## 3 Results and Discussions
### Assistance Effect of Bi-In Alloy Film  
Based on the above analysis, the optimal laser fluences that could form structures on bare silicon and Biln-Si were 1.02 and 2.55 J/cm\({}^{2}\), respectively. To analyze the assistance effect of the Bi-In film accurately, modified surface morphologies with different scanning speeds were observed on bare silicon (Figure 3a-c) and on Biln-Si (Figure 3d-f) at their respective optimal laser fluences. For bare silicon, the ripple structures were irregular. For example, at a scanning speed of 40 \(\upmu\)m/s (Figure 3b), the ripples were sharp in the middle and blurred at the edge. At a higher speed (Figure 3c), the ripples were discontinuous due to the discontinuity of the laser energy caused by the high scanning speed. In Figure 3d-f, for comparison, well-defined and distinct ripples were induced on Biln-Si. The LIPSSs on Biln-Si were more uniform with clear ridges and grooves, indicating that the Bi-In film contributed to the formation of uniform LIPSSs. Figure 2: Scanning electron microscopy (SEM) images of the surface morphologies on bare silicon and Biln-Si with different laser fluences of (**a**,**e**) 1.02, (**b**,**f**) 1.53, (**c**,**g**) 2.04, and (**d**,**h**) 2.55 J/cm\({}^{2}\) at a fixed laser pulse number of \(N=200\). (**a–d**) represent situations on bare silicon. (**e–h**) represent situations on Biln-Si. The mechanism of the nanolayered Bi-In alloy film that assisted with the femtosecond laser fabrication of uniform periodic surface structures is discussed as follows. The formation of LIPSSs on the silicon surface is explained by the interference between the incident laser radiation and the SPP wave. The period of the LIPSSs is expressed as [32]:  
\[\Delta_{\text{LIPSS}}\ =\ \lambda_{\text{s}}=\lambda\bigg{(}\frac{\varepsilon_{1}+ \varepsilon_{2}}{\varepsilon_{1}\varepsilon_{2}}\bigg{)}^{1/2}=\ \lambda\bigg{(}\frac{1}{\varepsilon_{1}}+\frac{1}{\varepsilon_{2}}\bigg{)}^{1 /2}, \tag{1}\]  
where \(\Delta_{\text{LIPSS}}\) is the period of the ripples, \(\lambda\) is the wavelength of the laser, \(\lambda_{\text{s}}\) is the wavelength of the surface plasmon polariton wave, and \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are the dielectric constants of the adjoining media. In our experiments, \(\varepsilon_{1}\) and \(\varepsilon_{2}\) represent the dielectric constants of air and Si, respectively. \(\varepsilon_{2}\) is defined as:  
\[\varepsilon_{2}=1-\frac{\omega_{p}^{2}}{\omega^{2}}, \tag{2}\]  
where \(\omega_{p}\propto n_{\text{e}}{}^{1/2}\), and \(n_{\text{e}}\) is the free electron density. According to the above analysis, the period of the ripples is equal to the wavelength of the SPP wave. As the laser fluence increases, the free electron density of the plasma layer will increase, resulting in a decrease in \(\varepsilon_{2}\). Consequently, the period of ripples will increase. The surface morphologies of the ripple structures are affected by the energy distribution of the laser. As shown in Figure 4a, when the bare silicon was irradiated by the laser, the laser energy was mainly concentrated in the center of the spot according to the Gaussian distribution of the laser energy (Figure 4c), which caused the ripples to be clearer or even damaged at the center of the laser spot and blurry or nonexistent at the edge of the laser spot. This analysis agrees with our experimental results in Figure 3b. However, with the assistance of the Bi-In film, which contains massive free electrons, the electrons excited by the incident laser pulse can transport thermal energy quickly due to their high heat conduction performance. The thermal conductivity of Bi-In alloy contributed by the electrons can be calculated as 8.9 W/(m\(\cdot\)K) at 110 \({}^{\circ}\)C [33,34]. When the Bi-In film still existed on the silicon, the laser energy distribution in the laser spot on silicon was nearly uniform, as seen in Figure 4d. The circular blue dashed lines indicate the threshold of the laser fluence that led to the formation of ripple structures.