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Abstract—This paper presents a COMSOL Multiphysics 2D
axisymmetric model of an pH-ElecFET (pH-sensitive
electrochemical field effect transistor) microsensor. This device
combines an integrated microelectrode with a pH-sensitive
chemical field effect transistor (pH-ChemFET). Thus, by
triggering electrolysis phenomena owing to the integrated
microelectrode, associated local pH variations in microvolumes
are monitored thanks to the pH-ChemFET microdevice. Taking
into account (electro) chemical reactions and diffusion
phenomena in liquid phase, the proposed model points out the
role of the ElecFET geometrical design (microelectrode width w,
gate sensitive radius r
e
and distance between the pH-ChemFET
gate and the microelectrode d), as well as polarization
parameters, (polarization voltage V
p
and time t
p
), on the
microsensor response. It is first applied to water electrolysis in
order to validate pH impulsional variations in microvolume.
Then, oxidation of hydrogen peroxide in phosphate buffer (PBS,
pH
0
=7.2) solutions is studied, evidencing the H
2
O
2
potentiometric
detection in the [10–100mM] concentration range. This developed
model paves new ways for sensor applications, opening several
new opportunities for pH-ElecFET devices for H
2
O
2
-related
enzymatic detection of biomolecules.
Index Terms—Modelling, ElecFET, microelectrode, pH-
ChemFET, water electrolysis, hydrogen peroxide detection.
I. INTRODUCTION
n the last decade, the electrochemical microsensors have
received an increasing interest in a wide range of
applications such as clinical diagnostics, food analysis,
environmental monitoring due to their low cost, simple
operation, small size, and rapidity, sensitivity and real-time [1-
3]. The electrochemical sensors can be divided into three
groups depending on the measured electrical signal [4-6]:
amperometric, potentiometric, and conductometric. Even so,
the combination of amperometric and potentiometric
techniques is a very promising method in terms of detection
[7-10]. Diallo et al. have developed an electrochemical field
effect transistor (ElecFET) microsensor based on this
technique [8, 9]. This device is achieved through the
integration of a planar noble metal electrode around the
dielectric gate area of a pH-sensitive ChemFET microdevice.
By triggering pH-related electrochemical reactions thanks to
the microelectrode polarization and by monitoring the so-
N. Aoun and F. Echouchene are with the Laboratory of Electronics and
Microelectronics, University of Monastir, 5000, Tunisia (e-mail:
nejibaaoun@yahoo.com, frchouchene@yahoo.fr)
A. K. Diallo, J. Launay and Temple-Boyer are with the University of
Toulouse, UPS, LAAS, F-31400 Toulouse, France.
H. Belmabrouk is with the Department of Physics, College of Science
AlZulfi, Majmaah University, Saudi Arabia.
obtained pH variations thanks to the pH-ChemFET,
electrolysis phenomena and pH measurement are closely
embedded at the microscale, enabling new electrochemical
detection potentialities. Among the ElecFET microdevice
applications, the most frequent is the manufacturing of a pH-
related enzyme sensor. In this case, the ChemFET detects the
pH change resulting from the enzymatic reaction in the
membrane that covers the sensor [11]. The output voltage of
the ChemFET controls the current flowing through the sensor-
actuator system [12]. ElecFET has been successfully used to
determine acid or base concentration [13], to form the heart of
a carbon dioxide sensor [14] and detect different biomolecules
[8, 11].
Various mathematical models of microsensors have been
developed and successfully used to study and optimize
analytical characteristics of microsensors [15-18].
Meena and Rajendran [15] have derived analytical expressions
of concentration and current in order to describe and evaluate
the performances of amperometric and potentiometric
biosensors using homotopy perturbation method. A numerical
study of potentiometric and amperometric electrochemical gas
sensors based in a solid-state ion conducting electrolyte has
presented by López-Gándaraa et al. [16] in order to optimize
the diffuse layers covering one of their catalytic electrodes.
The model describes the current-voltage characteristics in the
system layer/electrode/electrolyte/electrode. A theoretical
study and numerical simulation of potentiometric and
amperometric enzyme electrodes and of enzyme reactors have
been developed by Morf et al. [17, 18]. The response
characteristics of potentiometric and amperometric sensor
systems, as well as the product release from enzyme reactors,
are analyzed, and the influence of the relevant parameters on
the steady-state response is demonstrated and discussed [17].
In this paper, we apply the concept of the combination of
amperometric and potentiometric techniques to simulate the
ElecFET microdevice detection principles, in order to monitor
water (H
2
O) electrolysis phenomena in a first stage and
hydrogen peroxide (H
2
O
2
) electrochemical detection in the
second stage. We then focus on the study of the influences of
the main parameters, i.e. (i) polarization voltage V
p
and time t
p
on the integrated microelectrode, (ii) characteristic of the
microelectrode width w, (iii) distance between the gate
sensitive radius and the integrated microelectrode d and (iv)
gate sensitive radius r
e
.
II. PRESENTATION OF THE SIMULATION MODEL
The modelling approach used takes into account the
different chemical, electrochemical and physical phenomena
occurring in the frame of the ElecFET detection principles:
▪ Oxido-reduction on the integrated microelectrode;
Finite-element simulations of the pH-ElecFET
microsensors
N. Aoun, F. Echouchene, A. K. Diallo, J. Launay, P. Temple-Boyer and H. Belmabrouk
I
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▪ Diffusion phenomena;
▪ (H
3
O
+
/H
2
O) and (H
2
O/OH
-
) and acid-base analysis of
aqueous solutions at pH
0
=7.2.
The ElecFET detection properties were thus modeled by
studying the diffusion phenomena of the main chemical
species in the electrolyte, focusing on the H
3
O
+
/OH
-
water-
based ions, and finally by analyzing the pH detection
properties of the silicon nitride Si
3
N
4
ChemFET gate.
A. Geometry of ElecFET: comparison between real and
simulated model
Since their fabrication process used silicon-based
microtechnologies and therefore photolithography, the real
ElecFET microdevices are based on a rectangular concentric
geometry [9]. In order to decrease calculation times, the
simulated model was simplified by using r-z cylindrical
geometry, leading to a 2D axisymmetric geometry (Fig.1).
The geometrical parameters are: the gate sensitive radius r
e
,
the distance between the sensitive gate and the electrode d,
and w the microelectrode ring width. The depth of the
sensitive gate z
e
is 0.5µm and the height of the modeled
geometry is h=300 µm. The standard values of the parameters
(r
e
, d, w) are (10µm, 50µm, 100 µm). At the end of the paper
these values will be modified in order to enhance the
performance of pH-ElecFET. The dimensions of electrolyte
domain are indicated in Fig. 1.
B. Modelling of the electrochemical reactions (H
2
O &H
2
O
2
)
The ElecFET concept was initially used for the monitoring
of water (H
2
O) hydrolysis and secondly of the hydrogen
peroxide (H
2
O
2
) oxidation in water based solutions:
4eO O4HO6H :E
2320p
V
(1)
4OH2H4e O4H :E
220p
V
(2)
232221
O 2eO2HO2H OH :E
p
V
(3)
where
are equilibrium potentials of the
O
2
/H
2
O, the H
2
/H
2
O and O
2
/H
2
O
2
redox couple, respectively.
The values of the constants are:
[9]
and
[8].
C. Modelling of the diffusion phenomena in water
Diffusion phenomena of the most influential chemical
species, i.e. H
3
O
+
and OH
-
ions in case of H
2
O detection and
H
3
O
+
, OH
-
and H
2
O
2
species in case of hydrogen peroxide
detection, into water, have been modeled using the Fick law:
i
iii
i
i
R
z
c
r
c
r
r
c
D
t
c
)
1
(
2
2
2
2
(4)
where t denotes the time, c
i
is the concentration of the
studied chemical species, D
i
is its diffusion coefficient and R
i
is an additional term accounting for the
production/consumption rate of the ion species through a
possible chemical reaction. The reaction term can be deduced
using the water protolysis reaction:
(5)
where k
f
and k
b
are the forward and backward reaction kinetic
rates, respectively.
One can thus express the reaction for the production of proton
and hydroxide ions as [19]:
]OH][OH[
]OH[]OH[]OH[
3
32
3
ef
fb
OHOH
Kk
kkRR
(6)
where K
e
= k
b
[H
2
0]/k
f
is the equilibrium constant of water.
The forward rate constant k
f
of the water protolysis reaction
is estimated by values taken from literature [20] while the
backward rate constants k
b
is obtained from where K
e
denotes
the water dissociation constant.
Buffer solution is of great importance in biosensor
applications. Experimentally, the buffer concentration could
be optimized. So, a lot of experiments have been reported on
the buffer properties which enhance the response and the
stability of the biosensor [21, 22]. In our kinetic model the
chemical effect of the buffer solution was neglected and was
not taken into account. In the frame of a kinetic approach, the
influences of acid/bases other than the water-based ones are
limited by diffusion phenomena (Eq. 4). In another way, we
have been interested only on the protonation reaction because,
as a solvent, water is in excess in solution. As a result, we can
assume that the buffer solution does not have an effect on the
biosensor response which can be expressed with the chemical
effect modeled with physical equations.
D. Initial and boundary conditions
Boundary conditions are crucial for a correct description of
phenomena with partial differential equations. For our model,
several important conditions have to be set. The initial
condition related to mass transport of species is given by:
h0
300µm0
500;,
100;,
100;,
22
0
0
3
OH
pH pKe
OH
pH
OH
z
r
mMtzrc
tzrc
tzrc
(7)
Fig. 1.Cross-section on the ElecFET device in r–z cylindrical coordinates.
k
f
k
b
H
3
O
+
+ OH
-
2H
2
O
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On the axis of symmetry, the boundary condition reads:
0),0(
t,zr
r
c
i
(8)
At the upper interface of the electrolyte (z=h) and the lower
interface (z=0 or z
e
), the interface is assumed to be
impermeable:
0=)0( ,t or zr,z=h or
z
c
e
i
(9)
In order to do not disturb the diffusion phenomena
operating from the surface of the microelectrode, the outer
surface of the device is assumed to be at a constant
concentration:
),,300(
0,ii
ctzµmrc
(10)
An oxido-reduction reaction takes place at the electrode for
t<t
p
. Thus, the boundary condition reads:
w ; =) (
,
drrdri
FN
tt,z=zr,
z
c
D
eej
j
ji
pe
i
i
(11)
where N
j
is the number of electron transferred for reaction “j”,
i,j
is the stoichiometric coefficient, F is Faraday’s constant
and t
p
is the polarization time. i
j
denotes the current density
given from the kinetic equations for the electrochemical
reactions at the electrode surface based on the Butler–Volmer
expression[23]:
i
i
j
jc
jqi
refi
i
j
ja
jpi
refi
i
refjj
RT
F
c
c
RT
F
c
c
ii
)exp(
)exp(
,
,
,
,
,
,
;0
(12)
where i
0j,ref
is the exchange current density due to reaction “j”
at the reference concentrations in A/cm
2
,c
i
is the concentration
of species “i” adjacent to the surface of electrode in mol/cm
3
,
c
i,ref
is the reference concentration of species “i” in mol/cm
3
,
α
aj
is the anodic transfer coefficient for reaction “j”, α
c,j
is the
cathodic transfer coefficient for reaction “j”, p
i, j
=
i,j
is the
anodic reaction order of species “i” in reaction “j”, q
i, j
=-
i,j
is
the cathodic reaction order of species “i” in reaction “j”, R is
the gas constant, T is the temperature and η
j
is the
overpotential of reaction “j” in volts (V), and it is measured
with respect to a reference electrode of a given kind in a
solution at the reference concentrations.
The overpotential for electrochemical reaction “j”, (η) in Eq.
12 is given by:
jp
V
0,j
E-
(13)
where V
p
is the applied potential surface in V, E
0,j
is the
equilibrium potential for reaction “j”.
Total current is obtained by numerical integration of the local
current density over the entire ElecFET area. It is given by:
A
j
dAitI )(
(14)
where A is the surface area of the electrode.
E. Numerical method
The governing equations with initial and boundary conditions
are solved numerically using the finite element software
COMSOL Multiphysics 4.3b [24]. An electroanalysis module
has been chosen for solving the mass transport of diluted
species in electrolytes using the diffusion equation.
The overall computational domain is discretized using an
unstructured triangular mesh Fig.2. It is noticed that the region
nearby the reaction surface is refined with a better mesh
quality.
For the time discretization we have employed First-order
backward differentiation formula (BDF), with the time steps
controlled by the numerical solver during the computations.
Total current, given by Eq. (14), is performed using a fourth
order integration method.
III. RESULTS AND DISCUSSION
To describe the pH-ChemFET response, we can use the
threshold voltage variation. The pH-ElecFET threshold
voltage variation is related to the pH at the silicon nitride
Si
3
N
4
surface according to the following equation [20]:
)pH-)(pH(0,s)(
pzc00
tVtV
TT
(15)
where pH(0,t) is the pH at the Si
3
N
4
sensitive surface when
the diffusion phenomena "steady state" is reached and V
T0
is a
constant parameter depending on the SiO
2
/Si
3
N
4
pH-
ChemFET technology [25], pH
pzc
is the point zero of charge
which is estimated around 4 for Si
3
N
4
[23, 26]). In the
following, since the V
T0
value is only related to the pH-
ChemFET technological fabrication, it is of no influence
concerning the ElecFET detection properties and it will not be
taken into account, i.e. it will be chosen equal to zero [27, 28].
s
0
is an ideal sensitivity of ISFET based pH sensor when pH is
measured by the means of Nernst potential given by the
following equation [29]:
pH/2.59)10ln(s
0
mV
q
kT
(16)
Fig. 2. Two-dimensional unstructured mesh with triangular elements.
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where k=1.38×10
-23
J/K is the Boltzmann constant, T=300K is
temperature and q=1.6×10
-19
C the elementary charge.
A. Mesh sensitivity
To ensure that the convergence has been obtained and the
numerical results are independent of the mesh size,
Fig. 3 shows the pH local at z=150 μm of the electrolyte for
several mesh grids. There was no significant difference
between the curves obtained using these grids (6818, 13643,
27719, 53534 elements) and we may conclude that the
numerical convergence has been reached with all the grids. In
the results section, all simulations were done with a total
elements number 13645 [30, 31].
B. Study of the most influential parameters
The kinetic parameters and the constants used in this
simulation are listed in Table I and Table II [9, 32, 33].
ElecFET detection/transduction principles were first studied
for water electrolysis monitoring H
2
O in aqueous solutions
(pH
0
=7.2). Then, the ElecFET detection properties were tested
for the hydrogen peroxide H
2
O
2
also in aqueous solutions
(pH
0
=7.2) solutions containing different stabilized
concentrations [H
2
O
2
] ranging from 10 to 100mM because of
their properties in terms of activity, stability and cost.
According to theoretical equations, the most influential
parameters are the polarization voltage V
p
, the time of
polarization t
p
, the concentration [H
2
O
2
], the distance between
the gate sensitive radius and the microelectrode (parameter d),
the surface of the microelectrode (associated with the
parameter w) and gate sensitive radius (parameter r
e
).
All series of simulation have been devoted to modelling the
sensor response, i.e. the dependence of the threshold voltage
versus time. The curves of this threshold voltage, measured at
pH
0
=7.2, are shown in Figs.4-9.
Case1: water electrolysis monitoring:
Before testing the sensor performance for the H
2
O
2
detection, one should ensure that the sensor is able to provide
a response in the case of water electrolysis.
Fig. 4 presents the temporal evolution of the threshold
voltage V
T
in the case of H
2
O redox phenomena for different
polarization voltages while maintaining a constant the
polarization time (t
p
= 5s). Since V
p
is positive (respectively
negative), oxidation (respectively reduction) of H
2
O takes
place near the platinum microelectrode.
Therefore, a production of hydronium H
3
O
+
(respectively
hydroxide OH
-
) ions, so for a local pH changes sharply and
finally the threshold voltage V
T
increases (respectively
decreases). In this case, phenomena occur at higher than 1.2V
(positive polarization) and/or lower than -0.8V (negative
polarization) polarization voltages V
p
according to the
associated equilibrium potential values
and
.
Fig. 4.Temporal variations of the pH–ChemFET threshold voltage for
different polarization voltages.
TABLE II
PHYSICO-CHEMICAL INPUT VALUES USED IN THE SIMULATION MODEL
Parameter
Value
Unit
F
96352
C/mol
D
H30+
9.3×10
-9
m
2
/s
D
OH
-
5.3×10
-9
m
2
/s
D
H2O2
3.1×10
-10
m
2
/s
c
H3O+,ref
10
-pH0
mol/L
c
OH
-
,ref
10
pKe-pH0
mol/L
c
H2O2,ref
50×10
-3
mol/L
pH
0
7.2
k
f
1.5×10
11
L/mol/s
K
e
1×10
-14
mol
2
/L
2
0 200 400 600 800 1000 1200
-350
-300
-250
-200
-150
-100
-50
0
50
polarization time: 5s
Threshold voltage (mV)
Time (s)
-0.9V
-0.95V
-1V
1,35V
1,3V
1,4V
TABLE I
PARAMETERS USED IN THE SIMULATIONS
Reaction 1
Reaction 2
Reaction 3
i
0j,ref
(A/m
2
)
1.115×10
-6
10
-6
9.64×10
-6
E
0,j
(V)
1.2
-0.8
0.7
α
a,j
0.5
0.5
0.5
α
c,j
0.5
0.5
0.5
H3O+
+1
+1
OH
-
+1
H2O2
-1
N
j
4
4
2
Fig. 3. pH at z = 150 μm of the electrolyte for several mesh grids.
0 50 100 150 200 250 300
5,4
5,6
5,8
6,0
6,2
6,4
6,6
6,8
7,0
7,2
7,4
pH
r (µm)
3569 elements
6818 elements
13643 elements
27719 elements
53534 elements
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The amplitude of the peak is so much greater than the value
of the applied potential increases. When the polarization is
interrupted, the ElecFET microsensor response follows a
return to equilibrium of the system because of the diffusion
laws.
Subsequently, the influence of polarization time t
p
was
studied. Fig. 5 illustrates the temporal variations threshold
voltage for different polarization times (t
p
= 5, 10, 10 and3 s)
for two values of the polarization voltage on the integrated
microelectrode (V
p
= 1.4 or -1V). In agreement with the
Equation (11), the polarization time increase is responsible for
a local pH decrease and therefore a pH-ChemFET threshold
voltage increases (Eq. 15). Nevertheless, threshold voltage
variations are lower and tend to reach saturation. Fig. 4 and
Fig. 5 show clearly that the microsensor has a response in the
case of water electrolysis. Therefore, we can continue our
analysis and assess the performance of the sensor for H
2
O
2
detection.
Case2: hydrogen peroxide detection:
The ElecFET concept was studied by taking into account
the H
2
O
2
oxidation on the integrated microelectrode.
According to the oxidation reaction (Eq.3), in presence of
hydrogen peroxide H
2
O
2
, a positive polarization V
p
on the
platinum microelectrode produces hydronium H
3
O
+
ions.
Therefore, the local pH decreases around the sensitive area of
the microsensor and finally the threshold voltage V
T
increases.
For this purpose, the polarization voltage V
p
was chosen less
than
to avoid any interference with water hydrolysis.Since
the
is roughly equal to 0.7V, a similar polarization voltage
V
p
was applied on the platinum microelectrode at the different
polarization times (t
p
= 5, 10, 15, 20, 30, 40 and 60s) while
keeping constant [H
2
O
2
] concentration at 50mM in a solution
of pH
0
=7.2, with a constant polarization voltage (Fig. 6). V
T
tends toward increasingly positive values (i.e local pH
decreases). As previously for the water electrolysis, the
amplitude of the peaks increases with t
p
. The maximum
threshold voltage increases steeply over a short period of time
and thereafter reaches a plateau value. It is clear that the
influence of polarization time appears only in transient state.
The equilibrium state is reached for t
p
=10s.
In the same way, Fig. 7 represents the H
2
O
2
-ElecFET
response as a function of time for different polarization
voltages V
p
. This figure has been obtained with [H
2
O
2
] =
50mM in a solution of pH
0
=7.2 and t
p
= 30s.
We found that the asymptotic value of threshold voltage is
essentially linearly related to the polarization voltage V
p
. As
soon as the polarization is interrupted, the ElecFET
microsensor response tends to turn to back equilibrium of the
system because of diffusion phenomenon.In the case of
hydrogen peroxide detection, the Butler-Volmer theory
emphasizes on the influence of the [H
2
O
2
] concentration of
H
3
O
+
ion production kinetics (Eq. 3).
Fig. 8 shows temporal variations of the pH-ChemFET
threshold voltage for different H
2
O
2
concentrations.
Simulation results prove that the amplitude of the threshold
voltage increases with the [H
2
O
2
] concentration in solution,
and saturates for the highest values. This saturation
Fig. 7.Temporal variations of the pH–ChemFET threshold voltage for the
different polarization voltages at [H
2
O
2
] =50mM, t
p
=30s, d=50µm,
w=100µm and r
e
=10µm and (inset) ElecFET response V
p
.
Fig. 6.Temporal variations of the pH–ChemFET threshold voltage for the
different polarization times at [H
2
O
2
] =50 mM, V
p
=0.7V, d=50µm,
w=100µm and r
e
=10µm and (inset) ElecFET response versus t
p
.
-100 0 100 200 300 400 500 600 700
-200
-150
-100
-50
0
50
0,70 0,75 0,80 0,85 0,90
-0,20
-0,15
-0,10
-0,05
0,00
0,05
V
sat
T
(V)
V
p
(V)
V
sat
T
=0.99V
p
-0.86
Threshold voltage (mV)
Time (s)
0.7
0.75
0.8
0.85
0.9V
Fig. 5.Temporal variations of the pH–ChemFET threshold voltage for
different polarization times.
0 200 400 600 800 1000
-195
-190
-185
-180
-175
-170
-165
0 10 20 30 40 50
-190
-185
-180
-175
-170
-165
Threshold voltage(mV)
t
p
(s)
50
40
30
25
15
5
10
4
3
2
1
Threshold voltage (mV)
Time (s)
0.1
0 200 400 600 800 1000 1200
-350
-300
-250
-200
-150
-100
-50
0
50
Threshold voltage (mV)
Time (s)
positive polarization: +1,4V
negative polarization: -1V
5s
10s
20s
30s
5s
10s
30s
20s
![Fig. 9.Temporal variations of the pH–ChemFET threshold voltage for various: (a) surface of the microelectrode at d=50µm and re=10µm (b) positions of the microelectrode at w=100µm and re=10µm, and (c) gate sensitive radius at d=50µm and w=100µm and to all at Vp=0.7V, tp=30 s, [H2O2] =50 mM.](/figures/fig-9-temporal-variations-of-the-ph-chemfet-threshold-26jdsqdf.webp)
