Superior dielectric properties of epoxy-based photoresist thin film nanocomposites with carbon-coated Cu@C nanoparticles

In order to verify the structure of the carbon shell and its integrity during the deagglomeration step, Raman spectroscopy was performed on sono-mechanically dispersed as-received Cu@C nanoparticles. The damaging of this protective shell during the manufacturing process could lead to the oxidation of the metallic copper core that can worsen the dielectric properties of nanocomposites. It can be noted that the thin carbon shell may be deteriorated also by the power of the beam used. For this reason, different laser powers were used to investigate the carbon structure. Firstly, the raw nanoparticles were excited with a beam power of 0.2 mW at a wavelength of 532 nm. The result shown in figure 2(a) presents the characteristic peaks of CuO which can be seen at 290 cm⁻¹, 340 cm⁻¹ and 630 cm⁻¹ [23]. Furthermore, the specific peaks for the graphene-like carbon [24] located at 1587 cm⁻¹ (G band) and 2700 cm⁻¹ (2D band) are still visible, suggesting that the fragile carbon shell was partially destroyed due to the beam power. Thus, in order to avoid this damaging effect, the measurement was performed on another sample of the same composition at the same wavelength (532 nm) but at a lower laser power of 0.01 mW. In this case, Raman spectrum (figure 2(b)) does not reveal CuO peaks while the characteristic G band and 2D band are more intense. It can be concluded that the ultrasonicated as-received NPs exhibit no detectable oxidation and that the morphology of the carbon shell corresponds to a graphene-like structure. Despite the presence of a D band indicating the presence of defects inside the graphene crystalline structure, the carbon shell is efficient to protect the metal core from oxidation. Moreover, the widen of the 2D band and the ratio of ${I}_{2D}/{I}_{G}\ne 2$ specify that we do not have a monolayer of graphene.

Zoom In Zoom Out Reset image size

To reach a manufacturing processing level, achieving a homogeneous dispersion of nanoparticles along the whole film thickness is essential. To ensure this goal, cross-sectional SEM micrograph coupled with EDS elemental mapping were performed on previously dielectric characterized MIS devices and are shown in figure 3.

Zoom In Zoom Out Reset image size

Figure 3(a) presents a cross-sectional micrograph of the films, cut along the diameter of the circular electrodes. The images in figure 3 show a low surface roughness with a highly nanostructured nanoparticles distribution, with different NPs size and shape in the overall film thickness. Moreover, a thickness of 15 μm film was measured, agreeing with the profilometry technique. This further elemental characterization confirms the efficiency of the sono-dispersion process on the homogenisation of the functionalised nanoparticles in the polymeric host (figures 3(b) and (c)).

The dielectric behaviour of the (Cu@C)-PyrPS//SU8 (MIS) devices were characterized using a sinusoidal stimulation of ±3 V_AC between 10² Hz and 10⁶ Hz at room temperature. The frequency dependence of the characteristic dielectric features is shown in figure 4.

Zoom In Zoom Out Reset image size

The results have been averaged over 20 capacitors. Sampling on different locations of the deposited films on the same sample allowed to verify the distribution of Cu@C nanoparticles on it. No significant variation of the dielectric properties was detected confirming an equal distribution in the entire surface of the films. As frequently reported in literature, high-permittivity is often associated to high dielectric losses. Phase shift response was analysed to ensure the capacitive behaviour of formulated nanocomposites. Figure 4(a) shows no significant variation of the phase angle with the volume fraction, up to 2.4%vol. In details, the phase angle remains close to −90° (pure capacitive behaviour) in the whole frequency range Hence, in this condition, the device can be modelled as a CPE (Constant Phase Element) at low volume fraction (lesser than 2.4%vol) and a RC parallel circuit exhibiting a typical frequency dependence of phase shift at higher volume fraction [25]. Indeed, for the formulation at 3.0%vol of Cu@C the phase shift is close to −60° (mainly capacitive behaviour) at high frequencies ($f\,\gt$ 1 kHz) then abruptly rises close to 0° (resistive behaviour) at low frequency. As shown in figure 4(b), dielectric losses increase with volume fraction of Cu@C NPs. Nonetheless all the devices present losses inferior to the threshold value of 1 between 400 Hz and 10⁶ Hz. However (Cu@C)-PyrPS//SU8 3.0%v shows an increase of $tan\,\delta$ below 400 Hz with a maximum value of 4.30. This critical variation of losses is in agreement with the previously discussed phase shift frequency dependence. It can be attributed to the low inversion of electric field applied that facilitates charges mobility, thus, preventing the storage of charges.

The frequency dependence of AC conductivity is shown in figure 4(c). A linear response of AC conductivity was measured for all formulated nanocomposites except for the highest loaded composite which exhibits a constant value of AC conductivity at low frequency, typical of a resistive behaviour. Finally, it is shown in figure 4(d) an increment of the relative permittivity of the formulated nanocomposites as the volume fraction increases. The highest permittivity obtained at the reference frequency value of 5 kHz was measured for the sample at the highest concentration, with a permittivity value of 124. This value is one order of magnitude higher of pure SU8™ polymer. In table 1 below are reported the values of the previously discussed dielectric parameters at the reference frequency of 5 kHz.

This variation of permittivity could be explained by the Maxwell-Wagner-Sillars theory (MWS) [26, 27]. The MWS theory also known as interfacial polarization takes place when two phases present an ${\varepsilon }_{r}$ and σ different. Under the influence of an external electric field, electrical charges accumulate at the interface between the matrix and the fillers. In this study, the charges accumulate at the interface between the SU8™ and the functionalized (Cu@C)-PyrPS. Consequently, increasing the filling volume fraction of nanoparticles rise the quantity of charges inside the material leading to an enhancement of capacitance, and thus relative permittivity. However, this is only true before electrical percolation. Once electrical percolation is reached current can flow through the material and the capacitance drops while the losses rise drastically. The results are also supported by the percolation theory stating that permittivity and losses follow a power law with an exponential increase at the vicinity of the percolation threshold [6]. Indeed, as the number of nanoparticles in the matrix increases, the interparticular distance lowers easing conduction mechanisms. Considering the values presented in table 1 the variation of all four dielectric parameters suggests that none of the presented nanocomposites reached the percolation threshold. The large variation of permittivity between 2.4%vol and 3.0%vol on the contrary seems to indicate percolation threshold is not reached yet.

By Comparing the obtained experimental results with the literature, the capacitive nanocomposites produced does not exhibit giant permittivity in the proximity of percolation threshold. However, at the reference frequency of 5 kHz the dielectric losses $tan\,\delta$ is 0.65. This obtained value for the highest capacitive nanocomposite (3.0%vol) is not so low but still usable in practical applications. As a comparison, Wang et al [9] presented PDMS filled with carbon nanotube with ${\varepsilon }_{r}$ of 60 and $tan\,\delta$ of 10 (@ 10 kHz) for MWCNTs/PDMS 2%wt and Cao et al [8] showed a SiC-PVDF 20%wt nanocomposite with ${\varepsilon }_{r}$ of 200 and $tan\,\delta$ of 8 (@ 5 kHz). In consequence, our most charged formulation presents a direct improvement of nanocomposite thin film, as capacitor, with high permittivity and low losses.

The value of percolation threshold was estimated by using the generalized power laws of percolation as shown below in equations (1) and (2). Equation (1) details the variation before percolation threshold while equation (2) details the variation after percolation threshold:

$$\begin{eqnarray}\begin{array}{ccc}{\varepsilon }_{eff}={\varepsilon }_{m}{\left(\displaystyle \frac{{\varphi }_{C}-\varphi }{{\varphi }_{C}}\right)}^{-s} & {\sigma }_{eff}={\sigma }_{m}{\left(\displaystyle \frac{{\varphi }_{C}-\varphi }{{\varphi }_{C}}\right)}^{-t} & \varphi \lt {\varphi }_{C}\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}\begin{array}{ccc}{\varepsilon }_{eff}=\displaystyle \frac{1}{{\varepsilon }_{m}{(\varphi -{\varphi }_{C})}^{s}} & {\sigma }_{eff}={\sigma }_{NP}{\left(\displaystyle \frac{\varphi -{\varphi }_{C}}{1-{\varphi }_{C}}\right)}^{t} & \varphi \gt {\varphi }_{C}\end{array}\end{eqnarray} \tag{ 2 }$$

Where ${\varepsilon }_{eff}$ is the effective relative permittivity, ${\varepsilon }_{m}$ is the relative permittivity of the polymeric matrix, ${\sigma }_{eff}$ is the effective conductivity, ${\sigma }_{m}$ is the conductivity of the matrix, ${\sigma }_{NP}$ is the conductivity of a nanoparticle, $s$ and $t$ are the critical exponents for permittivity and conductivity respectively. In figure 5 is shown the obtained values at 5 kHz of AC conductivity and relative permittivity with the fit obtained with the percolation theory power laws.

Zoom In Zoom Out Reset image size

This model fits quite precisely the experimental obtained data and estimates the percolation threshold at the proximity of ${\varphi }_{C}\approx$ 3.2%vol with $s\,=$ 1.1 and $t\,=$ 3. The critical exponents are in agreement with what is reported in literature although these values slightly vary according to the specific conductivity of nanostructured system [28–30]. In agreement with the estimation of percolation threshold the highest loaded sample of 3.0%vol displays all the dielectric features of a classic behaviour of a near percolated system. That is why samples at higher volume fraction were not investigated in this study.

The dielectric responses of the formulated Cu@C based nanocomposites in response to an applied DC electric field obtained with AIXACCT TF2000E are reported on figure 6. In details, the maximum value of sustained DC electric field is represented for each nanocomposite. It is worthy to note that above these reported values, the conduction mechanisms of charges transport increase significantly turning the devices into highly leaky capacitors. As a matter of fact, above these values it is prevented to make measurements with this technique due to the abrupt increase of dissipative current.

Zoom In Zoom Out Reset image size

The obtained relative permittivity values obtained through C-V loop measurements are in accordance with the previously characterized ones obtained by dielectric spectroscopy (@ 5 kHz) as shown in figure 6(a). No variations of permittivity are visible on the range of electric field applied. DC voltage do not seem to have an impact on the polarisation of the material. However, the sustained DC voltage is dependent of the filling volume fraction. Particularly, the high loaded nanocomposite (Cu@C)-PyrPS//SU8 3.0%vol can stand an electric field of $\pm \,$6.01 kV cm⁻¹ while the (Cu@C)-PyrPS//SU8 0.8%vol can withstand an electric field of $\pm \,$33.88 kV cm⁻¹.

The effects of a DC bias electric field are highlighted in the evolution of dielectric losses as shown in figure 6(b). Indeed, for the formulation at 3.0%vol the dielectric losses response assumes a flat trend with a value of 0.68, in accordance to dielectric spectroscopy, at low applied DC electric field up to the threshold value of 3.51 kV cm⁻¹ where the dielectric losses suddenly increase leading to a leaky capacitor. This effect is present in all formulated nanocomposites with the DC electric field threshold value decreasing with the increase of volume filling fraction.

In order to evaluate the conduction mechanisms involved in this dramatically increase of dielectric losses under the application of an DC electric field, the charge transport regimes were investigated. Figure 7(a). shows the non-linear dependence of current density under DC applied electric field, following the same trend as dielectric losses.

Zoom In Zoom Out Reset image size

A greater level of understanding can be achieved through the representation of logarithm of current density over electric field as a function of the inverse of applied electric field [31, 32]. This representation (figure 7(b)) allows to distinguish a minimum value that correspond to a transition between two different conduction mechanisms. These phenomena are the Direct Tunnelling and Fowler-Nordheim Tunnelling conduction.

The conduction mechanisms which takes place in the material are dependant of the nanostructured system. In details, the mobility of charges that flow through the nanofillers is function of the distance between them and thus depending on their distribution and quantity. Indeed, at low applied DC electric field the energy given to the charges is enough to go through small energy barrier. As a result, the displacement of charges will only be on close fillers (Direct Tunnelling).

However, above the threshold E_Trans determined by the inflection of the curves as shown in figure 7(b), charges which are intrinsic of the metallic nanofillers are emitted on long distances (Fowler-Nordheim Tunnelling) brutally increasing the current density of the nanocomposites. Thus, with the increase of volume filling fraction the energy barrier length through the nanofillers decrease with the occurrence of the Fowler-Nordheim tunnelling at lower applied DC electric field. The obtained E_Trans values determined for each nanocomposite is summarized in table 2.