## 4 Experimental Characterization of Si-SC Structures with SLARC
### Optical Reflectivity Characteristics  
Theoretically, the Fresnel equations describe the reflection and transmission of light when it encounters an interface between two different media. For normal incidence, the reflectivity **R** at an interface between two materials with refractive indices \(n_{1}\) and \(n_{2}\) is given by:  
\[\textbf{R}=\left(\frac{n_{1}-n_{2}}{n_{1}+n_{2}}\right)^{2} \tag{2}\]  
When a thin film of refractive index \(n_{2}\) and thickness \(d\) is applied to a substrate with refractive index n\({}_{3}\), and the incident medium is air (\(n_{1}\approx 1\)), the total reflectivity \(\textbf{R}_{total}\) is influenced by interference effects. The reflectivity can be calculated using the following formula, which considers the constructive and destructive interference of light reflected from the top and bottom surfaces of the thin film:  
\[\textbf{R}_{total}=\left|\frac{r_{12}+r_{23}e^{2i\delta}}{1+r_{12}r_{23}e^{2i \delta}}\right|^{2} \tag{3}\]  
Figure 2: Refractive index spectra of single-layer thin films comprising SiO\({}_{2}\), Si\({}_{3}\)N\({}_{4}\), CdSe/ZnS NQDs, and LiF deposited on n-type Si wafers. Measurements were conducted at room temperature over a wavelength range of 350 to 1000 nm. Reference data for intrinsic silicon at 300 K are included ([PERSON] and [PERSON] [15; 16]). where \(r_{12}\) is the reflection coefficient at the air-film interface, \(r_{23}\) is the reflection coefficient at the film-substrate interface, and \(\delta\) is the phase difference due to the path length in the film. These parameters can be calculated as follows:  
\[\textbf{r}_{12}=\left(\frac{n_{1}-n_{2}}{n_{1}+n_{2}}\right)\ \ \ \ \textbf{r}_{23}=\left(\frac{n_{2}-n_{3}}{n_{2}+n_{3}}\right)\ \ \ \ \ \delta=\frac{2\pi n_{2}d}{\lambda} \tag{4}\]  
The optical reflectivity of n-type silicon substrates was systematically investigated, both in bare form and with the application of SiO\({}_{2}\) or Si\({}_{3}\)N\({}_{4}\) SLARCs. A series of samples were prepared, incorporating SLARC thicknesses of 90 nm, 100 nm, and 150 nm. Figure 3 presents the spectral reflectivity of these structures across a wavelength range of 350 nm to 1000 nm, with comparative data for intrinsic silicon included as a reference point [15,16]. Figure 3 presents a comparative analysis of reflectivity spectra for various n-type silicon substrates both with and without the application of SLARCs within the wavelength range of 350 nm to 1000 nm. The baseline reflectivity of n-type Si is established in Figure 3a, revealing comparable reflection characteristics to the reference intrinsic silicon spectrum. The introduction of SiO\({}_{2}\) and Si\({}_{3}\)N\({}_{4}\) SLARCs significantly reduces reflectivity, particularly within the visible spectrum, as evident in Figure 3b,c, with varying thicknesses. A correlation between SLARC thickness and reflectivity is observed, although interference effects can occur at greater thicknesses. However, The correlation between thickness and reflectivity exhibits variability across different wavelengths. While the refractive index remains relatively constant within the measured wavelength range, the relationship between SLARC thickness and reflectivity is not straightforward. Other factors, such as interference effects and material properties, likely influence the observed behavior. Figure 3d contrasts the reflectivity of SiO\({}_{2}\) and Si\({}_{3}\)N\({}_{4}\) SLARCs (both 90 nm-thick) with that of n-type Si, and highlights the superior anti-reflective properties of Si\({}_{3}\)N\({}_{4}\) compared to SiO\({}_{2}\) across a  
Figure 3: Optical reflectivity of (**a**) bare n-type silicon and intrinsic silicon (reference data from [PERSON] and Keevers [15,16]), (**b**) n-type silicon with SiO\({}_{2}\) SLARC, (**c**) n-type silicon with Si\({}_{3}\)N\({}_{4}\) SLARC, and (**d**) comparative reflectivity of bare silicon, SiO\({}_{2}\) SLARC (90 nm), and Si\({}_{3}\)N\({}_{4}\) SLARC (90 nm). Measurements were performed at room temperature over a wavelength range of 350 to 1000 nm.