Optical characterization and dispersion analyses of plasma polymerized methyl acrylate thin films

Abstract

This work reports the structural characteristics, surface morphology, linear and nonlinear optical properties of 110 to 225 nm thick plasma polymerized methyl acrylate (PPMA) thin films. X-ray diffraction analyses confirm the amorphous nature of the films. Field emission scanning electron micrographs of the films display cluster-based surface morphology. Attenuated total reflectance Fourier transform infrared spectroscopy confirms the chemical structural changes in the films. The optical properties were studied based on the absorbance, transmittance, and reflectance spectra measured by an ultraviolet–visible spectrophotometer within the wavelength ranges from 200 to 800 nm. The direct optical band gap and Urbach values are increased from 3.66 to 3.83 eV and 0.28 to 0.45 eV, respectively with increasing film thickness. The extinction coefficient and refractive index were evaluated, and discussed a correlation between the refractive index and the optical bandgap. The real and imaginary dielectric constants, volume/surface energy loss functions and skin depth were deduced. The oscillator energies and parameters were analyzed using the concept of Wemple-DiDomenico and Sellmeier models, respectively for a single oscillator. Static linear refractive index for the studied films exhibits normal dispersion behavior with film thicknesses and satisfied Moss, Ravindra-Gupta, and Herve-Vandamme rules. The linear susceptibility, third-order nonlinear susceptibility and the non-linear refractive index are considerably reduced from 0.20, 29.5 × 10⁻¹⁴ esu, and 5.89 × 10⁻¹² esu with increasing optical band gap energies. The outcomes from the analyses of PPMA demonstrated their potential for usage in electronic, optoelectronic, and non-linear device applications.

Highlights

• •Plasma polymerized methyl acrylate thin films were prepared by a glow discharge reactor at 22 W.
• •Optical constants and other parameters were studied using A, T, and R-spectra.
• •The electronic transition occurred due to changes in the surface/volume energy loss function values.
• •The dispersion energies and parameters were deduced using WDD and Sellmeier models.
• •The linear and third-order nonlinear susceptibilities decreased with increasing film thicknesses.

1. Introduction

Plasma polymerization (PP) depicts a most convenient and versatile technique which has been used as a powerful tool over the past few decades. PP organic polymeric thin films have been recognized as one of the widely studied materials due to their outstanding physical and chemical properties [1,2]. The different characteristics of thin films depends on various parameters, such as monomer flow rate, discharge power, substrate temperature, and steady-state pressure in the reactor chamber [3,4]. The PP organic thin films have found extensive biocompatible applications in solar cells [5], gas and humidity sensors [6], transistors [7], and optical waveguides [8]. Organic devices are relatively more affordable and simpler to fabricate in comparison to their inorganic counterparts. PP organic polymer films have attracted the attention of materials and solid state scientists who are keen to learn more about their structural, electrical, electronic and optical properties in order to develop high-quality polymer thin films utilizing a versatile technique for a range of significant applications. The special practical advantages of the PP technique are confirmative ultra-thin film fabrication, superior substrate adhesion, and chemically and physically viable surfaces [9]. It can be used to adhere thin films almost any substrates. Furthermore, while conventional polymer coating of a substrate necessitates multiple processes, PP completes all of them in practically one step [10]. Additionally, it may be used to create organic thin films from any volatile organic or organometallic molecule. Normally, light states are used for the deposition to reduce fragmentation modes. Most importantly, PP is environmentally friendly and has good deposition features which produce thin films that are homogeneous, biocompatible, and biodegradable and have special optoelectronic behaviours [11]. However, the disadvantages of the PP technique involve design complexity, necessitate certain fittings like expensive vacuum system, and cause unintended change of surface chemical composition. Moreover, determining the optimal conditions is time-consuming task due to the impact of process parameters on the chemical composition of the resultant polymer [12]. The significant techniques have been successfully utilized for synthesizing functional polymer thin films, including chemical vapor deposition [13], PP [14], spin/spray coating [15], atomic layer deposition [16], plasma enhanced chemical vapor deposition [17], sol gel [18], etc. The PP technique is strongly recommended since it can generate polymer thin films from almost any organic vapors and can fabricate thin films that cannot be made using other techniques. This process yields polymer thin films that are suitable for industrial usage. These films have exceptional mechanical, thermal, and chemical durability, are cross-linked and pinhole-free, and adhere well to almost all surfaces.

A large number of researchers have extensively studied PP thin polymer films in order to determine the morphological, thermal, structural, optical, and electrical properties to find their potential applications [[19], [20], [21], [22], [23]]. Hammani et al. [24] found values of the direct band gap energy ${(E}_g^d)$ ranges from 3.8 to 4.1 eV for polymethylmethacrylate/polyethylene glycol polymer blends. El-naggar et al. [25] determined the $E_g^d$ values for polymethyl methacrylate polymer between 4.46 and 4.52 eV. Haleshappa et al. [26] obtained the $E_g^d$ values from 3.77 to 3.83 eV for methyl methacrylate thin films. Nasrin et al. [27] noted that PP n-butyl methacrylate thin films exhibited a smooth and pinhole-free surface and found $E_g^d$ values between 3.64 and 3.80 eV. Hassanein et al. [28] found $E_g^d$ values between 2.67 and 2.90 eV values for ZnSe thin films. Hassanein and Sharma [29] found the absorption coefficient values in the range of 10⁴ cm⁻¹ for Cu_25-x (ZnGe)_25-xSe_50+2x thin films and they also determined the values of oscillator resonance energy (E_o) which increase from 2.939 to 3.422 eV, whereas the oscillator dispersion energy (E_d) values decrease from 30.831 to 24.342 eV. Park et al. [30] demonstrated that the surface morphology is largely homogeneous and amorphous in nature of PP methyl methacrylate utilizing attenuated total reflectance Fourier transform infrared (ATR-FTIR).

It is discerned from review of the past literature that the derivatives of methyl acrylate (MA) play a pivotal role in the field of science and technology. So, MA has been selected as the monomer precursor for the deposition of PPMA thin films. MA monomer is highly toxic through ingestion, inhalation, and skin absorption. If ventilation is insufficient in the laboratory, researchers must be used vapor-certified respirators, hand gloves, a lab coat, and splash goggles for safety during working with MA. But after plasma polymerization, MA becomes non-hazardous which is also environmentally friendly, biocompatible, and biodegradable [11].

The aim of this article is to prepare plasma polymerized methyl acrylate thin films samples of various thicknesses generated in a capacitively coupled plasma reactor operating at 22 W. Then comes the study and discuss the structural, optical, and dispersion parameters of PPMA thin films of various thicknesses. The X-ray diffraction analysis (XRD), FESEM, and ATR-FTIR were all used in this work to investigate the structural nature, surface morphology, and chemical bonding of PPMA thin films The ultraviolet visible (UV-VIS) spectroscopy were used to estimate thickness-dependent optical parameters such as direct band gap ${(E}_g^d$), linear refractive index (η), Urbach energy (E_U), real dielectric constants (ε₁) and imaginary dielectric constants (ε₂), quality factor (Q), the volume energy losses (VELF) and surface energy loss function (SELF), oscillator energy (E_o), dispersion energy (E_d), optical conductivity (σ_opt), skin depth (δ), reflection loss (RL), metallization parameter (M), optical surface resistance (R_s), high frequency and static dielectric constant, linear susceptibility (χ⁽¹⁾) and 3rd order nonlinear susceptibility (χ⁽³⁾), the nonlinear refractive index $\left({\eta }^{\prime }\right)$, are calculated and discussed in details. The optical properties of PPMA thin film could be controlled by altering both linear and nonlinear parameters as thickness is increased. These characteristics may reveal the suitability of PPMA for use in electronic and optoelectronic devices.

2. Experimental

2.1. Thin film preparation on glass substrate

Transparent MA was purchased from VWR Inter. Ltd., BH15 1TD England and utilized exactly as it was delivered. The chemical structure of MA is shown in Fig. 1 while the general properties of MA are presented in Table 1. Before cutting to the proper size, the borosilicate glass substrates of dimensions 0.0254 m × 0.0762 m × 0.0012 m (Model: Sail Brand, China) which have strong chemical stability were first cleaned with a solution of detergent and water for the deposition of PPMA thin films. After that, an ultrasonic cleaner was utilized to fully clean the substrates. Then the substrates were rinsed in deionized water, and dried in a dryer. A cylindrical shaped plasma reactor chamber with two parallel stainless steel electrodes of thicknesses 0.001 m, placed parallel to one another, separated by a distance of about 0.039 m, serves as the setup for glow discharge polymerization. The entire setup is shown in Fig. 2 which consists of a vacuum pressure gauge, a pumping unit, a monomer injection system, an AC power supply (50 Hz) and a flow meter. A rotary pump was used to evacuate the glow discharge plasma reactor chamber. Over the capacitively coupled electrodes, the plasma glow discharge was produced. Glass substrates have been placed on the lower electrode after being cleaned and dried. A rotary pump was used to progressively lower the pressure within the reactor chamber to around 13.3 Pa. The plasma glow was created by applying electric power across the two parallel electrodes in the chamber. A tiny injection valve controlled the monomer flow rate (20 cm³/min) to keep the working pressure steady throughout the deposition process. In the reactor, the monomer molecules were split up or fragmented before finally condensing onto the substrates. On the glass substrates, PPMA thin films were created for 45 to 90 min of deposition. The Fizeau interference technique was used to measure the thickness of the films. The following Eq. (1) was used to determine film thickness (d) [31]:

$$d=\frac{\lambda q}{2p}$$ (1)

Fig. 1.

Chemical structure of methyl acrylate.

Table 1.

General properties of methyl acrylate.

IUPAC name	Methyl acrylate
Molecular formula	C4H6O2.
Purity	≥ 99.5%
Physical state	Colorless liquid
Molecular weight	86.09 g/mol
Density	0.95 g/cm3
Boiling point	80 °C at 760 mm Hg
Refractive index	1.4021 (20 °C at 589 nm)

Fig. 2.

The Schematic diagram PP system for fabrication of the PPMA thin films.

; where λ is the wavelength of Na light = 589.3 nm, p is the fringe width and q is the step height which is the difference in height between two neighboring test surface sections of the fringe.

2.2. Devices and measurements

The structure of the PPMA thin films was examined by an X-ray diffractometer (XRD) (Model: Philips PW3040 X′Pert PRO, Germany) utilizing Cu-K_α as the target. The diffractometer reflections were taken at ambient temperature and the values of 2θ were swapped with a scan speed of 5° min⁻¹ between 10° and 70° with step sampling of 0.02°. The accelerating voltage and current for the XRD machine were 40 kV and 30 mA, respectively. The incident X-ray wavelength is 1.541 Å.

A field emission scanning electron microscope (FESEM) (Model: 7600F, JEOL, JSM, Japan; resolution: 1 nm) was used to collect the surface morphological information of the thin films. To stop charging effects during FESEM, a small coating of platinum was also deposited onto the films using a platinum sputtering coater.

ATR-FTIR spectra of the PPMA thin film samples were acquired using a FTIR double-beam spectrophotometer (Model: FTIR Bruker Alpha, Germany).

The bandgap was also determined using information from UV–visible spectra obtained from a UV–Vis spectrophotometer (Model: UV-1601, SHIMADZU, Japan) at ambient temperature.

3. Results and discussion

3.1. XRD analysis

A representative of the XRD data of the PPMA thin films of thickness 200 nm is shown in Fig. 3, and it is clear that there are no clearly defined Bragg peaks in the XRD patterns which confirms the amorphous nature of the PPMA thin films. During plasma polymerization, the continual scattering of ions and electrons with the film surface may be the cause of the thin film's amorphous nature [32,33].

Fig. 3.

A representative XRD pattern of the studied film of thickness 200 nm at 22 W.

3.2. Surface analyses

Fig. 4(a–d) displays the FESEM images of PPMA thin films of thickness 200 nm taken with magnification of × 30 k, × 50 k, × 100 k and × 150 k, respectively. At lower magnification, the surface of the PPMA thin films appear smooth and without any fractures. However, at higher magnification, a water wave-like structure becomes visible, suggesting the presence of aggregated portions within the films which is a result of prolonged polymerization and cross linking processes [34].

Fig. 4.

The FESEM micrographs of the PPMA thin film of thickness 200 nm were taken with magnification of (a) × 30k, (b) × 50k, (c) × 100k and (d) × 150k at 22 W.

3.3. ATR-FTIR analyses

ATR-FTIR spectra shown in Fig. 5 reveal significant changes, demonstrating the fragmentation of MA structure owing to plasma polymerization. The types of vibrations corresponding to the absorption bands in the spectra are registered in Table 2. In the spectrum of PPMA, the relative absorption bands intensity is significantly decreased compared to MA. For PPMA and MA, the C–H stretching between 2800 and 3100 cm⁻¹ is necessary for the methyl group to precisely identify the molecule as a molecular organic compound [35]. However, in the spectrum of PPMA, these bands appear as broad bands and are not detected due to very low intensity. The CH₂ stretching vibration are detected at 2917 and 2924 cm⁻¹, indicating the existence of these functional groups in both PPMA and MA [36]. Absorption bands from 1617 to 1637 cm⁻¹ in both PPMA and MA, represent C C stretching vibrations. The absorption bands at 1439 for PPMA and 1438 cm⁻¹ for MA are depicting the asymmetric CH₃ bending vibrations. The absorption peaks observed from 1382 to 1402 cm⁻¹ of PPMA and MA, are attributed to CH₂ bending vibrations. In the case of PPMA, these peaks are shifted towards lower wavenumbers. This shift is caused by the hydrogen atoms being removed from the CH₃ [37]. The C–O and C C bending vibrations are displayed from 800 to 1200 cm⁻¹ [38]. Overall, the FTIR spectra of PPMA significantly differ from that of the MA, demonstrating that the presence of extremely energetic electrons and ions during plasma polymerization causes structural alterations and fragmentation of the monomer.

Fig. 5.

ATR-FTIR spectra of the MA and studied films fabricated at 22 W.

Table 2.

ATR-FTIR vibration bands for MA and PPMA deposited at 22 W.

Assignment	Wavenumber (cm−1)
	MA	PPMA Thin films
Stretching OH	–	3395
Stretching CH3	2957	2957
Stretching CH2	2917	2924
Stretching C–H	2856	Merged in broad band 2871
Stretching C O	1727	1708
Stretching C C	1635	1625
Bending CH3	1439	1438
Bending CH2	1403	1382
C–O	1069–1276	Merged in broad band 1094 - 1262
Bending C C	811–987	Merged in broad band 802 - 1020

3.4. Optical properties

3.4.1. Absorbance, transmittance and linear absorption co-efficient

The UV–Visible absorbance (A) and optical transmittance (T) spectra of PPMA films of thicknesses 110, 160, 200, and 225 nm were investigated at ambient temperature and are depicted in Fig. 6a and b, respectively. An interesting observation in the absorption spectra is the sharp rise of A in shorter wavelengths, reaching a maximum at around 301 nm for various film thicknesses, with the UV zone experiencing the highest absorption. Beyond this point, as the wavelength increases, the A for all of the PPMA thin films quickly begins to decrease up to around 375 nm. The A drops at a slower pace beyond 375 nm, with the UV zone experiencing the highest absorption. The minor shift in the wavelength at which the highest A occurs with film thickness, as shown in Table 3, is an important feature. This change is a result of the conjugated system in PPMA becoming more prevalent [39].

Fig. 6.

Variation of (a) A with λ, (b) T with λ, and (c) α with hν for the studied films at 22 W.

Table 3.

Linear optical parameter of the studied films of various d at 22 W.

Parameters	Thickness, d
	110 nm	160 nm	200 nm	225 nm
λmax (nm)	299	300	301	301
Amax	0.69	1.39	1.79	2.05
$E_g^d$ (eV)	3.66	3.79	3.82	3.83
EU (eV)	0.45	0.34	0.28	0.31
σs	0.057	0.076	0.092	0.083
Ee-p	11.7	8.82	7.26	8.04

Correspondingly, the FTIR spectra reveal the appearance of a C C band in the range of 1625–1635 cm⁻¹, which serves as an indication of an expanding conjugated π-system. This observation further supports the notion of increased conjugation within the PPMA thin films. Regarding the T spectra (Fig. 6b), it is evident that the T increases with longer wavelengths up to 425 nm for various thicknesses. Beyond this point, the T reaches a nearly constant value. PPMA films of different thicknesses are translucent and display an 80 to 90% high T in the visible range. Between 110 and 225 nm, the A increases in the visible range while T displays opposite patterns of these films. The inset Fig. 6b illustrates, the absorption edge's position is dependent on the thickness of the thin films and has been moved to lower wavelengths.

At room temperature, the linear absorption co-efficient (α_lco) in terms of absorbance (A) and thickness (d) for PPMA films was evaluated using the following Eq. (2) [40,41]:

$${\alpha }_{lco}=2.303\frac{A}{d}$$ (2)

Analyzing Fig. 6c, it can be observed that the values of α_lco start increasing at approximately 3.0 eV. Beyond 3.5 eV, this increase becomes more rapid. The optical linear absorption coefficient (α_lco) is nearly visible and has high values in between 10⁴ and 10⁵ cm⁻¹. The inset Fig. 6c illustrates, the absorption edge's position has been moved to lower wavelengths with increasing film thicknesses. The existence of several optical transitions inside PPMA is confirmed by the nonlinear character of each curve. Additionally, the exponential edge seen in the absorption spectra indicates the existence of defects in the PPMA thin films.

3.4.2. Optical bandgap calculation

Optical band gap is one of the crucial parameters associated with the electronic structure [42]. There is a significant amount of absorption in the thin films because the incoming photons have sufficient energy to drive electrons into the conduction band from the valence band. This straightforward approach reveals the position of the optical absorption edge and clarifies the band structure of the film's characteristics. Using this approach, the optical absorption edge was discovered. The following Eq. (3) known as Tauc's technique was utilized to conduct an investigation into the optical absorption edge [43,44]:

$${\alpha }_{lco}h\nu =B{\left(h\nu -E_g\right)}^m$$ (3)

; where B = proportionality factor or band-tailing parameter which depends on the type of the electronic transition, and E_g = optical band gap. Exponent ‘m’ is dependent on the nature of transition which determines electronic transition type in the gap. It has various values, such as m = 1/2 (allowed direct), m = 2 (allowed indirect), m = 3/2 (forbidden direct) and m = 1/3 (forbidden indirect) transitions. The following Eq. (4) is a representation of Eq. (3) [45].

$$\frac{d\left[\mathit{ln}\left({\alpha }_{pco}h\nu \right)\right]}{d\left(h\nu \right)}=\frac{m}{h\nu -E_g}$$ (4)

The plot of d[ln(α_lcohv)]/d(hv) against hv that is delineated in Fig. 7a, displays a break or discontinuity that was noticed at the point from equation (4). The discontinuity is appeared at a specific energy, E_g = 3.27 eV. Based on the slope of the ln(α_lcohv) versus ln(hv - Eg) curves shown in Fig. 7b, it is discovered that the value of m is about 1/2. Therefore, it appears from the observed value of m that the allowed direct transitions produce the fundamental edge of absorption inside the films. During the transition phase, the integrity of the total momentum and energy of the photon-electron system must be maintained. The plot of (α_lcohv)² versus h $\nu$ for different d of PPMA is shown in Fig. 7c. The $E_g^d$ values are varied from 3.66 to 3.83 eV with d at 22 W that are tabulated in Table 3 and found to have a slightly lower direct band gap value by comparing with previous research at 35 W for PPMA [46]. The amorphous nature of these films is confirmed by the computed optical band values, which rise with increasing d. The thin films can be utilized as an insulating material in a nonvolatile organic digital memory because their band gaps can be easily tuned by changing the thicknesses [47]. When a photon is absorbed by an electron at the valence band edge, the electron becomes excited and moves toward the bottom of the conduction band.

Fig. 7.

(a) d[ln(α_lcohv)]/d(hv) against hv (b) ln(α_lcohv) versus ln(hv- Eg) and (c) (α_lcohv)² versus hv curves for the studied films at 22 W.

3.4.3. Urbach energy, extinction co-efficient, and refractive index

The Urbach tail indicates the defect levels exist inside the forbidden gap. The Urbach energy (E_U) was calculated using Eq. (5) [48]:

$$E_U=\left[\frac{d\left(h\nu \right)}{d\left(\mathit{ln}{\alpha }_{lco}\right)}\right]$$ (5)

Fig. 8a illustrates the lnα_lco versus hν curves for PPMA films of different d. The values of E_U ranges from 0.28 to 0.45 eV are calculated and tabulated in Table 3. Because the structural disorders are decreasing in the band gap, the E_U values decrease as film thickness increases up to 200 nm, then it increases.

Fig. 8.

The plots of (a) lnα vs hν, (b) k vs hν, and (c) η vs λ of the studied films at 22 W.

The steepness parameter (σ_s = k_BT/E_U) indicates the broadening in the optical absorption edge because of electrons-phonon interaction. The σ_s values have been calculated considering T = 298 K and k_B = Boltzmann's constant = 1.38 × 10⁻²³ JK⁻¹ and are listed in Table 3. The observed lower values of σ_s demonstrate a lower rate of phonon-electron scattering and a narrower optical absorption edge due to lower density of states close to the optical absorption edge [49].

Electron-phonon interaction (E_e-p= 2/3σ_s) indicates an interaction strength between electrons and phonons. The value of E_e-p exhibits the opposite relationship of the σ_s and the results are tabulated in Table 3. This knowledge may be helpful for a variety of applications, including optoelectronics and solar cell technologies. The E_e-p values suggests a broadening of the filled energy bands of PPMA films that vary in thickness from 110 to 200 nm whereas for 225 nm, E_e-p value is decreased which points to a reduction of the filled energy bands expansion according to the strong binding approximation [50].

The extinction co-efficient (k) indicates the polarization ability of the material. The k can be obtained using α with the assistance of Eq. (6) [51].

$$k=\frac{\alpha \lambda }{4\pi }$$ (6)

The relationship between k and hν is shown in Fig. 8b. With increasing hν, the value of k increases, possibly indicating a reduction in electron transmission across the mobility gap. The linear refractive index (η) provides information on how light moves through a material. The following Fresnel's formula in Eq. (7) was used to compute $\eta$ [52]:

$$\eta =\left(\frac{1+R}{1-R}\right)+\sqrt{\frac{4R}{{\left(1-R\right)}^2}-k^2}$$ (7)

Fig. 8c exhibits η at various λ, depicting the normal dispersion behavior of the PPMA films of various d. The value of η is larger in the lower wavelength regime, whereas in the wavelength regime $\left(300nm\le \lambda \le 550nm\right)$, it decreases drastically. However, above this photon wavelength, $\eta$ has no significant variation. For high film thickness, η is lower. Greater changes in the direction of light within the films are caused by a higher η which suggests slower light travel. As a result, the optical intensities rise which making the material more effective and useful for non-linear interactions [53,54].

The η displays normal dispersion behavior which satisfies the Moss relation [55], Ravindra and Gupta relation [56] and Herve and Vandamme relation [57]. In addition, this theoretical models are adequate for materials with a bandgap greater than 1.4 eV [58,59]. The η values of the films were also calculated from the $E_g^d$ values using the following Eqs. (8), (9), (10), respectively.

$$\eta \left(Moss\right)={\left(\frac{95}{E_g^d}\right)}^{\frac{1}{4}}eV$$ (8)

$$\eta \left(RG\right)=4.084-0.62E_g^d$$ (9)

$$\eta \left(HV\right)=\sqrt{1+{\left(\frac{A^{\prime }}{E_g^d+B^{\prime }}\right)}^2}$$ (10)

;where $A^{\prime }$ = -13.6 eV = the ionization energy of hydrogen and $B^{\prime }$ = 3.47 eV. The η_max(Vis) values are listed in Table 4. The η_max(Vis) values are almost independent of d. According to Table 4, η (Moss), η (RG) and η (HV) values are decreased with increasing d as well as $E_g^d$. This trend indicates that PPMA thin films allow light to pass more freely through and have less absorbing nature in the vis-NIR region [60].

Table 4.

Optical dispersive parameter of the studied films of various d at 22 W.

Dispersive parameters	Thickness, d
	110 nm	160 nm	200 nm	225 nm
ηmax(Vis)	2.62	2.63	2.62	2.63
η (Moss)	2.26	2.24	2.23	2.22
η (RG)	1.81	1.73	1.72	1.71
η (HV)	2.15	2.12	2.11	2.10
ε∞(Moss)	5.09	5.01	4.99	4.98
ε∞(RG)	3.29	3.01	2.94	2.92
ε∞(HV)	4.64	4.51	4.48	4.47
ε∞ (Adachi)	6.06	5.88	5.84	5.82
ε0 (Adachi)	7.25	6.85	6.75	6.72
$E_g^d$ (eV)	3.66	3.79	3.82	3.83
E0 (eV)	6.9	7.38	7.13	6.99
Ed (eV)	17.7	14.19	12.39	11.45
E0/$E_g^d$	1.90	1.95	1.87	1.83
${\eta }_0$	1.89	1.71	1.65	1.62
ε∞	3.56	2.92	2.74	2.64
f = E0Ed	122.13	104.72	88.34	80.04
nopt	1.92	1.97	1.98	1.99
M-1	2.57	1.92	1.74	1.64
M-3	0.0539	0.0353	0.0342	0.0335
λ0 (nm)	304	342	287	424
S0 (m−2)	2.93 × 1013	1.75 × 1013	2.25 × 1013	1.13 × 1013

3.4.4. Dielectric constants, quality factor, SELF and VELF

The complex dielectric constants (ε*), real dielectric constants (ε₁) and imaginary dielectric constants (ε₂) were calculated utilizing the following Eqs. (11), (12), (13), respectively [61,62]:

$${\epsilon }^{*}={\epsilon }_1+i{\epsilon }_2={\left(\eta +ik\right)}^2$$ (11)

where

$${\epsilon }_1={\eta }^2-k^2$$ (12)

and

$${\epsilon }_2=2\eta k$$ (13)

The ε₁ describes the de-acceleration of a light wave as it travels through the film material for any damped oscillator. As a result, it links to the energy contained in the substance and explains how electromagnetic waves disperse. On the other hand, the ε₂ indicates how much energy is received or lost in light. It is therefore regarded as a damping factor as it has to do with the energy lost and dissipated within the material when the light wave passes. Thus, numerous dielectric characteristics, including the dielectric loss factor, the quality factor, the volume and surface energy loss functions, and optical conductivity, etc., may be inferred from the known values of the dielectric constant [63]. From Fig. 9a and b, it is noted that the values of ε₁ is more than ε₂ for all these films of various thicknesses because ε₁ are highly dependent on the refractive index (η) where η≫k whereas ε₂ is only depends on k values where small k values decreases the product of n and k. Initially ε₁ and ε₂ dramatically decreased up to wavelength 550 nm and then no significant changes are observed. The variation of the dielectric constants with the incident photon energy indicates that there are some interactions have occurred between free electrons and incident photons in the wavelength range from 300 nm to 550 nm.

Fig. 9.

The variations of (a) ε₁ and (b) ε₂ and (c) Q as a function of λ for the studied films at 22 W.

The dielectric loss tangent ($\mathit{tan}\delta$) describes how an incoming electromagnetic radiation's energy or amplitude is reduced as it passes through the film medium. The ratio between the imaginary dielectric constant (${\epsilon }_2$) and real dielectric constant (${\epsilon }_1$) is known $\mathit{tan}\delta$. The inverse of $\mathit{tan}\delta$ is called the quality factor (Q).

The $\mathit{tan}\delta$ and Q were calculated with the assistance of Eqs. (14), (15), respectively [64,65]:

$$tan\delta =\frac{{\epsilon }_2}{{\epsilon }_1}$$ (14)

and

$$Q=\frac{1}{\mathit{tan}\delta }=\frac{{\epsilon }_1}{{\epsilon }_2}$$ (15)

Fig. 9c depicts the relationship between Q of PPMA films and the change in wavelength for various d. In comparison to the high and medium wavelength regions, the Q values are observed to be lower at lower wavelengths. The Q values are also observed to drastically decrease up to 800 nm as the d rises. Additionally, the Q values increase as d increase. The Q values for each of the investigated films decrease significantly in the high wavelength area. In comparison to lower thicknesses, films of higher thicknesses are more effective [66].

The surface (SELF) and volume (VELF) energy loss functions were utilized to determine the probability of energy which is caused by the rapidly moving electron inside the materials. The oscillation is dependent on the SELF and VELF. It is suggested that the activation of plasma oscillations in the ocean of conduction electrons is responsible for this loss. The values of ${\epsilon }_2$ and ${\epsilon }_1$ are used to determine surface energy losses. The SELF and VELF were calculated using Eqs. (16), (17), respectively [67,68].

$$SELF=\frac{{\epsilon }_1}{\left[{\left({\epsilon }_1+1\right)}^2+{\epsilon }_2^2\right]}$$ (16)

$$VELF=\frac{{\epsilon }_2}{\left({\epsilon }_1^2+{\epsilon }_2^2\right)}$$ (17)

The spectral behavior of the SELF is depicted in Fig. 10a. It is noted that in the lower λ region $\left(300nm\le \lambda \le 550nm\right)$, the SELF values are increased dramatically but above the λ region, the values are almost saturated. The behavior of the VELF is depicted in Fig. 10b along with the λ, which decreases with increasing the d. The SELF are greater than VELF for PPMA films of various d. Increases in SELF with d increases may be caused by an increase in disorder or defects, which results in an increase in the carrier's collisions while traveling through the material. Thus, the optical conductivity may be responsible for the variations in the values of the VELF and SELF loss functions [69].

Fig. 10.

Variation of (a) SELF with λ and (b) VELF with λ for the studied films at 22 W.

3.4.5. Optical conductivity and skin depth

The optical conductivity $,{\sigma }_{opt}$ is a powerful optical parameter for implementing the optical response as well as electronic state of the thin films. The following Eq. (18) in terms of the speed of light (c) was used to evaluate the σ_opt of PPMA thin films [70]:

$${\sigma }_{opt}=\frac{{\alpha }_{lco}\eta c}{4\pi }$$ (18)

The values of σ_opt are seen to significantly fall notably up to 550 nm wavelength in PPMA thin films. Beyond this limit, as the thin films interact with light photons, the σ_opt values remain almost constant and decrease toward zero as seen in Fig. 11a. Further, it could be noted that for thicker PPMA films, the σ_opt, values are lower. This variation between σ_opt and d is thought to be the result of localized states forming at PPMA thin film defect sites [71,72].

Fig. 11.

Variation of (a) σ_opt with λ and (b) δ, with hν for the studied films at 22 W.

Skin effect is measured using skin depth (δ) metric, which measures how well incident photons penetrate a medium. The following Eq. (19) was used to examine how the k depends on the δ [73]:

$$\delta =\frac{\lambda }{2\pi k}$$ (19)

The spectrum of δ versus hν of the PPMA films is shown in Fig. 11 b. At the lower energy region ranges between 2 and 2.5 eV, the δ values are very larger for various d but with increasing energy, it drops dramatically and nearly independent of d. The δ values are large in the lower energy range indicates that there are more electron collisions in this region [74].

3.4.6. Dispersive energy parameters

A thorough physical explanation of the examined parameters is provided by the single effective oscillator model. The Wemple-DiDomenico relationship in Eq. (20) was used to explain the dispersion analysis of η [75,76]:

$${\eta }^2=1+\frac{E_0{E}_d}{{E_0}^2-E^2}Or,{\left({\eta }^2-1\right)}^{-1}=\frac{E_0}{E_d}-\frac{E^2}{E_0{E}_d}$$ (20)

;where E_d is the dispersion energy, E (=hν) is the photon energy, and E₀ is the oscillator energy. Fig. 12a displays a plot of the ($\eta$²–1)⁻¹ against $\left(h\nu \right)$² for PPMA films of various d results in a straight line that cuts the Y-axis in the upward direction. The slope of this straight line is equal to (E_oE_d)⁻¹, and its intersection provides the ratio between E_o and E_d. The calculated E_o and E_d values are listed in Table 4 that are fluctuating with d. According to Tanaka [77,78], E_o is nearly equal to two times of $E_g^d$. For validation of these results, the values of the ratio $\frac{E_o}{E_g^d}$ for PPMA thin films were calculated and obtained results are fit in with the Tanaka relationship which are listed in Table 4. The obtained results are quite reasonably support the Tanaka relationship. The fluctuation of E_o may be related to variations in the number of scattering centers with respect to PPMA thin film thicknesses.

Fig. 12.

(a) ${\left({\eta }^2-1\right)}^{-1}vs{\left(h\nu \right)}^2$ and (b) ${\left({\eta }^2-1\right)}^{-1}vs{\lambda }^{-2}$ of the studied films at 22 W.

According to Maxwell relation [79], the theoretical high frequency dielectric constants, ${\epsilon }_{\infty }$ of PPMA films of various d were computed with the assistant of Eq. (21) using η (Moss), η (RG), and η (HV) values:

$${\epsilon }_{\infty }={\eta }^2$$ (21)

Adachi proposed the theoretical formula for evaluating both the high frequency dielectric constants, ${\epsilon }_{\infty }$ and static dielectric constants, ${\epsilon }_0$. The ${\epsilon }_{\infty }$ and ${\epsilon }_0$ values were calculated using Eqs. (22), (23), respectively [80]:

$${\epsilon }_{\infty }=11.26–1.42E_g^d$$ (22)

$${\epsilon }_0=18.52–3.08E_g^d$$ (23)

Table 4 shows that ε_∞ (Moss), ε_∞ (RG), ε_∞ (HV), ε_∞ (Adachi) and ε₀ (Adachi) values signify decreasing trends with increasing d.

The values of E_o and E_d were computed from the ($\eta$²–1)⁻¹ against $\left(h\nu \right)$² plot in Fig. 12a. So, the experimental high frequency dielectric constant (ε_∞) and static refractive index (${\eta }_0$) were calculated using the following Eq. (24) and tabulated in Table 4 [81]:

$${\epsilon }_{\infty }=1+\frac{E_d}{E_0},{\eta }_0=\sqrt{{\epsilon }_{\infty }}$$ (24)

The ε_∞ values is correlated with the ε_∞ (Moss), ε_∞ (RG), ε_∞ (HV), ε_∞ (Adachi) and ε₀ (Adachi) values where ε_∞ values are decreased with increasing d of PPMA films. It can be said that increasing thickness will help reduce the power loss in the PPMA thin films and increase the suitability of the material for high frequency and power device applications [82].

The first order moments of spectra $\left(M_{-1}=\frac{E_d}{E_0}\right)$ and third ($M_{-3}=\frac{M_{-1}}{E_0^2}$) order moments of spectra are computed which are tabulated in Table 4. The obtained M_-1 and M_-3 values are decreased with increasing d of the PPMA films. The oscillator strength (f = E₀E_d) of the material decreased with increasing d that are shown in Table 4.

The optical electronegativity (n_opt) values were computed using the following Eq. (25) [83]:

$$n_{opt}={\left(\frac{C}{{\eta }_0}\right)}^{\frac{1}{4}}$$ (25)

;where C = 25.54. The calculated values of n_opt are increased with increasing d that are tabulated in Table 4. The optical electronegativity influences the non-linear parameters because of n_opt is correlated with the static refractive index.

The values of both wavelength (λ₀) and the average strength of the oscillator (S₀) were obtained from the plot of ($\eta$² − 1)⁻¹ against λ⁻² according to the following Sellmeier's dispersion Eq. (26) [84]:

$${\left({\eta }^2-1\right)}^{-1}=\frac{1}{{S_0\lambda }_0^2}-\frac{1}{{S_0\lambda }^2}$$ (26)

In Fig. 12b–a straight line can be drawn with a slope of $\left(\frac{1}{S_0}\right)$ and an intersection with the Y-axis at a value equal to ${\left({S_0\lambda }_0^2\right)}^{-1}$. Consequently, the λ₀ and S₀ values are determined which are tabulated in Table 4.

3.4.7. Reflection loss, mettalization parameter, and optical surface resistance

The reflection loss (RL) of PPMA films of different d were computed utilizing Eq. (27) in terms of linear refractive index ($\eta$) [85]:

$$RL=\frac{{\eta }^2-1}{{\eta }^2+2}$$ (27)

The fluctuation of the RL with increasing d of PPMA thin films is shown in Fig. 13a. There are certain losses in electromagnetic wave strength when light travels through thin coatings. The propagation velocity is reduced as a result of these losses. This rise in the reflection loss values is likely caused by an increase in the k values and SELF and VELF, which demonstrate an increase in scattering, losses, and absorption.

Fig. 13.

Variation of (a) RL with λ, (b) M with λ, and (c) R_s with λ, for the studied films at 22 W.

Metallization parameter, M denotes the insulating or metallic properties of the materials which was calculated using the following Eq. (28) [86]:

$$M=1-\frac{{(\eta }^2-1)}{\left({\eta }^2+2\right)}=1-RL$$ (28)

If M > 1, the materials' metallic nature is confirmed, and if M < 1, the studied samples' non-metallic behavior is indicated. Fig. 13b displays the M-values, which range between 0.3 and 0.7 for PPMA films of various d. It has been noted that the obtained M values of the current film samples are less than unity and more than zero, indicating that PPMA films are insulating materials.

The Kirchhoff's functions are the resistance of the thin film's surface that results from the excitation of electrons by photons striking the surface. The estimated static refractive index, ${\eta }_0$ was utilized to compute the optical surface resistance (R_s) using the following Eq. (29) [87,88]:

$$R_s=\frac{-4\pi }{c}\times \frac{1}{{\eta }_0\mathit{ln}\left(T\right)}$$ (29)

The R_s values are increased with increasing d shown in Fig. 13c. The photon wavelength and d rise with an increase in Kirchhoff's functions.

3.4.8. Non-linear optical properties

Nonlinear optical properties of the substance were also investigated to better understand the nonlinear properties of PPMA films that are essential for utilization in device applications, notably in optoelectronics [89]. The linear susceptibility (χ⁽¹⁾) and 3rd order nonlinear susceptibility (χ⁽³⁾) and the non-linear refractive index $\left({\eta }^{\prime }\right)$ which connected with the static refractive index (${\eta }_0$) were computed using the following Eqs. (30), (31), (32), respectively [[90], [91], [92]]:

$$x^{\left(1\right)}=\frac{{\eta }_0^2-1}{4\pi }$$ (30)

$$x^{\left(3\right)}=K{\left[x^{\left(1\right)}\right]}^4$$ (31)

$;\text{where}\mathrm{C}=\text{constant}=1.7\times {10}^{-10}\text{esu}$

$${\eta }^{\prime }=\frac{12\pi x^{\left(3\right)}}{{\eta }_0}$$ (32)

The calculated values of χ⁽¹⁾, χ⁽³⁾ and ${\eta }^{\prime }$ are listed in Table 5. The values of χ⁽¹⁾, χ⁽³⁾ and ${\eta }^{\prime }$ are 0.20, 29.5 × 10⁻¹⁴ esu, and 5.89 × 10⁻¹² esu are decreased with increasing d. χ⁽³⁾ is a crucial indicator of a material's structural symmetry and provides details on the strength of the chemical bonds forming between the thin film's molecules. High χ⁽³⁾ has advantages for several prospective applications, including frequency converters, switching devices, and electro-optic modulators [93].

Table 5.

Non-linear optical parameters of the studied films of various d at 22 W.

Parameters	Thickness, d
	110 nm	160 nm	200 nm	225 nm
$x^{\left(1\right)}$	0.20	0.15	0.14	0.13
$x^{\left(3\right)}$ (esu)	29.5 × 10−14	9.32 × 10−14	6.22 × 10−14	4.91 × 10−14
${\eta }^{\prime }$ (esu)	5.89 × 10−12	2.05 × 10−12	1.42 × 10−12	1.14 × 10−12

4. Conclusions

Plasma polymerized methyl acrylate thin films has been generated using glow discharge plasma polymerization technique. A water wave-like structure becomes visible at higher magnification which suggesting the existence of aggregated portions within the films. The new absorption peak in PPMA spectrum suggests monomer fragmentation during plasma polymerization. The obtained absorption coefficient values ranges from 10⁴ to 10⁵ cm⁻¹ for all d. The direct band gap ${(E}_g^d)$ and Urbach energy (E_U) values are increased from 3.66 to 3.83 eV and from 0.28 to 0.45 eV, respectively with increasing d. X-ray diffraction analyses (XRD) analysis, metallization parameters and high value of $E_g^d$ confirms the dielectric nature of the films. The real dielectric constant is much greater than the imaginary dielectric constant (ε₁ ≫ε₂) which confirms that polymeric material responses to light falling on it. The higher quality factor (Q) values are observed for the 225 nm that means thicker films are more effective than thinner for device applications. Theoretical high frequency dielectric constants (${\epsilon }_{\infty }$) values are fitted with the ε_∞ (Moss), ε_∞ (RG), ε_∞ (HV), ε_∞ (Adachi) and ε₀ (Adachi) values where ε_∞ values are decreased with increasing d. The electronic transition occurs for the variations in the values of the surface energy loss function (SELF) and volume energy loss function (VELF). The skin depth (δ) fluctuates with d that indicates more electron collisions at lower energy range, but it becomes very low and independent of d in the higher energy range. The obtained dispersion energies (E_d) values ranges from 11.45 to 17.7 eV and the oscillator energies (E₀) values ranges from 6.90 to 7.38 eV. The estimated values of the optical electronegativity (n_opt) are slightly increased from 1.92 to 1.99 while the third-order nonlinear susceptibility (χ⁽³⁾) of PPMA thin films decreased from 29.5 × 10⁻¹⁴ esu to 4.91 × 10⁻¹⁴ esu by increasing d. The PPMA thin films is a suitable candidates for optoelectronic, electronics device and non-linear optics.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

S.D. Nath: Writing – original draft, Visualization, Software, Methodology, Investigation, Conceptualization. A.H. Bhuiyan: Writing – review & editing, Supervision, Resources.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.