# Dielectric permittivity modulation at nanoscale in plasma synthesized silver nanoparticles based nanocomposites for in-memory computing

Christina Villeneuve-Faure, Laurent Boudou, Gilbert Teyssedre, Kremena Makasheva

Makasheva

► To cite this version:

Christina Villeneuve-Faure, Laurent Boudou, Gilbert Teyssedre, Kremena Makasheva. Dielectric permittivity modulation at nanoscale in plasma synthesized silver nanoparticles based nanocomposites for in-memory computing. IEEE Open Journal of Nanotechnology, 2025, 6, pp.131-145. 10.1109/OJ-NANO.2025.3620878. [https://doi.org/10.1109/OJ-NANO.2025.3620878](https://doi.org/10.1109/OJ-NANO.2025.3620878). This content is licensed under a Creative Commons Attribution 4.0 International License.

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<figure><img src="image_1.png" /></figure>
Dielectric permittivity modulation at nanoscale
in plasma synthesized silver nanoparticles based
nanocomposites for in-memory computing

Christina Villeneuve-Faure, *Senior Member, IEEE*, Laurent Boudou, Gilbert Teyssedre, *Senior Member, IEEE*, and Kremena Makasheva, *Senior Member, IEEE*

**Abstract:** The intense work on development of unconventional approaches for computing and signal processing involves efforts on design and engineering of materials with tunable dielectric properties and switchable electrical state as conduction state. This is the case of in-memory computing using emerging non-volatile memories which has successfully opened up new prospects for neuromorphic computing via the option of high volume data traffic between processor and memory units but faces materials-related challenges mostly attributed to the intrinsic and non-ideal device properties and expresses complexity in hardware implementation. In the effort to advance on the concept we describe here a way for controlled modulation at nanoscale of the dielectric response of plasma synthesized silver nanoparticles (AgNPs)-based nanocomposites and a method for mapping their dielectric permittivity via Electrostatic Force Microscopy. By embedding a 2D-network of AgNPs close to the surface of thin SiO₂-layers, one can locally modulate the relative dielectric permittivity (εᵣ) of the device in a large range. The presence of AgNPs in the dielectric layer leads to a nanostructuration of the relative dielectric permittivity, with lower εᵣ-values above the AgNPs and higher ones in-between them, when compared to the εᵣ-value of a homogeneous SiO₂. A nanostructuration factor is introduced to account for this effect. The nanostructured dielectric response is related to modulation of the electric field inside these AgNPs-based nanocomposites. The results in this work generate important contributions towards the practical applicability of such AgNPs-based nanocomposites for neuromorphic computing, which is considered as an important step towards device engineering.

***Index Terms***— AFM, dielectric permittivity, AgNPs, nanostructured dielectrics, plasma nanotechnology

I. INTRODUCTION<fnref n="1" />

According to a recent roadmap for European Nanoelectronics, the scope of Beyond CMOS (Complementary Metal Oxide Semiconductor) device era encompasses novel information processing paradigms and goes with the development and implementation of new materials and/or architectures to address the challenges at nanoscale, among others the heat dissipation [1], [2]. This critical evolution needs emerging technologies to improve electronic devices, particularly those supporting neuromorphic computing [3], [4], [5], [6]. In neuromorphic computing, improved computational efficiency and reduction of power consumption are expected by electronic circuits that mimic the neuronal system. These neuromorphic

circuits can be obtained by integration of non-volatile
memory cells (NVMs), which represent the synapse, in
CMOS circuity that act as neurons (Figure 1a). Such in-
memory computing (IMC) using emerging NVMs has
recently been demonstrated and successfully opened up new
opportunities for future computing paradigm [5], [7], [8].

The development of IMC with NVMs needs materials or
architectures that present two or more stable states of at least
one physical property (resistivity, capacitance, magnetic
moment...) and can be switched by external stimuli (e.g.,
electric field, magnetic field, light...) Various NVM devices
are currently explored to meet this challenge. The most
spread of them are phase change memory, Conductive-
Bridging Random Access Memory (CBRAM), filamentary
and non-filamentary Resistive RAM (RRAM), spin devices
or memories derived from Metal Oxide Semiconductor
(MOS) devices. The common point for all these devices is

All authors are with LAPLACE (Laboratoire Plasma et Conversion d'Energie), Université de Toulouse, CNRS, INPT, 118 route de Narbonne, F-31062 Toulouse, France.

Corresponding authors: Christina Villeneuve-Faure (email: christina.villeneuve@laplace.univ-tlse.fr) and Kremena Makasheva (email: kremena.makasheva@laplace.univ-tlse.fr).

<footnote n="1">¹ This work was supported by l'Agence Nationale de la Recherche in France, project ANR BENDIS (ANR-21-CE09-0008).</footnote>

<footnote>For the purpose of open access, the authors have applied a CC-BY public
copyright license to any Author Accepted Manuscript (AAM) version
arising from this submission.</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Non-Volatile Memory cells (NVMs) suitable for in-memory computing (IMC). (a) Schematic of a neuromorphic device with a NVM cell above a classical CMOS device (D-drain, C-channel and S-source). NVMs designed as: (b) FGMOS (G-gate), (c) NOMFET, (d) filamentary RRAM, (e) non-filamentary RRAM.</figcaption></figure>

the importance of material development and the clear trend
towards application of nanocomposites (NCs) [3], [4], [5].
For example, in Floating Gate Metal Oxide Semiconductor
devices (FGMOS) the information is stored in the floating
gate as trapped charges with amount controlled by the
floating gate properties due to a capacitive coupling [9]. The
requirements to engineer the device in terms of materials are:
(i) long-term charge retention in the floating gate and
(ii) insulating layer with high dielectric permittivity and low
leakage current. The most explored structure is silicon-
oxide-nitride-oxide-silicon (SONOS), because of the very
high spatial trap density of silicon nitride ( > 9.0 × 10¹⁸ cm⁻³)
[10]. However, despite of the high relative dielectric
permittivity of Si₃N₄ (εᵣ = 7.5 [11]), the large leakage current
(1.06 × 10⁶ nA/cm², especially for Si-rich silicon nitride
films [12]) prevents from use of silicon nitride as floating
gate. A way to improve the performance of FGMOS devices
is to use nanocomposite materials for the floating gate
(Figure 1b) [2], [13]. Nanocomposite materials are also used
in Nanoparticle Organic Memory Field Effect Transistor
(NOMFET), for which metallic nanoparticles are introduced
in the insulating layer to act as artificial electronic traps to
store the information and to modulate the channel
conductivity (Figure 1c) [13], [14], [15]. Resistive switching
is observed for different metallic (Au [13], [15], Ag [16],
[17]) or semiconductor (CdSe [18]) nanoparticles and the
effect is related, as previously, to the electrical charge
trapping, but in this case in the nanoparticles. In NOMFET
devices, the nanoparticles are processed by chemical
methods and incorporated in a thin layer of an organic
matrix. The main advantage of the applied wet chemical way
for material synthesis is related to the low temperature of the

process; however, its main issue is the lack of compatibility
with standard microelectronic technologies.

Considering filamentary RRAM devices (Figure 1d), metal oxides such as HfOx, AlOx or TiOx are required to induce the conductive channel which is at the origin of the memristor effect [2], [3], [4]. Combining memory and resistor, memristors have emerged as the most important electronic component for brain-inspired neuromorphic computing. The main issue in such architectures is primarily related to the uncontrolled variability in the high/low resistivity state.

Recently, Ma *et al.* demonstrated that the memristor effect
can be initiated in thin native silica layers by protruding
bumps situated on the adjacent silver (Ag)-electrode [19].
Protrusions with size around 1.5 nm are sufficient to induce
conductive filaments in a 2.7 nm–thick native silica layer.
These advances describe the principle and open up
opportunities in mass production of Si-compatible
memristors for ultradense neuromorphic hardware.
However, the changeability of the composition of native
silica, which differs from that of a stoichiometric SiO₂ matrix
by the presence of C-, OH- and other chemical groups in it,
and its poor electrical performance on one side, and on the
other side the uncontrolled way of inception of the filament,
depending on the random distribution of protrusions on the
metal electrode surface, bring uncertainty in the response and
thus leave ample room for improvement and compromise. A
way to produce well controlled protruding areas and to
increase the electrical performance of the filamentary
RRAM devices is to use silver nanoparticles (AgNPs) with
known size and interparticle distance which would replace
the random protrusions on the electrode and thus allow
achieving more predictable resistance states. 2D-networks of
AgNPs can also be utilized to create non-filamentary RRAM devices. Recently, it was demonstrated that neuromorphic devices can be developed on the basis of AgNPs immobilized on the surface of a silica layer to form a 2D-network between two electrodes (Figure 1e) [6], [20]. In this case the resistive switching occurs through different electron conduction pathways for which the mechanisms of charge transport are defined by the AgNPs percolation level.

Clearly, components based on AgNPs appear promising for creating in-memory computing devices. Possible architectures, appropriate for filamentary and non-filamentary RRAM, imply also NCs made of a 2D-network of AgNPs embedded in silica matrix at a controlled distance from the surface [21], [22]. Embedding the AgNPs in a dielectric matrix has the advantage to protect them from aggregation and fast oxidation processes. The device can be realized in a plasma process which is compatible with the current microelectronic technologies but requires optimization of the dielectric matrix properties in order to limit/control the leakage current. As already demonstrated, AgNPs-based NCs exhibit tunable and well controlled dielectric properties, particularly in terms of artificial charge trapping, with fine control over the charge injection and release phenomena [21], [22], [23], [24]. The extremely high number of interparticle contact points and density of interfaces between amorphous and crystalline parts in such AgNPs-based NCs, and the crystalline orientation mismatch, in case of twinned and/or polycrystalline AgNPs, deeply affect the electrical conduction. On the other hand, such nanostructures appear highly suitable to achieve non-linear electrical behaviour and non-local effects [25]. However, before being considered for IMC with NVMs these AgNPs-based NCs require additional studies. The combination of dielectric permittivity gradients, huge electrical conductivity contrasts and charge trapping in the nanocomposite may lead to unpredictable macroscopic current in transient and steady states. For example, the influence of AgNPs on the relative dielectric permittivity of the nanocomposite material remains poorly addressed in the literature, especially at nanoscale. This is regrettable since charge injection and transport are favored in low dielectric permittivity areas due to the higher electric field there. Results on the relative dielectric permittivity of AgNPs-based NCs can be found for the global dielectric response of the nanocomposite, as probed by dielectric spectroscopy (DS) in the low frequency range ($10^1 - 10^4$ Hz) [26]. They clearly demonstrate that the dielectric response of AgNPs-based NCs is modulated by the presence of AgNPs in the silica matrix. Indeed, the relative dielectric permittivity of the nanocomposite goes up to $\epsilon_r = 4.2$ when the AgNPs are embedded at 6 nm beneath the $SiO_2$ surface. Then, it gradually decreases for AgNPs embedded further from the surface to get down to the $\epsilon_r$-value measured for a bare plasma $SiO_2$ layer of $\epsilon_r = 3.8$, when the AgNPs are located at more than 50 nm under the surface. Such modulation of the dielectric response of AgNPs-based NCs is surmised to originate from AgNPs-induced modulation of the designed electric field

distribution. Such electric field distortion can trigger local and non-local effects on the charge transport in the dielectric. However, only a nanoscale study can bring the necessary confirmations for the size of action of such phenomena. Mapping the dielectric permittivity of AgNPs-based NCs at nanoscale, on relatively large areas ($1 \mu m^2$ or larger), and particularly knowledge on the variations of the dielectric loss part, will add value to the description of the effective electronic conductivity of non-filamentary RRAM components in resistive arrays [4], [20]. In addition, modulation of the dielectric permittivity of the material can bring the required variations of capacitance states (nonzero capacitance window at DC zero bias) in capacitive crossbars, as recently proposed in order to overcome the disadvantages of the resistive arrays, and engender a new paradigm of parallel computing [27], [28].

Furthermore, to qualify the electrical performance and reliability of such AgNPs-based NCs for IMC, their characterization should involve studies at nanoscale to address the physical processes occurring at nanoparticle level and especially the interfaces between metallic and dielectric parts in the nanocomposite. In the last decade, the electrical properties of nanocomposites were investigated successfully at nanoscale using electrical modes derived from Atomic Force Microscopy (AFM). Indeed, Electrostatic Force Microscopy (EFM), Kelvin Probe Force Microscopy (KPFM) or Conductive AFM (C-AFM) could provide relevant information on the electrical behaviour of the nanocomposites at nanoscale: charges injection, trapping and transport phenomena [29], dielectric permittivity mapping [30], [31], current-voltage I(V)-measurements [32]. Combining these characterization methods, the influence of metal inclusions, namely the AgNPs, on the charge trapping and transport in the dielectric matrix ($SiO_2$) can be revealed.

In this work, plasma synthesized nanocomposite dielectric materials consisting of a 2D-network of AgNPs embedded in silica ($SiO_2$) matrix and positioned at a controlled distance from the surface are explored in terms of modulation of the relative dielectric permittivity of the material due to the presence of metallic inclusions (AgNPs). The impact of AgNPs size, interparticle distance and distance from the surface on the relative dielectric permittivity of the NCs is investigated at nanoscale to relate the 2D-nanostructuration of the material to the electrical performance of the device. The analysis is based on mapping the relative dielectric permittivity with nanometer resolution on relatively large surfaces, approximately $0.16 \mu m^2$. The originality of our approach stems from coupling of the EFM measurements with Finite Element Modeling (FEM) to identify the impact of inclusion of metallic component (AgNPs) on the relative dielectric permittivity of a dielectric silica matrix at nanoscale and its modulation. The numerical analysis is limited to geometric factors only (AgNPs size, interparticle distance, cover layer thickness). Given the small volume fraction of AgNPs in the $SiO_2$ matrix the dielectric structure is considered linear (weakly anisotropic), so that it can
reasonably well be characterized with a scalar (angle-average) susceptibility, i.e., a dielectric permittivity.

## II. MATERIALS AND METHODS

### A. Plasma synthesized nanocomposite dielectric materials

In line with the above reasoning, nanocomposite dielectric layers composed of a 2D-network of AgNPs embedded in a silica ($SiO_2$) matrix appear promising architectures to advance in the development of IMC with NVMs (Figure 2). Indeed, such nanocomposite structures can be elaborated in a low pressure hybrid plasma process successfully combining in the same reactor metal sputtering (Physical Vapor Deposition – PVD) for the growth of silver nanoparticles and Plasma Enhanced Chemical Vapor Deposition (PECVD) for the silica deposition. Moreover, this plasma-based process is a material process compatible with the current CMOS-technologies. The AgNPs-based NCs with total thickness $d_{tot}$ were synthesized in an axially-asymmetric RF ($f = 13.56$ MHz) capacitively-coupled plasma maintained at low gas pressure in argon [21, 22, 23, 33]. The RF-driven top electrode (smaller, 10 cm in diameter, covered by a silver target, purchased from Codex Int., with purity of 99.99%) was placed in front of a bottom electrode (larger, 12 cm in diameter) at a gap distance between the two electrodes of 3.5 cm. The bottom electrode and the walls of the plasma reactor were grounded.

Due to the axially-asymmetric design of this reactor the produced plasma induces a negative self-bias dc voltage ($V_{dc}$) on the smaller in size RF-driven electrode (the silver target). The self-bias voltage results from the dc voltage drop between the plasma bulk and the electrodes across the plasma sheaths. In general, the voltage drop across the plasma sheaths is inversely proportional to the sheath capacitance, thus the sheath with smaller area (the one adjacent to the smaller electrode) has smaller capacitance and therefore a larger voltage drop there. As a consequence, the induced self-bias voltage on the adjacent electrode is higher. The self-bias voltage scales up, in modulus, with the injected power, at a constant pressure, and can achieve values beyond -1000 V for injected power above 80 W. It is at the origin of acceleration of the argon ions from the plasma towards the silver target to bombard it and perform sputtering of silver atoms necessary to form the AgNPs. The same plasma reactor is used for the deposition of $SiO_2$ layers, one as a basis and a second one as cover layer to complete the stratified structure, as shown in Figure 2. More details on the plasma reactor, the deposition procedure, the real-time monitoring of the plasma process, and the plasma parameters are given elsewhere [21, 33].

Briefly, the AgNPs-based NCs synthesis was performed in a three-step process: 1) plasma deposition of base $SiO_2$ plasma layers with different thicknesses (80-180 nm) on Si-wafers (Sil'tronix), 2) silver sputtering to obtain the 2D-network of AgNPs followed by 3) a second plasma deposition to create the silica cover layer to complete the

<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic cross-section view of a AgNPs-based NC: $d_{tot}$-thick nanocomposite containing a 2D-network of AgNPs (size $d_{AgNPs}$ and interparticle distance $d_{in}$) embedded in a $SiO_2$ layer at a distance $d_c$ beneath the surface (the cover layer thickness is denoted $d_c$).</figcaption></figure>

structure. The plasma operating parameters for all AgNPs-based NCs studied in this work are summarized in Table I.

The $SiO_2$ plasma layers were obtained in the plasma maintained in an argon (Air/Liquid AlphaGaz 2 – 99.9995%) – hexamethyldisiloxane (HMDSO, $Si_2O(CH_3)_6$) – oxygen ($O_2$) mixture at total gas pressure of $p_{tot} = 7.7$ Pa, and input RF power of $P = 120$ W ($V_{dc} = -840$ V). The thickness of each $SiO_2$ plasma layer was controlled by the deposition time. A strong originality of this process is the pulsed injection of HMDSO which allows deposition of high quality plasma silica layers. The thickness of the cover layer ($d_c$) actually determines the depth at which the 2D-network of AgNPs is positioned in the $SiO_2$ matrix.

The AgNPs were synthesized in the same plasma reactor in a plasma maintained in pure argon at pressure of $p = 5.4$ Pa with various input RF power of $P = 20, 40$ and $80$ W inducing self-bias voltages around $V_{dc} = -550, -750$ and $-1000$ V, respectively. The self-bias voltage is used in this work to control the size ($d_{AgNPs}$) and interparticle distance ($d_{in}$) of the AgNPs-network (Figure 2). For all samples the silver sputtering time was fixed to 5 s. One shall note here the very good reproducibility of the elaborated AgNPs-based NCs.

### B. Material characterization

#### Morphological and structural characterization

AFM measurements were performed on a Bruker MultiMode 8 setup. Surface topography was probed in tapping mode using the same tip as for the electrical characterization, a PtIr-coated Si-tip (curvature radius $R_c \approx 25$ nm).

Structural characterization and statistical analysis on the AgNPs-based NCs in general, and the AgNPs in particular, were achieved on the basis of a Transmission Electron Microscopy (TEM) study. The latter was performed with a JEOL 2100F TEM equipped with a field emission source. The applied acceleration voltage was of 200 kV for a resolution of 2.3 Å. Images were acquired with a CDD Gatan 794 camera. The observations were made in both plane- and cross-section view. TEM image processing was performed with ImageJ 1.54d. Crystallographic patterns of the AgNPs were derived from electron microdiffraction. To achieve
thickness required for TEM observations the samples were prepared with a precision ion polishing system (PIPS 691) according to a standard procedure [33].

The thickness of the SiO₂ layers was measured by spectroscopic ellipsometry with a Semilab SE-2000 ellipsometer in the 250 – 850 nm spectral range with an incident angle of 75°. Forouhi-Bloomer dispersion law was applied to extract the thickness and the optical properties of the silica layers.

## Nanoscale electrical characterization

Electrostatic Force Microscopy was applied to investigate the dielectric response of the AgNPs-based NCs at nanoscale. EFM is a derivative mode of AFM that measures long range electrostatic forces between the sample and a conductive AFM tip [30], [34], [35]. The EFM provides simultaneously the surface topography and the resonance frequency shift Δf₀(Vᵢ) for an applied dc voltage Vᵢ to the tip (sample backside is grounded). It is a double-scan AFM technique. The surface topography is acquired in a first scan using AFM tapping mode and then during the second scan, the AFM cantilever is lifted at a preset height, driven at its resonant oscillation frequency, and excited electrically. The interaction between the voltage-biased AFM tip and the sample is a combination of capacitive forces due to surface potential and dielectric screening, and Coulomb forces between surface static charges and their image charges on the tip. These electrostatic interactions induce changes in the cantilever resonance frequency and phase. Record of the changes as a function of the tip position on the sample provides information on the dielectric properties of the probed material.

In our experiment, the EFM measurements were performed on a Bruker MultiMode 8 setup, using a PtIr-coated Si-tip with resonance frequency of f₀ = 66.1 kHz, tip curvature radius R_c of around 25 nm and a cantilever spring constant k = 2.32 N/m. The EFM measurements of the resonance frequency shift Δf₀ were achieved using a lift-

height h of 20 nm and an applied potential on the AFM tip of Vᵢ = 0 and 5 V, sample backside being grounded.

### C. Methodology to extract dielectric permittivity from EFM measurements

The effective relative dielectric permittivity map is extracted from the resonance frequency shift measured by EFM using a method derived from the one reported by C. Riedel et al. [30]. In this study, the frequency shift is probed at Vᵢ = 0V and 5V with a lift-height h, and the resulting resonance frequency shift parameter a<sub>Δf</sub> is obtained for each point over the entire studied surface to create its experimental map, using the following equation:

$$a_{\Delta f} = \frac{\Delta f_0(5V) - \Delta f_0(0V)}{5^2} \quad (1)$$

From theoretical point of view, the resonance frequency shift parameter a<sub>Δf</sub> is related to the capacitance C between the AFM tip and the sample by the following relation [30]:

$$a_{\Delta f} = \frac{f_0}{4k} \frac{d^2C}{dz^2}, \quad (2)$$

where f₀ is the resonant frequency, k is the cantilever spring constant and z is the vertical distance. The second derivative d²C/dz² is determined in the frame of an electrostatic approximation by using a 2D-axisymmetric Finite Element Model (FEM) developed on COMSOL platform. The geometrical description of the AFM tip is implemented in the FEM model. The AFM tip is represented by a truncated cone of 10 µm height and 14° aperture angle, ending by a semi-spherical apex (curvature radius R_c) [29]. It is surrounded by an air box with large enough dimensions to avoid edge effects (Figure 3a). The thickness of the dielectric layer (d<sub>tot</sub>) is taken, as determined from spectroscopic ellipsometry measurements.

The electric field E(r, z) is computed in air and in the dielectric matrix using Poisson's equation. The electrostatic potential is applied to the tip and the Si-substrate backside is grounded. No charge (zero potential) is applied as boundary condition on the free boundaries of the simulation box. The electrostatic force F_e, at different lift positions, is obtained

<figure><img src="image_4.png" /><figcaption>Fig. 3. (a) Schematic representation of the FEM model of electrostatic interaction with a dielectric layer, (b) flowchart of the methodology to extract the relative dielectric permittivity map from EFM measurements and FEM modeling (h is the experimental lift-height for the EFM measurements) and (c) schematic representation of the FEM model of AgNPs-based NCs (total thickness d<sub>tot</sub>).</figcaption></figure>
after integration of the electric field $E(r, z)$ over the AFM tip surface (Γ) according to the equation:

$$F_e = \iint_{\Gamma} \frac{\epsilon_0 \epsilon_r}{2} |E|^2 dS, \qquad (3)$$

where $\epsilon_0$ is the vacuum dielectric permittivity. It allowed to determine $d^2C/dz^2$ and thus the $a_{\Delta f}$ (equation 2). The relative dielectric permittivity map is then extracted for the corresponding values of the measured frequency shift parameter.

Figure 3b represents the flowchart of different steps in obtaining the $\epsilon_r$-map through combination of the developed FEM model and the EFM measurements. The frequency shift parameter $a_{\Delta f}$ is computed for relative dielectric permittivity $\epsilon_r$ ranging from 1 to 10 and an interpolation function $a_{\Delta f} = f(\epsilon_r)$ is created. Resonance frequency shift maps $\Delta f_0(V_i)$ corresponding to matrices with resolution of 384 × 192 points are recorded experimentally, and equation (1) is applied at each point to obtain the frequency shift parameter $a_{\Delta f}$ map. After that, the theoretical relationship $a_{\Delta f} = f(\epsilon_r)$, provided by the FEM modeling, is used to compute the effective relative dielectric permittivity at each point in order to reconstruct the map. This approach was first tested on the bare $SiO_2$ sample and then applied to the AgNPs-based NCs.

### D. Finite Element Modeling of the dielectric structure: a 2D-network of AgNPs embedded in $SiO_2$ matrix

To get inside the impact of nanostructuration imposed by the AgNPs on the relative dielectric permittivity a nanostructure close to the experimental one is modeled (Figure 3c) by FEM. In this configuration the relative dielectric permittivity of $SiO_2$ and Si-parts are taken as 3.9 and 11.4, respectively. The total amount of Ag is considered in the model via the geometrical parameters of the AgNPs. The AgNPs are modelled by metallic spheres periodically distributed in a plane whose size ($d_{AgNPs}$), interparticle distance ($d_{in}$) and cover layer thickness ($d_c$) i.e., the distance from the surface at which the 2D-network of AgNPs is embedded into the $SiO_2$ matrix, are the varying parameters. The surface of AgNPs is considered at floating potential and free of oxidation. A surface waviness due to closely

embedded AgNPs is imposed in the 2D-model. The electric field distribution $E(r, z)$, the electrostatic force $F_e$ and the frequency shift parameter $a_{\Delta f}$ are obtained as previously described (equations 2 and 3).

## III. RESULTS

### A. Structural and morphological properties of the studied AgNPs-based nanocomposites

The plasma synthesized AgNPs-based NCs were structurally studied prior to their electrical characterization. A large number of samples, as summarized in Table I, with gradual change in both, the nanostructure and the AgNPs characteristics were selected for the study on the relative dielectric permittivity mapping: a bare $SiO_2$ plasma layer, a $SiO_2$ plasma layer with AgNPs anchored on its surface and AgNPs-based NCs for which the three main parameters of the 2D-network of AgNPs: 1) size of AgNPs, 2) interparticle distance and 3) distance to the $SiO_2$ surface, were varied. The total thicknesses of the samples and the corresponding to each sample plasma operating conditions are also reported in Table I.

The structural analysis of the plasma elaborated AgNPs-based NCs indicates a very good agreement with the targeted architecture of the nanocomposite dielectric layers (Figure 4). TEM observations in plane-view show a 2D-network of randomly distributed in a plane AgNPs (Figure 4a). The size and interparticle distance of AgNPs depend on the plasma operating conditions (Table I). The statistics on AgNPs in the network were made on more than 200 AgNPs for each sample. The general trend, already observed in our previous studies, is clearly confirmed here. Increasing the injected power in the plasma increases the self-bias voltage (in modulus) which in turn leads to the synthesis of larger in size AgNPs, for constant gas pressure and sputtering time. As reported in Table I the increase of AgNPs size is accompanied by a decrease of the interparticle distance. For all samples containing AgNPs the nanoparticle size distribution is Gaussian. A histogram, presented in insert of Fig. 4a gives an overview of the size distribution for the sample with the largest AgNPs. As shown in Table I, decreasing the size of AgNPs narrows the size distribution.

<table><caption>TABLE I
SUMMARY OF THE STUDIED SAMPLES. PLASMA OPERATING CONDITIONS. STRUCTURAL CHARACTERISTICS OF BARE $SiO_2$ AND AGNPS-BASED NCs: AGNPS SIZE ($d_{AgNPs}$), INTERPARTICLE DISTANCE ($d_{in}$), COVER LAYER THICKNESS ($d_c$) AND TOTAL THICKNESS ($d_{tot}$).</caption><thead><tr><th>Sample</th><th>Plasma power P (W)</th><th>Self-bias voltage V<sub>dc</sub> (V)</th><th>Description of the final structure</th><th>Size of AgNPs d<sub>AgNPs</sub> (nm)</th><th>Interparticle distance d<sub>in</sub> (nm)</th><th>Distance from the SiO<sub>2</sub> surface d<sub>c</sub> (nm)</th><th>Total thickness d<sub>tot</sub> (nm)</th></tr></thead><tbody><tr><td>S1</td><td>120</td><td>-840</td><td>bare SiO<sub>2</sub></td><td>-</td><td>-</td><td>-</td><td>150.6 ± 1.8</td></tr><tr><td>S2</td><td>40</td><td>-700</td><td>AgNPs on the surface of SiO<sub>2</sub></td><td>11.3 ± 2.4</td><td>6.9 ± 2.4</td><td>-</td><td>80.0 ± 1.0</td></tr><tr><td>S3</td><td>20</td><td>-540</td><td rowspan="7">AgNPs-based NCs</td><td>8.0 ± 1.8</td><td>7.4 ± 2.3</td><td>5.0 ± 0.1</td><td>136.7 ± 1.7</td></tr><tr><td>S4</td><td>40</td><td>-700</td><td>11.3 ± 2.4</td><td>6.9 ± 2.4</td><td>5.0 ± 1.5</td><td>97.0 ± 3.4</td></tr><tr><td>S5</td><td>40</td><td>-720</td><td>12.0 ± 2.6</td><td>6.8 ± 2.6</td><td>5.0 ± 0.1</td><td>130.2 ± 2.7</td></tr><tr><td>S6</td><td>80</td><td>-950</td><td>18.5 ± 4.8</td><td>5.6 ± 2.5</td><td>5.0 ± 0.1</td><td>135.0 ± 4.6</td></tr><tr><td>S7</td><td>80</td><td>-1000</td><td>19.6 ± 7.8</td><td>5.2 ± 2.8</td><td>7.0 ± 1.8</td><td>203.0 ± 9.6</td></tr><tr><td>S8</td><td>80</td><td>-1000</td><td>19.6 ± 7.8</td><td>5.2 ± 2.8</td><td>21.0 ± 2.0</td><td>193.0 ± 8.4</td></tr></tbody></table>
The small in size AgNPs (below 11 nm) are spherical in shape, while the larger AgNPs (above 15 nm) show an evolution trend towards a prolate spheroid shape, however keeping a low eccentricity level (ε_c < 0.4) which means that the major axis of the prolate spheroid remains less than 8% longer than its minor axis. Despite the AgNPs shape evolution such a low eccentricity level suggests that the AgNPs can be considered spherical ones for further analyses. Moreover, plasma synthesis of AgNPs prevents from oxidation since the nucleation and growth of the AgNPs happens in a well-controlled argon plasma characterized by a gas temperature of 700 - 800 K. Such environment does not allow formation of Ag₂O or AgO, given the thermal instability of these oxides and their complete calcination for gas temperatures higher than 673 K [36], [37]. The AgNPs are metallic and polycrystalline, and some of them exhibit complex structuring (twined or high-order mixing). The metallic nature of AgNPs was further confirmed by UV-visible reflectance spectra which exhibits a strong absorption at 415 nm [33]. The AgNPs are connected to the surrounding SiO₂ matrix *via* Ag-O-Si bridges [37]. Embedding the AgNPs in SiO₂ matrix protects them from oxidation and prevents from aggregation.

The TEM cross-section view images of the samples confirm the stratified structure (Figure 4b). A well-aligned in the plane 2D-network of AgNPs is embedded in a silica matrix close to its surface. The total thicknesses of the samples vary in the 80 – 200 nm range, depending on the structure constituents: base SiO₂ layer, size of AgNPs and thickness of the SiO₂ cover layer, with the latter defining the distance from the surface at which the 2D-network of AgNPs is embedded in the silica matrix (Table I). The optical properties of the plasma silica layers show high quality SiO₂, with refractive index of n = 1.45 and extinction coefficient

<figure><img src="image_5.png" /><figcaption>Fig. 4. Bright field (a) plane-view, and (b) cross-section TEM images of the AgNPs-based NCs (sample S6, $d_{AgNPs} = 18.5 \pm 4.8$ nm). Surface topography maps obtained with EFM in tapping mode of (c) plasma deposited SiO₂ (sample S1), (d) AgNPs anchored on the plasma SiO₂ surface (sample S2, $d_{AgNPs} = 11.3 \pm 2.4$ nm) and (e) AgNPs embedded in plasma SiO₂ (sample S8, $d_{AgNPs} = 19.6 \pm 7.8$ nm and $d_c = 21.0 \pm 2.0$ nm). Inserts: in (a) a histogram of the AgNPs, in (c), (d) and (e) topography profiles over a horizontal line.</figcaption></figure>

$k_{ext} < 0.02$ at $\lambda = 632.8$ nm, as extracted from spectroscopic ellipsometry measurements. As typical for plasma deposition processes, the SiO₂ cover layer is conformal to the shape of AgNPs. It envelops the AgNPs and spreads between them, finally imposing a slight waviness on the surface (Figure 4b). The surface waviness varies depending on the thickness of the SiO₂ cover layer and the size of the AgNPs, being more pronounced for large AgNPs or for thinner SiO₂ cover layers. It decreases considerably with increasing the distance at which the 2D-network of AgNPs is embedded in the silica layer.

To analyze the surface topography of different samples we have performed AFM measurements. Comparing to the nanostructures, a noticeable difference is observed for the surface topography of the homogeneous plasma SiO₂ layer (S1, Figure 4c). The silica layer surface is flat, exhibiting a very low arithmetic surface roughness $S_a = 0.2 \pm 0.1$ nm. The observed correspondence between the obtained arithmetic surface roughness and the topography profile recorded over one horizontal line (insert of Figure 4c) further supports the observation of flat surface of the plasma silica.

For the AgNPs anchored on the silica surface, the surface topography is entirely defined by the size and interparticle distance of the 2D-network of AgNPs. A regular structuration of the surface is observed in this case (S2, Figure 4d). The structuration amplitude and the lateral width of peaks and pits in the topography profile over a horizontal line are in the same range as the AgNPs size *i.e.*, approximately 11.0 nm for AgNPs with $d_{AgNPs} = 11.3$ nm (insert of Figure 4d). This surface structuration implies a variation of the total thickness of the AgNPs-based NCs with an increase of 12.5% above the AgNPs. The arithmetic surface roughness is found $S_a = 3.2 \pm 0.3$ nm which is 16 times higher than the obtained one for bare silica and reflects the surface waviness of the nanostructure.

Embedding the AgNPs in the silica layer leads to a decrease of the surface waviness. This is related to the smoothing effect induced by the conformal plasma deposition of the silica cover layer. As observed in the TEM study, the surface waviness is progressively reduced when the 2D-network of AgNPs is positioned in the silica layer further from the surface. The surface waviness recorded by the AFM measurements are similar to those observed in TEM in cross-section view. As previously, the surface topography presents a regular structuration. For the 2D-network of AgNPs embedded at 21.0 nm beneath the silica surface, the lateral width of the peaks of the topography profile over a horizontal line is in the same range as the AgNPs size *i.e.*, $d_{AgNPs} = 20$ nm (S8, Figure 4e). However, the amplitude of the topography profile peaks is not any more comparable to the AgNPs size. Its variation is comprised in the ¼ of the AgNPs size. This is a significant difference compared to the 2D-network of AgNPs anchored on the silica surface. It implies a variation of the total thickness of this AgNPs-based NCs of only 2.5%. The arithmetic surface roughness is reduced to $S_a = 2.0 \pm 0.2$ nm, but still remains
much higher (10 times) than the one measured for bare
plasma silica.

## B. Nanoscale investigation of the relative dielectric permittivity of AgNPs-based nanocomposites

The relative dielectric permittivity was studied at
nanoscale for all samples listed in Table I according to the
methodology described in Section 2.C. The nanoscale study

allows analyses of possible spatial variations of the dielectric permittivity in the sample induced by its heterogeneous structure, with the latter being intentional, like the case here by introducing metallic nanoparticles, or non-intentional, simply due to the elaboration process. Such information on the spatial modulation of the electrical properties of the structure is crucial on device level. The analysis needs to be

<figure><img src="image_6.png" /><figcaption>Fig. 5. Nanoscale relative dielectric permittivity of AgNPs-based NCs: (a) surface topography and (b) dielectric permittivity map for a 2D-network of AgNPs anchored on the surface of a plasma SiO₂ layer (sample S2, d<sub>AgNPs</sub> = 11.3 ± 2.4 nm); (c) surface topography and (d) dielectric permittivity map for a 2D-network of AgNPs embedded in a plasma SiO₂ layer close to the silica surface (sample S7, d<sub>AgNPs</sub> = 19.6 ± 7.8 nm and d<sub>c</sub> = 7.0 ± 1.8 nm); (e) surface topography and (f) dielectric permittivity map for a 2D-network of AgNPs embedded in a plasma SiO₂ layer away from the surface (sample S8, d<sub>AgNPs</sub> = 19.6 ± 7.8 nm and d<sub>c</sub> = 21.0 ± 2.0 nm); (g) surface topography and (h) dielectric permittivity map for a 2D-network of AgNPs embedded in a plasma SiO₂ layer close to the silica surface (sample S3, d<sub>AgNPs</sub> = 8.0 ± 1.6 nm and d<sub>c</sub> = 5.0 ± 0.1 nm); (i) surface topography and (j) dielectric permittivity map for a 2D-network of AgNPs embedded in a plasma SiO₂ layer close to the silica surface (sample S5, d<sub>AgNPs</sub> = 12.1 ± 2.6 nm and d<sub>c</sub> = 5.0 ± 0.1 nm); (k) surface topography and (l) dielectric permittivity map for a 2D-network of AgNPs embedded in a plasma SiO₂ layer close to the silica surface (sample S6, d<sub>AgNPs</sub> = 18.5 ± 4.8 nm and d<sub>c</sub> = 5.0 ± 0.1 nm); (m) EFM relative dielectric permittivity above (open symbols) and in-between (full symbols) the AgNPs as function of the cover layer thickness d<sub>c</sub> for different 2D-networks of AgNPs with different size groups; (n) comparison of the apparent relative dielectric permittivity measured by DS and EFM as function of the position of the 2D-networks of AgNPs beneath the silica surface. DS data are at a frequency of 1 kHz [26]. The black line is to guide the eye only.</figcaption></figure>
performed with nanoscale resolution on micrometer scale surface areas as in the current work.

Before going to the AgNPs-based NCs, the plasma deposited SiO₂ homogeneous layer (S1, Table I) was characterized. A relative dielectric permittivity of εᵣ = 3.7 ± 0.1 was obtained. The strong flatness of the sample surface (very low surface roughness) and the thickness homogeneity of the silica layer provided a unique value of the relative dielectric permittivity of this SiO₂-layer on the entire studied surface. The small dispersion, only 2.5%, around the mean value is related to the EFM measurement noise. The obtained εᵣ-value differs a bit, but is very close to the relative dielectric permittivity of a stoichiometric thermal SiO₂ layer which is 3.9 [11]. One should recall here that the studied SiO₂ layer is plasma deposited, which can explain the difference due to the presence of some structural disorder or to a very slight difference of the matrix density, both induced by the plasma deposition process. However, it is consistent with results obtained by dielectric spectroscopy (DS) on similar plasma deposited SiO₂ homogeneous layers [26].

The nanoscale dielectric response of the AgNPs-based NCs is very different (Figure 5). Let's consider first the 2D-network of AgNPs anchored on the silica layer surface. Comparing the surface topography (Figure 5a) and the extracted relative dielectric permittivity map (Figure 5b) one can notice that εᵣ is not constant over the studied surface. Indeed, εᵣ is lowered in the zones where the AgNPs are found (2.1 ± 0.2) and increased in the areas in-between the AgNPs (5.3 ± 0.2). Since the dielectric permittivity extraction is sensitive to the layer thickness [38], the observed variation here requires verification of the thickness modifications induced by the surface topography waviness. According to Figure 5a, the surface waviness implies a thickness increase of 12.5% above the AgNPs which in terms of relative dielectric permittivity corresponds to a decrease by 0.4, i.e., 10% compared to the εᵣ-value of silica. Thus, the thickness variation above the AgNPs cannot be the only reason for the obtained decrease of the relative dielectric permittivity by 1.6, when compared to the εᵣ-value obtained for silica (3.7 ± 0.1). It is even more appealing when looking on the increased εᵣ-value in the areas in-between the AgNPs, for which one naturally expects to find the silica relative dielectric permittivity or an εᵣ-value close to it. Accordingly, the εᵣ-map structuration is not related to the surface waviness only. Phenomena occurring at the nanoscale are also at play.

The same is observed for the AgNPs-based NCs with AgNPs embedded in the silica matrix at 7 nm from the surface. Comparison of the surface topography (Figure 5c) and relative dielectric permittivity (Figure 5d) maps demonstrates that εᵣ is lowered above the AgNPs (2.8 ± 0.2) and increased in-between the AgNPs (4.9 ± 0.2). However, the contrast between these two εᵣ-values is reduced. As previously, the existence of a contrast is not related to the surface waviness only. Indeed, a thickness variation of 5%, like the one characterizing this sample, can induce a relative dielectric permittivity modification only by 0.2, when

compared to the silica εᵣ-value. This low modification factor is insufficient to describe the observed difference here. In contrary, when the 2D-network of AgNPs is embedded at 21 nm from the surface, the AgNPs-based NCs exhibits a smooth relative dielectric permittivity map (Figure 5f) while the AgNPs are still observable on the topography map (Figure 5e). The relative dielectric permittivity varies insignificantly in this case, having a value of 3.7 ± 0.1 which is the same as for the homogeneous plasma silica sample.

Variation of the size of AgNPs, when the 2D-network of AgNPs is embedded at the same distance from the silica surface, does not bring additional complexity in the εᵣ-nanostructuration (Figure 5g-l). In confirms the already observed trends of variation of the relative dielectric permittivity of AgNPs-based NCs. Nevertheless, it shows that one can successfully modulate the contrast between the εᵣ-values above the AgNPs and in-between them in a quite large range. Such large εᵣ-window is a valuable property for capacitive crossbars.

Figure 5m summarizes all these findings about nanostructuration of the relative dielectric permittivity due to the presence of a 2D-network of AgNPs embedded in a silica matrix. The εᵣ-evolution above the AgNPs and in-between them is plotted as function of the distance from the silica surface *i.e.*, of the cover layer thickness d_c for various AgNPs-based NCs. These results clearly demonstrate that both the distance from the silica surface (the cover layer thickness) and the size of AgNPs impact the dielectric permittivity contrast. Indeed, the εᵣ-enhancement in-between the AgNPs is more significant, as well as the contrast of the εᵣ-values, when the AgNPs are positioned closer to the silica surface or when their size is larger for the same distance from the silica surface.

For comparison between the EFM and DS results, the average εᵣ-value was obtained after integration over the entire εᵣ-map. The resulting EFM apparent relative dielectric permittivity was compared to DS results for 2D-networks of AgNPs embedded at different distances from the silica surface (Figure 5n). The black line on Figure 5n is to guide the eye only. Both methods provide very similar results which definitely validates the local probing methodology of the relative dielectric permittivity and the mapping technique presented in this work. A strong advantage of the EFM method, when compared to the DS one, is to provide local information about the εᵣ-nanostructuration due to the presence of a 2D-network of AgNPs embedded in the silica layer. Moreover, since the EFM tip acts as an electrode, this technique permits contactless measurements of the εᵣ-map and appears promising way to investigate dielectric properties of soft materials (2D-materials, biological materials as cells, proteins...) and single nanoobjects immobilized on dielectric surfaces.

Whatever the methodology, Fig. 5n demonstrates that the apparent relative dielectric permittivity decreases with the cover layer thickness d_c and tends to the silica permittivity for d_c higher that 20 nm. Similar trend was reported in the
<figure><img src="image_7.png" /><figcaption>Fig. 6. Influence of the AgNPs-based NCs geometrical parameters on their dielectric response. Distribution of the electric field norm for AgNPs-based NCs ($d_{AgNPs} = 10$ nm, $d_{in} = 5$ nm and $d_{tot} = 200$ nm): (a) for $d_c = 0$ nm, i.e., no silica cover layer and (b) for $d_c = 2.5$ nm, (c) Evolution of electric field on the sample surface in the area above the AgNPs and in-between them as function of the distance of the 2D-network of AgNPs to the surface $d_c$ ($d_{AgNPs} = 10$ nm, $d_{in} = 5$ nm, $d_{tot} = 200$ nm and applied voltage to the tip $V_i = 10$ V). Evolution of the structuration factor $S_F$ on the sample surface in the area above the AgNPs as function of the distance to the silica surface $d_c$ on (d) and as function of the ratio $d_{in}/d_{AgNPs}$, for $d_c = 0$ nm on (e).</figcaption></figure>

literature on nanocomposite pellets processed by pressing of core-shell particles (AgNPs within silica shell) even though the structural properties are different (porous material with AgNPs dispersed in the entire volume) [39]. Although this trend was reproduced by the effective medium approximation applied to the integral measurements, the approach failed to explain the underlying physical phenomena occurring at nanoparticles scale. Consequently, to understand the impact of AgNPs (size, interparticle distance and cover layer thickness) on the relative dielectric permittivity a finite element model at AgNPs scale is needed.

## IV. DISCUSSION

### A. Phenomena at the origin of nanostructuration of the relative dielectric permittivity of AgNPs-based nanocomposites

The dielectric response, either global or local, of such complex materials as the considered here AgNPs-based NCs is always a combination of different factors, mainly related to the intrinsic properties of each constituent of the nanocomposites and to the geometric parameters of the nanostructuration. To get inside the contribution of the nanocomposite geometrical parameters on the dielectric response of the AgNPs-based NCs, we have employed the

complex finite element model that takes into account the nanoscale structuration (Section II.D, Figure 3c) to compute the frequency shift parameter $a_{Af}$ (equation 2) for several physical situations. As for the experimentally obtained ones, the AgNPs are considered in the model spherical in shape, with a diameter $d_{AgNPs}$ and interparticle distance $d_{in}$. A lift-height of 20 nm has been used in all of the simulations.

Since the numerical model is based on solution of Poisson's equation, the electric field distribution is one of its outcomes. Figure 6a displays the 2D-axisymmetric distribution of the electric field norm for a 2D-network of AgNPs of size $d_{AgNPs} = 10$ nm and interparticle distance $d_{in} = 5$ nm anchored on the surface of a 200 nm-thick $SiO_2$ layer. The applied voltage to the tip is $V_i = 10$ V. According to the results two main conclusions can be drawn: The electric field is constant in the silica layer whereas it is strongly enhanced close to the AFM tip. A strong electric field enhancement is also observed in-between the AgNPs, even for those positioned far from the AFM tip (red arrows in Figure 6a).

The electric field distribution changes substantially for the same 2D-network of AgNPs ($d_{AgNPs} = 10$ nm, $d_{in} = 5$ nm and $d_{tot} = 200$ nm) but embedded in the silica matrix at a distance of $d_c = 2.5$ nm from the surface (Figure 6b). As previously the electric field is constant in the silica layer and enhanced
<table><caption>TABLE II
COMPARISON OF THE MEASURED AND THE COMPUTED BY FEM FREQUENCY SHIFT PARAMETER $a_{\Delta f}$ ABOVE THE AGNPS FOR DIFFERENT AGNPS-BASED NCs CONFIGURATIONS. EVALUATION OF THE RELATIVE ERROR $\Delta$ BETWEEN EXPERIMENT AND FEM.</caption><thead><tr><th rowspan="2">Total thickness d<sub>tot</sub></th><th rowspan="2">AgNPs characteristics</th><th rowspan="2">Distance from the surface d<sub>c</sub></th><th colspan="2">a<sub>Δf</sub> above AgNP</th><th rowspan="2">Relative error Δ</th></tr><tr><th>Experiment</th><th>FEM</th></tr></thead><tbody><tr><td rowspan="2">200 nm</td><td>d<sub>AgNP</sub> = 20.0 nm</td><td>7.0 nm</td><td>-1.46 Hz/V<sup>2</sup></td><td>-1.51 Hz/V<sup>2</sup></td><td>3.3%</td></tr><tr><td>d<sub>in</sub> = 5.0 nm</td><td>21.0 nm</td><td>-1.81 Hz/V<sup>2</sup></td><td>-1.83 Hz/V<sup>2</sup></td><td>1.1%</td></tr><tr><td>130 nm</td><td>d<sub>AgNP</sub> = 8.0 nm</td><td rowspan="2">5.0 nm</td><td rowspan="2">-3.20 Hz/V<sup>2</sup></td><td rowspan="2">-3.27 Hz/V<sup>2</sup></td><td rowspan="2">2.1%</td></tr><tr><td></td><td>d<sub>in</sub> = 7.5 nm</td></tr></tbody></table>

close to the AFM tip. A strong coupling is observed between the AFM tip and the AgNPs located under the tip. The electric field enhancement in-between the AgNPs is less pronounced. Figure 6c compares the evolution of the electric field above and in-between the AgNPs as function of the distance from the silica surface (the cover layer thickness). Opposite behavior is observed for the electric field above and in-between the AgNPs. Indeed, the electric field above the AgNPs increases when the AgNPs are embedded at larger distances from the silica surface and tends to a value obtained for the homogeneous silica layer in this tip-to-plane geometrical configuration. On the contrary, the electric field in-between the AgNPs decreases when the distance from the silica surface is increasing and tends to zero for distances of $d_c = 20$ nm and beyond.

Afterward, the model was used to compute the frequency shift parameter $a_{\Delta f}$ for AgNPs-based NCs with geometrical configurations similar to the experimental ones. The electric field distribution was used to compute the electrostatic force (equation 3) and to deduce the second derivative of the capacitance. This permits to determine the $a_{\Delta f}$ parameter (equation 2), which is related to the local relative dielectric permittivity of the material under the AFM tip. The results are reported in Table II and demonstrate a very good agreement between the experimental and theoretical values of the frequency shift parameter $a_{\Delta f}$. This is further confirmed by the fact that the relative error $\Delta$ remains less than 5%. The finite element model successfully reproduces the experimental physical situation. The results clearly confirm that the relative dielectric permittivity nanostructuration observed experimentally i.e., $\varepsilon_r$-value decreasing above the AgNPs and increasing in-between them, is mainly related to the modulation of the electric field.

For application purposes, it is important to predict the modulation of the relative dielectric permittivity in order to tune it at a target value i.e., low/high dielectric permittivity. The impact of the AgNPs-based NCs geometrical parameters on the $\varepsilon_r$-value were investigated via a factor $S_F$ that defines the degree of nanostructuration of the dielectric:

$$S_F = \frac{a_{\Delta f} (\text{above NPs})}{a_{\Delta f} (\text{matrix})}, \quad (4)$$

with $a_{\Delta f}$ (above NPs) corresponding to the frequency shift parameter $a_{\Delta f}$ computed in the areas above the AgNPs and $a_{\Delta f}$ (matrix) is the frequency shift parameter related to a homogeneous silica matrix without AgNPs. As the $a_{\Delta f}$

increases monotonously with the relative dielectric permittivity (equation 2), a $S_F \to 1$ implies that the $\varepsilon_r$ of the AgNPs-based NCs tends to the one characterizing the dielectric host matrix. If $S_F = 1$, there is no nanostructuration effect. When structuring the dielectric matrix, the $S_F$-factor decreases. A nanostructuration factor less than 1 ($S_F < 1$) means that the $\varepsilon_r$-value above the AgNPs is lower than the one corresponding to the dielectric host matrix. Such physical situation represents an increase of the AgNPs screening effect i.e., the electric field is decreasing above the nanoparticles.

Figure 6d represents a parametric study of the evolution of the structuration factor $S_F$ as function of the distance $d_c$ to the silica surface for 2D-networks of AgNPs with different AgNPs sizes and interparticle distances. For a fixed interparticle distance (here $d_{in} = 10$ nm), the AgNPs screening effect increases when the AgNPs size increases. Regardless the AgNPs size the dielectric response of the AgNPs-based NCs tends towards the silica one when the 2D-network of AgNPs is deeply embedded in the matrix. The distance from the silica surface required to minimize the AgNPs influence on the dielectric response of the AgNPs-based NCs increases with the AgNPs size from $d_c = 10$ nm for $d_{AgNPs} = 5$ nm to $d_c = 50$ nm for $d_{AgNPs} = 20$ nm. For a fixed AgNPs size, increasing the interparticle distance implies a decrease of the AgNPs influence on the relative dielectric permittivity. These results demonstrate a coupled influence of the nanoparticle size and distance between them. To evaluate this effect, the structuration factor $S_F$ was plotted as function of the ratio of interparticle distance to the AgNPs size, for a fixed distance of their position to the silica surface $d_c = 5.0$ nm (Figure 6e). When the ratio $d_{in}/d_{AgNPs}$ is higher than 1, the interparticle distance influence is weak and the $\varepsilon_r$-value is mainly determined by the AgNPs size. Moreover, larger nanoparticles entail more pronounced decrease of $\varepsilon_r$ above the AgNPs. On the contrary, when the ratio $d_{in}/d_{AgNPs}$ is lower than 1, the relative dielectric permittivity of AgNPs-

<table><caption>TABLE III
STRUCTURATION FACTOR $S_F$ COMPUTED FOR VARIOUS DIELECTRIC MATRICES ($d_{AgNPs} = 20$ nm, $d_{in} = 10$ nm, $d_c = 5$ nm AND $d_{tot} = 200$ nm).</caption><thead><tr><th></th><th>SiOC:H</th><th>SiO<sub>2</sub></th><th>Si<sub>3</sub>N<sub>4</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th></tr></thead><tbody><tr><th>ε<sub>r</sub></th><td>3.0</td><td>3.7<sup>a</sup></td><td>7.5</td><td>9.0</td></tr><tr><th>S<sub>F</sub></th><td>0.45</td><td>0.56</td><td>0.78</td><td>0.83</td></tr></tbody></table>

<footnote>a Value obtained in this work for a plasma synthesized SiO<sub>2</sub>.</footnote>
based NCs is determined by both the AgNPs size and the interparticle distance.

## B. Role of the dielectric host matrix in AgNPs-based nanocomposites on the nanostructuration of the relative dielectric permittivity

The global dielectric response of the AgNPs-based NCs is strongly affected by four main features: AgNPs size, shape, interparticle distance and surrounding medium of the metallic nanoparticles. Thus, variations of the composition of the host dielectric matrix brings additional degree of adjustment. To account for this influence, the structuration factor was computed for a 2D-network of AgNPs with $d_{AgNPs} = 20$ nm and $d_{in} = 10$ nm, embedded at $d_c = 5$ nm from the dielectric surface, the total thickness being constant $d_{tot} = 200$ nm, for dielectric host matrices with different relative dielectric permittivity [11]. The results emphasize that the modulation of the apparent relative dielectric permittivity is more pronounced for AgNPs-based NCs with dielectric host matrices of low relative dielectric permittivity (Table III).

## C. Implication of the dielectric response of AgNPs-based nanocomposites for in-memory computing

As described in the introduction, development of in-memory computing using emerging NVMs is in demand for materials with tunable dielectric properties and switchable electrical state as conduction state. We have shown above that in order to obtain a strong spatial variation of the relative dielectric permittivity, the 2D-network of AgNPs needs to be embedded close to the surface and to be made of large and closely situated AgNPs i.e., with a ratio $d_{in}/d_{AgNPs}$ ideally lower than 1. The developed and applied here unconventional approach on mapping the $ε_r$-spatial variation is an important achievement for capacitive crossbars, for example, for which modulation of the dielectric permittivity of the material brings the required variations of capacitance states. The achieved in this work $ε_r$-window is 4. Such large

<figure><img src="image_8.png" /><figcaption>Fig. 7. Electric field distribution along the axis in tip-to-plane geometry for tip-electrodes with curvature radii of $R_t = 3.0$ nm and $R_t = 4.5$ nm. Insert: 2D-representation of the area of electrical contact between an electrode and a AgNPs-based NCs (topography of sample S8, $d_{AgNPs} = 19.6 \pm 7.8$ nm, $d_{in} = 5.2 \pm 2.8$ nm and $d_c = 21.0 \pm 2.0$ nm, Figure 4e), emphasizing two of the tip-electrodes.</figcaption></figure>

window has been reported for high-k dielectrics only [27]. However, the main issue of high-k dielectric materials is the important charge trap density which causes a reduced stability in the electric states. The resistive arrays can be impacted too, since $ε_r$-spatial variations, and particularly the dielectric loss part, provide valuable information on the effective electronic conductivity of non-filamentary RRAM.

The presented AgNPs-network configuration produces enhanced electric field in-between the AgNPs which induces an electrostatic coupling between nanoparticles under applied electric field. The process is well described by the electrostatic modeling presented in this work (Figure 6). The nanostructuration of the dielectric by 2D-networks of AgNPs, so designed, is surmised to express high plasticity in synaptic networks due to the extremely localized field effects brought by the surface topography of the device and the capability of AgNPs to act as artificial traps for charges when embedded in an insulating matrix [22]. Such localized effects can represent opportunities as well as threats for synaptic networks, both related to the performance and energy efficiency of the device. Due to the enhancement of the electric field in-between the AgNPs, non-linear effects, like tunneling and Poole-Frenkel, will be at play at low interparticle distances, thus representing ways to modulate lateral charge transport.

Surface waviness due to the conformal silica deposition on the 2D-networks of AgNPs constitutes another strong source of electric field distortion and non-linear behavior when an electrode is deposited over the structure surface to create the electrical contact and a voltage is applied to it. The main reason resides in the tip-electrodes, that will appear in the dips between the AgNPs, with dimensions depending on the AgNPs size, the interparticle distance and the depth at which the 2D-network of AgNPs is embedded in the silica matrix. These tip-electrodes may serve as protrusion bumps to induce conductive filaments, for example. Figure 7 presents the electric field enhancement along the axis of such tip-electrodes with curvature radius of $R_t = 3.0$ nm and $R_t = 4.5$ nm. 2D-representation of the electrical contact area between an electrode and a AgNPs-based NCs emphasizing two of the tip-electrodes is shown in the insert of Figure 7 for the topography of sample S8, $d_{AgNPs} = 19.6 \pm 7.8$ nm, $d_{in} = 5.2 \pm 2.8$ nm and $d_c = 21.0 \pm 2.0$ nm (Figure 4e), for which the nanostructuration of the relative dielectric permittivity of the nanocomposite is very small (Figure 5e and 5m).

Assimilating the tip-electrode to a parabolic curve of curvature radius $R_t$, the electric field distribution along the axis of this tip-to-plane geometrical configuration is in the form [40]:

$$E(z) = \frac{2V_g}{(R_t + 2z) \ln(2d_{tot}/R_t + 1)}, \quad (5)$$

where $V_g$ is the applied voltage, $R_t$ is the curvature radius of the tip-electrode, $d_{tot}$ is the tip-to-plane distance and $z$ is variable along the axis.
For a flat silica layer of thickness $d_{tot} = 150$ nm (sample S1, Table I) and under an applied voltage of $V_g = +5$ V, the electric field is homogeneous, with a strength of $3.3 \times 10^7$ V/m. If a tip-electrode with curvature radius of $R_t = 3.0$ nm is introduced, the electric field at the tip is amplified by a factor of 20 (up to $7.2 \times 10^8$ V/m) in respect to the homogeneous electric field value. For a tip-electrode with curvature radius of $R_t = 4.5$ nm the electric field amplification at the tip is a bit lower (up to $5.3 \times 10^8$ V/m) but a tip-electrode with curvature radius of $R_t = 1.5$ nm will give a higher amplification (up to $1.3 \times 10^9$ V/m). It is clear that at such high electric fields, approaching the breakdown strength of thin $SiO_2$-layers ($2.7 \times 10^9$ V/m) [41], charges can be injected into the dielectric and will lead to a strong modification of the behavior of the device. Moreover, the computation here is achieved for the surface topography of a 2D-network of AgNPs deeply embedded in the silica and without accounting for the presence of AgNPs in the structure or for possible coupling effects between the AgNPs in the network, or between the AgNPs and the electrode, as previously reported [22], which can introduce further distortion.

Besides modifying the electric field strength and its distribution, the AgNPs have the capability to store electrical charges and thus to impact the behavior of the device. Such capability of the metallic nanoparticles to store electrical charges –as nano-capacitors– has been used to constitute the memory effect in organic nano-circuits that mimic synapse activity [14]. The leaky behavior of the nanocomposites is used to provide a dynamic character to the memory. The leakage time is an important parameter of the device. Pre-charging of the AgNPs can be a way to tune the interparticle electric field. With an isolating matrix as $SiO_2$, the conductive character of the layer could be tuned by the charging state of the AgNPs. The memristive character of the device would originate from a capacitive memory. As large local fields can be at play, combined with charge tunneling between the AgNPs owing to short interparticle distances, and the possibility to tune the effective relative dielectric permittivity, a large range of dielectric time constants could be reached. The charge retention time of the AgNPs, as isolated (non-percolated) nanoparticles at floating potential in an insulating matrix, is a challenging question to address but represents a possibility of application of the current AgNPs-based NCs for IMC using emerging NVMs among many others to be conceived.

## V. CONCLUSION

In conclusion, we presented in this work a way for controlled modulation at nanoscale of the dielectric response of plasma synthesized AgNPs-based nanocomposites and a method for mapping their dielectric permittivity via Electrostatic Force Microscopy. The architecture of the studied samples comprises a 2D-network of AgNPs embedded in a silica matrix at a controlled nanometric distance from the surface. Both, the AgNPs and the silica matrix are synthesized in the same plasma reactor that

successfully combines sputtering of a metallic target to obtain the AgNPs and plasma polymerization to deposit the silica layers. Different configurations of the 2D-network of AgNPs are studied by varying the size of the AgNPs ($d_{AgNPs} = 8.0 – 20.0$ nm), the interparticle distance ($d_{in} = 5.0 – 8.0$ nm), and the depth at which the AgNPs are located ($d_c = 5.0 – 25.0$ nm) for total thicknesses of the structure in the range $d_{tot} = 80 – 200$ nm. Their structural characterization confirms the versatility of plasma-based synthesis of complex nanocomposites and the possibility of strict control over their nanostructuration.

A methodology based on coupling of EFM measurements with FEM-electrostatic modeling is developed to perform $\epsilon_r$-mapping of the structures with nanometer resolution. The $\epsilon_r$-maps and the corresponding surface topography maps are obtained on relatively large surfaces, approximately $0.16 \ \mu m^2$, which attests for the robustness of the proposed here method.

It is shown that by embedding the 2D-network of AgNPs close to the $SiO_2$-surface ($d_c < 10.0$ nm), the permittivity of the device can be locally modulated in a large range. The presence of AgNPs in the dielectric layer leads to a $\epsilon_r$-nanostructuration, with lower $\epsilon_r$-values above the AgNPs and higher ones in-between them, when compared to the $\epsilon_r$-value of homogeneous $SiO_2$. The obtained $\epsilon_r$-window is 4. The nanostructured dielectric response is related to modulation of the electric field inside these AgNPs-based nanocomposites. Proper selection of the geometrical parameters of the AgNPs-based NCs can open up operation $\epsilon_r$-windows, as large as twice the one of the host dielectric matrix, which is extremely advantageous for capacitive crossbars.

To account for the $\epsilon_r$-modulation at nanoscale a nanostructuration factor $S_F$ is introduced. It is upper limited by 1, which corresponds to the case when the nanostructuration of the dielectric has no influence on its global dielectric response. In case of nanostructuration, the relative dielectric permittivity of the nanocomposite is modulated at nanoscale and the modulation is more pronounced for AgNPs-based NCs with dielectric host matrices of low relative dielectric permittivity.

Additional localized effects brought by the surface waviness and the capability of AgNPs to act as artificial traps for charges are also discussed. They are expected to modify the electrical behaviour of the AgNPs-based NCs due to the enhancement of the electric field in-between the AgNPs and can lead to strong modification of the performance and energy efficiency of the device.

Further work will be directed to analyses of the electrical behaviour of these AgNPs-based NCs when integrated in device: energetics of injected charges and description of charge trapping and transport in the 2D-networks of AgNPs, as well as in assemblies of multiple stacks of nanoparticles.

## ACKNOWLEDGMENT

The authors acknowledge support from the Centre de microcaractérisation Raimond Castaing (UAR 3623) of
CNRS and University of Toulouse, and thank Dr. Alessandro Pugliara for the TEM observations.

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