One-dimentional periodic structure infiltrated by (PVA/CV + CF)-polymer for high-performance sensitivity

In the current work, we demonstrate a design to act as a Gamma-ray radiation dosimeter based on the one-dimensional photonic crystal (1D-PhC). The basic concept of the present dosimeter is based on a Porous Silicon (PSi) infiltrated by poly-vinyl alcohol (PVA)-polymer doped with crystal violet (CV) and carbol-fuchsine (CF) dyes. The mechanism of suggested dosimeter is based on the shift of the photonic bandgap (PBG) to higher wavelengths as exposed to gamma-ray radiation doses from 0 to 70 Gray (Gy). The basic axes of the current theoretical treatment are the transfers matrix method (TMM), Bruggeman's effective medium equation, and the fitted experimental data to the refractive index of the doped PVA-Polymer. The obtained results showed the proposed sensor is characterized by high stable sensitivity varied from (178–186 nm/ RIU) along an applied γ-dose from (10–70 Gy) in the visible range. In addition, we compared these results with previous researches. In addition, based on the our knowledge may be it is the first time that a 1D-PhC has been used for gamma-ray detection by using (PVA/CV + CF) based on Porous Silicon.


Introduction
Radiations of varied degrees cause and induce many Physico-chemical changes in the materials that come into contact with them in the environment. Radiations influence various materials by varying degrees, depending on the type of radiation, radiation dosage level, exposure time, material characteristics, environmental conditions, etc. (Chandrappa et al. 2021;. Radiation dosimetry is the main point of much research due to the use of radiation in various applications (Baccini, et al. 2019;Andreo, et al. 2017). A dosimeter is any instrument that can produce an output value that represents the average absorbed dose deposited in its sensitive volume by ionizing radiation (Baccini, et al. 2019; Polymers, metals, semiconductors, liquid crystals, superconductors, metamaterials, and dielectrics are all utilized in the design of PhCs (Hadi Al-kadhemy et al. 2014;Elsayed et al. 2021;Wu 2021;Iwamoto et al. 2021;Park et al. 2021). The incorporation of porous silicon (PSi) layers in PhCs as a novel sensor design to improve sensitivity is the focus of recent research (Ivanov et al. 2022; Van 2022). PSi layer is commonly fabricated by an electrochemical etching route. Due to its simplicity of manufacture, different pore sizes and morphologies, vast surface area, and controlled surface modification and reactivity, it is highly recommended and considered to be a promising candidate (Al-Syadi et al. 2021;Yue et al. 2019;Zhong et al. 2020;Zaky and Aly 2021).
In this work, we develop a highly sensitive radiation dosimeter; 1D-PhC based on PSi layers infiltrated by PVA-polymer doped with crystal violet (CV) and carbol fuchsine (CF) dyes. Also, we studied the behavior of this structure when exposed to different doses of gamma rays emitted from a 60 Co-radioactive source. In addition, the results show how the PSi-layer enhanced the optical properties of the doped PVA-Polymer, and how the porosity of PSi-layers affects our structure. Then, the effect of gamma-ray doses ranging from 0 to 70 Gy on our structure is studied. Finally, the effect of thicknesses of the two layers on our structure and how much they affect the sensitivity of this radiation-dosimeter are discussed.

Theoretical framework
In this part, we design a gamma-ray dosimeter by a 1D-PhC based on the Porous Si layer. As shown in Fig. 1, the structure is configured as [Air (PSi 1 /PSi 2 ) N 1 substrate]. Where, PSi 1 , PSi 2 are the first and second porous silicon layers with porosity P 1 , P 2 , respectively, and N 1 represents the number of periods. For gamma-ray detection, we used PSi-layer to be infiltrated by the doped PVA-Polymer. The transfer matrix method (TMM) is used to study the transmittance spectra of our structure (Ahmed and Mehaney 2019;Aly and Sayed 2020;Aly et al., 2009;Aly and Mohamed. 2015). As a result, the Porous Silicon layer, the doped PVA-Polymer, and the transfer matrix method are the main points to illustrate our theoretical study.

Optical properties of the porous silicon layer
The optical refractive index of the PSi layer (n PSi ) that is filled with Polymer (n Polymer ) with porosity (P) is calculated using Bruggeman's effective medium equation (Zaky and Aly 2021;Ahmed and Mehaney 2019).
where, n (Si) is the refractive index of the silicon, and is equal to 3.7 ).

Optical properties of the PVA-polymer
The film samples of the (PVA/CV + CF) polymer were prepared by using a solvent casting method. These films were irradiated At room temperature with gamma-ray doses of 0-70 (Gy) emitted from 60 Co-source (Antar 2014).
The refractive index of the (PVA/CV + CF) polymer is given as a function of wavelength and gamma-ray radiation doses D γ (Gy) by fitting the experimental results using the Matlab program (Antar 2014). Applying the cubic fitting to the experimental data, the following fitted equations can be used to express the refractive index of the polymer as follows.
where, A, B, C, and C are the fitted coefficients and are listed in Table 1. The R-square value of the fitting is equal that the value of 0.015963 through gamma-ray radiation doses ranging from 0 (unirradiated sample) to 70 Gy. (1) (4) n(D) = Aλ 3 + Bλ 2 + Cλ + D

Transfers matrix method (TMM)
The transfer matrix method (TMM) is used to determine the optical properties of the presnt structure (transmittance, reflectance, and absorbance spectra) because of electromagnetic waves interaction with our structure. Many previous studies have investigated the details of TMM Sayed et al. 2022;Zaky and Aly 2021;Aly et al. 2022;Abadla et al. 2021;El-Shemy et al. 2022;Mehaney et al. 2019;Mehaney 2019). The following matrix (M) represents the total transfer matrix for the proposed structure with the number of periods (N 1 ) of PSi 1 and PSi 2 -layers: Then, the transmittance spectra of our structure could be described according to the previous matrices as:where, P o , P s are the propagation matrix of air and substrate for TE-polarization, respectively.

Results and discussion
Herein, the numerical results of our 1D-PhC gamma-ray dosimeter based on PSi-layer are discussed in this section. These results include the transmittance spectra of our structure in the visible region for a transverse electric (TE) polarization. The refractive indices of Si, air and glass are n Si = 3.7, n Air = 1, and n s = 1.52, respectively (Zimek 2017). The refractive index of the PSi and Polymer are mentioned in Eqs. (1) and (4). By injecting the polymer at the top of the structure, the pores will be infiltrated with the polymer as shown in Fig. 1. The thickness of the first layer (PSi 1 ) and the second layer (PSi 2 ) are d 1 = 30 nm, and d 2 = 73 nm with porosity of P 1 = 20%, P 2 = 80%, respectively. Furthermore, the period of numbers is N 1 = 20.
The first point in this section explains the effect of radiation on the dimension of our radiation dosimeter and the reason for choosing these materials. The radiation damage is critical for devices that operate in radiation-prone environments. Wherein, radiation dosimeters are exposed to pressure, temperature, or strain from external sources during Gamma-radiation. The reason behind choosing Si material is that the refractive index of Si changes below (5 × 10 -5 ) at (Dγ = 1000 kGy). Also, the thermo-optic coefficient of Si is equal (2.3 × 10 -4 ) at (Dγ = 66.5 kGy, and 32 °C) (Baccini, et al. 2019;Cocorullo et al. 2002). And the maximum rise in the temperature of Si is equal to (3.2 °C) due to the radiation effect. Besides, the thermal expansion coefficient of the Si is very small and equals (≈ 2.6 × 10 -6 ) (Okada and Tokumaru 1984). Therefore, the change in the refractive index of Si caused by the radiation processes across a γ-dose range from 0 to 70 Gy can be ignored. Additionally, the effect of radiation on the geometrical dimensions (thermal expansion) of the proposed sensor (radiation dosimeter) is ignored. The thermal strain caused by radiation can thus be ignored (Ibrahim et al. 2021). To sum up, we think the proposed structure is suitable for measuring gamma rays without being destroyed.
For, the effect of radiation on the refractive index of the (PVA/CV + CF) polymer is shown in Fig. 2. The fitting of the experimental results examined in reference (Antar 2014) is discussed in this figure. Based on this figure, the fitting parameters in Table 1 are calculated. Through the varied values of Dγ (Gy), the figure demonstrates a sufficient matching with the experimental results. This indicates that the fitting process produces the same results as the experimental data, and the fitting parameters are suitable for calculating the (PVA/CV + CF) polymer's refractive index. Figure 2, shows the (PVA/CV + CF) refractive index for unirradiated and irradiated polymer in the range (10-70 Gy) γ-ray doses from wavelength 380 nm to 550 nm. The refractive index reduces gradually as the wavelength increases, and the changes become larger as the wavelength increases. Whereas crystallization, density, electronic structure, and defects are all potential causes for changes in the refractive index induced by γ-radiation (Antar 2014). The refractive index increases with doses of irradiation, as shown in Fig. 2; for example, when doses irradiation increases from 0 to 70 Gy, the n changes from 2.24 to 2.40 at the wavelength (λ = 555 nm). The increase in the polymer's refractive index after irradiation could be due to ionization, and/or atomic displacements caused by a gamma-ray collision with the samples, which could alter the internal structure of the polymer films (Antar 2014). . Indeed, the refractive index increased from 2.53 to 2.82 at λ = 400 nm, and from 2.25 to 2.63 at λ = 560 nm, respectively. According to Bruggeman's effectivemedium approximation as Eq. (1), the refractive index of porous silicon depends on the refractive index of silicon and the refractive index of the material inside the pores. So, any change in the refractive index of the material inside the pores, reflects on the refractive index of porous silicon material. This is the essential point on which our gammaray dosimeter is based. Whereas any change in the refractive index of doped polymer induced by γ-radiation will reflect on the refractive index of the material. In addition, the refractive index of porous silicon depends on the porosity value, as shown in Eq. (1). Figure 3b, shows the dependence of the refractive index of [PSi (PVA/CV+CF) ] on the variation of porosity. The refractive index of [PSi (PVA/CV+CF) ] decreases with an increase Fig. 2 The response of the refractive index of PVA-Polymer doped with CV + CF to the Gamma-Ray radiation variation based on the fitting of the experimental data (Antar 2014) in the porosity value from λ = 350 nm to λ = 690 nm, then increases with an increase in the porosity value for λ > 690 nm. The refractive index equals 3.12, 2.82, and 2.69 for P = 30%, 65%, and 80% at λ = 400 nm. Figure 4, shows the effect of γ-doses in the range (0-70 Gy) on the refractive index of [PSi (PVA/CV+CF) ] with porosity equal to 65%. The refractive index firstly slightly increases with the increase in the γ-ray doses and then decreases with the increase in the γ-ray doses in all wavelength ranges. Figure 5, represents the transmittance spectra of our proposed structure of the gamma-ray dosimeter for TE-modes calculated by the TMM method. The initial geometrical parameters of this structure are set as d 1 = 30 nm, and d 2 = 73 nm with porosity P 1 = 20%, and P 2 = 80%, respectively, and N 1 = 20. The photonic bandgap (PBG) appears in the visible range with the left side wavelength (λ L = 527.5 nm), right side wavelength (λ R = 678.7 nm), and the width of PBG equal ( Δ = L − R = 151.2nm ). The principle behind this structure is that the PBG works as a sensor for gamma-ray radiation. When the structure is exposed to gamma-ray radiation, the refractive index of materials will be changed and then the PBG will change as well. Before showing the effect of gamma-ray radiation on the PBG, we are doing optimization for the parameters of this structure.  Figure 6, shows the transmittance spectra of our structure at the different number of periods. We note that the PBG became sharper and steeper as the number of periods increased. In addition, there is no change in the transmission spectra of this structure, and the width of the PBG doesn't affect by increasing the number of periods. In other words, we choose N 1 = 35 in the following calculation to the PBG become more suitable for the detection of gamma-ray radiation. Figure 7, shows the effect of porosity of the first and the second layer of our structure on the PBG sensor. As shown in Fig. 7a, b with the increase in the porosity of the first layer (P 1 ) and the second layer(P 2 ), the width of the PBG decreases. We choose P 1 = 30% and P 2 = 85% for the width of the PBG to appear in a wide and suitable form. Because the primary focus of this study is on the development of radiation-resistant FBGs for use in nuclear environments in temperature and strain measurement applications. Now, we show the effect of γ-doses (Gy) from (0-70 Gy) on the PBG sensor of our radiation dosimeter, as shown in Fig. 8a. It can note that with an increase in the value of γ-doses (Gy), the left side of the PBG shifts to a higher wavelength, and the width of the PBG is affected by this radiation. This shift is due to the change in the refractive index of the Psi-layer which is induced by gamma-ray radiation.
We examine the performance of our radiation dosimeter by calculating the sensitivity of the dosemeter. The sensitivity (S) is defined as the difference in the wavelength ( Δ L ) Fig. 5 Transmittance spectra of 1D-Binary structure with thickness d 1 = 30 nm, d 2 = 73 nm, N-period = 20, and porosity of P 1 = 20%, P 2 = 80% at zero gamma-ray radiation Fig. 6 Transmittance spectra of 1D-Binary structure with thickness d 1 = 30 nm, d 2 = 73 nm, and porosity P 1 = 20%, P 2 = 80% at zero gamma-ray radiation at different N-period Page 9 of 16 755 to the difference in the refractive index of doped PVA-polymer and units of (nm/RIU), as the following Eq. (7). Figure 8b, shows the effect of γ-doses (Gy) on the left band side of the PBG L and the sensitivity of this radiation dosimeter. We noted that with an increase in γ-doses from (10 Gy) to (70 Gy), the L an increase from (521.3 nm) to (536.7 nm), and the sensitivity decrease from (176.5 nm/RIU) to (133.3 nm/RIU). We will study the geometrical parameters that will maximize the shift of the PBG's left band side, and therefore sensor sensitivity, under various radiation doses. The effect of thickness of the first layer PSi 1 with values of (33, 35, 38, and 40 nm) at different γ-doses (Gy) on the PBG and sensitivity of this will be studied, while the other parameters are kept constant. As shown in Fig. 9a, b, c, and d, generally, it noted that with an increase in the thickness of the first layer, the left side of the PBG an increase and shift to longer wavelengths at the same value of γ-dose (Gy). Eg; At γ-dose is equal (10 Gy), with an increase of d 1 (33, 35, 38, and 40 nm), the L increase with values (534.3, 543.5, 559.1, and 571.6 nm), respectively. In addition, at each value for this thickness, we study the effect of γ-doses (Gy), and we noted that the L shifted (a) (b) (c) (d) Fig. 9 The effect of the thickness of first layer PSi 1 (PVA/CV+CF) on the properties of our design for TE at d 2 = 73 nm, N 1 = 35, and porosity P 1 = 30%, P 2 = 85% at γ-doses (Gy) from (0-70 Gy) Fig. 10 The effect of the thickness of first layer PSi 1 (PVA/CV+CF) on the sensitivity of our design for TE at d 2 = 73 nm, N 1 = 35, and porosity P 1 = 30%, P 2 = 85% at γ-doses (Gy) from (0-70 Gy) Page 11 of 16 755 to higher wavelengths with an increase in the value of γ-doses (Gy). Then, we study the sensitivity of the different thicknesses of the first layer at different γ-doses (Gy), as shown in Fig. 10. We conclude from Fig. 10 that, when the thickness of the first layer equals the value of 38 nm, our radiation dosimeter gives sensitivity with very high stability and equals ≈ 195 nm/RIU. Consequently, the thickness of the first layer is taken as 38 nm. Secondly, we study the effect of the thickness of the second layer PSi 2 with values (72, 74, 76, and 77 nm) at different γ-doses (Gy) on the PBG and the sensitivity of this radiation dosimeter. The effect of the thickness of the second layer gives the same behavior as the first layer. As shown in Fig. 11a, b, c, and d, at γ-dose is equal (10 Gy), with an increase of d 2 (72, 74, 76, and 77 nm), the L increase with values (554.6, 563.9, 575.1, and 581.6 nm), respectively. With an increase in the value of the γ-doses (Gy) at each value of the thickness of the second layer, the L shifted to higher wavelengths. The sensitivity at each thickness of the second layer and at different values of the γ-doses (Gy) was studied as shown in Fig. 12. We note that at each value of the thickness of the second layer, with the increase in the value of the γ-doses (Gy), the sensitivity gradually increases. When the thickness of the second layer equals the value of 72 nm, the sensitivity is characterized by very high stability at each of the applied γ-doses (Gy) and equals ≈186 nm/RIU. Therefore, the thickness of the second layer is taken as 72 nm.

(a) (b)
(c) (d) Fig. 11 The effect of the thickness of second layer Psi 2 (PVA-Polymer) on the properties of our design for TE at d 1 = 38 nm, N = 35, and porosity of P 1 = 30%, P 2 = 85% at γ-doses (Gy) from (0-70 Gy) The relation between the left side of the PBG and the γ-doses (Gy), in addition to the relation between the sensitivity and the γ-doses (Gy) at the optimized parameters, is given by the following equations based on the data fitting in the form of the 4th-degree polynomial: Finally, a comparison between our study and previous experimental radiation dosimeter used is shown in Table 2. This table shows firstly the proposed gamma-ray dosimeter based on 1D-photonic crystals and using porous silicon layers is a unique study and did not exist before. Furthermore, this radiation dosimeter achieved the highest sensitivity of 186 nm/ RIU compared to published results in this part with very stability along the range of visible wavelengths when the design is exposed to gamma-ray doses from 0 to 70 Gy.

Conclusion
We developed a highly sensitive 1D-PhC radiation dosimeter based on PSi-layers infiltrated by PVA-polymer doped with crystal violet (CV) and carbol fuchsine (CF) dyes. The theoretical analysis is investigated by fitting the experimental data of the doped PVA-polymer, the Bruggeman's effective medium equation of PSi-layer, and the transfer matrix method for calculating the optical properties of the dosimeter structure. The numerical results demonstrated that the PSi-layers enhanced the refractive index of the doped PVA-Polymer. In addition, they illustrated the idea of this radiation dosimeter is based on the shift in the PBG when it is exposed to gamma-ray radiation. Physically, this shift is due to the refractive index of doped PVA-Polymer depending on the γ-doses (in Gy unit). Therefore, the refractive index of PSi-layers is changed when exposed to γ-doses. The novelty of this pepper lies in the fact that this radiation dosimeter achieved a high sensitivity of 186 nm/RIU 1R = 0.84006 Fig. 12 The effect of the thickness of second layer Psi 2(PVA-Polymer) on the sensitivity of our design for TE at d 1 = 38 nm, N = 35, and porosity P 1 = 30%, P 2 = 85% at γ-doses (Gy) from (0-70 Gy) with very stability along of the range of visible wavelengths when the design is exposed to gamma-ray doses from 0 to 70 Gy. Furthermore, the effects of the thickness of the PSilayers are studied to achieve the highest sensitivity. To the author's knowledge, this is the first time 1D-PhC based on PSi-layers has been used as a gamma-ray dosimeter. Finally, the other purpose of this radiation dosimeter is to be used as radiation-resistant FBGs for usage in nuclear environments in temperature and strain measurement applications.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
Data availability Requests for materials should be addressed to Arafa H. Aly.
Code availability Requests for materials should be addressed to F. Sayed

Conflict of interest
The authors declare they have no conflicts of interest.
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