## 5 Summary  
This study explores the dominant failure mechanisms in high-temperature MEMS devices with a heater element made of tungsten, focusing on the combined effects of temperature, current density, and hydrostatic stress on atomic migration. Steady-state simulations were performed to extract critical parameters, including temperature distribution, current density, hydrostatic stress, and vacancy flux contributions caused by diffusion, electric fields, temperature gradients, and stress gradients.  
The results highlight that the regions of maximum temperature, current density, and hydrostatic stress coincide in the structure, particularly at the curved portion of the heater arm near the hotplate. This overlap leads to concentrated vacancy fluxes and accumulated vacancy transport, correlating with real-life device failures where void formation is observed. Among the driving forces for atomic migration, electromigration (flux due to the electric field) was found to dominate, contributing 84.73% to the total vacancy flux. Vacancy fluxes caused by diffusion (8.17%) and hydrostatic stress gradients (7.06%) also play significant roles, whereas the temperature gradient had a negligible contribution to the driving force of the vacancies (0.03%).  
The simulations further revealed that vacancies migrate from regions of positive hydrostatic stress to regions of negative stress, causing void accumulation. This nothing effect aligns with physical observations of failure sites and the subsequent hotspot formation in heater arms. Void growth accelerates local current density, leading to a positive feedback loop of increased stress, further void expansion, and eventual structural failure.  
This study underscores the critical role of temperature and current density in device reliability, as reflected in the mean time to failure (MTTF) equation. MTT has exponential dependence on temperature and inverse-square dependence on current density, illustrating how extreme conditions significantly shorten the operational lifetime of high-temperature MEMS devices. This work provides valuable insights into the underlying failure mechanisms and emphasizes the importance of mitigating electromigration and stress-driven degradation to improve MEMS device robustness and longevity.  
Conceptualization, W.L.S., M.I. and A.J.D.; methodology, W.L.S. and A.J.D.; software, W.L.S.; validation, W.L.S., M.I. and A.J.D.; resources, J.B.; writing--original draft preparation, W.L.S. and M.I.; writing--review and editing, W.L.S., M.I., J.B. and A.J.D.; funding acquisition, M.I. and J.B. All authors have read and agreed to the published version of the manuscript.  
This work has received funding from the Swiss State Secretariat for Education, Research and Innovation (SERI), OMICSENS-23.00547, 101129734. This project has also received funding from the European Union's Horizon Europe EIC 2023 Pathfinder Open program under grant agreement No 10112973.4 Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or European Innovation Council and SMEs Executive Agency (EISMEA). Neither the European Union nor the granting authority can be held responsible for them.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The support of the University of Bern during this project is gratefully acknowledged. Special thanks are extended for the provision of advanced simulation tools, technical resources, and a collaborative research environment, which were essential for the successful completion of this work. Acknowledgment is also given to 4K-MEMS for providing the hotplate MEMS devices used in this research.  
Conflicts of InterestAuthor [PERSON] was employed by the company 4K-MEMS S.A. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.