## 1 Introduction
### High-Temperature MEMS Performance  
The performance and reliability of MEMS devices in high-temperature environments differ significantly to those operating at lower temperatures. Most of the MEMS structures,which are used for higher-temperature applications, such as microhotplates (MHPs), have operating temperatures up to 1000 \({}^{\circ}\)C. Several examples of such structures can be found in the literature, with heater materials including platinum [5; 6; 7], polysilicon [8], titanium nitride [9], or tungsten [10; 11; 12; 13]. Some limited examples of MEMS structures operating above 1000 \({}^{\circ}\)C can be found, where the heater material is platinum [14], molybdenum [15], or boron-doped polycrystalline diamond PCD [16]. Failure mechanisms with corresponding failure temperatures for different heater materials used as microhotplates are shown in Table 1.  
The operating temperature significantly impacts the performance of these devices, making stability and failure mechanisms at high temperatures crucial for MHPs. In accelerated life testing, the Arrhenius relationship is commonly used to model how temperature influences device reliability over time. The atomic migration failure can be described by this relationship. This failure mechanism is strongly temperature-dependent as the atomic mobility increases with the temperature and so does diffusivity [19]. The failure caused by hotspot formation is also significantly influenced by Arrhenius kinetics as the higher temperatures can cause larger temperature gradients, leading to failure [5; 17]. The Arrhenius relationship shows that the mean time to failure (MTTF) has an exponential temperature dependence, expressed by the following equation [19]:  
\[MTTF=A_{0}\text{exp}\bigg{(}\frac{E_{a}}{kT}\bigg{)} \tag{1}\]  
In this formula, \(A_{0}\) is a pre-exponential factor that varies depending on the material properties, device design, and environmental factors of the system being analyzed, \(E_{a}\) is the activation energy related to the failure mechanism, and \(k\) is the Boltzmann constant. Even small increases in temperature \(T\) can greatly reduce the lifespan of a device as higher temperatures significantly accelerate failure mechanisms [19]. This exponential temperature dependence makes it essential to study failure modes at elevated temperatures in order to improve the reliability of high-temperature devices. Failure mechanisms such as electromigration [6; 7; 13], hotspot formation [5; 18], the rupture of the membrane [9; 11; 15], and the displacement of the suspended structure [18] have been observed in MEMS structures operating at temperatures up to 1000 \({}^{\circ}\)C.  
Despite the increasing interest in high-temperature MEMSs, the current literature lacks a comprehensive discussion on the specific failure mechanisms that occur in devices operating above 1000 \({}^{\circ}\)C. Much of the existing research on MEMS reliability focuses on low- to moderate-temperature environments, leaving a gap in understanding how high tem \begin{table}
\begin{tabular}{c c c c} \hline
**Heater Material** & **Temperature Reached at the Time of Failure** & **Failure Mechanism** & **Reference** \\ \hline Pt & 870 \({}^{\circ}\)C & Hotspot formation & [5] \\ Pt & 700 \({}^{\circ}\)C & Electromigration & [7] \\ W & 750 \({}^{\circ}\)C & Rupture of membrane & [11] \\ Pt & 820 \({}^{\circ}\)C & Electromigration & [6] \\ TiN & 720 \({}^{\circ}\)C & Rupture of membrane & [9] \\ Al & 350 \({}^{\circ}\)C & Hotspot formation & [17] \\ Pt & 550 \({}^{\circ}\)C & Displacement of & [18] \\  & & suspended structures & \\ W & 850 \({}^{\circ}\)C & Electromigration and & [13] \\ Pt & 1057 \({}^{\circ}\)C & Thermomigration & [14] \\ Mo & 1360 \({}^{\circ}\)C & Rupture of membrane & [15] \\ \hline \end{tabular}
\end{table} 
Table 1: Failure temperatures and failure types for different heater materials used as microhotplates. peratures influence failure modes and overall performance.