicts an important trait: graphene EGFET
intrinsic gain is virtually independent of channel length. This behavior is apparent
for larger channel lengths, where the effect of contact resistance is negligible.
Intrinsic gain only begins to roll off at lower channel lengths because of decreasing
transconductance due to contact resistance. This reduction in transconductance
occurs because at short channel lengths, the contact resistance flattens out the
current-voltage characteristic. With this understanding, the intrinsic gain curve can
be shifted left to produce constant intrinsic gain across an even larger range of
channel lengths by reducing contact resistance.
An alternative to maximizing the intrinsic gain is to focus on optimizing
EGFETs with
matching graphene
performance and
transconductance
for
the two-stage
model
signal
the
small
3.34
depicts
Fig.
transresistance amplifiers.
amplifier circuit. The voltage gain for the circuit is given by Eq. 3.18.
39
R+
I +
gmv,
Vg
ro
Ri
i'
Ki
-
RL
V
+
+in
Output Stage
Fig. 3.34: Graphene EGFET small signal model with
transresistance output amplifier stage.
G =
rV)(K=K
_(
(
gmr+R
Vin
(3.18)
R)
RL+Ro
where G, is the overall voltage gain, vin is the small signal gate voltage, vout is the
small signal output voltage, g. is the graphene EGFET transconductance, ro is the
graphene EGFET output impedance, Rin is the input impedance of the second stage,
K is the gain of the second stage, R0 is the output impedance of the second stage, and
RL is the load impedance.
Given a fixed process technology, the most
straightforward way to increase transconductance in graphene EGFETs is to
increase the W/L ratio. For certain applications such as electrogenic cell sensing,
the maximum width is dictated by cell diameter. The only means to optimize
transconductance then becomes channel length reduction. As seen previously, this
works to a limited extent. As the channel length becomes infinitesimal, the entirety
of the drain-source voltage drops across the contact resistances leaving no current
to be modulated by the graphene region.
Figs. 3.35, 3.36 depict the
transconductance behavior as a function of channel length along with the
corresponding current consumption.
50
10
3
40
103
30
-
0
102
102
0
10
10
10
10
0
-0.2
20
10
100
-50
100
0
0.2
0.4
0.6
0.8
VGS (V)
1
1.2
1.4
-5
Fig. 3.35: Simulated transconductance as a function
of channel length for VDS = 100 mV.
010
-0.2
0
0.2
0.4
0.6
0.8
VGS (V)
1
1.2
1.4
Fig. 3.36: Simulated current versus channel length
for VDS = 100 mV.
For the flexible polyimide substrate process and a set channel width of 10 Im, the
optimal channel length is around 5 km. This unintuitive and rather modest W/L
ratio demonstrates the utility of graphene EGFET models in sensor design. Fig. 3.35
also reveals that slightly longer than optimal channel lengths provide
transconductance performance over a broader VGS range. Substantially shorter
channel lengths, on the other hand, only serve to restrict the range of acceptable VGS
biases and increase power consumption.
40
Sensor designs focusing on high transconductance sensors coupled with
transresistance amplifiers also require the input impedance of the second stage to
be much less than the output impedance of the first stage. Using the developed
model, the graphene EGFET output impedance can be readily determined enabling
appropriate design of the second stage amplifier.
8
0.8
50.66
>
0.4
4
0.2
-0.2
0
0.2
0.4
0.6 0.8
VGS (V)
1
1.2
1.4
1
1.6 2
Fig. 3.37: Output impedance as a function of VGS
and VDS for a graphene SGFET with W/L = 10
ptm/5 gm.
References
[1]
J. Xia,
[2]
L. H. Hess, M. V. Hauf, M. Seifert, F. Speck, T. Seyller, M. Stutzmann, I. D. Sharp,
and J. A. Garrido, "High-Transconductance Graphene Solution-Gated Field
Effect Transistors," Appl. Phys. Lett., vol. 99, no. 3, p. 033503, 2011.
[3]
N. Schwierz, D. Horinek, and R. R. Netz, "Reversed Anionic Hofmeister Series:
The Interplay of Surface Charge and Surface Polarity," LangmuirACSJ.
surfaces colloids, vol. 26, no. 10, pp. 7370-9, May 2010.
[4]
S. Birner, "Modeling of Semiconductor Nanostructures and Semiconductor
Electrolyte Interfaces," 2011.
[5]
1. Meric, M. Y. Han, A. F. Young, B. Ozyilmaz, P. Kim, and K. L. Shepard, "Current
Saturation in Zero-Bandgap, Top-Gated Graphene Field-Effect Transistors,"
Nat. Nanotechnol., vol. 3, no. 11, pp. 654-9, Nov. 2008.
[6]
1. J. Umoh, S. Member, T. J. Kazmierski, S. Member, and B. M. Al-hashimi, "A
Dual-Gate Graphene FET Model for Circuit Simulation - SPICE
Implementation," IEEE TranactionsNanotechnol., vol. 12, no. 3, pp. 427-435,
2013.
-
F. Chen, J. Li, and N. Tao, "Measurement of the Quantum Capacitance of
Graphene," Nat. Nanotechnol., vol. 4, no. 8, pp. 505-9, Aug. 2009.
41
[7]
M. Magallo, C. Maneux, H. Happy, T. Zimmer, and S. Member, "Scalable
Electrical Compact Modeling for Graphene FET Transistors," IEEE Tranactions
Nanotechnol., vol. 12, no. 4, pp. 539-546, 2013.
[8]
V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, and N. Kirova, "Device Model for
Graphene Bilayer Field-Effect Transistor," J. Appl. Phys., vol. 105, no. 10, p.
104510, 2009.
[9]
H. Wang, S. Member, A. Hsu, J. Kong, D. A. Antoniadis, and T. Palacios,
"Compact Virtual-Source Current-Voltage Model for Top- and Back-Gated
Graphene Field-Effect Transistors," IEEE Trans. Electron Devices, vol. 58, no. 5,
pp. 1523-1533, 2011.
[10]
D. Jimenez, "Explicit Drain Current, Charge and Capacitance Model of
Graphene Field-Effect Transistors," IEEE Trans. Electron Devices, vol. 58, no.
12, pp. 4377-4383, 2011.
[11]
E. F. Transistors, C. Mackin, L. H. Hess, A. Hsu, Y. Song, J. Kong, J. A. Garrido,
and T. Palacios, "A Current-Voltage Model for Graphene Electrolyte-Gated
Field-Effect Transistors," IEEE Trans. Electron Devices, vol. 61, no. 12, pp.
3971-3977, 2014.
[12]
M. Kilic, M. Bazant, and A. Ajdari, "Steric Effects in the Dynamics of
Electrolytes at Large Applied Voltages. I. Double-layer Charging," Phys. Rev. E,
vol. 75, no. 2, p. 021502, Feb. 2007.
[13]
J. Martin, N. Akerman,
G. Ulbricht, T. Lohmann, J. H. Smet, K. von Klitzing, and
A. Yacoby, "Observation of Electron-Hole Puddles in Graphene using a
Scanning Single-Electron Transistor," Nat. Phys., vol. 4, no. 2, pp. 144-148,
Nov. 2007.
[14]
S. Adam, E. H. Hwang, V. M. Galitski, and S. Das Sarma, "A Self-Consistent
Theory for Graphene Transport," Proc. Natl. A cad. Sci. U. S. A., vol. 104, no. 47,
pp. 18392-7, Nov. 2007.
[15]
B. Mailly-Giacchetti, A. Hsu, H. Wang, V. Vinciguerra, F. Pappalardo, L.
Occhipinti, E. Guidetti, S. Coffa, J. Kong, and T. Palacios, "pH Sensing Properties
of Graphene Solution-Gated Field-Effect Transistors,"J. Appl. Phys., vol. 114,
no. 8, p. 084505, 2013.
[16]
H. Ji, X. Zhao, Z. Qiao, J. Jung, Y. Zhu, Y. Lu, L. L. Zhang, A. H. MacDonald, and R.
S. Ruoff, "Capacitance of Carbon-Based Electrical Double-Layer Capacitors,"
Nat. Commun., vol. 5, p. 3317, Jan. 2014.
=
C
Ot
xax]
42
Chapter 4 - Graphene EGFET Applications
1. pH Sensing
A number papers exist describing pH sensitivity of graphene field-effect transistors
(FETs). pH sensitivity for graphene FETs is typically measured by the shift in Dirac
point per unit change of pH. The reported pH sensitivities range anywhere from 18
mV/pH to above 99 mV/pH [1]-[5].
The shift in Dirac point versus pH can be understood through the Nernst-Planck
equation [6]. This equation is essentially a drift-diffusion equation for electrolytes.
The Nernst-Planck equation states that total ion flux is due to diffusion, drift from
electric fields, and convection. The convection term is zero for many pH sensing
applications and is omitted.
Oc= Ji = -Di a-
p.cjzjF
7
(4.1)
where ci is the ion concentration,J is the ion flux, Di is the ion diffusivity, Yj is the
ion mobility, zi is the ion charge number, F is the Faraday constant, and V) is the
electric potential. The Einstein relation describes the relationship between ion
diffusivity and mobility.
(4.2)
= RT
where R is the gas constant, T is the temperature.
equation to be rewritten as the following.
This allows the Nernst-Planck
[RT Lc-' + cizi F
= -pi
(4.3)
This Nernst-Planck equation can then be further rewritten from the perspective of
charged species moving along potential gradients.
Ji oc Vpi
(4.4)
where p traditionally represents what is termed the electrochemical potential.
-pac
RT=
T In (c1 ) + zLF
L
(4.5)
The electrochemical potential must have the following form in order to satisfy the
original Nernst-Planck equation.
43
p
t==
j
(4.6)
In (ci)
+
where pf is a constant potential term. Whenever an electrode such as graphene is
brought into contact with an electrolyte an interface potential develops. This occurs
because the electrode possesses a different electrochemical potential from that of
the electrolyte. The electrochemical potentials are given by the following equations.
ISeiectrode
flelctrde
=Ipiectrode
+ -In
Peectode
zF
fleiectrolyte = Itelectrolyte
+
(Celectrode)
(4.7)
In (celectrolyte)
(4.8)
The yo parameter is a constant that is independent of ionic concentrations.
Electrochemical potentials may be converted to electric potentials by dividing by
Faraday's constant and the appropriate charge number.
(4.9)
zF
zF
To determine the magnitude of the interface potential drop, subtract the two
potentials.
electrode-~electroyte -
Aelectrode~Ielectrolyte +RT
zF
zF
In
Celectrode
\Celectrolyte)
(4.10)
The first term, which is independent of ion concentration, may be combined to yield
the Eq. 4.11. The concentration of a solid electrode is equal to unity.
4'electrode-+electrotyte
4electrode-+electrolyte
=
= V)
+
-
(4.11)
In
i'o + 2.3 ZFT log(1\Celectrolyte/
(4.12)
Thus it becomes evident that the interface potential is a function of ion
concentration. This equation applies to any solid-electrolyte interface. pH is
defined as pH = -log (cH+), where CH+ is the concentration of hydronium. The
electrode-electrolyte interface potential equation may then be rewritten as Eq. 3.13.
For monovalent ions at room temperature, the potential slope is ideally around 58.8
mV/dec.
4'electrode-+electrolyte
=
4'6 + 2.3
RT
pH
(4.13)
It is important to note, however, that the location of the Dirac point is determined
not only by the potential drop at the graphene-electrolyte interface but also by the
44
potential drop present at the gate electrode-electrolyte interface. The gate
electrode-electrolyte interface potential may also be a function of pH. This is shown
in Fig. 4.1 where a Pt pseudoreference electrode is measured with respect to an
Ag/AgCl reference electrode. Ag/AgCl reference electrodes are known to produce a
relatively constant interface potential drop with changing pH. Therefore, the change
in the overall potential is largely due to the potential drop at the Pt interface.
4
--- ----0 --
5
6
7
8
9
10
-50
s
-lo-10
__
-150
---
-250
-
-200 ----300
2
_
-350
-400
_
I-450
-500
pp H
Fig. 4.1: Platinum electrode potential with respect to Ag/AgCl
reference electrode for varying pH.
A pH meter from Hanna Instruments was calibrated using a 3-point calibration and
buffer solutions with pH 4, 7, and 10. The buffer solutions were then mixed to
produce a range of pH solutions varying from 4 to 10 in unit increments of pH. Each
buffer solution was deposited on top of a graphene EGFET and the IDS current was
measured as a function of VGS and VDS repeatedly until the current-voltage
characteristic stabilized. This was achieved using a Pt wire as a pseudoreference
electrode. The graphene EGFET was then rinsed for thirty seconds using deionized
water and the measurement was repeated using a different pH solution. The Dirac
points for various VDS voltages were then extracted from the current-voltage data as
a function of pH. The entire experiment was repeated twice: once going from pH 4
to pH 10 and a second time going from pH 10 to pH 4. The data from these
experiments is given in Figs. 4.1, 4.2. The slopes for the two experiments were -46.7
mV/pH and -54.8 mV/pH. The data is considerably less linear in the second plot
suggesting that the Dirac point should have been given more time to stabilize.
600
-VDS = 20mV
-VDS = 40mV
-VDS = 60mV
EVDS = 8OmV
VDS= 1OOmV
500
0 400
-VDS
-VDS
-VDS
-VDS
VDS
500
= 20mV
= 40mV
= 60mV
= 80mV
100mV
40
0:
'~300-
204
600
5
6
7
8
9
10
pH
Fig. 4.2: Graphene EGFET Dirac point location
versus pH. The slope is roughly 46.7mV/pH.
2004
5
6
7
pH
8
9
10
Fig. 4.3: Graphene EGFET Dirac point location
versus pH. The slope is roughly 55.8 mV/pH.
45
2. Monitoring Real-Time Polymerase Chain Reactions
One potential application for graphene EGFETs is monitoring the replication of
deoxyribonucleic acid (DNA) in real-time polymerase chain reactions (RTPCR). PCR
is commonly employed for DNA sequencing and for the detection of foodborne
pathogens such as Escherichia coli [7], [8]. RTPCR is differentiated from simple PCR
in that it allows the concentration of DNA to be monitored in real-time by optically
monitoring molecules that fluoresce when attached to DNA. Performing RTPCR
requires a thermocycler and several reagents: template DNA, DNA polymerase,
deoxyribonucleotide triphosphates (dNTPs), primers, buffer solution, and probes.
The template DNA is the double-stranded DNA being replicated. The PCR process
begins with an initial denaturation step, which splits all double-stranded template
DNA into single-stranded DNA by breaking the hydrogen bonds holding the two
strands together. This denaturation step occurs at around 100*C. The mixture of
PCR reagents is then cooled to approximately 60*C. This allows the primers to fuse
to their complementary segments on the single-stranded DNA. Only once the
primers are fused, can the DNA polymerase incorporate complementary nucleotides
using the dNTPs to rebuild each single-stranded DNA into double-stranded DNA.
Ideally, each temperature cycle doubles the concentration of DNA present within the
PCR mix.
RTPCR also requires a buffer solution because the DNA polymerase is only active
within a limited pH range. The probes used in the following experiments are
fluorescent molecules consisting of a fluorophore and a quencher. This probe binds
to the DNA along with the primer molecule previously discussed. However, when
the DNA polymerase passes over the probe during the extension phase, it detaches
the quencher segment of the probe from the fluorophore. The quencher then
diffuses away into the PCR mix. With the quencher molecule far away, the
fluorophore may now fluoresce when excited by a suitable light source. This
fluorescence can be detected optically and is directly proportional to the DNA
concentration in real time [9]. Because PCR doubles the amount of DNA (and
fluorescence) with each temperature cycle, the fluorescence increases exponentially.
Eventually, however, a one of the reagents will limit the reaction and the
fluorescence will saturate. This produces s-shaped curves such as the one depicted
in Fig. 4.4.
46
Vic
LL
FAM
Cycles
FAM 1
FAM 40
VIC 1
VIC 40
Fig. 4.4: RTPCR experiment using FAM and VIC fluorophores for the detection of a DNA sequence
associated with the inability to process clopidogrel, a common antiplatelet medication. Insets below
show the increase in fluorescence for the actual PCR mix droplet over the course of the experiment.
Graphene EGFETs with W/L = 100 ptm / 20 prm were fabricated on the topside of a
RTPCR chip along for use in a custom thermocycler system. The RTPCR chip
includes both a temperature sensor and resistive heating element (Fig. 4.5). Each
graphene EGFET is surrounded by a polycarbonate well capable of storing
approximately 30 pL of solution. A silicone adhesive was used to attach the
polycarbonate wells to the RTPCR chip. Each well was filled with approximately 20
ptL of mineral oil to prevent evaporation of the PCR mix during the denaturation
phase. A 5 iL volume of PCR mix was then micropipetted underneath the mineral
oil. The RTPCR chip was then placed inside of carrier designed for the RTPCR
system. Thin insulated wires were glued to large metal source drain terminals using
conductive silver paste. The wires were fed outside of the thermocycler system so
that a voltage VDS could be applied to the graphene EGFETs and the resulting current
measured over the course of the RTPCR experiment. The bottom side of the RTPCR
chip contains a resistive heating network as well as a temperature sensor.
47
Thermocycler
PCR Chip
Graphene FET
.Graphene
Ac
fluSensor
Resistive
Heating
Fig. 4.5: Graphene EGFETs fabricated on the topside of a RTPCR chip. Thin insulated wires are
adhered to large source-drain pads using silver paste. The RTPCR chip may then be inserted into the
thermocycler using the grey button (left), which opens the system. The lid contains all of the optical
excitation and detection systems.
At present, RTPCR systems rely on optical systems along with fluorescent
chemistries to detect DNA replication. The use of graphene EGFETs to detect DNA
replication could reduce both the size and complexity of the PCR system by
eliminating the need for optical detection systems as well as fluorescent chemistries.
A graphene EGFET approach relies on fine-tuning the PCR buffer mix and
correlating pH changes to changing DNA concentrations [10]. This is possible
because DNA chain extension is accompanied by proton release (Fig. 4.6) and
because graphene has been shown to exhibit pH sensitivity.
B4
B3
8I
B3
82
B2
08B1
+
H
P_0
OH
B4
---
0P4
1
OH
U
=U
0-
P =0
dNTP
DNA primer to be extended
+
O-P-O
Extended DNA chain
OH
H+
proton
+
4
P2 7
pyrophosphate
Fig. 4.6: DNA extension chemistry illustrating the incorporation of nucleotide bases and subsequent
proton release. Deoxyribonucleotide triphosphates are abbreviated as dNTP.
The graphene EGFET channel current was recorded for an RTPCR experiment using
just mineral oil as a control run. This run determined to what extend the graphene
channel conductivity would be modulated by changes in temperature only (Fig. 4.7).
The sharp changes in the graphene EGFET current represent the denaturation phase
of each cycle. Therefore, the graphene EGFET covered with mineral oil produced
higher currents at lower temperatures. The overall baseline current remained
relatively stable. Once the PCR mix was added underneath the mineral oil, the
graphene EGFET channel current dropped markedly. The denaturation phase now
results in an increase in channel current. The reverse in behavior of the channel
current combine with the dramatic drop in the baseline current, suggests that the
Dirac point was shifted by the introduction of the PCR mix. Unfortunately, the
baseline current of the EGFET with PCR mix did not change with the increased
concentration of DNA. This led to the conclusion that RTPCR did not release enough
protons to affect the pH of the PCR mix. The PCR chemistry will requires further
48
optimization to allow the pH to change enough to shift the Dirac point but not
enough to render the DNA polymerase ineffective.
2001
150
-Mineral Oil
-PCR Mix
E 100
Readout
-Optimized
50j_"jhUILL j
0
I1
.iiW
-L -
5
10
I--
15
20
25
30
35
40
45
Time (minutes)
Fig. 4.7: Graphene FET sensor readouts over the course of an RTPCR
experiment for mineral oil baseline (blue), PCR mix with excessive
buffer concentration (green), hypothesized readout for optimized
buffer concentration (magenta).
Subsequently, the Dirac point voltage was measured as a function of temperature to
verify that the spikes in current in Fig. 4.7 result from changing temperatures during
the PCR cycle. Changing temperatures are known to affect rate constants in
chemical reactions via the Arrhenius equation. Because the PCR is a complex
chemical process consisting of many reactions with different activation barriers, it
makes sense that changing temperature may affect the graphene doping and
therefore the location of the Dirac point. The location of the graphene EGFET Dirac
point as a function of temperature is depicted in Fig. 4.8.
-100r
-120
E -140
5 -160
-VDS
=
20 mV
T-180
-200
-VDS =80 mV
VDS=00
-22 h
100mV
100
90
80
70
60
50
Temperature 0C
Fig. 4.8: Graphene EGFET Dirac point temperature dependence. A
tungsten probe was used as a pseudoreference electrode. The
average slope is approximately -0.73 mV/C.
30
40
49
3. Action Potential Sensing
Action potentials are electrical signals transmitted in both the central and
peripheral nervous systems. Neurons are the cells at the core of the nervous system
and consist of four components: the soma, axon, synapse, and dendrite. The soma is
the cell body and the axon is responsible for transmitting the action potential from
the soma to the synapse. At the synapse the electrical signal is transmitted
chemically to the other side of the synaptic cleft via neurotransmitters. The
dendrite is then responsible for the continued propagation of the post-synaptic
action potential.
Action potentials may be described by four phases: a resting potential,
depolarization, repolarization, and a refractory period in which hyperpolarization
occurs. The neuron membrane must be depolarized beyond a certain threshold for
an action potential to evolve. A changing membrane potential for an action
potential is illustrated in Fig. 4.9.
Action
potential
+40
CC
-55
initiations
SResting
StimulusRefractory
period
-70
0
1
3
2
Time (ms)
Fig. 4.9: Membrane potential
depiction of an action potential.
4
versus
state
5
time
The occurrence of action potentials was initially explained and modeled by the
pioneering work of Hodgkin-Huxley [11]. The essence of the Hodgkin-Huxley model
can be explained by examining two ionic species: sodium and potassium. Each of
these ions species possesses its own ion channels, which allow the ions to diffuse
through the cell membrane. Because the extracellular and intracellular ion
concentrations are not equal, the ions diffuse along concentration gradients, which
in turn create an electric field across the cell membrane. At equilibrium, the force
exerted by the ions due to the electric field is equal and opposite to the force exerted
on the ions due to diffusion. The potentials due to each sodium and potassium ions
are defined as ENa and EK, respectively. The potentials ENa and EK may be calculated
II
50
using the extracellular and intracellular ion concentrations in conjunction with the
Nernst equation. The model of the cell membrane as originally described by
Hodgkin-Huxley is depicted in Fig. 4.10.
Outside
E
~~ EKRN
E~.
+
+
CM+
Inside
Fig. 4.10: Hodgkin-Huxley model of a neuron cell membrane. RNa,
RK, and RL represent the conductivities of the sodium, potassium,
and leakage ion channels, respectively. RNa and RK exhibit
voltage-dependent conductivities. ENa, EK, and EL represent the
Nernst potentials due to sodium, potassium, and leakage ions. CM
is the membrane capacitance [11].
Extracellular sodium concentration is greater than the intracellular sodium
concentration. On the other hand, the intracellular potassium concentration is
Because membrane
greater than the extracellular potassium concentration.
potentials are defined as the extracellular potential with respect to the intracellular
potential, the sodium ions attempt to establish a negative membrane potential, ENa,
whereas the potassium ions attempt to establish a positive membrane potential, EK.
These two ionic species compete to define the overall membrane potential. At the
resting potential, however, conductivity of the sodium ion channels is much higher
than the conductivity of the potassium ion channels. Therefore the overall
membrane potential is ENa, which is approximately -70 mV as determined by the
sodium ion concentrations (Fig. 4.9).
If the neuron receives some stimulus and becomes depolarized beyond a certain
threshold, the conductivities of the potassium ion channels will temporarily become
greater than conductivities of the sodium ion channels. Therefore, the membrane
potential will climb to a positive value as defined by the potassium ion
concentrations, EK. Eventually, the conductivities of the sodium ion channels will
again become greater than the conductivities of the potassium ion channels. When
this occurs, the cell membrane repolarizes with a slight over shoot and eventually
51
recovers to the resting potential, ENa. For in-depth description of voltage dependent
ion channel conductivities, the reader is referred to the Hodgkin-Huxley model [11].
If a neuron is in close proximity to the gate region of a graphene EGFET and
produces an action potential, the resulting change in ion concentrations alter the
composition of the electric double layer at the graphene surface. This, in turn,
changes the carrier concentration in the graphene channel, which results in a
modulated channel current IDS. In this way, the generation of an action potential can
be detected by monitoring the current of a graphene EGFET under constant bias
conditions. This experimental setup is depicted in Fig. 4.11.
GS
reference electrode
neuron
Drain
Fig. 4.11:
Experimental
gold contact
Source
setup
for
graphene
EGFET as
an
electrogenic cell sensor.
Graphene EGFET devices were disinfected by autoclaving and subsequent
immersion in ethanol. Mouse hippocampal neurons were then extracted and
cultured on top of graphene EGFETs. A high K+ Tyrode's solution was used to
chemically stimulate neurons and generate action potentials. The current process
results in a cell culture with healthy neurons as indicated by dendrite formation in
Figs. 4.12, 4.13. The process, however, produced low-density cell culture with no
neurons located over the graphene EGFET channel regions. Current efforts aim to
increase the cell culture density so as to increase the likelihood that neurons are
positioned on top of graphene EGFET channel regions.
52
Fig. 4.12:
Optical
microscope
image of
hippocampal mice neurons cultured on top of
graphene EGFET device.
Fig. 4.13:
Optical
microscope
image of
hippocampal mice neurons cultured on top of a
second graphene EGFET device.
References
[1]
J.-U. Park, S. Nam, M.-S. Lee, and C. M. Lieber, "Synthesis of Monolithic
Graphene-Graphite Integrated Electronics," Nat. Mater., vol. 11, no. 2, pp. 1205, Feb. 2012.
[2]
P. K. Ang, W. Chen, A. T. S. Wee, and K. P. Loh, "Solution-Gated Epitaxial
Graphene as pH Sensor,"J. Am. Chem. Soc., vol. 130, no. 44, pp. 14392-3, Nov.
2008.
[3]
B. Mailly-Giacchetti, A. Hsu, H. Wang, V. Vinciguerra, F. Pappalardo, L.
Occhipinti, E. Guidetti, S. Coffa, J. Kong, and T. Palacios, "pH Sensing Properties
of Graphene Solution-Gated Field-Effect Transistors,"J. AppL. Phys., vol. 114,
no. 8, p. 084505, 2013.
[4]
Y. Ohno, K. Maehashi, Y. Yamashiro, and K. Matsumoto, "Electrolyte-gated
graphene field-effect transistors for detecting pH and protein adsorption,"
Nano Lett., vol. 9, no. 9, pp. 3318-3322, 2009.
[5]
J. Ristein, W. Zhang, F. Speck, M. Ostler, L. Ley, and T. Seyller, "Characteristics
of Solution Gated Field Effect Transistors on the Basis of Epitaxial Graphene
on Silicon Carbide,"J. Phys. D. AppL. Phys., vol. 43, no. 34, p. 345303, Sep. 2010.
[6]
R. Brumleve, Timothy, Buck, "Numerical Solution of the Nernst-Planck and
Poisson Equation System with Applications to Membrane Electrochemistry
and Solid State Physics,"J. Electroanal. Chem., vol. 90, pp. 1-31, 1978.
[7]
J. M. Rothberg, W. Hinz, T. M. Rearick, J. Schultz, W. Mileski, M. Davey, J. H.
Leamon, K. Johnson, M. J. Milgrew, M. Edwards, J. Hoon, J. F. Simons, D. Marran,
J. W. Myers, J. F. Davidson, A. Branting, J. R. Nobile, B. P. Puc, D. Light, T. a Clark,
M. Huber, J. T. Branciforte, 1. B. Stoner, S. E. Cawley, M. Lyons, Y. Fu, N. Homer,
53
M. Sedova, X. Miao, B. Reed, J. Sabina, E. Feierstein, M. Schorn, M. Alanjary, E.
Dimalanta, D. Dressman, R. Kasinskas, T. Sokolsky, J. a Fidanza, E. Namsaraev,
K. J. McKernan, A. Williams, G. T. Roth, and J. Bustillo, "An Integrated
Semiconductor Device Enabling Non-Optical Genome Sequencing," Nature, vol.
475, no. 7356, pp. 348-52, Jul. 2011.
[8]
D. R. Pollard, W. M. Johnson, H. Lior, S. D. Tyler, and K. R. Rozee, "Rapid and
Specific Detection of Verotoxin Genes in Escherichia coli by the Polymerase
Chain Reaction," J. Clin. Microbiol., vol. 28, no. 3, pp. 540-545, 1990.
[9]
C. a Heid, J. Stevens, K. J. Livak, and P. M. Williams, "Real Time Quantitative
PCR," Genome Res., vol. 6, no. 10, pp. 986-994, Oct. 1996.
[10]
C. Toumazou, L. M. Shepherd, S. C. Reed, G. I. Chen, A. Patel, D. M. Garner, C. A.
Wang, C. Ou, K. Amin-desai, P. Athanasiou, H. Bai, I. M. Q. Brizido, B. Caldwell,
D. Coomber-alford, P. Georgiou, K. S. Jordan, J. C. Joyce, M. La Mura, D. Morley,
S. Sathyavruthan, S. Temelso, R. E. Thomas, and L. Zhang, "Simultaneous DNA
Amplification and Detection using a pH-sensing Semiconductor System," Nat.
Methods, vol. 10, no. 7, pp. 641-646, 2013.
[11]
A. F. Hodgkin, A. L., Huxley, "A Quantitative Description of Membrane Current
and its Application to Conduction and Excitation in Nerve,"J. PhysioL, vol. 117,
no. 4, pp. 500-544,1952.
54
Chapter 5 - Summary & Conclusions
This thesis provides an introduction to graphene and the theory behind graphenebased electrolyte-gated field-effect transistors (EGFETs). The thesis then moves on
to provide a detailed description of the graphene EGFET fabrication process and
measurement setups. A current-voltage model for graphene EGFETs is then
developed to better understand and optimize graphene EGFET performance. This
was accomplished by combining models for metal-insulator-gated graphene FETs
with models for the graphene-electrolyte interface. The developed graphene EGFET
model was shown capable of producing as little 2% error in the current-voltage
characteristic. The model can be used to compute other device characteristics
required for circuit design such as transconductance, output impedance, and
intrinsic gain.
The model allows for heterogeneous top-gate capacitances, which enable the study
of different passivation schemes and cases where the graphene channel is only
partially modulated (e.g. partial coverage by an electrogenic cell). The model shows
partial channel passivation acts to increase the overall series resistance. This was
experimentally verified and graphene EGFETs with partial channel passivation were
compared to those with recessed passivation.
Fitting the model to experimental data represents a convenient method to estimate
device parameters such as minimum carrier concentration, mobility, contact
resistance, effective double layer capacitance, and charged impurity concentration.
The alternative requires fabricating specialized devices and a number of different
measurements (e.g. Hall, TLM, Mott-Schottky). In addition, graphene EGFETs were
shown capable of substantial intrinsic gains making them suitable for use in
amplifier circuits. Alternatively, graphene EGFET sensors may be optimized for
transconductance performance and coupled with transresistance amplifiers. A basis
for determining an optimal channel length given certain design constraints is
established.
Graphene EGFETs were shown also capable of substantial intrinsic gains making
them suitable for use in amplifier circuits. The intrinsic gain of graphene EGFETs is
shown to be virtually independent of channel length provided the effect of contact
resistance remains negligible. Alternatively, graphene EGFET sensors may be
optimized for transconductance performance and coupled with transresistance
amplifiers. A basis for determining an optimal channel length given certain design
constraints is established. The developed graphene EGFET model may now be
employed for application-specific sensor optimization and as a tool to inform the
design of large-scale graphene sensors systems.
Lastly, this work describes several potential applications for graphene EGFETs
ranging from pH sensors to real-time polymerase chain reaction (RTPCR) sensors to
55
electrogenic cell sensors. Fabricated graphene EGFETs are shown to produce pH
sensitivity of -50.8 mV/pH.
Graphene EGFETs are also fabricated for use in a
RTPCR system. RTPCR is run successfully to identify DNA segments thought
responsible for the metabolism of clopidogrel, a popular antiplatelet medication.
The graphene EGFETs, however, failed to sense an increase in DNA concentration.
Further optimization of the PCR buffer concentration is required to ensure that
increased DNA concentration lowers the PCR mix pH without rendering the DNA
polymerase ineffective.
Graphene EGFETs were fabricated for electrogenic cell sensing using the optimized
parameters from the newly developed graphene EGFET current-voltage model.
Hippocampal mouse neurons were successfully cultured on top of the graphene
EGFETs. At present, however, the graphene EGFETs are unable to sense action
potentials due to the low density of the cell cultures. Current efforts aim to increase
the density of neurons and improve adhesion between neurons and the graphene
EGFET channel region. Chemical and optogenetic methods of neural stimulation are
under current investigation.