## 1 Introduction  
Since [PERSON] obtained surface periodic structures by using pulsed laser irradiation on a semiconductor surface in 1960 [1], laser-induced periodic surface structures (LIPSSs) have been studied extensively due to their simple and fast fabrication process compared with conventional lithography technology. Meanwhile, LIPSSs can be observed on almost all classes of materials when irradiated near their ablation threshold [2, 3]. Recently, considerable research works have focused on tuning the surface structures by changing the parameters, such as laser fluence (F) [4, 5], laser pulse number (N) [6], polarization [7, 8], and processing environment [9, 10]. Formation mechanisms of LIPSSs have been proposed, including a radiation residual model [11], self-organization [12], and surface defects [13]. The interference between the laser radiation and the surface plasmon polariton (SPP) wave is widely accepted as the dominant mechanism for the ripple formation on metals and semiconductors [14, 15, 16, 17].  
Silicon wafers with patterned surface structures have important applications in many fields [18, 19, 20, 21]. In the past few decades, numerous investigations and promising results of LIPSSs on silicon have been made. However, the fabrication of large-area LIPSSs with uniformity remains a bottleneck. Therefore, nonlinear feedback mechanisms [22] and a polishing technique [23] were proposed to improve the quality of surface nanostructures over a large area. Depositing gold film as a buffer layer is another promising method, as shown be [PERSON] et al., who obtained large-area uniform structures on silicon [24]. Materials assisted by gold films were subsequently investigated, such as indium-tin-oxide(ITO)films [25],sapphire [26], and aluminum [27]. However, present studies on different buffer layers are still limited. Liquid metals are referred to as metals and alloys with melting points below 330 \({}^{\circ}\)C [28], including post-transition and zinc group metals, such as indium (In), bismuth (Bi), and tin (Sn). These metal alloys with different morphologies and properties offer extraordinary capabilities regarding the synthesis of new materials [29]. Bi-In alloys are regarded as outstanding liquid metals and ideal buffer materials that can decrease the energy of peeling off the surface film. Compared with gold, Bi-In alloys can reduce processing costs. In addition, Bi-In alloys are convenient for fabricating flexible components and have high potential in industrial production and applications due to the splendid stretchability of liquid metals. Therefore, Bi-In alloys are superior substitutes for gold.  
In this work, we employed a pre-deposited Bi-In film to improve the quality of laser-induced ripple structures on silicon. The experimental results proved the validity of the buffer layer for improving the quality of LIPSSs. A physical model in terms of the high thermal conductivity contributed by the free electrons in the metal film that homogenize the thermal distribution caused by laser irradiation in the early stage of the formation of LIPSSs was proposed for theoretical analysis. Moreover, the effects of the laser fluence on the period and the laser pulse number on the depth were revealed experimentally.