# Exploring Surface-Driven Mechanisms for Low-Temperature Sintering of Nanoscale Copper
## 1 Introduction  
With chips evolving towards extremely small manufacturing processes, the electronic packaging density has surged dramatically [1, 2]. The rise in the number of connector contacts has pushed traditional soldering methods for high-density connections to their limits [3, 4, 5, 6]. Solder not only lacks sufficient structural strength but also falls short in thermal dissipation and electromigration resistance [7, 8]. Consequently, copper-copper direct bonding is emerging as a popular technique in advanced packaging [9, 10, 11, 12, 13]. However, copper's high melting point makes direct diffusion bonding challenging under conventional conditions, making low-temperature copper-copper bonding a research focus [14, 15]. Currently, techniques to achieve low-temperature Cu-Cu bonding include thermocompression bonding [13, 16], hybrid bonding [17], and nanomaterial sintering processes [18, 19]. These new methods and processes are expected to effectively overcome the shortcomings of traditional solder, providing possibilities for high-quality, ultra-high-density packaging. However, these techniques are still facing challenges, as the contradiction between bonding quality and sintering quality persists. At a low temperature, sintering often results inporosity, and the porosity rate of the sintered material is difficult to control precisely [19; 20]. This has become a critical factor limiting the development of low-temperature Cu-Cu bonding technology. In all these methods, the primary achievement for direct bonding at low temperatures is controlling the surface to enhance the diffusion rate of Cu atoms and applying pressure to facilitate the deformation and contact bonding of copper at low temperatures [15; 21; 22; 23; 24; 25]. From this perspective, there is a uniformity among the three in the mechanism of low-temperature welding, which has been well investigated. Simulation methods, particularly molecular dynamics simulations, have recently been employed to investigate relevant mechanisms, yielding some effective results [26; 27]. In our preliminary research, we also identified the rapid surface dynamic state of nanoparticles and proposed a low-temperature sintering mechanism for these particles. It demonstrated the low-temperature sintering process under various temperature and pressure coupling conditions and further demonstrated the positive role of the rapid surface dynamic state of nanoparticles in promoting sintering [28; 29]. Obviously, the current research appears to be quite comprehensive from the perspective of bonding driving forces, which are inherently determined by temperature and pressure. However, the actual copper-to-copper bonding process involves the coupling of multiple mechanisms, such as dislocation, slip, surface diffusion, and plastic flow processes, which are challenging to emerge in a simple bonding model with only two interfaces or two grains in most research [30; 31]. These mechanisms may exert their effects on the sintering process in a specific order or act collectively at lower temperatures. Clarifying the bonding mechanisms within complex interfaces or systems is crucial for the extrapolation of microscopic mechanisms to macroscopic scales, thereby facilitating a comprehensive understanding of macroscopic phenomena. In this work, a multi-particle periodic system is utilized with different sintering temperatures, simulating the actual low-temperature sintering process to further consider the coupling of various atomic-level mechanisms during low-temperature sintering. A substantial random particle database is employed as the particle sample used during the sintering process, and through random drift and rotation during the initial arrangement of the particles, the distribution is made to closely resemble a random state to reflect the real sintering process. Through this method, the changes in porosity and mechanical properties during the sintering process are monitored carefully.