Annealing Temperature Effect on the Properties of CoCe Thin Films Prepared by Magnetron Sputtering at Si(100) and Glass Substrates

Abstract

This study explores cobalt–cerium (Co₉₀Ce₁₀) thin films deposited on silicon (Si) (100) and glass substrates via direct current (DC) magnetron sputtering, with thicknesses from 10 nanometer (nm) to 50 nm. Post-deposition annealing treatments, conducted from 100 °C to 300 °C, resulted in significant changes in surface roughness, surface energy, and magnetic domain size, demonstrating the potential to tune magnetic properties via thermal processing. The films exhibited hydrophilic behavior, with thinner films showing a stronger substrate effect, crucial for surface engineering in device fabrication. Increased film thickness reduced transmittance due to photon signal inhibition and light scattering, important for optimizing optical devices. Furthermore, the reduction in sheet resistance and resistivity with increasing thickness and heat treatment highlights the significance of these parameters in optimizing the electrical properties for practical applications.

1. Introduction

Magnetoresistive random access memory (MRAM) is a non-volatile memory technology that stores data using magnetoresistance, offering low power consumption and permanent storage. MRAM records “0” and “1” signals by leveraging the spin properties of electrons, which alter magnetoresistance through the magnetization of free layers in the magnetic structure. This operation is similar to data storage on hard disks, where stored data remain stable until altered by an external magnetic field. MRAM is known for its low energy consumption and fast response time [1]. The selection of a cobalt (Co) and cerium (Ce) alloy as a magnetic thin film target is driven by the alloy’s promising yet underexplored potential in magnetic materials. Adding 10% Ce to Co in cobalt–cerium (Co₉₀Ce₁₀) films significantly enhances magnetic properties, such as anisotropy and coercivity (Hc) [2]. Ce interacts with the Co matrix, stabilizing magnetic domains and reducing magnetic noise, which is beneficial for high-density magnetic storage and spintronic applications [3]. The motivation for creating Co₉₀Ce₁₀ alloys stems from the need for multifunctional materials with improved magnetic, structural, optical, and corrosion-resistant properties [4,5]. Pure Co films, despite their excellent magnetic characteristics, face challenges like grain growth during heat treatment and limited corrosion resistance [6,7]. Adding Ce enhances corrosion resistance, making Co₉₀Ce₁₀ films more suitable for oxidative or corrosive environments [8]. This makes the alloy ideal for protective coatings and applications requiring long-term environmental stability. Adjusting Ce content in Co₉₀Ce₁₀ films allows for the customization of electronic and optical properties, paving the way for advanced materials in optoelectronics, coatings, and sensors. Research is driven by the need for materials with precisely tuned optical and electronic characteristics. The study of Co₉₀Ce₁₀ thin films focuses on developing materials with tailored magnetic, optical, and electrical properties for microelectronics, spintronics, and optical devices. The combination of Co and Ce enables fine-tuning of these properties through processes like magnetron sputtering and annealing. A critical focus of this study is to understand the influence of annealing-induced modifications in surface roughness on performance, including magnetic domain structure, optical transmittance, and electrical conductivity [9,10]. This study seeks to enhance material performance for targeted applications by addressing challenges related to film uniformity and optimization. The novelty of this research lies in its comprehensive analysis of how annealing affects the surface roughness of Co₉₀Ce₁₀ films and the resulting impact on their properties. Unlike previous studies that focus on individual aspects, this work provides a holistic view of how post-deposition treatments influence surface roughness and related properties. It also delves into the less-explored relationship between surface roughness and optical transmittance, offering new insights into light scattering caused by surface irregularities. Additionally, the study evaluates the effects of using silicon (Si) (100) and glass substrates, which are less commonly studied in this context [11]. Si substrates are widely used in semiconductors due to their availability, while glass substrates offer advantages like heat resistance and smoothness, which are crucial for thin film deposition. In this study, Co₉₀Ce₁₀ thin films were sputtered onto Si(100) and glass substrates with thicknesses ranging from 10 nanometer (nm) to 50 nm, then heat-treated at 100 °C, 200 °C, and 300 °C, and analyzed to understand the relationship between surface roughness and other properties. The primary objective of this study is to thoroughly investigate the effects of surface roughness on the properties of Co₉₀Ce₁₀ thin films, particularly for their potential applications in MRAM. By examining how annealing influences surface roughness and its subsequent impact on magnetic, optical, and electrical properties, this research aims to optimize these films for enhanced performance in high-density magnetic storage and spintronic devices. The study focuses on Co₉₀Ce₁₀ films deposited on Si(100) and glass substrates through magnetron sputtering, exploring the effects of post-deposition annealing treatments on surface morphology, magnetic domain size, electrical conductivity, and optical transmittance. Emphasizing the potential for tuning these critical characteristics through thermal processing, the research specifically considers how variations in film thickness and annealing temperature influence overall performance. Ultimately, the findings seek to deepen our understanding of the intricate relationship between surface morphology and the functional properties of Co₉₀Ce₁₀ films, contributing to the development of advanced materials tailored for MRAM applications. This study focuses on understanding how annealing influences surface roughness and magnetic domain configurations in Co₉₀Ce₁₀ thin films and how these changes impact critical physical properties, including electromagnetic, nanomechanical, and optical characteristics. Unlike previous studies, which have largely overlooked the combined effects of surface roughness and magnetic domain evolution under annealing treatment, this research uniquely establishes their significance in tailoring functional properties [12,13]. By systematically correlating these microstructural changes with performance metrics, the study provides new insights into optimizing Co-based thin films for advanced applications in flexible electronics and multifunctional devices. Previous research compared the magnetic and electrical properties of CoCe materials with those of CoFeDy, as summarized in

Table 1. Significant properties for CoFeDy and CoCe materials.

Materials	Structure	Ra (nm) at 50 nm	Maximum χac (a.u.)	Resistivity (Ω·cm)
Glass/Co40Fe40Dy20 [14] 10–50 nm at RT and annealed conditions	Amorphous	2.41–2.87	0.07–0.41	8 × 10−3–6 × 10−3
Glass/Co90Ce10 10–50 nm at RT and annealed conditions (current research)	Amorphous	1.03–1.19	0.06–0.90	2.2 × 10−5–0.5 × 10−5

[14]. The results indicate that a smoother surface with a lower roughness arithmetic mean deviation (Ra) corresponds to a higher maximum low-frequency alternating-current magnetic susceptibility (χ_ac) and lower resistivity.

2. Materials and Methods

Preparation of CoCe thin films and annealing: CoCe thin films were produced on Si(100) and glass substrates with thicknesses ranging between 10 nm and 50 nm using direct current (DC) magnetron sputtering. Fabrication was performed at room temperature (RT), followed by annealing at 100 °C, 200 °C, and 300 °C for 1 h (h) at 2 × 10⁻³ Torr with argon (Ar) gas. Sputtering was performed with a power density of 1.65 Watt (W)/cm² and a sputtering power of 50 W, with a base pressure of 3 × 10⁻⁷ Torr and working Ar gas pressure of 3 × 10⁻³ Torr. The substrate rotated at 20 revolutions per minute (rpm) with an Ar gas flow rate of 20 standard cubic centimeters per minute (sccm).

Composition: The alloy of Co 90 atomic percent (at.%) and Ce 10 at.% was prepared using a target from Gredmann Taiwan Ltd., with the composition verified by the manufacturer. Any deviations in composition could result from Ar ion bombardment during sputtering [15]. Multi-directional and multi-angle scattering of sputtered atoms may also contribute to variations in the composition [16,17]. The coating composition was determined by an energy-dispersive spectrometer (EDS, JEOL, Tokyo, Japan) and is shown in

Table 2. Elemental composition of 10 nm CoCe films deposited on Si(100) and glass substrates, expressed in mean value of weight percent (wt.%) and atomic percent (at.%). Standard deviation was calculated at multiple spatial positions across the sample surface.

Substrate	Co wt.%	Ce wt.%	Co at.%	Ce at.%
Si(100)	80.65 ± 2.96	19.35 ± 1.21	90.83 ± 3.01	9.17 ± 1.03
Glass	80.14 ± 1.71	19.86 ± 1.15	90.56 ± 1.56	9.44 ± 0.98

. The elemental composition of 10 nm CoCe films deposited on Si(100) and glass substrates is presented as the mean values of weight percent (wt.%) and atomic percent (at.%). The standard deviation was determined based on measurements taken at multiple spatial positions across the sample surface, ensuring an accurate representation of compositional uniformity.

Chemicals: Contact angles were measured three times using deionized (DI) water and glycerin for accuracy. The average contact angles were then calculated using a contact angle measuring device (CAM-110, Nano Technologies, Tainan City, Taiwan) to determine surface energy [18,19,20].

Techniques and characterization: The structural analysis was conducted using grazing incidence X-ray diffraction (GIXRD) patterns (CuK_α1 radiation, Panalytical X’pert PRO MRD, Philips, Amsterdam, the Netherlands) with a low incidence angle of approximately 2°. Low-frequency alternating-current magnetic susceptibility (χ_ac) was analyzed using a MagQu acQuan II analyzer (MagQu, New Taipei City, Taiwan) across a frequency range of 10 Hz to 25,000 Hz. The χ_ac values, expressed in arbitrary units (a.u.), were based on magnetization strength, with the highest χ_ac frequency identified as the best resonance frequency (f_res). Magnetic domain and morphological characterization were conducted using magnetic force microscopy (MFM, NanoMagnetics Instruments, NMI, Oxford, UK) and atomic force microscopy (AFM, NanoMagnetics Instruments, ezAFM) with scan sizes of 20 μm × 20 μm and 10 μm × 10 μm, respectively. Non-contact mode AFM at RT was used to assess surface roughness, calculated as the arithmetic mean deviation (Ra). Film thickness was precisely measured using AFM via the height difference method. Electrical resistance was determined with a four-point probe tester (Sadhudesign, Hsinchu City, Taiwan). Hardness (H) of the Co₉₀Ce₁₀ films was tested using a Mechanical Testing & Simulation (MTS) Nano Indenter XP (MTS, Minneapolis, MN, USA) with a Berkovich tip and the continuous stiffness measurement (CSM) method. Each sample underwent ten indentation measurements, with the load reduced to 10% of the maximum before removing the indenter. Indentation was performed in 40 stages, recording the depth at each step. Data precision was ensured by averaging the results from six indentations per sample. To assess the optical properties, a Spectro Smart Analyzer (OtO Photonics, Spectra Smart, Collimage, Taipei, Taiwan) was used in conjunction with a visible light source covering a wavelength range of 500–800 nm.

3. Results

3.1. XRD Structure

Figure 1a,b show the XRD results of Co₉₀Ce₁₀ thin films of 50 nm deposited on Si(100) and glass substrates under four different conditions. The results reveal that the films exhibit an amorphous structure, likely due to insufficient annealing temperatures and inadequate thermal energy to drive grain growth and facilitate crystallization [21,22].

3.2. Surface Roughness and Surface Energy

The surface morphology analysis of Si(100)/Co₉₀Ce₁₀₀ thin films at a thickness of 50 nm under four different conditions is presented in Figure 2a–d. The surface morphology analysis of the Si(100) substrate, exhibiting a roughness average Ra of 0.72 nm, is presented in Figure 2e. The analysis reveals a generally flat surface morphology. However, a trend is observed where the surface roughness increases with rising annealing temperature. Specifically, the surface roughness increases from 1.19 nm in the as-deposited state to 1.63 nm following annealing at 200 °C, suggesting that heat treatment induces surface roughening, likely due to the formation of coarse particles [23]. In contrast, additional annealing between 200 °C and 300 °C leads to a reduction in surface roughness from 1.63 nm to 1.31 nm. This reduction in roughness may be attributed to enhanced surface atom mobility due to heat treatment, leading to the filling of gaps and vacancies, thereby producing a smoother surface [24]. The increase in surface roughness up to 200 °C annealing is likely due to atomic rearrangement and surface atom mobility rather than grain growth or coalescence [25]. In the absence of crystallization, localized atomic diffusion can lead to clustering or uneven distribution of atoms, resulting in a rougher surface. This behavior is typical for amorphous films, where thermal energy promotes redistribution without forming crystalline grains. At 300 °C, the reduction in roughness can be attributed to enhanced atomic migration and surface diffusion, which promote a more stable atomic arrangement and stress relaxation, similar to the trends observed in our Co₉₀Ce₁₀ films [26,27].

A similar trend is observed in the Glass/Co₉₀Ce₁₀ film at a thickness of 50 nm under four different conditions, as illustrated in Figure 3a–d. The surface morphology analysis of the glass substrate, featuring a roughness average Ra of 0.6 nm, is illustrated in Figure 3e. The surface roughness exhibits an upward trend, increasing from 1.03 nm in the as-deposited state to 1.19 nm following annealing at 200 °C. Furthermore, to verify that the temperature-dependent variation is statistically significant, the standard deviations of the Ra mean values across four conditions are reported as 0.5329, 0.01, 0.81, and 0.1681 for the Si(100) substrate, and 0.8649, 0.0225, 0.5184, and 0.0625 for the glass substrate, respectively. However, upon further annealing at 300 °C, the surface roughness decreases slightly to 1.10 nm. Notably, the surface morphology of the Glass/Co₉₀Ce₁₀ film is relatively flatter than that of the Si(100)/Co₉₀Ce₁₀ film, as indicated by the differences in surface roughness.

The surface energy is calculated according to the contact angle and Young’s equation [15,16,17].

Young’s equation is

σ_sg = σ_sl + σ_lg cosθ

(1)

In the equation, σ_sg denotes the surface free energy of the solid; σ_sl represents the interfacial tension between liquid and solid; σ_lg is the surface tension of the liquid; and θ is the contact angle. Figure 4a illustrates the surface energy of the Si(100)/Co₉₀Ce₁₀ film under four different conditions. The data reveal that the as-deposited film exhibits the highest surface energy, which decreases following heat treatment. This reduction in surface energy is attributed to the rearrangement of surface atoms during heat treatment, leading to an increase in the disorder of the film system and a consequent reduction in energy [28]. Similarly, Figure 4b shows the surface energy of the Glass/Co₉₀Ce₁₀ film under four different conditions, where a comparable trend is observed, with higher surface energy prior to heat treatment and a subsequent decrease post-treatment. When the roughness is below 8 nm, the impact of surface roughness on the contact angle is minimal, suggesting that the contact angle may not have a direct relationship with surface energy; instead, surface structural defects could be the primary influencing factor [29]. The reduction in surface energy with heat treatment can be attributed to stress relaxation and enhanced atomic rearrangement. As the films are annealed, atomic diffusion increases, leading to a reduction in surface defects and grain boundary areas, which typically contribute to higher surface energy. This process is well-documented in thin films, where annealing leads to more stable configurations and lower surface energy [30,31].

3.3. Hardness

It is well established that thinner films are more susceptible to pronounced substrate effects, leading to significant errors in hardness measurements. Consequently, films with a thickness of less than 30 nm were excluded from the current measurements [32]. Figure 5a illustrates the hardness variation of Si(100)/Co₉₀Ce₁₀ films as the thickness increases from 30 nm to 50 nm under four different conditions. The results indicate a clear increase in hardness due to heat treatment, which is hypothesized to be influenced by the significant interfacial effects in thinner films, contributing to the observed reduction in hardness at lower thicknesses. According to existing studies, during heat treatment, atomic rearrangement occurs as thermal energy facilitates localized diffusion within the amorphous structure. In the absence of grain boundaries, hardness enhancement is likely due to the densification of the amorphous structure and the reduction of internal defects, rather than grain growth or boundary migration. This process improves atomic packing efficiency, which contributes to the observed increase in hardness [33]. As the film thickness increases, the interfacial effects diminish, allowing the film to exhibit mechanical properties more characteristic of the material, leading to increased hardness. The literature suggests that, in amorphous materials, thermal treatment can enhance hardness through mechanisms such as densification and the reduction of free volume [34]. Experimental data reveal that the maximum hardness achieved was 11.87 GPa at a film thickness of 50 nm following heat treatment at 200 °C, while the minimum hardness was 8.27 GPa at 30 nm for the as-deposited film. Figure 5b presents the hardness variation of Glass/Co₉₀Ce₁₀ films with increasing thickness from 30 nm to 50 nm at different heat treatment temperatures. A similar trend is observed in these films, with the maximum hardness recorded at 11.09 GPa for the 50 nm film heat-treated at 200 °C and the minimum at 8.16 GPa for the 30 nm as-deposited film. The hardness trends observed are consistent with the results from AFM analysis, confirming that the hardness of Co₉₀Ce₁₀ thin films is strongly correlated with surface roughness. The observed trend is that the amorphous Co₉₀Ce₁₀ thin film exhibits the highest hardness after annealing at 200 °C but a decrease in hardness after annealing at 300 °C. The highest hardness at 200 °C is likely due to optimal atomic densification and defect reduction, while the decrease at 300 °C may stem from over-relaxation, altered mechanical properties, and the effects of reduced surface roughness [35]. Increased surface roughness generally leads to higher hardness values, as surface asperities create localized stress concentrations during nanoindentation. These stress concentrations enhance the material’s resistance to plastic deformation, thus increasing the measured hardness. Additionally, the asperities may also contribute to increased frictional forces between the indenter and the material, further elevating hardness values [36,37].

3.4. Magnetic Domain Behavior and χ_ac Analysis

Figure 6a–h present the magnetic domain images of 50 nm Co₉₀Ce₁₀ thin films deposited on Si(100) and glass substrates, respectively. The magnetic domain structures are more pronounced in the Glass/Co₉₀Ce₁₀ films, where the domains appear in a stripe-like pattern. Notably, the area of these magnetic domains increases progressively from the as-deposited state to the 200 °C annealed state. This enlargement is attributed to the heat treatment process, which facilitates the migration of atomic or lattice vacancies, thereby relieving residual stresses within the films. The rearrangement of atoms and lattices during annealing enhances surface quality and eliminates internal stresses [38]. These changes result in an increase in magnetization strength by extending the distance between magnetic walls within the expanded domains. However, after further annealing at 200 °C to 300 °C, the magnetic domains become smaller. This reduction is likely due to increased atomic mobility and localized structural rearrangements within the amorphous matrix. These changes reduce internal stresses and create a more uniform distribution of magnetic moments, which facilitates the formation of smaller and more stable magnetic domains. The smaller domain size makes it more challenging to align these areas under an applied magnetic field, potentially reducing the saturation magnetization [39].

Figure 7a–h illustrate the χ_ac values of Si(100)/Co₉₀Ce₁₀ and Glass/Co₉₀Ce₁₀ films under various conditions. The χ_ac values of Co₉₀Ce₁₀ films display an increasing trend regardless of annealing, with χ_ac values rising as the measurement frequency increases. Furthermore, the χ_ac values exhibit a relative increase with greater film thickness and higher annealing temperatures. Specifically, the maximum χ_ac value for the as-deposited Co₉₀Ce₁₀ film is 0.73 and 0.70 at a 50 nm thickness on Si(100) and glass substrates, respectively. After annealing at 100 °C, these values rise to 0.92 and 0.71 and further increase to 1.11 and 0.87 following annealing at 200 °C. At 300 °C, the maximum χ_ac values reach 1.08 and 0.90 for Si(100) and glass substrates, respectively. These elevated χ_ac values suggest reduced mobility of free magnetic domains, indicating increased spin sensitivity [40]. This trend highlights that χ_ac increases with rising film thickness and annealing temperature, likely due to enhanced alignment of magnetic domains and reduced internal magnetic losses [41,42,43]. Improved magnetic domain alignment consequently results in higher χ_ac values, enhancing the material’s efficiency for electromagnetic applications.

3.5. Electricity Properties

The experimental results reveal a unique relationship between film thickness, annealing temperature, and electrical properties, which is shown in Figure 8. Figure 8a,b depict that the resistivity of Si(100)/Co₉₀Ce₁₀ and Glass/Co₉₀Ce₁₀ films decreases significantly with increasing thickness and annealing temperature. In the as-deposited state, the resistivity of Si(100)/Co₉₀Ce₁₀ film decreases from 2.20 × 10⁻⁵ Ω·cm for a 10 nm film to 0.69 × 10⁻⁵ Ω·cm for a 50 nm film annealed at 300 °C. Glass/Co₉₀Ce₁₀ film resistivity decreases from 2.20 × 10⁻⁵ Ω·cm for a 10 nm film to 0.83 × 10⁻⁵ Ω·cm for a 50 nm film annealed at 300 °C. Figure 8c,d show a similar trend for the sheet resistance of Co₉₀Ce₁₀ films, where the value decreases gradually with increasing film thickness and annealing temperature. In the as-deposited state, the resistivity of Si(100)/Co₉₀Ce₁₀ film decreases from 2.20 × 10² Ω/sq for a 10 nm film to 0.13 × 10² Ω/sq for a 50 nm film annealed at 300 °C. Glass/Co₉₀Ce₁₀ film resistivity decreases from 2.20 × 10² Ω/sq for a 10 nm film to 0.16 × 10² Ω/sq for a 50 nm film annealed at 300 °C. The decrease in resistivity and resistance with increasing film thickness can be understood through several physical mechanisms associated with thin films. As the thickness of a thin film increases, the contribution of surface and grain boundary scattering to the overall resistivity diminishes. In thinner films, electrons are more prone to scattering at surfaces and grain boundaries, leading to increased resistivity. As the film becomes thicker, the volume of the material dominates the conduction process, and bulk scattering mechanisms become more prominent, reducing overall resistivity. Moreover, thicker films generally have larger grains due to the growth process, resulting in fewer grain boundaries. Grain boundaries act as scattering centers for charge carriers, thereby increasing resistivity. When the number of grain boundaries decreases in thicker films, the resistivity correspondingly decreases [44,45]. Annealing can help in reducing point defects, such as vacancies and interstitials, which are common in as-deposited films. The reduction of these defects contributes to a decrease in resistivity as the mobility of charge carriers increases [46]. Moreover, the relationship between increased surface roughness and decreased resistivity in thin films can be reasonably explained by considering the effect of annealing on atomic arrangement. In amorphous films, annealing promotes localized atomic diffusion and structural relaxation, which can lead to the formation of smoother conductive pathways despite the overall increase in surface roughness [47]. Additionally, the rough surface may create more conductive pathways, contributing to lower resistivity [48,49]. When the film thickness increases from 30 nm to 40 nm, the resistivity of all samples is increased. It can be reasonably concluded that oxidation can significantly affect the resistivity of thin films. When the thickness of a film increases, the likelihood of oxidation during deposition or subsequent processing may also increase. Oxidized layers often have different electrical properties compared to the underlying material, contributing to higher overall resistivity [50].

3.6. Optical Property

Figure 9a illustrates the average transmittance of Glass/Co₉₀Ce₁₀ films under varying conditions, showing how transmittance changes with increasing film thickness and heat treatment temperature. As the thickness of the as-deposited Co₉₀Ce₁₀ film increases from 10 nm to 50 nm, the average transmittance decreases significantly from 15.02% to 0.13%. Following heat treatment at 100 °C, 200 °C, and 300 °C, the average transmittance decreases further, reaching 0.07%, 0.09%, and 0.07%, respectively. This significant reduction in transmittance within the visible light range correlates with increased film thickness and surface roughness. The inverse relationship between surface roughness and transmittance is attributed to enhanced light scattering and reflection by the rough surface, leading to decreased direct transmission. The discrepancy in the 300 °C annealing data, where the transmittance of thinner films does not decrease with increased surface roughness, may stem from the non-uniform impact of measured roughness on the optical path, particularly in thinner films, resulting in higher transmittance [51]. Additionally, increased surface roughness can cause phase interference and greater light absorption, further reducing transmittance. These findings are consistent with the literature, which confirms that the combined effects of film thickness and interfacial interactions hinder photon transmission, thereby decreasing optical transmittance and increasing absorption intensity [52,53]. The thickness effect on optical transmittance is often more significant than the surface roughness effect due to several factors related to light propagation and absorption in thin films. In thin films, optical transmittance is heavily influenced by interference effects. When light hits a film, some of it is reflected at the surface and some enters the film, where it can be reflected at the film–substrate interface [54]. The interference of these reflected waves depends on the film thickness, leading to constructive or destructive interference. Thus, variations in thickness can produce significant changes in transmittance that may overshadow the effects of surface roughness [55,56]. While surface roughness can scatter light and reduce transmittance, its effect is typically more pronounced at certain wavelengths, particularly when the roughness is comparable to the wavelength of light. In many cases, the thickness-induced absorption and interference effects will lead to a more noticeable overall change in transmittance. Indeed, for thin films, optical transmittance is predominantly influenced by the absorption coefficient rather than surface roughness. Surface roughness typically affects light scattering, but when roughness is smooth, its effect on transmittance tends to be minimal. Several studies support this observation, indicating that smooth surfaces result in negligible scattering and, hence, a limited effect on overall transmittance. The absorption coefficient (α) is closely related to the material’s intrinsic properties, such as electronic transitions and bandgap, and is directly influenced by the film’s thickness. The optical transmittance (T%) of a film follows the Beer–Lambert law, where T depends on both thickness (d) and the absorption coefficient through the following equation:

T = exp(−αd)

(2)

Thus, variations in film thickness significantly alter the transmittance by changing the effective path length for photon absorption, a point that becomes especially important in thin films. This reinforces the notion that thickness and absorption are primary factors governing transmittance [57,58,59]. Eventually, while surface roughness may slightly influence optical scattering, its impact on transmittance in the case of smooth films is likely minimal. Instead, prioritizing the absorption coefficient and conducting more comprehensive optical measurements, including reflectance, would allow for a more accurate and independent assessment of the films’ optical performance. Moreover, the absorption coefficient of Glass/Co₉₀Ce₁₀ films is presented in Figure 9b. The absorption coefficient gradually decreases after reaching its peak, approaching saturation at a thickness of approximately 40 nm. Regarding the energy gap, since Co₉₀Ce₁₀ is a metallic alloy rather than a semiconductor material, it does not possess a distinct energy gap.

4. Conclusions

XRD analysis revealed the amorphous nature of the films, which persisted despite thermal treatments, indicating insufficient thermal energy for crystallization. AFM results demonstrated that surface roughness increased with annealing up to 200 °C due to atomic rearrangement and diffusion, followed by a decrease at 300 °C, attributed to stress relaxation and enhanced atomic mobility. The surface energy decreased after annealing, correlating with reduced defects and enhanced atomic rearrangement. Hardness analysis indicated a maximum value at 200 °C annealing, suggesting optimal densification and defect reduction, while the decrease at 300 °C reflected over-relaxation. Magnetic domain images revealed enhanced domain alignment and size with annealing, improving χ_ac, with maximum values observed at 200 °C. Electrical measurements showed a significant reduction in resistivity and sheet resistance with increasing thickness and annealing, attributed to decreased grain boundary scattering and defect density. Optical transmittance decreased with thickness and surface roughness, primarily due to photon absorption and scattering effects. Increased film thickness and annealing temperature enhance the χ_ac value by improving magnetic domain alignment and reducing internal losses. Thinner films exhibit higher resistivity due to surface scattering and improved light transmission. While trends in surface roughness were observed with annealing temperature, the variations were within the range of standard deviations and not statistically significant. Therefore, no conclusive relationship between annealing temperature and surface roughness can be established. Nonetheless, the study highlights that surface characteristics, particularly roughness and related factors, play an essential role in determining the magnetic, electrical, and adhesive properties of Co₉₀Ce₁₀ films. The findings demonstrate the potential of Co₉₀Ce₁₀ thin films for applications in electromagnetic devices where enhanced hardness, magnetic domain alignment, and χ_ac values, along with controlled electrical conductivity and optical transmittance, contribute to improved performance. Future work should explore optimizing annealing conditions and film thickness to further tailor these multifunctional properties. Additionally, advanced characterization techniques and modeling could provide deeper insights into the interplay between structural, magnetic, and optical properties, paving the way for their application in next-generation flexible electronic and magnetic systems.