EIS measurements in molecular electronics

Meiling Su, Kieu Ngo, Jean-Christophe Lacroix, Mireille Turmine, Vincent Vivier

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Meiling Su, Kieu Ngo, Jean-Christophe Lacroix, Mireille Turmine, Vincent Vivier. EIS measurements in molecular electronics. Current Opinion in Electrochemistry, 2026, 57, pp.101830. 10.1016/j.coelec.2026.101830. hal-05528626

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## Review Article

# EIS measurements in molecular electronics

Meiling Su¹, Kieu Ngo¹, Jean-Christophe Lacroix², Mireille Turmine¹ and Vincent Vivier¹

<figure><img src="image_2.png" /></figure>

Although electrochemical impedance spectroscopy (EIS) has already demonstrated its reliability in electrochemistry and organic semiconductors as a tool for tracking charge-carrier transport, its potential in molecular electronics has not yet been fully realized. In this emerging field, where DC-based measurements often obscure key physical processes, EIS provides an indispensable frequency-resolved perspective capable of disentangling interfacial, dielectric, and molecular contributions. The aim of this review is to revisit prior studies and highlight how impedance measurements reveal information that remains hidden or ambiguous in static J-V analysis—ranging from contact resistance and dielectric response to polarization dynamics and environment-induced effects. By surveying the current state of the art, we underscore the unique diagnostic power of EIS and outline the challenges that must be overcome for it to become a standard metrological tool in molecular electronics.

### Addresses

¹ Sorbonne Université, CNRS UMR 7197, Laboratoire de Réactivité de Surface (LRS), 75005 Paris, France

² Université Paris Cité, ITODYS, CNRS UMR 7086, 75205 Paris, France

Corresponding author: Vivier, Vincent (vincent.vivier@sorbonne-universite.fr)

### Current Opinion in Electrochemistry 2026, 57:101830

This review comes from a themed issue on **Electrochemical Impedance Spectroscopy (EIS) (2025)**

Edited by Mark E. Orazem and Vincent Vivier

For a complete overview see the Issue and the Editorial

Available online 5 February 2026

https://doi.org/10.1016/j.coelec.2026.101830

2451-9103/© 2026 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

## Introduction

Over the past fifty years, the continuous drive toward smaller and faster devices has pushed transistor dimensions from the micrometer scale down to just a few nanometers. At these dimensions, molecular electronics has emerged as a fascinating frontier, where individual molecules become the functional elements

of circuits [1–4]. Molecular junctions (MJs) embody this concept, from single-molecule contacts to ordered molecular films engineered to achieve specific electronic functions. Advances in chemical design now enable control over molecular-level conduction, bridging chemistry and device physics. However, understanding how charge travels through a molecule or an ultrathin film remains challenging, as transport reflects a subtle interplay between electronic coupling, molecular conformation, and dynamic electrode interfaces that fluctuate under bias. This coupling between molecular structure, interfacial order, and contact quality dictates the reproducibility and performance of nanoscale devices.

Traditionally, charge transport has been described by current-voltage (J-V) characteristics and tunneling models such as the Simmons equation [5] in MJs whose thickness is below 5 nm:

$$J = J_0(V) \cdot e^{(-\beta \cdot d)} \quad (1)$$

in which $J_0$ is the theoretical current for a layer with $d = 0$, $\beta$ the tunneling decay constant, and $d$ the thickness of the layer.

When molecular layers exceed a few nanometers, transport shifts from direct tunneling to multistep hopping or polaron-mediated conduction, as described by Marcus theory [6]. In this regime, carriers move through localized states, and activationless long-range transport arises when electronic coupling approaches half the molecular reorganization energy. This transition from coherent to thermally activated behavior underscores the value of frequency-resolved techniques such as impedance spectroscopy, which can disentangle interfacial and molecular contributions [7,8].

Although impedance spectroscopy of molecular layers on electrode surface has been extensively studied in solution [9–11], impedance measurements in solid-state MJs are in their initial stage and few proven examples and potential prospects have been reported. They are discussed in this review providing the assessment of interfacial and dielectric properties, and the complement of physical picture from mesoscopic perspectives, alongside an examination of their underlying challenges and limitations.
Among several techniques for fabricating thickness-controlled molecular layers at nanoscale, self-assembly is widely used to conveniently construct well-defined self-assembled monolayers (SAM) on metal surfaces. SAM-based MJs thus represent an ideal platform for probing fundamental charge transport mechanisms and for developing functional devices, such as thermoelectric devices [12–14]. Both tunneling and dielectric properties can be addressed by impedance analysis. A common architecture of SAM-based MJs and the corresponding equivalent circuit are illustrated in Figure 1. Notably, the equivalent circuit might differ for distinct device configurations and molecular systems. For simplicity, this model considers monolayers rather than mixed SAMs or multilayer films, which remain less well understood. The molecular layer is deposited on the bottom electrode by self-assembly. In a second step, a top electrode is deposited onto it using various methods [7,8,15–19]. The molecule/electrode interface plays a decisive role in electron propagation [1,15]. Electrons driven by the external power source travel through the wire to the first molecule/electrode interface. They can either tunnel through the molecular layer, contributing to the resistance of the SAM ($R_{SAM}$), or accumulate at the interface, resulting in a charged state at the opposite plane of molecular chain ends. The partially impeded electrons generate an electric field across the molecular layer; therefore, the electrode planes at both ends of the molecular chains can be modeled as a parallel-plate capacitor, defined as the capacitance of the SAM ($C_{SAM}$). The parallel-plate capacitance relation (Eq. (2)) shows that the apparent dielectric constant can be derived from thickness-dependent EIS experiments:

$$C_{SAM} = \frac{\epsilon_0 \epsilon_r A_{geo}}{d} \qquad (2)$$

where $\epsilon_0$ is vacuum permittivity, $\epsilon_r$ the apparent dielectric constant of the SAM, $d$ the thickness of the SAM, and $A_{geo}$ the geometrical area of the junctions.

Electrons transferred through the molecular layer subsequently pass through the second molecule-electrode interface. As indicated in the commonly adopted equivalent circuit, the overall series resistance $R_c$, originating from the two aforementioned interfaces and the wires in the external circuits, cannot be separated in EIS analysis. It is important to emphasize that equivalent-circuit representations of impedance data are not unique, as different circuit topologies can often reproduce the same impedance spectra. This non-uniqueness reflects the inferential nature of impedance spectroscopy and implies that equivalent circuits should be viewed as descriptive models rather than unique physical representations of physico-chemical processes [20].

Covalent anchoring at metal/molecule interfaces strengthens electronic coupling by promoting orbital hybridization and favorable energy-level alignment, thereby minimizing intrinsic contact resistance. It is worth noting that the covalent link is not specified here (Figure 1), although thiol-based SAMs are popular, ultrathin films generated by diazonium electroreduction [21–23] and N-heterocyclic carbene based SAMs [12,24] have been demonstrated to improve chemical stability of the connection. For densely packed self-assembled monolayers, covalent bonds result in an effective specific contact resistance at the bottom

<figure><img src="image_3.png" /><figcaption>Figure 1</figcaption></figure>

(a) Schematic illustration of large-area molecular junctions. Two molecule/electrode interfaces are highlighted by red boxes. Yellow wavy lines are used to depict the simplified molecular backbones. Black bonds represent covalent links between the electrode surface and the molecules. The first molecule/electrode interface is defined as the interface between the bottom electrode plane and the covalent anchoring plane of the molecular layer, with the corresponding resistance denoted as $R_b$. The second molecule/electrode interface corresponds to noncovalent contact, characterized by the resistance $R_t$; (b) The capabilities of EIS measurements according to equivalent circuit analysis. The proposed equivalent circuit consists of a series resistance $R_c = R_b+R_t+R_s$ ($R_s$ is the resistance of the external circuit), while the bulk of the molecular layer is modeled as a parallel combination of $R_{SAM}$ and $C_{SAM}$.
electrode, R<sub>θ</sub>, of approximately 10<sup>-11</sup>–10<sup>-10</sup> Ω cm<sup>2</sup>, which is approximated from the quantum conductance of single-molecule junctions [25]. For electrode areas ranging from 20 to 400 µm<sup>2</sup>, this corresponds to absolute contact resistances below 1 mΩ, effectively rendering the covalent bottom contact non-limiting. In contrast, non-covalent or mechanically compliant top contacts exhibit substantially weaker electronic coupling and therefore much larger contact resistances, R<sub>t</sub>, which often dominate the overall junction response. In such asymmetric configurations, the apparent resistance of the molecular layer can be strongly overestimated, obscuring the intrinsic transport properties. This effect is particularly pronounced in SAM-based junctions, where reported resistance–area products span several orders of magnitude, reflecting variations in contact quality rather than molecular structure. Reliable determination of intrinsic SAM properties therefore requires low-resistance, ohmic and temperature-independent contacts on both sides of the junction.

The series resistance associated with metallic leads and
wiring, R<sub>s</sub>, was estimated from the conductor geometry

and independently verified by high-frequency imped-
ance measurements, yielding values below 1 mΩ
(Figure 1). This contribution is independent of the
electrode area and therefore negligible compared to
interfacial and molecular resistances.

**Impedance spectroscopy as a diagnostic**

Electrochemical impedance spectroscopy (EIS) has thus become a frequency-resolved probe capable of deconvoluting resistive and capacitive components and quantifying dielectric response at the molecular scale [16,17]. In benchmark work, Sangeeth et al. [17] analyzed Ag<sup>TS</sup>–SAM//GaOx/EGaIn junctions and identified contributions from molecular resistance (R<sub>SAM</sub>), capacitance (C<sub>SAM</sub>), and contact resistance (R<sub>t</sub>). R<sub>t</sub> was nearly thickness-independent, while R<sub>SAM</sub> increased exponentially with length, consistent with tunneling models (Figure 2a). EIS thus disentangles molecular from contact effects, offering a geometry-insensitive complement to static J–V curves.

Beyond resistance extraction, EIS probes dielectric
behavior. Chen and Nijhuis [18] showed that dense

<figure><img src="image_4.png" /><figcaption>Figure 2</figcaption></figure>

(a) Length dependence of R<sub>SAM</sub> (black squares) compared to R<sub>S</sub> (blue dots). Reprinted with permission from [17]. Copyright 2014 American Chemical Society. (b) Dielectric constant of Au–S(CH<sub>2</sub>CH<sub>2</sub>O)<sub>n</sub>·<sub>eg</sub>CH<sub>3</sub>//GaO<sub>x</sub>/EGaIn junctions as a function of molecular length under ambient and vacuum Reprinted with permission from [18]. Copyright 2020 American Chemical Society. (c) Capacitance as a function of device area for a C14 SAM. The dielectric constant, ε<sub>r</sub>, extracted from the fit is 2.09 ± 0.05; (d) Logarithmic plot of a C12 monolayer resistance-area product (R × S) as a function of applied voltage. The resistance multiplied by the area, rather than the resistance alone, is used because it more accurately reflects the validity of the model. The triangle data points represent the measurement. The solid line and the dash line represent the fits from the Simmons model with a barrier height of 4.16 eV (obtained from the J–V characteristics) and with a barrier height of 4.30 eV, respectively. The former shows a discrepancy from the experiment below 0.3 V, while the latter cannot describe the overall data within the experimental error Ref. [19] © 2007 National Academy of Science. (e) J–V curves of the eC/FL<sub>4.5</sub>/LiBa<sub>4</sub>/eC junction in vacuum (red curve) and acetonitrile vapor (blue curve); (f) The schematic illustration shows the potential profile for the four distinct states: separated molecular layers, and the formed junction under open-circuit, positive, and negative bias Reprinted with permission from Ref. 26. Copyright 2018 American Chemical Society.
conjugated SAMs exhibit collective dipolar responses with effective permittivity up to a value of about 15, far above bulk organic values (Figure 2b). Such enhancement originates from molecular tilt, conjugation, and donor–acceptor substitution, as supported by DFT [7,27].

## Image potential correction and dielectric constant

In a seminal study, Akkerman et al. [19] showed that transport through alkane dithiol SAMs follows the Simmons model when image potential corrections are included. By combining impedance spectroscopy and J–V measurements, they determined a dielectric constant of $ε_r \approx 2.1$ (the thickness of the SAM is 2.3 nm) and demonstrated that tunneling current and capacitance can be measured simultaneously for a limited range of device area because of experimental and instrumental constraints (Figure 2c). The dielectric constant allowed quantification of image potential effects, which reduce the effective barrier height. The J–V curves of varying length SAMs (C8 to C14) were reproduced using a single electron effective mass for data fitting ($m^* \approx 0.28 m_e$) and barrier heights of about 4–5 eV, without additional fitting parameters. Although the improved model showed deviations at low bias (<0.3 V), revealing the limitations of purely static models (Figure 2d), the results indicate the potential of EIS as a metrological tool for identifying dynamic polarization or interfacial dipole effects in future investigation.

At the molecular level, dielectric behavior depends on intrinsic polarizability and supramolecular organization. Adjusting molecular tilt and packing modulates both resistance and capacitance. For example, in hydroxide-based systems, impedance spectra exhibit dispersive capacitive features well-described by constant phase elements (CPEs), revealing inhomogeneous polarization and surface disorder [28,29]. CPEs are routinely used to capture non-ideal capacitive responses in impedance data, yet their widespread use largely reflects the persistent conceptual uncertainty surrounding the electrochemical interface itself. CPE parameters cannot be interpreted as a capacitance, except under restrictive and model-specific assumptions on time-constant distributions [28,30]. As a result, CPEs should be regarded as phenomenological descriptors of interfacial dispersion rather than as physically resolved elements, and any attempt to extract quantitative capacitance values from them must be approached with particular caution [28,31].

## Polarization dynamics of polar solvent and mobile ions

EIS proves especially informative when internal fields are perturbed by polar molecules or mobile ions. In carbon-based junctions, McCreery and co-workers

[32,33] showed that exposure to acetonitrile vapor or $Li^+$ ions drastically alter conductance and hysteresis (Figure 2e). Slightly increased capacitance of $FL_{8.5}$ MJs in acetonitrile vapor compared to that in vacuum implies solvent reorganization. For $FL_{4.5}/LiBA_4$ MJs, capacitance increased from ~1 µF cm⁻² (dry conditions) to > 5 µF cm⁻² (in acetonitrile solvent), with frequency roll-offs from 10 kHz to 1 MHz shifting with temperature, highlighting sub-microsecond to millisecond relaxation-times for ion motion. These observations naturally raise questions about the fundamental time-scale of ionic displacement across nanometer-thick layers, particularly the time required for a mobile ion to travel several nanometers within a 10-nm-thick molecular film. Based on order-of-magnitude considerations and previous discussions, this transit time may be as short as ~1 ns. This hypothesis calls for clear experimental validation.

Ionic screening reshapes internal potential profiles and lowers the effective electric field (see Figure 2f for more details), i.e., phenomena that EIS can resolve by distinguishing dipolar polarization from ionic migration, which static J–V measurements merge. This highlights the need to design iono-electronic architectures using thin layers and materials with high ionic mobility. It also emphasizes that clearly demonstrating nanosecond-scale ionic motion would represent a significant breakthrough, paving the way for GHz-frequency iono-electronic devices.

## Solvent-induced rectification

At the single-molecule scale, Shi et al. [34] extended EIS to STM break-junctions, measuring tip/solvent/substrate capacitance and demonstrating how solvent-induced dipoles tune rectification. Changes in the interfacial dielectric environment altered potential-drop asymmetry and charge-injection barriers, corresponding to effects that are invisible to static I–V analysis. Thus, EIS emerges as a sensitive probe of electrostatics and environmental polarization in single-molecule devices.

## Bioelectronic junctions and contact-limited transport

The same principles extend to bioelectronic junctions, where proteins serve as the molecular bridge. Recent work demonstrated efficient electron transport across protein films tens of nanometers thick [35]. As shown in Figure 3a, using DC and impedance analyses, the total junction resistance, $R_p$, was separated into intrinsic film resistance and a contact-limited term, $R_C$, derived from extrapolated zero-length ($R_{ZLR}$) and series resistances ($R_S$). Across Si–Au, Au–EGaIn, and Au–Pd micropore configurations, impedance data revealed that transport efficiency depends critically on interfacial electrostatics and oxide layers. Minimizing $R_C$ in the micropore geometry yielded exponential length-dependent transport
<figure><img src="image_5.png" /><figcaption>**Figure 3**</figcaption></figure>

(a) The equivalent circuit proposed for protein-based molecular junctions with components including series resistance ($R_S$), protein capacitance ($C_p$), protein resistance ($R_p$), and $R_C$ contributing to contact resistance (a dimensionless term calculated from $\bar{R}_C = \frac{R_{ZLR}}{R_S}$, $R_{ZLR}$ is resistance deduced from the protein resistance-length plot when the length is 0) [35]; (b) Schematic illustration of the quantum RC circuit with a quantum point contact (QPC) on top of a submicrometer two-dimensional electron gas quantum dot. The equivalent circuit on top considers the QPC and the geometric capacitance separately. The equivalent circuit on the bottom represents the coherent RC behavior of the system; (c) Nyquist representation of the conductance in the coherent regime at T = 295 mK (blue line) and in the high temperature regime at T = 4.2 K (red line); The black dashed lines show fits to an RC circuit using a tunable resistance and a fixed capacitance. The blue and red dashed lines represent fits where the capacitance is tunable and the resistance is constant at $R_q = h/2e^2$ ($R_K = h/e^2$) [36] © IOP Publishing. Reproduced with permission. (d, e) The frequency response of S parameter $|S_{21}|(\propto|Y(\omega)|)$ and phase angle $\phi$ measured on 1 G₀, 3 G₀, 10 G₀ Au contacts [37] © IOP Publishing. Reproduced with permission.

with decay constants $\beta \approx 0.7 - 1.1 \text{ nm}^{-1}$, confirming that proteins can sustain long-range conduction beyond tunneling. Impedance fitting provided access to an apparent “protein capacitances” ($C_p$, where both ends of the protein layer are simplified as equivalent parallel plates), which reflects the collective dielectric response of the protein film and its interfacial regions. The extracted $C_p$ thus defines an effective dielectric constant for the protein layer, incorporating both the intrinsic polarizability of the molecules and the contributions of the interfaces, enabling qualitative evaluation of dielectric and charge-transfer properties. These results exemplify how contact engineering guided by impedance isolates intrinsic bioelectronic transport from parasitic effects.

## Quantum and mesoscopic admittance

At the mesoscopic limit, impedance acquires a quantum dimension. The pioneering experiments of Gabelli et al. [36] demonstrated that a phase-coherent quantum conductor behaves as a quantum RC circuit (Figure 3b): its capacitance reflects the electronic density of states in

the confined region, while the charge-relaxation resistance takes the universal value $R_q = \frac{\hbar}{2e^2}$ for a single transmission channel. The resistance remains constant even when transmission decreases, whereas capacitance oscillates, i.e., a non-classical behavior governed by electron dwell time (Figure 3c). This concept provides the microscopic foundation of frequency-dependent admittance in nanoscale systems and directly connects mesoscopic transport theory with the complex conductance measured in molecular EIS.

## Atomic contacts and admittance limits

At the atomic limit, admittance replaces static conductance as the relevant descriptor. Sakai [38] showed that single-atom metallic contacts exhibit extremely small imaginary components, with $|\Re m(Y(\omega))| = 0.01-0.1$ nS at 1 GHz, confirming that such junctions behave nearly purely resistively even at gigahertz frequencies (Figure 3d and e). Theoretical models, including the single-level and mesoscopic capacitor approaches derived from the use of Non-Equilibrium Green's Function, predict that the capacitance at this scale
originates from atomic geometry and field confinement rather than classical dielectric response. The correction term D (related to the electrode surface density of states) deduced from the distance-dependence of STM tip/cluster capacitance (reaching its maximum about 0.3 fF at a tip-cluster distance of 0.13 nm) suggests $|\Re m(Y(\omega))| \approx 0.15$ nS at 1 GHz, confirming that intrinsic imaginary part of the admittance becomes vanishingly small at the atomic limit, setting the lower boundary for detectable molecular or dielectric contributions using the imaginary part of the admittance [38,39]. Importantly, a small imaginary admittance relative to its real part signifies a predominantly resistive response, rather than a large imaginary impedance.

## Device geometry and parasitic effects

Because single-molecule junctions exhibit capacitances as small as $10^{-16}$ to $10^{-14}$ F, stray and fringe capacitances often dominate the response [40]. Capacitance for large-area molecular devices scale with interfacial area and are proportional to the inverse of layer thickness, while resistance depends on both layer thickness and contact geometry. Accurate modeling thus requires including parasitic elements, and electrode design becomes critical for modulating the overall impedance profile. Sangeeth et al. [15] introduced CPEs captures deviations from ideal capacitive behavior due to interfacial disorder or defects in the SAM. Equivalent-circuit models, from simple RC to modified Randles types, remain invaluable. Validation of equivalent-circuit models in impedance analysis requires that the experimental data satisfy the assumptions of linearity, causality, and stability underlying the Kramers–Kronig relations. These relations express the interdependence between the real and imaginary parts of the impedance spectrum across the entire frequency domain. For a causal and stable system, each component can be derived from the other.

In practice, however, Kramers–Kronig consistency is not assessed by directly integrating the relations numerically, but rather through regression using Kramers–Kronig consistent models. These models simultaneously enable extrapolation to the zero and infinite frequency limits, as well as identification of frequency ranges affected by experimental artifacts, non-stationary behavior, or instrumental bias [28].

## Limitations and perspectives

Despite its versatility, EIS at the nanoscale faces intrinsic limitations. Parasitic capacitances and geometric stray fields can overshadow the tiny intrinsic response, and multiple equivalent-circuit fits can describe similar spectra. Yet, theoretical and experimental studies of single-atom contacts confirm that reactive components are negligible up to 1 GHz, and that most measured dispersion originates from the impedance of the interfaces rather than intrinsic

molecular polarization. The challenge is thus to disentangle real molecular contributions from artifacts through bias- and temperature-dependent EIS combined with operando spectroscopies.

## Concluding remarks

Electrochemical impedance spectroscopy has become an indispensable tool in molecular and bioelectronic research. Across single-molecule, SAM-based, ionic, and protein junctions, EIS bridges dielectric physics and charge transport, providing access to interfacial capacitances, dielectric constants, relaxation times, and polarization dynamics when probing the system over a wide frequency domain. Its main strengths are the ability to separate contact and molecular contributions, sensitivity to attofarad-scale elements, and robustness against morphological variability. Limitations stem from parasitic capacitances and the non-uniqueness of circuit models. Future progress will rely on integrating EIS with time-resolved spectroscopies and multi-scale modeling to unify the understanding of charge transport from coherent tunneling to Marcus-type hopping regimes.

## Declaration of competing interest

The authors declare no competing financial interests.

## Acknowledgements

The authors acknowledge the support of the Centre National de la Recherche Scientifique and the funding from the ANR (ANR-23-CE09-0028) – Project DEMOCRACY.

## Data availability

No data was used for the research described in the article.

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