## 1 Introduction  
Electronic materials naturally contain uranium (U), thorium (Th), and other radioactive elements, whose decay will release the very ionizing ability of alpha particles. When the alpha particles propagate inside the chip, it will generate a large number of electron-hole pairs along the direction of propagation, these electron-hole pairs are collected by an electric field to generate a current pulse, and when the charge collection exceeds the critical charge corresponding to the node of the chip, then a soft error will occur [1]. Distinguishing from hard errors [2], soft errors do not cause catastrophic damage to the device but can lead to varying degrees of data loss. Achieving high integration, high speed, and low power consumption is crucial in integrated circuit manufacturing processes [3]. Along with the development of its manufacturing process, the soft errors caused by alpha particles and other factors, such as increased integration, reduced operating voltage, and reduced node capacitance, pose a great threat to the reliability of integrated circuits, and in the chip industry, the problem of its reliability may directly affect the core competitiveness of the product [4, 5, 6]. In the atmospheric environment, soft errors mainly originate from \(\alpha\)-particles, energetic neutrons, and thermal neutrons [7, 8, 9]. Among them, the proportion of the soft error rate (SER) caused by \(\alpha\)-particles is closely related to the device process, package material grade, and usage environment [10] and is an important part of the overall SER. In order to reduce the soft error rate, common measures include improving the purity of packaging materials, adding a protective layer on the chip surface, changing the structural design, and changing the circuit design [11].  
Alpha particles within chips in terrestrial environments mainly originate from radionuclides in raw materials, such as solder joints composed of lead-based solder, bonding wires, and aluminum in ceramic packages, with alpha particles generated by the solder being the main factor [12; 13]. As an important and indispensable material in the new type of packaging, solder balls are used to replace the pins in the integrated circuit (IC) package structure to meet the requirements of electrical interconnections and mechanical connections.  
As the process size of ICs enters the nanoscale, related research in China and abroad focuses on the measurement of a-particle SERs of ICs, the contribution ratio to neutron SERS [14; 15; 16], as well as the morphology and properties of tin spheres. For example, in China, and [PERSON] et al. introduced the technique of ultra-low background \(\alpha\)-particle testing and radiometric characterization of the solder [17]. Overseas, [PERSON] et al. studied the effects of thermal cycling and current on the reliability of different solder ball weld joints [18], [PERSON] et al. did a study on the mechanics of the solder ball shear test and the effect of shear rate [19], and so on. The characterization and simulation of \(\alpha\)-particle radioactivity in tin spheres is lacking. The \(\alpha\)-particles emitted from tin spheres located at the bottom of the chip can directly enter into the chip, thus endangering the reliability of the chip. Therefore, it is of great significance to test the \(\alpha\)-particle emissivity and emission spectra of tin spheres, to confirm their internal emitting nuclides through the spectra, and to reveal the intrinsic mechanism through simulation.