Study of Utilization of Embedded Metal Nanoparticles in Dielectric Thin Film for Humidity Sensing

This paper presents a theoretical study of the utilization of the shift in the reflection peak of the thin dielectric film with embedded metal nanoparticles (NPs) towards humidity and vapor applications. The presence of the NPs in the film results in a complex effective index. Hence, the reflected light at the superstrate-film interface causes a phase shift when the index of the surrounding is changed. This alters the reflected spectrum of the formed Fabry-Perot, for both the reflection peak wavelength and intensity. Here, the dynamic range of the proposed sensor is optimized through the variation of the film thickness and nanoparticle metal type, as well as the volume fraction.


Introduction
Monitoring humidity is essential for comprehensive applications in electronic and chemical industries, optoelectronics devices, agriculture, medical diagnoses, metrology, and aerospace [1,2]. To adapt a comfortable life to human beings, it is important to control humidity levels inside buildings, cars, shops, and other places [3]. Therefore, it is necessary to monitor and measure humidity using low-cost, small-size, high-stability, and high-sensitivity humidity sensors. The development of humidity sensors differs according to the type of the structural material, e.g., organic and inorganic materials. Inorganic materials used in the fabrication of humidity sensor take different forms including nanowires [4], nanotubes [5], and nanofiber [6]. Organic and composite materials, such as nafion persulphonate, are used to fabricate the humidity sensors [7]. In addition, there are graphene oxide [8] and plasmonic materials [9] based sensors. These sensors work at different mechanisms including changes of the resistivity, capacity, optical properties, piezoresistivity, magnetism, and frequency (impedance) of the active material with the humidity level [6,10].
Nanomaterials' distinctive optical, mechanical, electrical, and magnetic properties make them a vital candidate for many applications including but not limited to sensors [1], solar cells [11,12], optoelectronic devices [13], and waveguides [14]. In particular, the sensor technology has a high leap in the technology world due to the use of nanotechnology and nanomaterials. This leads to an encroachment in the field of humidity sensors [15].

Photonic Sensors 156
Several types of nanoparticles (NPs) are used in fabricating the humidity sensor. For example, flexible impedance-type humidity sensors by using gold (Au) NPs in different nanocomposites are presented by different authors, e.g., in [16]. Silver (Ag) NPs in various nanocomposites are used to synthesize humidity sensors [17][18][19]. These sensors have been developed in different ways such as the chemical reduction process [17], the electrostatic spray deposition technique [18], and the vacuum deposition process [19]. Different parameters have been studied in the development of these sensors. Some considered the ageing of nanocomposite coatings and the influence of an aqueous environment on their internal structure properties [19]. The others considered the influence of the deposition times on properties of films [18].
Adhyapak et al. [20] used Au(c)-Ag(s) bimetallic NPs to fabricate resistors on ceramic rods to measure relative humidity response. Titanium dioxide (TiO 2 ) NPs that have a high surface area are waved in different nanostructures to build high sensitivity humidity sensor, i.e., LiCl-doped TiO 2 NPs sensors [2]. Other structures like CuO NPs [3], ZnO nanorods [21], and nickel (Ni) NPs [22] are also used to structure humidity sensors. In this work, we theoretically propose a device for humidity/vapor detection in air by the optimization of the shift in the reflection peak from a thin polymer film with different types of NPs impurities. Section 2 introduces the proposed humidity sensor. Section 3 presents the calculation results followed by conclusions in Section 4.

Proposed humidity sensing scheme
In this theoretical study, a simple alternative approach is used by utilizing the shift in the reflection peak from metal NPs impeded in a polymer host thin film that is coated on a glass substrate as illustrated in Fig. 1. The presence of metal NPs results in a complex effective index, n eff , of the thin film.
In (1), ε h is the host polymer permittivity, ε m is the NP metal permittivity, and f is the NP filling factor [23]. In the analysis, the effective index is calculated by using Maxwell's Garnett effective medium theory where the particles' sizes are assumed to be much smaller than the optical wavelength [24]. where m and j can be 1, 2 or 3. The refractive indices n 1 and n 3 are for the substrate and superstrate, respectively. The coefficient ψ j =1 is for TE polarization and ψ j =1/ε j is for TM polarization. In (2), the term added to r 12 on the right hand side depends on the Fresnel reflection and transmission at the two interfaces (film-substrate and film-superstrate) as well as the propagation/attenuation inside the film. The constant k 0 is the free space propagation constant. These coefficients are complex in nature due to the absorption of the metal NPs.
The proposed model in Fig. 1 assumes a glass substrate with fixed index n 1 . The superstrate index, n 3 , however changes with the presence of vapor; n 3 becomes an effective index composed of air with certain concentration of water. Its value ranges from 1 to a maximum of 1.33. The change of n 3 due to humidity alters the complex Fresnel reflection coefficient at the superstrate-film interface (r 23 ). This causes a shift in the amplitude and phase of the term added to r 12 on the right side of (2). Hence, it changes the total reflection coefficient, r. This by its turn affects the reflection spectrum in terms of the peak wavelength location and the maximum amplitude as illustrated in Fig. 2. The plots are calculated for gold NPs in a polymer (n h = 1.446) and a glass substrate (n 1 = 1.5) for f = 0.06 when TE wave is considered.
The calculated reflectance shows a reduction in the amplitude when n 3 increases from air (n 3 = 1) towards water (n 3 = 1.33). There is also a clear blue-shift in the peak wavelength. In order to optimize the response of the structure, two figures of merit are introduced as defined in (3a)  Three parameters are varied in this study: the type of metal NPs, the film thickness d, and the NP filling factor f.
It is worth mentioning that in the presented analysis, the change of the effective index around the NPs due to polymer swelling [25] or porosity in the host medium [26] is not considered. Only changes on the film surface are considered to cause a shift in the complex Fresnel reflection and hence the total Fabry-Perot reflectance spectrum. This is shown by the blue-shift in the reflection peak when an increase in the superstrate index is depicted in Fig. 2. This trend is opposite to the typical red-shift observed when the host medium index is increased by the change of the surrounding, duty porosity in the nanocomposite film.

Calculation results
The optimization process aims at maximizing the dynamic ranges through comparing different metal NPs inclusions as well as film thickness d and volume fraction f. Gold NPs are first tested when varying d and f as shown in Fig. 3. The plots in Fig. 3(a) indicate that the value of film thickness d, which causes the maximum peak reflection R max , decreases as the value of the filling factor f increases. This is logical as higher f causes larger absorption in the effective film. For example, for f between 0.05 and 0.06, d of 80 nm causes the highest R max . For f = 0.09, d causes that the highest R max decreases to 70 nm. Here, R max is calculated at n 3 =1. Figures 3(b) and 3(c) show that the wavelength dynamic range is maximized for d less than 40 nm. However, the intensity dynamic range is higher for d > 90 nm.
The changes of the wavelength and peak reflectance for these two limits are depicted in Fig. 4 for a volume fraction, f = 0.055. Here, R max is maximized for the higher film thickness when compared with gold (100 nm for f between 0.05 and 0.06). The intensity dynamic range is shown to increase for the higher thickness reaching a peak similar to that of R max . The plots in Figs. 4(c) and 4(d) show the calculated sensitivities for the peak amplitude detection and peak wavelength detection for the two selected film thicknesses.  The sensitivity duty peak amplitude seems to be almost constant for different thicknesses. However, the sensitivity due to the change of the peak wavelength with superstrate index decreases for larger thickness. The wavelength dynamic range in Fig. 5(c), however, shows three distinctive regions: high dynamics and low d, low dynamics, and a second high dynamics at high d. As illustrated in Fig. 6, high wavelength dynamic is caused by the broadening of the plasmonic peak for both the low and high film thicknesses. This is not the case when the peak is defined as in Fig. 6(b).
For the sake of comparison, the calculations have been repeated for Ni NPs. Figure 7 displays the intensity dynamic range as the function of d at different values of f. It can be seen that for d > 50 nm and f > 0.03 the intensity increases as f and d increase. At a low volume fraction such as f = 0.02, the intensity dynamic range decreases as d increases to reach the minimum at d = 110 nm. The inset of Fig. 7 shows the reflection at different values of n 3 as the function of the wavelength. It can be seen clearly that as n 3 goes from pure air to pure water, a decrease follows in the peak accompanied with blue shift for d = 80 nm.  Comparing the intensity dynamic values for the three nanoparticles, the dynamic range dependency on the film thickness and volume fraction seems to follow a similar trend for Au and Cu. This is however different in the case of Ni where a more dramatic change is observed when moving from lower to higher thicknesses. This can be due to high absorption of Ni nanoparticles.

Conclusions
In this work, a humidity sensor is proposed by using NPs hosted in polymer as a film layer on the top of glass substrate and covered by air superstrate. The NPs, which are used in this calculation, are Au, Cu, and Ni. The effect of changing the type of NPs, the filling factor, and the thickness of the film on the performance of the sensor is studied extensively. The calculation results for the three metals indicate that a film thickness between 70 nm and 100 nm results in the maximum intensity dynamic range for volume fractions more than 0.05. Sharp plasmonic peaks are also presented within the same operation region for Au and Cu giving wavelength dynamic ranges around 20 nm and 10 nm, respectively. Higher wavelength dynamic ranges can be achieved for the thinner film. However, the plasmonic peak for the thin film has a broader spectrum and hence can cause a large error in detection. Hence, for practicalities, a thickness range between 70 nm and 100 nm should be suitable for operation in both the intensity and wavelength modulations for the given host medium and metals.