Electronic and ionic transport in
organic materials and devices

3

Paolo Romele, Zsolt M. Kovács-Vajna and Fabrizio Torricelli
University of Brescia, Department of Information Engineering, Brescia, Italy

3.1

Charge transport in organic materials

Electronic charge transport in organic and polymeric materials impacts the electrical, optical, and thermal properties of organic devices. The wide range of organic
materials and fabrication techniques used for the material deposition and device
fabrication, provides organic materials with very different morphological structure
and properties. Organic devices are obtained by combining several materials including, for example, organic small molecules and polymers, polymer blends, polyelectrolytes, electrolytes, inorganic compounds (typically used as insulators), and
metals (typically used as electrodes).
This large variety of materials, processes, and device structures results in very
different bulk and interface charge transport properties of organic materials and
devices. It is quite common that the very same organic semiconductor can display
different charge transport properties depending on the solvent, annealing temperature, substrate, interaction with other materials used for the device fabrication, and
so on. In addition, depending on the operating conditions of the device (e.g.,
applied voltage, temperature, and electric field) and device geometries, only a small
“window” of the organic material properties can be assessed. By the way of example, organic light emitting diodes operate in space charge limited transport, with a
typical charge carrier concentration in the range 1014
1016 cm23 [1,2], while
organic field-effect transistors can operate in both weak and strong accumulation
spanning charge concentrations in the range 1016
1020 cm23 [3,4]. Interestingly,
organic ion-gated transistor, comprising both electrolyte-gate and electrochemical
transistors, can achieve charge concentrations as high as 1022 cm23 [5,6], making
them very interesting for the in; vestigation and understanding of the charge transport
at the transition between the semiconducting and conducting regimes [5].
Moreover, in the case of organic electrochemical transistors the charge concentration can be modulated in the whole bulk of the organic polymer by means of ionicelectronic charge interaction and/or electrochemical charge transfer [7].
In organic materials and devices, the energetic and spatial order of the molecules
and their interaction with the interface materials are reflected in the density of states
(DOS) distributed in the bulk and at the interface. In highly ordered (crystalline)
organic materials, the charge carriers are delocalized on several molecules, defining
a delocalized band energetically positioned at the lowest unoccupied molecular
Organic Flexible Electronics. DOI: https://doi.org/10.1016/B978-0-12-818890-3.00003-5
© 2021 Elsevier Ltd. All rights reserved.

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orbital (LUMO) in the case of electron transport and at the highest occupied molecular orbital in the case of hole transport. Although crystalline organic semiconductors, like rubrene, have been demonstrated, most of the organic semiconductors are
polycrystalline or amorphous. By the way of example, the chemical or physical
defects in conjugated polymer “brake” the polymer chains into subconjugation subunits. Charge carriers can easily move within a conjugation subunit while an energetic or spatial barrier have to be overcome when passing from one subunit to
another. In contrast to highly ordered organic materials where charge carriers hop
between closely spaced molecules forming a crystalline stack, in disordered organic
materials the charge transport is strictly related to the density of the localized
states.
Depending on the degree of disorder and on the position of the Fermi energy
level, the charge transport in organic semiconductors involves (1) the density of
delocalized states only, (2) the density of localized states only, and (3) both the density of delocalized and localized states. The aforementioned cases are described
with different charge transport theories. If there is no disorder and/or the Fermi
energy level is above the delocalized states (viz. all the traps are filled), charge carriers move like free particles in the delocalized DOS and the Drude model is conceptually appropriate for describing the charge transport [8]. In the case of a
medium level of structural disorder (e.g., polycrystalline organic materials) and/or
when the Fermi energy level is approaching the delocalized states, both delocalized
and localized states have to be considered and the charge transport is described by
the multiple trapping and release (MTR) model [9]. The MTR model, originally
developed for polycrystalline and amorphous silicon, assumes that most of the
charge carriers are trapped into the localized states and released in the delocalized
states upon thermal excitation (Fig. 3.1). Charge transport takes place only in delocalized states and only a small fraction of charge carriers contributes to the transport and the conductivity reads:
σMTR 5 qμds cds ;

(3.1)

where q is the elementary charge, μds is the charge carrier mobility in the delocalized states, and cds is the charge concentration in the delocalized states, that can be
calculated by solving the Fermi-Dirac integral expression and in the case of electrons and holes reads, respectively:
ð
nds ðEF Þ 5

gdes ðEÞ



ð
pds ðEF Þ 5

1

 dE
1 1 exp E k2B TEF

gdhs ðEÞ

exp

E 2 EF
kB T

1 1 exp



(3.2)



E 2 EF
kB T

 dE

(3.3)

Electronic and ionic transport in organic materials and devices

73

Figure 3.1 Schematic view of the MTR transport. A charge carrier (electron or hole)
moving in the delocalized states is trapped in a localized stated and then thermally released.
MTR, Multiple trapping and release.

where gdes(E) and gdhs(E) are the density of delocalized states of electrons and
holes, respectively, E is the energy, kB is the Boltzmann constant, T is the temperature, and EF is the Fermi energy level. Finally, the field-effect mobility due to the
overall charge concentration can be calculated as:
μMTR 5

σMTR
;
cds 1 cls

(3.4)

where cls is the trapped charge concentration in the localized states and can be calculated by replacing in Eqs. (3.2) and (3.3) the gdes(E) and gdhs(E) with the density
of localized states gles(E) and glhs(E), respectively. As a consequence, MTR charge
transport depends on the shape and energy position of both delocalized and localized DOS.
In the most common case of organic devices based on disordered organic materials, charge transport can take place in localized states by means of hopping, viz.
thermally assisted tunneling process. The hopping process between two small molecules or subconjugated units of a polymer can be described by considering the
equivalent energy site Es and position rs 5 (xs, ys, zs). The charge transport process
between two sites i and j is depicted in Fig. 3.2. A charge carrier occupies a site
with energy Ei and position ri. Upon phonon absorption, the energy of the charge
carrier increases (E 5 Ei 1 ΔE) and because of quantum tunneling there is a probability that the carrier can hop from site i to site j. At the end of this process, the particle has a new energy Ej and position rj. It is worth to note that a carrier may hop

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Organic Flexible Electronics

Figure 3.2 Representation of a hopping process. The two localized states are depicted as
potential wells with different energies. The absorption of a phonon with energy ΔE makes
the tunneling from the state i to the state j possible.

provided that the initial site is occupied and the target site is unoccupied. In order
to quantitative describe this hopping process a probability evolution equation,
named Master equation, is used [8]:
X


dfi ðtÞ X
5
υji fj ðtÞ½1 2 fi ðtÞ 2
υij fi ðtÞ 1 2 fj ðtÞ 2 λi fi ðtÞ;
dt
j6¼i
j6¼i

(3.5)

where fi(t) is the probability that site i is occupied by a carrier at a time t, [1 2 fj(t)]
is the probability that site j is unoccupied, ν ij is the transition rate from site i to site
j and λi is the decay rate of the excitation at site i. This is a nonlinear equation with
a potentially extremely large number of terms. For a given problem, the site locations ri need to be given as well as the decay rates for each site (often one assumes
that the recombination is only a small perturbation, and assumes that λi 5 0).
The hopping probability is then composed of two factors, the tunnel term and
the thermal activation term. Assuming an exponential decay of the wavefunction
tails Ψ(r)~exp(2αr), where α is the reverse of the localization length, the transfer
integral can be approximated as exp(22αrij). This term takes into account the
actual wavefunction overlap of the two sites, which depends not only on the decay
length of the wavefunctions but also on the reciprocal orientation of the molecules
which can affect the effective overlap of the π orbitals.
For upward hops (Ei , Ej), the energetic difference between the two sites is provided by phonons, so, the total hopping probability has to depend on the number of
available phonons with energy ΔE. Assuming the Boltzmann statistic for the phonon distribution, the thermal activation term has the following form: exp(ΔE/
(kBT)). On the contrary, for downward hops (Ei . Ej), no thermal activation is
required and only the tunneling term survives. Then the total hopping probability of
the jump can be calculated with the Miller-Abrahams hopping rate and reads [10]:


Ej 2 Ei 1  Ej 2 Ei 
υij 5 υ0 exp 2αrij exp 2
;
2kB T




(3.6)

where ν 0 is the phonon vibration frequency and it can be intuitively understood as
the jump-attempt rate or simply as a normalization factor. The variable range

Electronic and ionic transport in organic materials and devices

75

hopping (VRH) charge transport in disordered organic semiconductors is depicted
in Fig. 3.3. In this case, the charge carriers move through the localized DOS while
the delocalized states are not involved.
While the various charge transport models introduced before are based on very
different physical scenarios, all of them require the knowledge of the delocalized
and/or localized states. Indeed, depending on the amount of localized states, on the
relative energy position of the delocalized and localized states, and on the position
of the Fermi energy level in the material during the device operation, the charge
transfer from one molecule or polymer chain to another can be dominated by VRH
or by MTR or by band-like transport. This highlights the key role played by the
DOS. The shape of the DOS can be extremely complex, comprising peaks, valleys,
and exponential and linear decays. However considering only the energy range that
is practically relevant for experimental conditions, it can be approximated with a
Gaussian function, an exponential function or a combination of these functions
[2,4]. For example, in the case of organic diodes, a VRH transport in a Gaussian
DOS is most commonly used, but there are also cases where a Gaussian DOS with
a localized exponential tail is observed [11]. VRH or MTR transport in a singleexponential or double-exponential function can be used for the description of
organic thin-film transistors [12], while in the case of organic electrochemical transistors the explored DOS can be well approximated by the sum of two or more
Gaussian and exponential functions [7,13].

Figure 3.3 Schematic view of the VRH transport. A charge carrier (electron or hole) is
moving in the localized states by means of thermally activated quantum tunneling. Each
hopping can involve a variation of space and energy of the charge carrier. VRH, Variable
range hopping.

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3.2

Organic Flexible Electronics

Ionic transport in mixed ionic-electronic conductors

Transport phenomena in mixed conductive polymers can be described by the
thermodynamics of irreversible processes [14]. This relies on two fundamental
hypotheses: the continuum hypothesis and the local equilibrium hypothesis. The
state variables of the system, such as electric potential, pressure and energy, are
functions of the position r and time t. The continuum hypothesis states that each
volume element dV of the system, with position r in the space, is small enough
that infinitesimal calculus can be applied, but still it is macroscopic in the sense
that it contains a large number of molecules. The system can be described by
means of equilibrium thermodynamic relations, since the changes in the state variables take place over a time scale much larger than that of molecular motion. Thus
we can assume local internal equilibrium within the infinitesimal volume element
dV. Given these assumptions, the Gibbs energy of the volume element can be
defined as:
dG 5

X

μ~ i ni 5 dU 2 TdS 1 pdV

(3.7)

i

Where μ~ i and ni are the electrochemical potential and number of particles of the
specie i, respectively, U is the internal energy, T is the temperature, S is the
entropy, and p is the pressure. Dividing Eq. (3.7) by dV, we obtain the fundamental
thermodynamic equation that applies to the volume element:
g5

X

μ~ i ci 5 u 2 Ts 1 p;

(3.8)

i

where g 5 dG/dV is the Gibbs energy density, ci 5 dni/dV is the molar concentration
of the specie i, u 5 dU/dV is the internal energy density, and s 5 dS/dV is the
entropy density.
We consider a binary electrolyte completely dissociated into positively and negatively charged ions. Assuming charge numbers z1 5 2z2 5 1 and given the bulk
concentrations c1 and c2 of the cation and anion, respectively, it holds
c1z1 1 c2z2 5 0. The internal energy density and the entropy density can be
rewritten in terms of molar concentration and electrostatic potential ϕ. More in
detail, the energy density results [15]:
ε  2
u 5 2 rϕ 1 z1 qc1 ϕ 2 z2 qc2 ϕ:
2

(3.9)

Where the first term is the self-energy of the electric field, while the second and
the third terms are the electrostatic energies associated to the charged particles
in the electric field [16]. Assuming that cations, anions, and solvent molecules have
the same size a, the entropic contribution reads [15]:

Electronic and ionic transport in organic materials and devices

s5

77







kB 
c1 a3 ln c1 a3 1 c2 a3 ln c2 a3 1 ð1 2 c1 a3 2 c2 a3 Þln 1 2 c1 a3 2 c2 a3 :
3
a
(3.10)

The first two terms are the entropies of the positive and negative ions, while the
last term is the entropy of the solvent molecules. It is worth to note that Eq. (3.10)
takes into account the finite size of ions, which results in a maximum ion concentration cmax 5 1/a3. The electrochemical potential for each ionic specie can be
obtained as:
μ~ 6 5

dg
c6
5 z 6 qϕ 1 kB Tln
:
dc 6
cmax 2 c1 2 c2

(3.11)

Diffusion and migration of ionic species are given by gradients in the electrochemical potential, either because of a species concentration difference (a concentration gradient), or because there is a difference of ф (an electric field or potential
gradient). In general, a flux of species i will occur to alleviate any electrochemical
potential difference. More in detail, under quiescent conditions, the ionic flux can
be written as:
!
ji

52

Di ci !
r μ~ i ;
kB T

(3.12)

where Di is the ionic diffusion coefficient. Thus combining Eqs. (3.11) and (3.12),
we can derive the formulation for the Nernst
Planck equation describing ionic
fluxes in the binary electrolyte:
!
j6

52

!
D6 c6
r! c 6
r! ðc1 1 c2 Þ
zq r ϕ 1 kB T
1 kB T
:
cmax 2 ðc1 1 c2 Þ
kB T
c6

(3.13)

If we assume cmax!N, Eq. (3.13) simplifies to the Nernst
Planck equation for
diluted systems:
!
j6

52

!
D6 c6
r! c 6
zq r ϕ 1 kB T
:
kB T
c6

(3.14)

The direct measurement of ionic conduction in a mixed ionic-electronic conductive polymer is not straightforward, because of the difficulty to decouple the ionic
and electronic contributions in this kind of analysis. Stavrinidou et al. proposed the
moving front experiment as a brilliant approach for the measurement of ion mobility in the prototypical mixed conductive polymer PEDOT:PSS [17]. They took
advantage of electrochromism in organic electronic materials, where free electronic
carriers create states in the optical gap and change the color of the material [18].

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Organic Flexible Electronics

Figure 3.4 Experimental setup of the moving front experiment proposed in Ref. [17].

This phenomenon has been used to monitor the doping/dedoping process in the
polymer film. Fig. 3.4 shows a schematic representation of the proposed experimental setup.
A strip of PEDOT:PSS is contacted to one end by a gold electrode and covered
along its length by a passivation layer which acts as an ion barrier. The other end
of the strip is in contact with an electrolyte, and an Ag/AgCl electrode is immersed
into the electrolyte. By applying a potential between the gold and the Ag/AgCl
electrodes, ions drift into the polymer changing its doping state and hence its color.
More in detail, when a positive bias is applied at the Ag/AgCl electrode, cations are
pushed into the polymer and a dark dedoping front propagates from the electrolyte
toward the gold contact at the opposite end. The mobility of the cations is obtained
by tracking the propagation velocity of the dedoping front. A potassium mobility of
1.4 3 1023 cm2 V21 s21 was measured, which is higher than the electrophoretic
mobility of potassium cations in water at the limit of infinite dilution. This implies
first and foremost that the PEDOT:PSS film is highly hydrated, as confirmed by the
measurement of a 155% swelling of the film measured by optical profilometry.
Furthermore, the morphology of the nanometric-size ion propagation paths through
the PSS phase [19] suggests that electroosmotic flow mechanisms could contribute
to the increased ion mobility [20]. Interestingly, the ionic mobility in PEDOT:PSS
depends on the solvated ion size. H1 ions show larger mobility than K1 ions, which
in turn have higher mobility than Na1. It is worth noting that PEDOT:PSS is able
to efficiently transport choline (C5H14NO1) [17], which is an organic cation that is
essential in nutrient. This implies that the size of the ionic transport paths is larger
than the size of the choline ion, and prompts the question of what the maximum
size is for the efficient ionic transport in this material. An effective ion transport in
mixed conductivity materials is paramount as it determines the maximum operative
frequency of the device, with relevant implications for its fields of application.

3.3

Ionic-electronic coupling in mixed ionic electronic
conductors

The bulk ionic/electronic coupling is the core mechanism that makes mixed conductivity organic materials a powerful technology for bioelectronics and energy

Electronic and ionic transport in organic materials and devices

79

storage applications. It relies either on capacitive or faradaic coupling between ionic
and electronic charges, depending on the adopted material, on the electrolyte and
experimental conditions. Capacitive coupling takes advantage of the formation of
an electric double layer (EDL) involving ionic and electronic charge carriers, while
faradaic coupling is associated to electron transfer between the electrode and the
specie dissolved in the electrolyte through electrochemical reactions (Fig. 3.5).
The capacitive coupling occurs when an excess or deficiency of electrons is created on the electrode by applying a potential, and it is compensated by ionic
charges of the opposite sign provided by the electrolyte, which are attracted at the
electrode, originating an EDL. When a mixed ionic-electronic conductor is considered, the EDL involves the whole bulk of the electrode material, with ions penetrating through the ionically conductive paths in the material and electrostatically
compensating the electronic charges in the electroactive sites of the polymer. This
yields a capacitance that depends on the whole material volume, while in the case
of a classic metal electrode the accumulation of ionic and electronic charges
involves only the electrode/electrolyte interface and hence it scales with the electrode area. In the case of a metal electrode, the resulting EDL can be described
with the Gouy
Chapman
Stern (GCS) model [21]. Let us consider an initial interface potential drop at which there is no net charge accumulation. By increasing the
electrode potential with respect to the electrolyte potential, the electrode will
become positively charged, and charges of opposite sign will be attracted near the
electrode surface from the bulk electrolyte. It is worth to note that the electronic
charges on the metal plate are confined on the surface, while it may take some significant thickness to accumulate the excess charge needed to counterbalance the
electrode charge excess, especially at low concentrations of electrolyte. This “thick”
layer of ions is usually referred as diffuse layer. By increasing the applied electrode
potential, ions start packing at the intimate interface with the electrode, resulting in
a compact layer known as the Helmoltz layer. The Helmoltz layer is separated from
the electrode surface by a distance equal to the size of the solvated ion radius a,
and the maximum ion packing is given by the finite size of the solvated ions as
cmax 5 a23. This is a basic model that gives a simplified view of the ionic/electronic

Figure 3.5 Capacitive vs. faradaic coupling. (A) Capacitive coupling results in an EDL at
the interface between electronic and ionic charge carriers. (B) Faradaic coupling takes
advantage of electron transfer at the interface between the electrode and the electrolyte. EDL,
Electric double layer.

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interaction in an EDL at a metal/electrolyte interface, and a mathematical formulation can be found in Ref. [21]. It is worth noting that the GCS model usually fails
to capture the complexity of EDL in real applications, in which a quantitative
description of the system requires a deep knowledge of the adopted material characteristics and strictly depends on the operative conditions. An extensive analysis of
the problem is reported in Ref. [21]. Furthermore, the applicability of the classic
EDL model to the capacitive coupling in mixed ionic-electronic conductors is still
debated. Considering PEDOT:PSS as a relevant example, it has been demonstrated
that the ionic/electronic conversion involves a capacitive phenomenon, with ions
penetrating through the ionically conductive PSS phase and electrostatically compensating electric charge carriers in the electrically conductive PEDOT phase
[22,23]. It has been shown that the volumetric capacitance in PEDOT:PSS does not
show the typical concentration dependence of an EDL [22], and a model describing
the capacitive coupling in this widely used polymer is still missing.
When faradaic ionic/electronic coupling is involved, a potential difference at the
electrode/electrolyte interface yields an energetically favorable transfer of an electron from the electrode to a specie dissolved into the electrolyte (reduction of the
dissolved specie) or from the specie to the electrode (oxidation).
kR

O 1 e2 ! R
kO

R ! O 1 e2
This electron transfer is usually referred as an electrochemical redox reaction
and it involves three fundamental steps.
1. The reactant moves from the bulk electrolyte to the electrode interface: this is termed
mass transport.
2. Electron transfer occurs via tunneling between the electrode and reactant close to the electrode. The involved distance is on the nm scale.
3. The product moves away from the electrode and fresh reactant moves to the surface.

It follows that faradaic processes are controlled by two factors: the reaction rate
of the reactant at the electrode and the mass transport providing fresh reactant for
the reaction. Both reduction and oxidation take place simultaneously at the electrode, and the applied potential determines which reaction is occurring at higher
rate. This is described by the Butler
Volmer equation, suitably adapted to capture
the volumetric response in mixed ionic-electronic conductors:
i 5 iO 1 iR 5 FvkO cRð0;tÞ 2 FvkR cOð0;tÞ ;

(3.15)

where i is the total current resulting from the electron transfer at the interface, iO is
the current associated with the oxidation process, F is the Faraday constant, v is the
electrode volume, kO is the oxidation reaction rate coefficient, cR(0,t) is the timedependent concentration of the reduced specie at the interface. A similar notation is

Electronic and ionic transport in organic materials and devices

81

used for the reduction process current iR. Eq. (3.15) readily shows that the reaction
current depends both on the reaction rate, which is determined by the interface
potential, and on the concentration of the reactant at the interface. The supply of
fresh reactant from the bulk of the electrolyte is described by the ionic transport
equations reported in Section 3.2, while the reaction rate coefficient exponentially
depends on the applied potential ϕ as:

3
αzF ϕ 2 ϕeq
5;
kO 5 Zexp4
RT
2


3
ð1 2 αÞzF ϕ 2 ϕeq
5:
kR 5 Zexp4 2
RT

(3.16)

2

(3.17)

Where the preexponential factor Z can be estimated theoretically, but it also can be
treated as an empirically measured parameter, α is called transfer coefficient and is
typically found to have a value of 0.5, z is the number of charge of the specie
involved in the reaction, R is the ideal gas constant, ϕeq is the potential at which
the reaction is at the equilibrium, also known as the Nernst potential, and results:
ϕeq 5 ϕo 2

RT
c
ln R :
zF
cO

(3.18)

With cR and co are the bulk concentrations of the reduced and oxidized species.
A straightforward method to probe the nature of the ionic/electronic coupling
for mixed ionic/electronic materials is the cyclic voltammetry (CV). The typical
experimental setup adopts a three-electrodes configuration. The working electrode (WE) is the electrode to be studied, the reference electrode (RE) determines the electrolyte potential and typically an Ag/AgCl electrode or a saturated
calomel electrode is used, the counter electrode (CE) is usually a platinum or
another inert metal electrode which provides the current required by the WE
during the measurement. The WE potential (with respect to the RE potential) is
swept at a constant rate in the range of interest, from V1 to V2 and then back to
V1 and the WE current is measured. A box-shaped CV is the fingerprint of a
capacitive coupling. On the forward scan (from V1 to V2) a current IFW 5 CdV/dt
is displayed, where C is the capacitance of the EDL and dV/dt is the sweep rate,
on the backward sweep a current IBW 5 2IFW is measured, due to the opposite
sign of the sweep rate. A faradaic coupling is usually revealed by current peaks
in the CV. A redox peak is due to the two factors governing the reaction kinetic.
On the rising side of the peak the increasing potential is exponentially increasing the reaction rate at the interface. With increasing reaction rate at the interface, the supply of fresh reactant from the bulk electrolyte becomes insufficient,
the current stops increasing at the highest point of the peak and eventually starts

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decreasing, resulting in a mass-transport-limited process. On the backward
sweep the same mechanisms govern the reaction in the opposite direction.
Further details on the CV are provided in Section 3.4.
It is worth to note that in practical applications capacitive and faradaic mechanisms can be involved at the same time, with one phenomenon or the other dominating the overall process depending on the experimental conditions, and particularly
on the applied potentials. Considering, for example, PEDOT:PSS, the capacitive
coupling in the typical operating voltage window is displayed by a box-shaped CV,
while at larger potential the cyclic voltammogram is dominated by redox currents
due to the interaction between the polymer blend and the oxygen dissolved in water
[24]. The redox currents become negligible when the oxygen is removed from the
electrolyte, stressing once again the importance of the experimental setup on the
ionic-electronic coupling.

3.4

Mixed conduction in supercapacitors

Supercapacitors (SCs) are energy-storage devices that gained a lot of attention
owing to their unique features like high power, long cycle life, and environment
friendly nature [25,26]. SCs bridge the gap between batteries and capacitors to form
fast-charging energy-storage devices of intermediate specific energy (Fig. 3.6) [27].
They are a promising technology in fields requiring fast-storage capability, midrange energy density, and enhanced cycling stability. SCs have potential application
in renewable energy storage, regenerative breaking in hybrid electric vehicles, and
power supply in portable devices.

Figure 3.6 Ragone plot for energy-storage devices. Supercapacitors show intermediate
performances between batteries and capacitors in terms of power density and energy density.

Electronic and ionic transport in organic materials and devices

83

A traditional capacitor consists of two metal plates separated by an insulator.
Charge of opposite sign (Q) is accumulated on the metal plates by applying a potential difference (V) and reads:
Q 5 CV;

(3.19)

where C is the capacitance, which, in turn, depends on the capacitor geometries and
on the insulator properties as:
C5

εA
;
d

(3.20)

where A is the metal plates area, d is the insulator thickness, and ε is the insulator
dielectric constant. Typical capacitances per unit area Cs 5 C/A are in the order
of 1 μF cm22. The credit for the beginning of capacitor technology goes to the
invention of the Leyden Jar (1745
46) which was made of a glass jar with metal
foils covering the inside and the outside surfaces. The metal foils served as electrodes and the jar acted as the dielectric. In the 1920s came the first electrolytic
capacitor, where higher capacitances are achieved by incorporating an electrolyte
in the capacitor structure [25]. Interestingly, it took advantage of the formation
of an EDL at the interface between the electrode and the electrolyte. In an EDL,
ionic charges provided by an electrolyte are accumulated at the interface with an
electrode and compensated by electronic charges. In this charge configuration
the surroundings of the ionic charge separating ionic and electronic charges act
as a subnanometric thick insulator, allowing to achieve capacitances in the order
of 10
100 μF cm22. In 1957 the first SC consisting of two porous carbon electrodes separated by an electrolyte was patented by General Electric [28]. The
porous carbon electrodes yielded a larger effective area for the electrode/electrolyte interface, resulting in increased capacitance with respect to the traditional
electrolytic capacitor. When traditional conductive materials are used as electrodes, the ionic-electronic charge interaction takes place at the planar interface
between the electrode and the electrolyte. In modern SCs, conductive polymer
showing mixed ionic-electronic conduction are used as electrodes, allowing the
ionic charges to penetrate the bulk of the electrode and extending the ionicelectronic charge interaction from 2D to 3D. This results in higher equivalent
capacitances per unit area, dramatically increasing the charge-storage capability
of this class of devices.
When mixed conductive polymers are used as electrodes, the charge storage can
be obtained through a purely electrostatic phenomena (electric double layer capacitors, EDLCs) or a pseudocapacitive (PC) phenomena involving faradaic reactions at
the electrode-electrolyte interface. EDLCs usually show faster dynamics, while PC
SCs allow larger energy storage [26,27].
The main figures of merit of a SC are the cell-specific capacitance (F g21), specific energy (W h g21), specific power (W g21), and the cycle life. Other important
parameters are the operating voltage, the temperature stability, the reliability and

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Table 3.1 Performances comparison between capacitors, supercapacitors, and batteries.
Characteristic

Capacitor
21

Supercapacitor
1

Battery

Max. specific
energy
(W h kg21)

10

10

103

Max. specific
power
(W kg21)

107

105

103

Charge time (s)

1026
1023

1
102

103
104

Discharge time
(s)

1026
1023

1
102

103
105

Cycle life
(cycles)

Almost infinite

.500,000

About 1000

Operative
voltage
determinants

Dielectric
thickness and
composition

Electrode and electrolyte
stability window

Thermodynamics
of phase
reaction

Charge storage
determinants

Electrode area
and dielectric

Electrode structure and
composition, electrolyte
composition

Thermodynamics
and active
mass

Source: Adapted from W. Raza, F. Ali, N. Raza, Y. Luo, K. Kim, J. Yang, et al., Recent advancements in
supercapacitor technology, Nano Energy 52 (2018) 441
473 [26]; A.G. Pandolfo, A.F. Hollenkamp, Carbon
properties and their role in supercapacitors, J. Power Sources 157 (1) (2006) 11
27 [29].

safety of the device. Table 3.1 shows the performances of SCs compared to capacitors and batteries.
The main techniques used to evaluate the SCs performances are the CV, the galvanostatic charge/discharge (GCD), and the electrochemical impedance spectroscopy (EIS). The CV is a DC method where the properties of the SCs electrode/
electrolyte system are characterized as a function of the voltage. It is usually performed in a three electrodes configuration as shown in Fig. 3.7A, where the SC
electrode is the WE, a nonpolarizable electrode is the RE, and a polarizable electrode is used as the CE. The voltage applied to the WE (VI) is swept in the range of
interest from V1 to V2 at a rate dVI/dt, while the RE fixes the electrolyte voltage to
a reference level and the CE supplies the current required by the electrochemical
processes at the WE. The shape of the CV gives information on the charge-storage
mechanism at the electrode. Redox peaks are displayed in the case of PCs, while a
rectangle-shaped CV is typical for EDLCs (Fig. 3.7B and C).
The capacitance of the electrode-electrolyte system can be calculated as:
C5

Qtot
;
2jV1 2 V2 j

(3.21)

Electronic and ionic transport in organic materials and devices

85

Figure 3.7 The cyclic voltammetry. (A) Schematic experimental setup for the measurement
of a cyclic voltammetry. A1 ensures that the RE voltage is fixed to a reference level, while
the CE voltage is set to the voltage required to supply IO. A voltage source inputs VI to A2.
The generated voltage is replicated at the WE, and IO 5 (VO 2 VI)/R1. The reference
electrode is usually a nonpolarizable electrode such as an Ag/AgCl electrode or a saturated
calomel electrode. A nonpolarizable electrode is ideally able to exchange an infinite faradaic
current density with the electrolyte by applying an infinitesimal voltage between the
electrolyte and the electrode itself. This ensures that the input polarization current required
by A1 can be provided by the RE with a negligible voltage drop at the RE/electrolyte
interface, resulting in a stable reference voltage level. The counter electrode is usually a
polarizable electrode, made of an electrochemically inert material like platinum or gold.
Considering an ideally polarizable electrode, no redox current is exchanged with the
electrolyte even at large applied voltages. Thus the current required by the WE is provided
with a capacitive current by the CE, avoiding the formation of redox reactions products that
could interfere with the processes at the WE/electrolyte interface. (B) Example of a CV plot
in the case of faradaic reactions at the WE. The typical redox peaks are displayed. (C)
Example of a CV plot in the case of EDLC, with the typical rectangle-shaped characteristic.
CE, Counter electrode; CV, cyclic voltammetry; EDLC, electric double layer capacitor; RE,
reference electrode.

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Organic Flexible Electronics

where Qtot is the total charge stored and it is calculated as:
Ð
Qtot 5

V2
V1 IO dV

1

Ð V1
V2


IO dV

dVI =dt

:

(3.22)

The specific capacitance is:
Cs 5

C
;
m

(3.23)

where m is the electrode mass. The cycle life of the SC can be evaluated by monitoring the capacitance over repeated measurement cycles.

Figure 3.8 (A) Schematic setup for the GCD technique. The TE is grounded, the NPE is
polarized with a constant current II, while the VME measures the potential drop at the TE
interface. An Ag/AgCl pellet can be used for the NPE, while the VME is usually an
electrochemically inert electrode, like platinum or gold. (B) GCD plot in the case of PC
mechanisms. The VO-t plot shows nonlinear charge and discharge characteristics. (C) GCD
plot in the case of an EDLC. The VO-t plot shows linear charge and discharge characteristics.
EDLC, Electric double layer capacitor; GCD, galvanostatic charge/discharge; TE, tested
electrode; VME, voltage measurement electrode.

Electronic and ionic transport in organic materials and devices

87

The GCD is a DC technique where the electrode/electrolyte system is characterized by charging the electrode with a constant current II and measuring the voltage
drop VO at the interface. A schematic representation of the setup is shown in
Fig. 3.8A. A constant current is applied at a nonpolarizable electrode (NPE) and
charges the tested electrode (TE) which is polarized at a reference voltage, while
the voltage measurement electrode (VME) measures the potential drop at the TE.
The shape of the GCD curve allows to identify the charge-storage process: in the
case of an EDLC a linear increase and decrease of the interface potential is displayed over the time t, while in the case of PC mechanisms a deviation from the
linear behavior is shown (Fig. 3.8B and C).
The electrode capacitance can be estimated as:
C5

II
:
dVI =dt

(3.24)

And again, the specific capacitance is obtained as Cs 5 C/m, where m is the electrode mass. The capacitance extracted over repeated measurements gives information on the cycle life.
The CV and GCD methods give overall information on the charge storage over
the operative range of the SC. Nevertheless, the extracted capacitance yields a
global picture of a complex and highly nonlinear system, where, for instance, the
capacitance of the electrode depends on the voltage at the electrode/electrolyte
interface. Moreover, the same electrode/electrolyte system can behave as an EDLC
with no faradaic mechanism involved over a certain voltage range, while PC behavior can be displayed outside of this voltage window.
EIS is a powerful AC technique that can give precise information on the electrode
and electrolyte properties at a fixed applied voltage. It is performed with a three electrodes configuration as shown in Fig. 3.9A. The RE is a nonpolarizable electrode and
it determines the electrolyte potential, the characterized electrode (WE) is biased at a
fixed DC voltage and a small amplitude AC signal (usually 6 5 mV) is applied, while
a polarizable CE provides the current required by the WE. A sweep on the frequency
of the AC signal is performed and the impedance of the electrode/electrolyte system is
measured at each frequency. The information is usually displayed with a Bode plot,
showing the magnitude and phase of the impedance as a function of the frequency, or
a Nyquist plot, which shows the real part and imaginary part of the impedance on the x
and y axes of the plot, respectively (Fig. 3.9B and C).
The EIS measurement can be fitted by using the Randles circuit [30]
(Fig. 3.10A). It consist of a resistance (Rs) in series with the parallel of a capacitor
(Cp) and the series of a resistance (Rp) and a Warburg element (W). Fig. 3.10B
shows the frequency-dependent impedance formulation for each component of the
Randles circuit. Rs is the electrolyte resistance and describes the ion transport
through the electrolyte, Cp accounts for the ionic/electronic charge accumulation at
the WE, Rp describes the faradaic charge transport at the WE/electrolyte interface
and the Warburg element accounts for mass transport limited faradaic processes. In
practical cases, inhomogeneities on the nano- or microscale or adsorption

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Figure 3.9 (A) Schematic of the experimental setup for the EIS measurement. A1 ensures
that the RE voltage is fixed to a reference level, while the CE voltage is set to the voltage
required to supply IO. A voltage source inputs VI to the A2. The generated voltage is
replicated at the WE, and IO 5 (VO
VI)/R1. The output signal is filtered through a bandpass
filter and only the frequency equal to the input signal frequency is kept. The impedance at
the target frequency ω is Z(ω) 5 VI(ω)/[(VOF(ω)
VI(ω))/R1]. The reference electrode is
usually an Ag/AgCl electrode or a saturated calomel electrode, the counter electrode is
usually made of an electrochemically inert material, like platinum or gold. (B) Typical Bode
plot (impedance modulus |Z| and phase) of a Randles circuit. In the low-frequency regime the
impedance is dominated by the parallel resistance, resulting in a flat |Z| and phase close to 0.
In the medium frequency range the impedance is dominated by the parallel capacitance, |Z|
decreases with 20 dB dec21 and the phase approaches π/2. In the high-frequency range the
series resistance dominates the overall impedance, yielding a flat |Z| and phase close to 0. (C)
Corresponding Nyquist plot. The modulus of the impedance is given by the distance of the
characteristic from the origin of the plot, while the phase is given by the angle between Re
(Z) and the vector connecting the origin and the characteristic. The high-frequency
information, where the characteristic is dominated by the series resistor, is displayed near to
the origin of the plot, with Re(Z) . 0 Ω and Im(Z) 5 0 Ω. With decreasing frequency, the
characteristics move farther from the origin, showing capacitive behavior, with increasing
impedance modulus and phase. Further decreasing the frequency, the characteristic is
dominated by the parallel resistor, resulting in a decreasing phase and increasing modulus,
with Im(Z) approaching 0 Ω. CE, Counter electrode; EIS, electrochemical impedance
spectroscopy; RE, reference electrode; WE, working electrode.

Electronic and ionic transport in organic materials and devices

89

Figure 3.10 (A) The Randles circuit and (B) the Randles circuit elements.

Figure 3.11 Structure of polymers used for the fabrication of supercapacitor’s electrodes.
(A) Polyaniline (PANI). (B) Polypyrrole (PPy). (C) Poly(3,4-ethylenedioxythiophene).

phenomena at the WE/electrolyte interface yield a nonideal capacitance for the Cp
element [31
33]. This is usually modeled by replacing the Cp with a constant phase
element (CPE). The α parameter of the CPE (see Fig. 3.10B) ranges from 0 to 1
(usually α . 0.6), with values closer to 1 describing an almost ideal capacitive phenomena. The Q parameter for the CPE is the equivalent to the C parameter of the
ideal capacitor. The γ parameter in ZW is usually assumed equal to 0.5, but in practical cases it could range from 0 to 0.5.
The performances of a SC mostly depend on the electrodes and electrolyte materials. Typical conductive polymers for SCs electrodes are polyaniline (PANI), polypyrrole (PPy), and derivatives of polythiophene. PANI and PPy have been studied
extensively as SC electrode materials. Their structure is illustrated in Fig. 3.11.
They show high electrical conductivity in doped states (B100 2 10,000 S m21),
low environmental impact, low cost, and compatibility with large-area fabrication
techniques [34]. Their excellent specific capacitance typically ranges between 500
and 3400 F g21, depending on preparation conditions [35]. This value is larger than
that of conventional carbon-based electrodes (B100 2 200 F g21) and comparable
to PC metal oxides [36]. However both PANI and PPy suffer from structural

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Organic Flexible Electronics

breakdown and thus fast capacitance decay due to the swelling and shrinking as a
result of ion doping and dedoping. Apparently, most PANI- and PPy-based electrode lose more than 50% of the initial capacitance after cycling for 1000 times.
Therefore cycling instability is a major issue for practical applications of conductive polymer electrodes. A number of methods have been proposed to improve the
cycling stability of PANI and PPy, such as polymer blending with carbon nanotubes
or polymer encapsulation in carbonaceous shell, which yielded a capacitance retention up to 95% after 10,000 cycles [34]. Among polythiophene derivatives, poly
(3,4-ethylenedioxythiophene) (PEDOT, structure in Fig. 3.11) has gained large
interest due to commercial availability, good electrical conductivity, excellent electrochemical and thermal stability, and biocompatibility [37]. On the negative side,
because of its large molecular weight, it has a relatively low specific capacitance.
PEDOT thin film with a specific capacitance of 180 F g21 have been demonstrated,
but severe polymer degradation reduced the cycle life of the electrodes. Mixing
PEDOT with carbon nanotubes yields higher mechanical stability and hence a longer cycle life, with specific capacitance up to 160 F g21 [38].
The electrolyte plays a fundamental role in the SC structure, since it impacts
both the capacitance and the charge/discharge velocity. Furthermore, easy handling
and no leakage are required. Aqueous electrolytes, organic electrolytes, and ionic
liquids (ILs) are generally used in SCs. Aqueous electrolytes show good conductivity, at least 1 order of magnitude higher than that of ILs and organic electrolytes.
This results in a low electrolyte resistance and hence fast charge and discharge
kinetics. The size of the hydrated ions plays a fundamental role on the specific
capacitance, with smaller size yielding larger capacitances. Aqueous electrolytes
can be modified by adding different gels to create a mechanically stable electrolytic
system, resulting in easier handling and no leakage. Wang et al. [39] fabricated a
novel gel by dipping polyacrylamide gel (PAM-G) into an aqueous solution of 6 M
KOH for about 60 hours. The resulting system provided excellent cycling stability
and high specific capacitance (196 F g21 at GCD 1 A g21), probably due to the
homogeneous three-dimensional microporous structure of the PAM-G, which facilitated the ionic transportation. However aqueous electrolytes are not an optimal
choice for commercial electrochemical SCs because of their small electric potential
windows. This is one key reason why commercial SCs generally use organic electrolytes, with a potential window in the range of 2.5
2.8 V. Typically, the organic
electrolytes used for SCs are conductive salts [40], such as tetraethylammonium tetrafluoroborate (TEABF4) dissolved in propylene carbonate or ACN. Nevertheless,
organic electrolytes suffer from low conductivity, small specific capacitance, and
high cost. They are volatile, toxic, and flammable [41]. Moreover, they require
complex assembly and purification procedures under controlled environment to
eliminate impurities (i.e., moisture) that could degrade their performances. The
organic electrolytes used in SCs at the commercial level are not suitable for temperatures above 70 C because of their low ignition and detonation temperatures,
while the effectiveness of aqueous electrolytes is limited by the boiling temperature
of water and cannot be practically used above 80 C. Ionic liquids like 1-ethyl-3methylimidazolium acetate (EMIM Ac) are potential candidates for use at even

Electronic and ionic transport in organic materials and devices

91

very high temperatures because of their high chemical and thermal stabilities, with
wide operating voltage ranges, negligible vapor pressure, and nonflammability [41].

3.5

Mixed conduction in bioelectronics

The emerging field of bioelectronics provides a bidirectional connection between
biology and electronics. Bioelectronic devices can be used to specifically regulate
the physiology and the processes of cells, tissues, and organs through electrochemical stimulation. Conversely, bioelectronics enables high-precision monitoring of
biological phenomena and physiological signals. Typical examples of such devices
are electrodes for electrophysiology recording, biosensors for the monitoring of biomarkers, and drug-delivery iontronic devices enabling targeted pharmaceutical
treatment. While electronic signals are carried through electrons, signaling in biological systems relies on the transport of ions. Thus mixed ionic-electronic conduction in organic materials provides a seamless interface between biology and
electronics. Mixed conduction devices combine low-voltage operation due to efficient ionic/electronic coupling with the benefits typical of organic technologies,
such as biological compatibility, large-area deposition with simple and low-cost
techniques, chemically tunable properties, mechanical flexibility, and softness
[42
45]. Soft electronic materials with low Young’s module are suitable to operate
in contact with biological tissues with minimum risk of adverse reaction, while
mechanical flexibility enables comfortable wearable devices [46]. Large area electronics allow the monitoring of complex and dynamic structures such as organs
with high spatial resolution. Low cost is highly desirable in the case of bioelectronics, where the risk of contamination and infection requires the use of disposable
devices. Furthermore, devices can be fabricated on ultrathin, flexible, and biocompatible substrates [47]. Biocompatibility of the employed materials is paramount
when it comes to bioelectronics and it is strictly dependent on the involved cells
type. PPy is noncytotoxic for a wide range of cell types in vitro, it supports cell
adhesion and growth, and yields low inflammatory response in vivo, and similarly
encouraging results are reported for PEDOT:PSS and PANI [48]. Mixed conductors
like PEDOT:PSS show long-term stability in physiological environment [49], which
is fundamental for long-term implants for electrophysiology. Fueled by this unique
benefits combination, mixed ionic-electronic organic conductors are a promising
platform for the next-generation bioelectronics.

3.5.1 The organic electrochemical transistor
The organic electrochemical transistor (OECT) is a groundbreaking device with
huge potential for the biological to electrical information transduction in bioelectronic applications. It relies on mixed conduction to provide intrinsic ionic-electronic
conversion together with local signal amplification and low voltage operation. An
OECT comprises an organic semiconductor channel connected to source and drain

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Organic Flexible Electronics

metal electrodes. An electrolyte solution is in contact with the semiconductor, and a
gate electrode is immersed into the solution (Fig. 3.12A). Typical electrical characteristics (transfer characteristics) of an OECT based on a p-type semiconductor are
shown in Fig. 3.12B. By applying a positive gate voltage (VG) cations drift into the
polymer, reduce the hole concentration and lower the drain current (ID).
Analogously, when a negative VG is applied previously injected cations drift out of
the polymer while anions drift into the polymer, the hole concentration increases
and this results in a larger ID. The magnitude of the drain current increases by
applying a more negative voltage to the drain electrode.
Bernards and Malliaras described the operation of OECTs through a simple
model, providing the drain current as a function of the geometrical and physical
parameters and of the bias conditions [50,51]. The model reads:
ID 5


2
Wd
μCv Vt 2VG;eff
2L

ID 5



Wd
V2
μCv Vt 2 VG;eff VD 2 D
L
2

when VG 2 Vt . VD ;
when VG 2 Vt # VD ;

(3.25)

(3.26)

where W, d, and L are the channel width, thickness, and length, respectively. Cv is
the volumetric capacitance accounting for the electrostatic interaction between ionic
and electronic charges in the transistor channel. μ is the electronic carrier mobility
in the channel and Vt is the pinch off voltage. VG,eff accounts for the effective gating voltage and reads:
VG;eff 5 βVG 1 Vo ;

(3.27)

Figure 3.12 (A) Schematic structure of an OECT. (B) Typical transfer characteristics of a ptype OECT. OECT, Organic electrochemical transistor.
Source: Adapted from P. Romele, M. Ghittorelli, Z.M. Kovács-Vajna, F. Torricelli, Ion
buffering and interface charge enable high performance electronics with organic
electrochemical transistors, Nat. Commun. 10 (2019) 3044.

Electronic and ionic transport in organic materials and devices

93

where β is a parameter accounting for the gating efficiency in the OECT and it is
equal to 1 in the case that a nonpolarizable gate electrode is used (e.g., Ag/AgCl
electrode), while β 5 CG/(CG 1 CCH), with CG the gate capacitance, when a polarizable gate electrode is used (viz. gold). Vo is a voltage parameter accounting for the
work function differences in the gate-electrolyte-channel structure. Importantly, the
model captured the key feature of OECTs, that is, the volumetric response due to
the ion penetration into the transistor channel.
OECTs can be used to sense biological events, which usually involve potential
variations due to ionic currents. The potential variation is captured by the gate voltage (dVG) and results in a drain current modulation (dID). Thus the OECT transconductance, defined as gm 5 dID/dVG, gives the sensitivity of the device to a
biological event. When the OECT is integrated in an amplifying structure (e.g., an
inverter [22]), the gm parameter, combined with the output resistance ro 5 dID/dVD
of the device, allows to amplify the input signal by a factor that is proportional to
the product gmro. As a result, the OECT is able to provide simultaneous detection
and local amplification of a biological event, enabling biosensing with increased
signal-to-noise ratio (SNR). OECTs usually show an extremely large transconductance normalized to the channel geometries gmL/(Wd), in the order of 10 mS cm21,
resulting from the ionic-electronic interaction through the bulk of the polymeric
channel [52]. As shown in Eqs. (3.25) and (3.26), the transconductance of an OECT
depends on the channel geometry, on the applied bias and on the product of the
material dependent parameters μ and Cv. Thus the μCv product is a device-based
figure of merit that enables to determine the performances of a material when integrated in OECTs [53]. The μCv product can be directly estimated by the measurement of gm and considering the device geometries and biasing conditions.
Decoupling the μ and Cv contributions provides understanding on why one material
outperforms another. The μ parameter depends on the electronic charge transport
properties, and it can be extracted by measuring ID as a function of time while
applying a constant IG [50]. Considering an OECT operated in the linear regime, it
holds:
ID 5

Wd
Q
qμp0 1 2
Vd ;
L
qp0 WdL

(3.28)

where q is the elementary charge, p0 is the intrinsic hole concentration in the
Ð t polymer, and Q is the ionic charge injected into the channel and is equal to Q 5 t0 IG dt.
By considering a constant IG, it follows from Eq. (3.28):
μ5

L2 dID
IG VD dt

(3.29)

The volumetric capacitance, depending on the ionic and electronic charge storage capability of the polymer, can thus be determined knowing gm and μ. It can
also be measured through EIS as follows. The experimental setup is the same as
reported in Section 3.4, with the OECT source and drain shortened together and the

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channel acting as the WE, a nonpolarizable electrode as the RE and a polarizable
electrode as the CE. The gate electrode is intentionally excluded from the measurement (i.e., not connected), since we are probing a property of the OECT channel.
The typical bode plot for an OECT is shown in Fig. 3.13. In the low-frequency
regime the impedance depends on the frequency and a 220 dB dec21 variation with
2 π/2 phase is displayed, while Z is constant in the high-frequency regime, showing a 0 phase. The spectra can be described by means of a capacitance C, given by
the ionic/electronic charge accumulation on the channel volumetric capacitance, in
series with a resistance RS accounting for the ionic transport in the electrolyte. By
reproducing the data with this simple model, the device volumetric capacitance can
be derived as Cv 5 C/(WtL).
PEDOT:PSS is the most commonly employed material for the fabrication of
OECTs [54]. Among the reasons for its widespread use are the excellent electric
and ionic conductivity as well as its aqueous stability, easy processability, biocompatibility, and importantly, commercial availability. PEDOT:PSS OECTs fabricated
with the procedure reported in Ref. [52] show Cv is equal to 40 F cm23, with a
μ 5 2 cm2 V21 s21, for an overall record μCv product equal to 80 F cm21 V21 s21
[53]. The increasing interest in the field of OECTs for bioelectronics resulted in a
large effort in the synthesis of new and improved materials for the device channel
fabrication. The best performances are displayed by p(g2T-TT) [55], a p-type
OECT material which shows Cv 5 240 F cm23 and μ 5 1 cm2 V21 s21, resulting in
μCv 5 240 F cm21 V21 s21. N-type materials with stability in water have been
recently proposed for the fabrication of OECTs. BBL was proposed by Berggren’s
group [56], showing a Cv 5 930 F cm23, μ 5 7 3 1024 cm2 V21 s21 and
μCv 5 0.65 F cm21 V21 s21, while McCulloch’s group synthesized p(gNDI-gT2) with
Cv 5 400 F cm23, μ 5 3 3 1024 cm2 V21 s21, and μCv 5 0.12 F cm21 V21 s21 [57].

Figure 3.13 Typical EIS bode plot for an OECT. The low frequency regime is dominated by
the volumetric capacitance, while at high frequency the electrolyte resistance is the major
contribution. EIS, Electrochemical impedance spectroscopy; OECT, organic electrochemical
transistor.

Electronic and ionic transport in organic materials and devices

95

It is worth to note that the μCv product gives information on the steady-state performances of the polymer, while the transient behavior suitability of the polymer, as well
as other properties like the biocompatibility, have to be evaluated on a case-by-case
basis according to the considered application.
Owing to their intrinsic ionic/electronic transduction and local amplification,
OECTs have been successfully used in bioelectronics as electrodes or biosensors,
and the investigation of their fundamental properties is enabling the design of
OECT-based circuits, opening new opportunities for the future bioelectronic
applications.

3.5.2 Electrodes
Electrodes are used in electrophysiology both for the monitoring of biological processes and for the stimulation of cells and tissues.
High-precision monitoring of electrophysiological signals with high spatial and
temporal resolution is an invaluable tool for diagnostic purposes and for advancing
our understanding of physiology. The first stage in the recording of vital signals is
performed by electrodes, translating the biological information into an electronic
signal, which can be eventually processed and stored. The ionic-electronic transduction can happen either through capacitive or faradaic processes, depending on the
electrode material and on the electrolyte. When a capacitive mechanism is involved,
the sensed potential results in an accumulation of ions and electronic charge carriers
at the electrolyte/electrode interface and no chemical reaction is involved. This phenomenon can be modeled as an EDL, with a capacitance in the order of
10 μF cm22. On the other hand, in a faradaic mechanism the sensed potential results
in charge transfer across the electrolyte/electrode interface which can be described
by means of the Butler
Volmer equation [58]. Since redox processes with electron
transfer are involved, it could cause variations in the chemical environment, potentially creating chemical species or variations in the pH that could damage the biological tissues or the electrode [48].
Biological signals are usually weak, and the resulting electronic signal can range
from the μV (e.g., electroencephalography) to the mV (e.g., electrocardiography,
ECG) [59], with frequencies up to 1 KHz [60]. Thus the electrodes design is of paramount importance to obtain high-quality recordings. Metallic wires or discs are
usually adopted as electrodes. The miniaturization and integration of electrodes in
arrays allow to simultaneously record multiple signals with high spatial resolution,
and the small size results in less invasive recording procedures. However as the
area of the interaction between the electrode and the biological medium decreases,
so does the ionic-electronic coupling, viz. the electrode impedance increases. A
high electrode impedance is usually associated to higher noise voltage [60,61], dramatically lowering the recording quality of small electrophysiological signals. Low
impedance can be achieved with small surface electrode by using mixed conductivity organic materials such as PEDOT:PSS. In this class of materials, the ionicelectronic coupling develops through the whole bulk of the material, resulting in
lower impedances with respect to metal electrodes with the same area [62].

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PEDOT:PSS microelectrode arrays (MEAs) have been successfully used for in vitro
recording of the activity of hippocampal cell cultures treated with several drugs
[60] and of stimulus-locked cognitive responses to audiovisual stimuli with high
spatial specificity [63]. Hippocampal cells activity has been measured in vivo with
a nonpenetrating MEA allowing for high-SNR, long-term monitoring without the
risk of damaging the tissues [64]. In vivo monitoring of nerve signals in mice has
been demonstrated with PEDOT:PSS-based microelectrodes, showing improved
miniaturization features and enhanced mechanical stability with respect to standard
technologies [65] (Fig. 3.14). PEDOT:PSS was also integrated in tattoo electronics
for electromyography allowing for low cost, noninvasive, and conformal devices
with performances comparable to the Ag/AgCl commercial standard, providing
inherently low skin/electrode impedance without the use of electrolyte gels as
required by traditional electrodes [66].
When the biosignal to be measured is extremely weak, amplification near to
the signal source allows to achieve higher SNR. OECTs can be used to monitor
electrophysiological signals providing local amplification, resulting in improved

Figure 3.14 Chronic recording of rat sympathetic nerve activity (RSNA). (A) Scheme
showing the PEDOT:PSS-based electrode connected to the renal nerve. The elaboration and
transmission circuitry is located on the back under the skin. (B) Optical micrograph of
electrode located below renal nerve before sealing. (C) Trace of the recorded signals: renal
sympathetic nerve activity (RSNA), arterial pressure (AP), and heart rate (HR). (D) Detail of
RSNA (black) and AP (red) trace. (E) Cross-correlation of RSNA spiking activity and AP.
Source: Adapted from F. Decataldo, T. Cramer, D. Martelli, et al. Stretchable low impedance
electrodes for bioelectronic recording from small peripheral nerves, Sci. Rep. 9 (2019)
10598.

Electronic and ionic transport in organic materials and devices

97

recording quality. In vivo recording of mice brain activity has been demonstrated with PEDOT:PSS OECTs, showing improved SNR with respect to the
same signal measured with a PEDOT:PSS surface electrode and a penetrating
metal electrode [67]. ECG and electrooculography have been measured with
OECTs thank to the large amplification and bandwidth [59]. OECTs integrated
on stretchable and conformable substrates have been used for in vivo recording
of cardiac signals in rats showing blood compatibility, allowing for long-term
ECG signal monitoring [68].
In addition to monitoring electrophysiological signals, electrodes can be used to
stimulate cells or tissues. In vivo electrical stimulation can replace lost physiological functionality or treat diseases and injuries. A variety of clinical examples of
electrical stimulation have been proposed, including a cochlear implant to restore
hearing, deep brain stimulation to alleviate symptoms of neurological disorders
such as dystonia and Parkinson’s disease, and spinal cord stimulation for pain management [48]. Stimulation treatments are investigated for many other pathologies in
both clinical trials as well as preclinical studies [69] and their healthcare impact
will likely continue to expand over the next decades. Also in the case of electrical
stimulation, the ionic-electronic coupling can be capacitive or faradaic. Since faradaic reactions can generate undesired variations in the biological environment,
capacitive-coupled operation is highly desirable. In order to operate in capacitive
regime, it is fundamental to apply low voltages to the electrode, generally below
1 V. To achieve low-voltage operation and small electrode area for site-specific
stimulation, a high capacitance per unit area is required. Mixed ionic-electronic
conductors provide bulk ionic-electronic coupling, allowing to obtain high capacitances per unit area by increasing the electrode thickness. PEDOT:PSS-coated electrodes have been used for in vivo stimulation of the auditory system in rats [70].
The reduced size of the electrodes allowed to precisely stimulate the target neurons,
while the flexibility and conformability of the device allowed for improved stimulation due to closer contact to the site. The performances of PEDOT:PSS electrodes
have been tested in vivo for intracortical microstimulation applications, showing
better results than iridium oxide electrodes [71].
Although numerous hurdles have to be overcome for safe and reliable recording/
stimulation in patients, the integration of flexible, biocompatible, and high performances electrodes based on mixed ionic-electronic conductive materials has broad
applicability in the field of diagnostics as well as in the understanding of physiologic activity, and therapeutic stimulation for the treatment of diseases [72].

3.5.3 Iontronic delivery devices
As opposed to traditional electronic devices, where signals are carried by electrons,
in iontronic devices ions are the main information carriers. During the last decade,
a variety of iontronic devices based on organic materials have been developed,
from the iontronic resistor, also referred as organic electronic ion pump (OEIP), to
the ionic transistor [73]. This class of devices finds fundamental application in the
delivery of ions and drugs to a target biosystem at specific location and time. An

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OEIP is composed of an ionically conductive and electrically insulating ionexchange membrane (IEM) connecting an ion source reservoir and a target outlet
(Fig. 3.15). The ionic transport from the source to the target is accomplished by
applying an electric potential between the reservoir and the target electrolyte,
resulting in an electric field over the IEM. Similarly to an electronic resistor, the
ionic current in OEIPs is proportional to the applied voltage and to the IEM
ionic resistivity, which, in turn, depends on the material morphology and geometries. Diffusive “leakage” ionic currents can occur due to the charged molecules
concentration mismatch between the source and the target reservoir. An effective way to reduce such diffusive currents in OEIPs is to design long and narrow
IEM channels, nevertheless leading to high ionic resistances. When an electric
field is applied to the IEM, the resulting ionic current consists mostly of counterions (majority charge carriers) transported in the forward direction, but also a
small contribution from coions (minority charge carriers) arises. The coions contribution to the overall current is determined by the IEM selectivity, which
depends on the material adopted.
In conventional drug delivery systems such as microfluidics or microelectromechanical systems, the biomolecule is delivered together with a solvent, which
can interfere with the target biological environment. In contrast with conventional approaches, the electrophoretic ion transport in iontronic devices is not
flow based, meaning that only the ionic specie is delivered to the target.
Furthermore, iontronic devices can rely on well-established solid state
manufacturing techniques, allowing for easy miniaturization and integration
with electronic conditioning circuits. As a result, iontronic devices are characterized by precise control of the delivered drug amount as well as high spatial
resolution and speed comparable to that of biological events. A drawback for
this technology is that only charged species can be delivered and the molecule
size can in principle be a limitation.
The iontronic device electrodes can be made of a conducting polymer, while the
source reservoir can be an electrolyte solution containing the ionic specie to be
delivered. In principle, a solid state OEIP can be obtained by replacing the

Figure 3.15 Schematic representation of an organic electronic ion pump.

Electronic and ionic transport in organic materials and devices

99

electrically conductive polymer electrode and the liquid reservoir with a mixed
ionic-electronic conductor, simultaneously providing electric connectivity and ionic
reservoir. Furthermore, the mixed conductivity electrode yields lower impedance
per unit area, significantly improving the drug-delivery capacity. The most frequently used electrode material is PEDOT:PSS, providing both large electrical conductivity and ionic storage capacitance. IEMs are usually based on polyanions or
polycations, resulting in a cation-exchange membrane or anion exchange membrane, respectively. Several different materials have been used for IEM in iontronic
components, from linear polymers to advanced tailor-made hyperbranched (dendrolyte) materials [73]. The selectivity and resistivity of the IEM depend both on the
transported ionic specie and on the chemical and geometric microstructure of the
adopted membrane material. A high fixed charge concentration allows to achieve
selectivity through Donnan exclusion, and the ion mobility depends on the pore
size of the hydrated membrane. Linear IEM materials efficiently transport small
ions such as K1, Na1, Cl2, and Ca21 and small molecules with molar mass lower
than 200 g mol21, such as γ-aminobutyric acid, glutamate, aspartate, and acetylcholine. When larger molecules are involved, dendrolyte-based IEMs with large, welldefined porous structures can be used.
OEIPs have been used in vitro for the first time to induce physiological signaling
events in neuronal cells [74]. K 1 was delivered in high quantities in the neuron
environment, which in turn activated voltage-operated Ca21 channels. The localized
action of the OEIP allowed to activate an equivalent Ca21 response to that attainable by manual addition by delivering significantly lower K 1 concentration. The
miniaturization of the device enabled the individual stimulation of single neuronal
cells. The neurotransmitters glutamate, aspartate, and γ-amino butyric acid were
successfully delivered in vivo to the cochlea of guinea pigs, showing the possibility
to target specific hair cells inside the cochlea [75]. Chemical stimulation and electrical sensing functions at the same site were successfully performed by integrating
a PEDOT:PSS recording electrode and an OEIP on the same device [76]. The electrode recorded epileptiform discharges induced in mouse hippocampal preparation.
The inhibitory neurotransmitter, γ-aminobutyric acid (GABA), was then actively
delivered through the recording electrodes via OEIP. GABA delivery stopped epileptiform activity, recorded simultaneously and locally. This multifunctional “neural pixel” paves the way to implantable therapeutic devices with automated
feedback, where the drug release is activated by locally recorded signals. Moving
from iontronic devices to circuits, controlled chemical delivery was demonstrated
with independent release of several charged compounds in the milliseconds time
scale [77]. Bipolar membranes structures with diode-like characteristics allowed to
selectively switch off delivery paths with high on/off ionic current ratio.
Iontronics prospectively opens for new therapeutic procedures, as well as a new
paradigm of functional circuits. The integration of iontronics and electronics could
enable innovative tools for bioelectronic applications. The development of new materials specifically designed for use in iontronic devices, a deep understanding of the
device physics and improved microfabrication techniques could eventually enhance
the performances and the possibilities achievable with this novel class of devices.

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3.6

Organic Flexible Electronics

Conclusions

Mixed conduction organic materials exploiting ionic and electronic transport show
a huge potential for the future of bioelectronics and charge-storage devices. The
disruptive market of electric cars, as well as the pervasiveness of electronic devices
and the need to store renewable energy for power grids are urgently demanding for
charge-storage devices providing high-power and energy density, high durability
and safety [78]. State-of-the art SCs are a promising technology, usually showing
high-power density, long cycling life and safe operation. However their practical
application is limited by their poor-energy density, which is still far from that of
batteries [79]. The energy density of SCs is limited by a relatively low capacitance
and operating voltage window. Mixed conduction materials are able to provide
superior specific capacitances by exploiting a volumetric nanoscale ionic-electronic
interaction, but their voltage window and safety are still hampered by the choice of
the electrolyte. Furthermore, mechanical stability issues may arise due to the penetration of ions into the material, leading to swelling and cracking. The development
of new materials will drive the integration of improved mixed conductor-based
SCs. The tuning of the electronic and ionic conductivity could result in increased
energy density without compromising the power-density performance. The development of new solid state electrolytes could broaden the operative voltage window
and improve the safety of the devices, and the engineering of the electrodes
mechanical properties could eventually lead to high durability SCs.
The world of bioelectronics opens an even wider and more dynamic scenario.
The aim is to provide a ubiquitous and smooth link between biology and electronics, with potential applications in the fields of personalized medicine, continuous
health monitoring, early-stage diagnosis, treatment of neurological diseases, and targeted drug delivery. But we can also push our imagination further toward even
more futuristic applications, such as plant-based biohybrid systems [80] or
advanced brain-machine interfaces efficiently connecting humans and computers
[72]. Mixed conduction organic materials are the ideal platform for this scope,
inherently bridging the world of biology and electronics. The open challenges here
are diverse and each application has its own requirements. They involve not only
the development of new and improved functional materials, but also the progress of
microfabrication techniques and the integration of biocircuits with an application
aware design that must be able to meet the demands of the biological world, with
its complexity and delicateness.
The understanding of the ionic and electronic transport mechanisms and their
coupling in mixed conduction materials should guide the development of enhanced
materials and technologies, allowing to identify the physics under the weak points
of current technologies. The wide variety and the versatility of organic materials
make this a hard challenge, because very different electronic and ionic charge transport mechanisms can be involved when considering different materials. The multidisciplinary scenario makes the challenge even harder, demanding for the
collaboration of different backgrounds including physics, chemistry, biology,

Electronic and ionic transport in organic materials and devices

101

engineering, and medicine. Nevertheless, this results in an extremely dynamic field,
with a huge foreseen potential and an even larger panorama of unexplored
possibilities.

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