## 5 Conclusions  
In this paper, the surface \(\alpha\)-particle emissivity and energy spectrum characteristics of three typical tin spheres were investigated by a combination of experimental and simulation methods. The internal radionuclides were traced back and the intrinsic mechanism was thoroughly studied by combining Monte Carlo simulations. Firstly, surface \(\alpha\)-particle emissivity tests and energy spectrum characterization were carried out on two types of lead-containing tin spheres (Sn\({}_{10\%}\)Pb\({}_{90\%}\), Sn\({}_{63\%}\)Pb\({}_{37\%}\)) and one type of lead-free tin sphere (SAC305). The results showed that the \(\alpha\)-particle emissivity of the Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere is the highest; while the emissivity of the Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere, the second highest, is one order of magnitude lower than the \(\alpha\)-particle emissivity of the Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere; and the SAC305 tin sphere had the lowest emissivity, which was reduced by about 55.6% compared with the emissivity of Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere. The emission spectra of the tin spheres showed obvious single peak characteristics. The internal radionuclide traceability of the tin spheres, combined with the spectra, revealed that \({}^{210}\)Po was the main nuclide producing \(\alpha\)-particles, and that \({}^{210}\)Po originated from the decay of \({}^{210}\)Pb. The energy  
Figure 15: Emission energy spectra of \(\alpha\)-particles at 5.3 MeV obtained from simulation on the surface of Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere. There are four cases, a represents the emission energy spectrum of radionuclides on the surface within the a-layer, b represents the emission energy spectrum of radionuclides on the surface within the b-layer, c represents the emission energy spectrum of radionuclides on the surface within the c-layer and d represents the emission energy spectrum of radionuclides on the surface within the d-layer.  
spectrum of the purified low-alpha tin spheres showed a discrete distribution and its emissivity was reduced by three to four orders of magnitude.  
By establishing a simulation model of tin spheres and using Monte Carlo simulation to simulate the transport process of \(\alpha\)-particles inside the spheres, the corresponding surface emission spectra were obtained to reveal the distribution pattern of internal radionuclides. The results showed that the \(\alpha\)-particles with energies higher than 4 MeV in the emission spectra originated from the radionuclides within 5 \(\upmu\)m of the surface layer of the tin sphere, accounting for 60% of the total number of particles. According to the test results and simulation analyses, it was found that the internal radionuclides of the tin spheres used for the test show the characteristics of more surface layer and less internal layer. The above results are important for the establishment of \(\alpha\)-particle mitigation methods for tin spheres, which, in turn, will help to improve the reliability of chips from the material level and reduce the risk of soft errors in chips.  
Conceptualization, L.L.; methodology: L.L., Z.Z. and Z.L.; software: H.Z.; validation: H.Z.; formal analysis: J.L. and C.P.; investigation: L.L. and C.S.; resources: Z.Z. data curation, L.L.; writing original draft preparation, L.L.; writing review and editing: L.L. and H.L.; visu-alization, Y.H.; supervision, Z.Z.; project administration: Z.Z.; funding acquisition, Z.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China grant number 12175045, 12075065. The Key-Area Research and Development Program of Guangdong Province (Grant No. 2022B0701180002).  
Not applicable.  
The datasets presented in this article are not readily available because the data are part of an ongoing study. Requests to access the datasets should be directed to [EMAIL_ADDRESS].  
The authors declare no conflict of interest.