# Epoxy/Silicone Blend Loaded with N-Doped CNT Composites: Study on the Optoelectronic Properties

Authors: Younes Ziat; Hamza Belkhanchi; Maryama Hammi; Ousama Ifguis
Journal: International Journal of Photoenergy
 (2021)

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## Abstract

Thin films of epoxy/silicone loaded with N-CNT were prepared by a method of sol-gel and deposited on ITO glass substrates at room temperature. The properties of the loaded monolayer samples (0.00, 0.07, 0.1, and 0.2 wt% N-CNTs) were analyzed by UV-visible spectroscopy. The transmittance for the unloaded thin films is 88%, and an average transmittance for the loaded thin film is about 42 to 67% in the visible range. The optical properties were studied from UV-visible spectroscopy to examine the transmission spectrum, optical gap, Tauc verified optical gap, and Urbach energy, based on the envelope method proposed by Swanepoel (1983). The results indicate that the adjusted optical gap of the film has a direct optical transition with an optical gap of 3.61 eV for unloaded thin films and 3.55 to 3.19 eV for loaded thin films depending on the loading rate. The optical gap is appropriately adapted to the direct transition model proposed by Tauc et al. (1966); its value was 3.6 eV for unloaded thin films and from 3.38 to 3.1 eV for loaded thin films; then, we determined the Urbach energy which is inversely variable with the optical gap, where Urbach’s energy is 0.19 eV for the unloaded thin films and varies from 0.43 to 1.33 eV for the loaded thin films with increasing rate of N-CNTs. Finally, nanocomposite epoxy/silicone N-CNT films can be developed as electrically conductive materials with specific optical characteristics, giving the possibility to be used in electrooptical applications.


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## Body

## 1. Introduction

Photovoltaic solar energy is an electrical energy produced from solar radiation by photovoltaic solar cells [1]. This kind of energy is the smartest way to produce electricity, and it has many advantages, such as direct generation of electricity from sunlight [2, 3]. It is a renewable source and clean [4–11], as well as friendly to the environment [5, 8, 11–14]. Photovoltaic energy is useful in different applications and devices [15–21].The prices of the solar cells based on (Si) have declined so speedily that panel expenses now make up <30% of the costs of a fully installed “solar-electricity-system” [22]. Because of their fragility, Si thin sheets cannot be treated on their own, but they must be mechanically supported. The researchers proposed to scale thick substrates by adding different materials such as aluminum, silver, nickel, and epoxy [23–26]. They are generally composed of a mixture of inorganic particles embedded in a polymer matrix.In recent years, the research interest in the development of a new material of polymer-inorganic nanocomposites with improved properties has been very high [27–33], and most research has been directed towards the use of materials in the form of thin films. The nanocomposites allow improving mechanical, electrical, optical, optoelectronic, and magnetic properties. For this reason, many studies have shown that hybrid nanocomposites are used in optoelectronic or optical applications requiring high visible transparency and shielding against ultravisible transparency [34–40].Today, energetic deposition means are widely used for the manufacture of thin film optical components [41]. These processes allow the fabrication of thin film materials with excellent repeatability, whose optical properties are very close to those of the solid material, thus opening doors to higher performance treatments that are insensitive to the constraints of the external environment. This was only possible with the technology developments in thin film deposition using several physical deposition techniques such as reactive sputtering [42], electron beam evaporation [43], and arc deposition [44, 45]. In particular, the sol-gel method has emerged as one of the most promising processes, as it is economical and efficient in the production of thin films [46, 47] as well as transparent and homogeneous films which are suitable for a variety of substrates. In fact, many works are devoted to this method [48–51]. In this paper, we report a simple and economical method for elaborating thin films of epoxy/silicone blend loaded by nitrogen-doped carbon nanotubes (N-CNTs). The nanocomposites are thin films having interesting optical properties. These films may offer potential new opportunities for photovoltaic applications caused by their specific chemical and electrical properties [52–55].


## 2. Experimental Work

### 2.1. Material and Methods

The elaborated matrix contains epoxy which is a colorless viscous liquid of 99.9% purity, supplied along with the hardener from Toronto Research Chemicals and silicone gel from Keol having high purity level (>99%). The fillers are the nitrogen-doped carbon nanotubes (N-CNTs) which were prepared using physical vapor deposition according to explained protocol in our previous paper [50].Substrate cleaning is a very important step that takes place in a clean room, as this step determines the adhesion and homogeneity of the deposited layers. The substrates must be free of grease, dust, and scratches. The substrates chosen for our study are blades with Indium Tin Oxide (ITO). The procedure for cleaning the substrates is as follows:(1)
Brushing with detergent, rinsing with deionized water(2)
Ultrasonic cleaning for ten minutes in a beaker filled with detergent(3)
Rinse with deionized water(4)
Ultrasonic cleaning again, but this time in a beaker filled with deionized water, for seven minutes(5)
Steps 3 and 4 are performed three times(6)
Last rinsing with deionized water(7)
Dry at 150°C for 15 minutesFirst, epoxy and silicone were mixed in a 50 ml beaker with the weight percentage of epoxy which is always kept higher than that of silicone and after a strong stirring, the hardener is added to avoid anisotropy and in order to keep homogeneity. The neat matrix contains 75 wt% of epoxy, 10 wt% of silicone, and 15 wt% of hardeners. Afterward, the N-CNTs were added with weight percent (0.00, 0.07, 0.1, and 0.2% of N-CNTs) in order to obtain homogeneous nanocomposites with consideration that they are formulated using the same process.The resulting mixture was deposited on the ITO glass substrate at room temperature. The prepared films were thermally cured at 103 for 1 hour then at 115°C for 30 min in the oven to obtain the epoxy/silicone N-CNT films.


### 2.2. Technical Characterizations

After preparing the thin films of epoxy/silicone N-CNT, microstructural and optical characterizations were carried out, using, respectively, the scanning electron microscopy and UV–visible technique which is based on the property of material and its ability to absorb certain wavelengths of the UV-visible domain. This method determines the transmissionT (%) of a material for a given wavelength λ (nm) that has been judiciously chosen. The optical transmission spectrum for the elaborated thin films was registered using a UV–visible spectrophotometer (Jasco V-530) over the wavelength range of 300—800 nm. The microstructure of the processed composite thin films was examined through SEM micrographs which were picked up for epoxy/silicone blend loaded with 0.2 wt% N-CNTs using FEI Quanta FEG 450 scanning electron microscopy (SEM).


## 2.1. Material and Methods

The elaborated matrix contains epoxy which is a colorless viscous liquid of 99.9% purity, supplied along with the hardener from Toronto Research Chemicals and silicone gel from Keol having high purity level (>99%). The fillers are the nitrogen-doped carbon nanotubes (N-CNTs) which were prepared using physical vapor deposition according to explained protocol in our previous paper [50].Substrate cleaning is a very important step that takes place in a clean room, as this step determines the adhesion and homogeneity of the deposited layers. The substrates must be free of grease, dust, and scratches. The substrates chosen for our study are blades with Indium Tin Oxide (ITO). The procedure for cleaning the substrates is as follows:(1)
Brushing with detergent, rinsing with deionized water(2)
Ultrasonic cleaning for ten minutes in a beaker filled with detergent(3)
Rinse with deionized water(4)
Ultrasonic cleaning again, but this time in a beaker filled with deionized water, for seven minutes(5)
Steps 3 and 4 are performed three times(6)
Last rinsing with deionized water(7)
Dry at 150°C for 15 minutesFirst, epoxy and silicone were mixed in a 50 ml beaker with the weight percentage of epoxy which is always kept higher than that of silicone and after a strong stirring, the hardener is added to avoid anisotropy and in order to keep homogeneity. The neat matrix contains 75 wt% of epoxy, 10 wt% of silicone, and 15 wt% of hardeners. Afterward, the N-CNTs were added with weight percent (0.00, 0.07, 0.1, and 0.2% of N-CNTs) in order to obtain homogeneous nanocomposites with consideration that they are formulated using the same process.The resulting mixture was deposited on the ITO glass substrate at room temperature. The prepared films were thermally cured at 103 for 1 hour then at 115°C for 30 min in the oven to obtain the epoxy/silicone N-CNT films.


## 2.2. Technical Characterizations

After preparing the thin films of epoxy/silicone N-CNT, microstructural and optical characterizations were carried out, using, respectively, the scanning electron microscopy and UV–visible technique which is based on the property of material and its ability to absorb certain wavelengths of the UV-visible domain. This method determines the transmissionT (%) of a material for a given wavelength λ (nm) that has been judiciously chosen. The optical transmission spectrum for the elaborated thin films was registered using a UV–visible spectrophotometer (Jasco V-530) over the wavelength range of 300—800 nm. The microstructure of the processed composite thin films was examined through SEM micrographs which were picked up for epoxy/silicone blend loaded with 0.2 wt% N-CNTs using FEI Quanta FEG 450 scanning electron microscopy (SEM).


## 3. Results and Discussion

### 3.1. Optical Properties

Figure1 shows the transmittance (T) spectrum of the thin films of epoxy/silicone N-CNT as a function of wavelength at room temperature in the spectral range of 300—800 nm. The transmittance spectrum has a high transmittance of up to 88% in the visible range for neat epoxy/silicone blend, indicating a highly transparent material; it is pointed out that transmittance in the overall wavelength range is considerably reduced with the increased filler content ranging from 0.07 to 0.2 wt% N-CNT.Figure 1
Curves of epoxy/silicone film transmission as a function of wavelength for different N-CNT loading rates.Figure1 exhibits a sharp decrease in the optical transmittance around 360 nm; this conduct is observed in many compounds and composites [56, 57]. Also, the optical transmission, the optical band-gap values, and structural and morphological changes of thin films are related to annealing temperature [58] or lamp changing. The optical band-gap values could be varied employing different precursor ions as well as substrate types which will be helpful for a wide variety of optoelectronic applications [59, 60]This drastic reduction is caused by significant absorption increasing with the quantity of the N-CNT fillers; this effect is significant in the optimization of the fabrication of the optoelectronic devices. The spectrophotometer allows recording the optical transmission of the layers as a function of wavelength and allows determining the value of the energy of the optical gap (Eg) of the layer (characteristic of a semiconductor), the refractive index of the films, and their thicknesses. For this aim, we will use the following formulas given by the method of Swanepoel [61]. The thickness of the nanostructures is determined from the following equation:
(1)d=λ1λ22λ1n2−λ2n1,where 𝑛1 and 𝑛2 are the refractive indices at two adjacent maxima (or minima) at λ1 and λ2. The average values of thickness d of the studied thin films determined by this equation are about 700 nm.The refractive index in the spectral region of the high, low, and medium absorption zones can be calculated; it follows that the refractive index is given by the following expression:(2)n1=N1+N12−S21/21/2n2=N2+N22−S21/21/2.In addition, the Swanepoel coefficient (N) in the transparent spectral region can be calculated by the following expression:
(3)N1=2STmax1−TminTmax1×Tmin+S2+12,N2=2STmax2−TminTmax1×Tmin+S2+12,where S is the refractive index of the glass and Tmax and Tmin represent the maximum and minimum values for the transmission curve.The absorptionα of the epoxy/silicone N-CNT nanocomposite is linked to transmittance through Bouguer-Lambert-Beer relation [62]:
(4)T=exp−αd.If transmittanceT is expressed in %, the absorption coefficient is shown by
(5)α=1dln100T.From the transmittance spectra (T), we can calculate the optical gap value of semiconductors from the Tauc formula (Eg(eV)) defined by the following equation using [63–67]
(6)αhν=Bhν−Egn.The relation can be rewritten in a logarithmic form such as(7)lnαhν=lnB+nlnhν−Eg,where α is the absorption coefficient, ν is the absorption frequency, B is constant, h is Planck’s constant, and n is dependent on the type of optical transition. The constant n depends on the nature of the optical gap; it is 1/2 for a direct optical gap and 2 for an indirect optical gap.Note that the interband transitions are accompanied by a change of electronic dynamics. Because the laws of energy and momentum conservation must be satisfied, the indirect electronic band-to-band transitions are phonon-assisted, and phonons must be involved in the electronic interband transition to provide the necessary momentum. Their energetic contribution is negligible if, for instance, the exponent takes the value ofn=2 [68].To determine whether the electronic transition that has occurred in the samples studied is direct or indirect, the optical gapEg must first be determined using equation (6) to plot αhν versus hν; the value of the optical gap is obtained by extrapolating the linear part of the curve, at the intersection of this line with the x-axis given in Table 1; then, the photon energy lnhν−Eg is plotted versus lnαhν which has been fitted with equation (7) in the linear region of the curve, using the average-squares method, where Eg, n, and B are fitted parameters; this process can show that the type of optical transition of the pure epoxy/silicone mixture is direct with the power factor n=0.51, and the same result was obtained for the epoxy/silicone N-CNT w% loaded.Table 1
The optical parameters: optical gapEg, power factor (n), Tauc verified Eg, and Urbach energy Eu of the studied composite.
CompositeParameters obtained byαhν=Bhν−EgnTauc verifiedEg (eV)Urbach energyEU (eV)Eg (eV)Factor (n)Slope (eV·cm−1)1/nNeat epoxy/silicone blend3.610.514.201083.60.19Epoxy/silicone N-CNT 0.07 wt%3.550.503.181083.380.43Epoxy/silicone N-CNT 0.1 wt%3.420.543.201083.30.61Epoxy/silicone N-CNT 0.2 wt%3.190.512.981083.11.33To verify the validity of the method used, we plottedαhν2 versus hν as shown in Figure 2 according to the Tauc model [69], giving the value of the direct optical gap. The extrapolation of the linear part of the absorption edge αhν2 gives the band-gap energy. The use of the power factor n obtained gives a good agreement between the optical gap bands and the Tauc slopes; almost the same optical gap Eg is found (Table 1), so the correlation between experience and theory is compatible.Figure 2
Plot ofαhv2 versus photon energy hv, for “epoxy/silicone N-CNT @ wt%” (@=0.00, 0.07, 0.1, and 0.2).
(a)(b)(c)(d)Obviously, the optical gap obtained is high for neat epoxy (3.6 eV), because it is optically transparent, and this means that no absorption is possible in the visible; they cannot be excited without being loaded with another element to decreaseEg, so we load with N-CNT and we see that there is a diminution in Eg in 3.6 to 3.1 eV (Table 1); this decrease of the optical gap with the loading rate is essentially due to the distortions caused in the network following the introduction of impurity (loading) and the increase in the concentration of free electrons; this characteristic would seem to be related to the increase in the number of free carriers with increasing the concentration of nanocomposite loaded in 0.07, 0.1, and 0.2 wt% N-CNT (Table 1 and Figure 3).Figure 3
Variation of optical gap of epoxy/silicone nanocomposite films versus N-CNT wt% loaded.The system is progressively becoming more conducting with addition of N-CNT; this seems to change slightly the structure of the electronic bands of the neat epoxy. In addition, the variation of optical gap with increasing N-CNT loaded concentration can also be correlated with surface roughness and film density. When variations in interatomic distance, length, or angle of bonding are produced in the material, a so-called “disorder” occurs; in this case, the strip edges described in the case of crystalline networks and delimited by valence energyEv and conduction energy Ec can disappear (Figure 4); so-called localized states formed in band tails at the borders of the optical gap in the valence band and the conduction band are observed.Figure 4
Band structure of amorphous semiconductors.The forbidden gap is referred to as the pseudogap energy for amorphous semiconductors as in the case of our composites; we noteEg. The generation phenomena can only happen if the light energy is larger than the band-gap energy of a semiconductor. For a wide-band-gap semiconductor, this band-gap energy is correspondent to the visible or ultraviolet spectrum excitations. As a consequence, the increase of charge carriers’ concentrations in the conduction band may be slight, which maintains that such material type is quite an electrical insulator. The electrical conductivity of amorphous semiconductors can be tuned in several ways. The basic idea is to create free charge carriers (electrons or holes) in a wide-band-gap semiconductor through appropriate fillers. This can create extrinsic impurities in the amorphous insulating materials which play a critical role for improving their electrical conductivity. When the disorder becomes too great, with the appearance of dangling links or impurities in the material, one then recalls the notion of Urbach parameter EU that corresponds to the transition between the extended states of the valence band and the localized states [70]. This phenomenon is exemplified with the absorption coefficient (α) as a function of photon energy near the edge of the band, exhibiting an exponential tail as shown in Figure 5; according to Urbach’s law, the expression of the absorption coefficient is of the form [71]
(8)α=α0exphνEU,where h is Planck’s constant, α0 is a constant, ν is the frequency of absorption, and EU is Urbach energy. To determine the disorder (Urbach energy) of thin films, we plot the logarithm of α versus of hν:
(9)lnα=lnα0+hνEU.Figure 5
Determination of Urbach energyEU by the plot of lnα versus photon energy hv for “epoxy/silicone N-CNT @ wt %” (@=0.00, 0.07, 0.1, and 0.2).
(a)(b)(c)(d)It is shown that it is possible to obtain the information on the dynamics of the electronic excitations of condensed matter by Urbach’s rule. Thus, Urbach’s rule makes it fairly easy to find the degree of the location of the states in the network and to determine the effect of network disorder on the location of the excitement [72].Figure5 shows the plot of lnα versus energy hν for a series of thin films of neat epoxy (Figure 5(a)) and epoxy/silicone loaded at different concentrations (Figures 5(b)–5(d)). Therefore, Urbach energy is determined by the reciprocal slope of the adjusted experimental linear behavior; the results of the study are shown in Table 1. The evolution of the Urbach energy versus the wt% N-CNT loaded is presented in Figure 5; this figure shows that the Urbach energy values were higher in loaded epoxy/silicone than in the neat, and that the highest value was obtained in the most filled loaded epoxy/silicon.The increase in tail width can be explained by the creation of disorder and imperfections in the nanocomposite lattice by addition of N-CNT.The Urbach energy also depends on the optical energy bandEg. The Urbach energy increases from 0.19 to 1.33 eV while Eg decreases from 3.6 to 3.1 eV as the amount of N-CNT increases (Table 1 and Figure 6).Figure 6
Variation of optical gap and Urbach energy of epoxy/silicone composite films versus wt% N-CNT.The variation found inEU indicates that the N-CNT addition creates a certain disorder, which leads to the structural characterization of the deposits, and the defects are deduced from the Urbach energy exponential absorption tail caused by fluctuations within the matrix optical gap. Moreover, it can be seen that the increase in Urbach’s energy opposes the decreasing behavior of the optical gaps with increasing w% N-CNT as shown in Figure 6, so Urbach’s energy is consistent with the determined values of the optical gap energy. There is also a significant change in slope above the percolation threshold, in wt% 0.07 of epoxy/silicone composite film for optical gap and Urbach energy. Indeed, above the percolation threshold, the electron carrier concentration exceeds the density of the conduction band states, the composites become semiconducting, and their number of carriers increases significantly. Therefore, the optical gap must decrease significantly, and the results are in accordance with the theory of Burstein and Moss [73, 74].


### 3.2. Microstructural Insight

The cured composites exhibited a very dense and relatively smooth surface. The SEM photographs revealed that N-CNT particles were found to be uniformly dispersed throughout the epoxy/silicone blend matrix (Figure7). This result revealed that there is a good miscibility between the phases, in a good agreement with elsewhere findings [75]. These findings might have a positive impact on electrical conductivities of the studied thin films.Figure 7
SEM images of the surface of the thin film with 0.1 wt% N-CNT.


### 3.3. Electrical Properties of the Fabricated Thin Films

Conductivity is a particular concern for semiconductor materials. Measuring the conductivity of semiconductor films is not that easy as it seems because it depends on a series of inseparable factors, especially temperature. For Urbach energy and optical band gap, the entire curve shows a significant slope change at a specific threshold associated with the epoxy/silicone blend-based composite films. The decrease inEg and the increase in EU become faster above this threshold. In order to evaluate this behavior, it is more convenient to measure the relationship between the DC and the change in filler load conductivity at ambient temperature. DC conductivity is based on resistivity measurement. The two-point probe method [76] was used to measure resistivity (it is expressed in Ω·cm) at room temperature (RT). Note that resistivity represents its ability to stop the flow of current. The resistivity measurement at ambient temperature is performed by plotting the current-voltage characteristics: I=fV.TheI=fV curves are exploited to extract the electrical resistivity. We have measured the electrical resistivity of the studied samples. Then, sheet resistance can be effectively performed utilizing the following equation [77]:
(10)RSh=R·WL.Also,R=ρL/A=ρL/d·W=ρ/d×L/W in which
(11)RS=ρd,where ρ is the resistivity (Ω·cm), RSis electrical sheet resistance (Ω), W is the width (cm), d is the thickness (cm) which can be determined with optical measurements, and Lpresents the length (cm), given that the conductivity is given byσ=1/ρin (Ω·cm)-1. The curve of DC conductivity behavior versus filler concentrations is represented in the inset of Figure 8.Figure 8
Electrical conductivity of thin films (epoxy/silicone N-CNT wt%) versus conducting filler concentrations.As indicated in Figure8, it is worthy to take note that electrical conductivity of unloaded film is about 10-8 (Ω·cm)-1. It is nonlinearly improved when N-CNT filler content is raised. The fillers give rise then to the electrical conductivity.


### 3.4. Evaluation of Thin Film Performance through the Calculation of Figure of Merit

The optical and electrical properties of the film are very important properties for all known transparent conductive oxide (TCO) applications. Ideally, a good TCO is identified by the optical transmission coefficient and high electrical conductivity. Therefore, when both light transmission and electrical conductivity are important, the material is considered high performance. These two parameters are inversely proportional and are related by a single factor called the figure of merit (FOM). This later allows reasonable comparisons of film properties and allows estimation of their optoelectronic properties [78]. The films represent a compromise between conductivity and light transmission. The decrease in resistivity involves an increase in the carrier concentration or its mobility. Increasing the number of carriers leads to an increase in absorption. In the present paper, the FOM of the studied films can be evaluated, using the following equation [79]:
(12)1ρ.α=σα,where
(13)FOM=σα=−1RSh·lnT+R,where σ is the electric conductivity (Ω-1), α is the absorption coefficient (cm-1), RSh is the surface resistance (Ω/sq), T is the total transmission (%), and R is the total reflection (%). Here, the best FOM is related to good optical transmission and electrical conductivity. It has been shown that useful films must have a FOM greater than or equal to 7 [80, 81]. Therefore, considering expression (13), the variation of the FOM value of the studied film with the filler concentration is gathered in Table 2. We noticed that the figure of merit was improved by increasing the load concentration.Table 2
Variation of optical figure of merit versus conducting filler concentrations.
MaterialSurface resistance (Ω/cm2)Visible absorption coefficientα (cm-1)Figure of merit (Ω-1 cm)Neat epoxy/silicone blend2000.200.02Epoxy/silicone N-CNT 0.07 wt%30.123Epoxy/silicone N-CNT 0.1 wt%3.80.055Epoxy/silicone N-CNT 0.2 wt%50.037


## 3.1. Optical Properties

Figure1 shows the transmittance (T) spectrum of the thin films of epoxy/silicone N-CNT as a function of wavelength at room temperature in the spectral range of 300—800 nm. The transmittance spectrum has a high transmittance of up to 88% in the visible range for neat epoxy/silicone blend, indicating a highly transparent material; it is pointed out that transmittance in the overall wavelength range is considerably reduced with the increased filler content ranging from 0.07 to 0.2 wt% N-CNT.Figure 1
Curves of epoxy/silicone film transmission as a function of wavelength for different N-CNT loading rates.Figure1 exhibits a sharp decrease in the optical transmittance around 360 nm; this conduct is observed in many compounds and composites [56, 57]. Also, the optical transmission, the optical band-gap values, and structural and morphological changes of thin films are related to annealing temperature [58] or lamp changing. The optical band-gap values could be varied employing different precursor ions as well as substrate types which will be helpful for a wide variety of optoelectronic applications [59, 60]This drastic reduction is caused by significant absorption increasing with the quantity of the N-CNT fillers; this effect is significant in the optimization of the fabrication of the optoelectronic devices. The spectrophotometer allows recording the optical transmission of the layers as a function of wavelength and allows determining the value of the energy of the optical gap (Eg) of the layer (characteristic of a semiconductor), the refractive index of the films, and their thicknesses. For this aim, we will use the following formulas given by the method of Swanepoel [61]. The thickness of the nanostructures is determined from the following equation:
(1)d=λ1λ22λ1n2−λ2n1,where 𝑛1 and 𝑛2 are the refractive indices at two adjacent maxima (or minima) at λ1 and λ2. The average values of thickness d of the studied thin films determined by this equation are about 700 nm.The refractive index in the spectral region of the high, low, and medium absorption zones can be calculated; it follows that the refractive index is given by the following expression:(2)n1=N1+N12−S21/21/2n2=N2+N22−S21/21/2.In addition, the Swanepoel coefficient (N) in the transparent spectral region can be calculated by the following expression:
(3)N1=2STmax1−TminTmax1×Tmin+S2+12,N2=2STmax2−TminTmax1×Tmin+S2+12,where S is the refractive index of the glass and Tmax and Tmin represent the maximum and minimum values for the transmission curve.The absorptionα of the epoxy/silicone N-CNT nanocomposite is linked to transmittance through Bouguer-Lambert-Beer relation [62]:
(4)T=exp−αd.If transmittanceT is expressed in %, the absorption coefficient is shown by
(5)α=1dln100T.From the transmittance spectra (T), we can calculate the optical gap value of semiconductors from the Tauc formula (Eg(eV)) defined by the following equation using [63–67]
(6)αhν=Bhν−Egn.The relation can be rewritten in a logarithmic form such as(7)lnαhν=lnB+nlnhν−Eg,where α is the absorption coefficient, ν is the absorption frequency, B is constant, h is Planck’s constant, and n is dependent on the type of optical transition. The constant n depends on the nature of the optical gap; it is 1/2 for a direct optical gap and 2 for an indirect optical gap.Note that the interband transitions are accompanied by a change of electronic dynamics. Because the laws of energy and momentum conservation must be satisfied, the indirect electronic band-to-band transitions are phonon-assisted, and phonons must be involved in the electronic interband transition to provide the necessary momentum. Their energetic contribution is negligible if, for instance, the exponent takes the value ofn=2 [68].To determine whether the electronic transition that has occurred in the samples studied is direct or indirect, the optical gapEg must first be determined using equation (6) to plot αhν versus hν; the value of the optical gap is obtained by extrapolating the linear part of the curve, at the intersection of this line with the x-axis given in Table 1; then, the photon energy lnhν−Eg is plotted versus lnαhν which has been fitted with equation (7) in the linear region of the curve, using the average-squares method, where Eg, n, and B are fitted parameters; this process can show that the type of optical transition of the pure epoxy/silicone mixture is direct with the power factor n=0.51, and the same result was obtained for the epoxy/silicone N-CNT w% loaded.Table 1
The optical parameters: optical gapEg, power factor (n), Tauc verified Eg, and Urbach energy Eu of the studied composite.
CompositeParameters obtained byαhν=Bhν−EgnTauc verifiedEg (eV)Urbach energyEU (eV)Eg (eV)Factor (n)Slope (eV·cm−1)1/nNeat epoxy/silicone blend3.610.514.201083.60.19Epoxy/silicone N-CNT 0.07 wt%3.550.503.181083.380.43Epoxy/silicone N-CNT 0.1 wt%3.420.543.201083.30.61Epoxy/silicone N-CNT 0.2 wt%3.190.512.981083.11.33To verify the validity of the method used, we plottedαhν2 versus hν as shown in Figure 2 according to the Tauc model [69], giving the value of the direct optical gap. The extrapolation of the linear part of the absorption edge αhν2 gives the band-gap energy. The use of the power factor n obtained gives a good agreement between the optical gap bands and the Tauc slopes; almost the same optical gap Eg is found (Table 1), so the correlation between experience and theory is compatible.Figure 2
Plot ofαhv2 versus photon energy hv, for “epoxy/silicone N-CNT @ wt%” (@=0.00, 0.07, 0.1, and 0.2).
(a)(b)(c)(d)Obviously, the optical gap obtained is high for neat epoxy (3.6 eV), because it is optically transparent, and this means that no absorption is possible in the visible; they cannot be excited without being loaded with another element to decreaseEg, so we load with N-CNT and we see that there is a diminution in Eg in 3.6 to 3.1 eV (Table 1); this decrease of the optical gap with the loading rate is essentially due to the distortions caused in the network following the introduction of impurity (loading) and the increase in the concentration of free electrons; this characteristic would seem to be related to the increase in the number of free carriers with increasing the concentration of nanocomposite loaded in 0.07, 0.1, and 0.2 wt% N-CNT (Table 1 and Figure 3).Figure 3
Variation of optical gap of epoxy/silicone nanocomposite films versus N-CNT wt% loaded.The system is progressively becoming more conducting with addition of N-CNT; this seems to change slightly the structure of the electronic bands of the neat epoxy. In addition, the variation of optical gap with increasing N-CNT loaded concentration can also be correlated with surface roughness and film density. When variations in interatomic distance, length, or angle of bonding are produced in the material, a so-called “disorder” occurs; in this case, the strip edges described in the case of crystalline networks and delimited by valence energyEv and conduction energy Ec can disappear (Figure 4); so-called localized states formed in band tails at the borders of the optical gap in the valence band and the conduction band are observed.Figure 4
Band structure of amorphous semiconductors.The forbidden gap is referred to as the pseudogap energy for amorphous semiconductors as in the case of our composites; we noteEg. The generation phenomena can only happen if the light energy is larger than the band-gap energy of a semiconductor. For a wide-band-gap semiconductor, this band-gap energy is correspondent to the visible or ultraviolet spectrum excitations. As a consequence, the increase of charge carriers’ concentrations in the conduction band may be slight, which maintains that such material type is quite an electrical insulator. The electrical conductivity of amorphous semiconductors can be tuned in several ways. The basic idea is to create free charge carriers (electrons or holes) in a wide-band-gap semiconductor through appropriate fillers. This can create extrinsic impurities in the amorphous insulating materials which play a critical role for improving their electrical conductivity. When the disorder becomes too great, with the appearance of dangling links or impurities in the material, one then recalls the notion of Urbach parameter EU that corresponds to the transition between the extended states of the valence band and the localized states [70]. This phenomenon is exemplified with the absorption coefficient (α) as a function of photon energy near the edge of the band, exhibiting an exponential tail as shown in Figure 5; according to Urbach’s law, the expression of the absorption coefficient is of the form [71]
(8)α=α0exphνEU,where h is Planck’s constant, α0 is a constant, ν is the frequency of absorption, and EU is Urbach energy. To determine the disorder (Urbach energy) of thin films, we plot the logarithm of α versus of hν:
(9)lnα=lnα0+hνEU.Figure 5
Determination of Urbach energyEU by the plot of lnα versus photon energy hv for “epoxy/silicone N-CNT @ wt %” (@=0.00, 0.07, 0.1, and 0.2).
(a)(b)(c)(d)It is shown that it is possible to obtain the information on the dynamics of the electronic excitations of condensed matter by Urbach’s rule. Thus, Urbach’s rule makes it fairly easy to find the degree of the location of the states in the network and to determine the effect of network disorder on the location of the excitement [72].Figure5 shows the plot of lnα versus energy hν for a series of thin films of neat epoxy (Figure 5(a)) and epoxy/silicone loaded at different concentrations (Figures 5(b)–5(d)). Therefore, Urbach energy is determined by the reciprocal slope of the adjusted experimental linear behavior; the results of the study are shown in Table 1. The evolution of the Urbach energy versus the wt% N-CNT loaded is presented in Figure 5; this figure shows that the Urbach energy values were higher in loaded epoxy/silicone than in the neat, and that the highest value was obtained in the most filled loaded epoxy/silicon.The increase in tail width can be explained by the creation of disorder and imperfections in the nanocomposite lattice by addition of N-CNT.The Urbach energy also depends on the optical energy bandEg. The Urbach energy increases from 0.19 to 1.33 eV while Eg decreases from 3.6 to 3.1 eV as the amount of N-CNT increases (Table 1 and Figure 6).Figure 6
Variation of optical gap and Urbach energy of epoxy/silicone composite films versus wt% N-CNT.The variation found inEU indicates that the N-CNT addition creates a certain disorder, which leads to the structural characterization of the deposits, and the defects are deduced from the Urbach energy exponential absorption tail caused by fluctuations within the matrix optical gap. Moreover, it can be seen that the increase in Urbach’s energy opposes the decreasing behavior of the optical gaps with increasing w% N-CNT as shown in Figure 6, so Urbach’s energy is consistent with the determined values of the optical gap energy. There is also a significant change in slope above the percolation threshold, in wt% 0.07 of epoxy/silicone composite film for optical gap and Urbach energy. Indeed, above the percolation threshold, the electron carrier concentration exceeds the density of the conduction band states, the composites become semiconducting, and their number of carriers increases significantly. Therefore, the optical gap must decrease significantly, and the results are in accordance with the theory of Burstein and Moss [73, 74].


## 3.2. Microstructural Insight

The cured composites exhibited a very dense and relatively smooth surface. The SEM photographs revealed that N-CNT particles were found to be uniformly dispersed throughout the epoxy/silicone blend matrix (Figure7). This result revealed that there is a good miscibility between the phases, in a good agreement with elsewhere findings [75]. These findings might have a positive impact on electrical conductivities of the studied thin films.Figure 7
SEM images of the surface of the thin film with 0.1 wt% N-CNT.


## 3.3. Electrical Properties of the Fabricated Thin Films

Conductivity is a particular concern for semiconductor materials. Measuring the conductivity of semiconductor films is not that easy as it seems because it depends on a series of inseparable factors, especially temperature. For Urbach energy and optical band gap, the entire curve shows a significant slope change at a specific threshold associated with the epoxy/silicone blend-based composite films. The decrease inEg and the increase in EU become faster above this threshold. In order to evaluate this behavior, it is more convenient to measure the relationship between the DC and the change in filler load conductivity at ambient temperature. DC conductivity is based on resistivity measurement. The two-point probe method [76] was used to measure resistivity (it is expressed in Ω·cm) at room temperature (RT). Note that resistivity represents its ability to stop the flow of current. The resistivity measurement at ambient temperature is performed by plotting the current-voltage characteristics: I=fV.TheI=fV curves are exploited to extract the electrical resistivity. We have measured the electrical resistivity of the studied samples. Then, sheet resistance can be effectively performed utilizing the following equation [77]:
(10)RSh=R·WL.Also,R=ρL/A=ρL/d·W=ρ/d×L/W in which
(11)RS=ρd,where ρ is the resistivity (Ω·cm), RSis electrical sheet resistance (Ω), W is the width (cm), d is the thickness (cm) which can be determined with optical measurements, and Lpresents the length (cm), given that the conductivity is given byσ=1/ρin (Ω·cm)-1. The curve of DC conductivity behavior versus filler concentrations is represented in the inset of Figure 8.Figure 8
Electrical conductivity of thin films (epoxy/silicone N-CNT wt%) versus conducting filler concentrations.As indicated in Figure8, it is worthy to take note that electrical conductivity of unloaded film is about 10-8 (Ω·cm)-1. It is nonlinearly improved when N-CNT filler content is raised. The fillers give rise then to the electrical conductivity.


## 3.4. Evaluation of Thin Film Performance through the Calculation of Figure of Merit

The optical and electrical properties of the film are very important properties for all known transparent conductive oxide (TCO) applications. Ideally, a good TCO is identified by the optical transmission coefficient and high electrical conductivity. Therefore, when both light transmission and electrical conductivity are important, the material is considered high performance. These two parameters are inversely proportional and are related by a single factor called the figure of merit (FOM). This later allows reasonable comparisons of film properties and allows estimation of their optoelectronic properties [78]. The films represent a compromise between conductivity and light transmission. The decrease in resistivity involves an increase in the carrier concentration or its mobility. Increasing the number of carriers leads to an increase in absorption. In the present paper, the FOM of the studied films can be evaluated, using the following equation [79]:
(12)1ρ.α=σα,where
(13)FOM=σα=−1RSh·lnT+R,where σ is the electric conductivity (Ω-1), α is the absorption coefficient (cm-1), RSh is the surface resistance (Ω/sq), T is the total transmission (%), and R is the total reflection (%). Here, the best FOM is related to good optical transmission and electrical conductivity. It has been shown that useful films must have a FOM greater than or equal to 7 [80, 81]. Therefore, considering expression (13), the variation of the FOM value of the studied film with the filler concentration is gathered in Table 2. We noticed that the figure of merit was improved by increasing the load concentration.Table 2
Variation of optical figure of merit versus conducting filler concentrations.
MaterialSurface resistance (Ω/cm2)Visible absorption coefficientα (cm-1)Figure of merit (Ω-1 cm)Neat epoxy/silicone blend2000.200.02Epoxy/silicone N-CNT 0.07 wt%30.123Epoxy/silicone N-CNT 0.1 wt%3.80.055Epoxy/silicone N-CNT 0.2 wt%50.037


## 4. Conclusion

The optical properties were studied from UV-visible spectroscopy to examine the transmission spectrum, optical gap, Tauc verified gap, and Urbach energy, based on the envelope method proposed by Swanepoel.The study shows that the films obtained show a high transmittance for the unloaded thin films of neat epoxy/silicone blend about 88% and an average transmittance for the loaded thin film of epoxy/silicone N-CNT about 42 to 67% in the visible range and opaque in the UV range.The results indicate that the film has a direct optical transition with an optical gap of 3.61 eV for unloaded thin films and 3.55 to 3.19 eV for loaded thin films depending on the loading rate. The optical gap was appropriately adapted to the direct transition model proposed by Tauc; its value was 3.6 eV for unloaded thin films and from 3.38 to 3.1 eV for loaded thin films; then, Urbach’s energy is determined which is inversely tended withEg which varies from 0.19 eV for unloaded thin films and from 0.43 to 1.33 eV for loaded thin films. The obtained results show the success of the method sol-gel to elaborate epoxy/silicone loaded with N-CNT films with properties adapted to the physical applications. These results also show that it was possible to modify the loaded epoxy films by inserting a loading. In the near future, this gives hope for applications such like waveguides, electrochemistry, optical fibers, and solar cells.



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