论文和技术资料

Micro-Electro-Mechanical Systems (MEMS) infrared emitters are widely used as radiation sources in non-dispersive infrared (NDIR) gas sensing and are subjected to extreme thermal and electrical stress. Over time, electromigration alters the conductive tracks locally, leading to resistance drift, thermal hotspots, and ultimately device failure. Predicting this failure is critical for reliability assessment, yet simulating the highly dynamic, localised material degradation poses significant numerical challenges.

We present a robust, fully coupled 3D multiphysics proof of concept to simulate electromigration-induced ageing, implemented in COMSOL Multiphysics® using the AC/DC Module (Electric Currents interface), the Heat Transfer Module, and the Mathematics interface. To initiate and study the degradation process deterministically, the geometry was modified by using an artificially milled focused ion beam (FIB) defect to trigger local current crowding and associated temperature peaks. Corresponding test structures with amorphous MoSi2 tracks and a 1 µm FIB hole were fabricated using standard CMOS processing, and in-situ optical microscopy under constant current stress was used to capture the relevant damage mechanisms and benchmark the simulated degradation behaviour against real devices.

The core methodological contribution lies in stabilising an empirical damage variable. Electromigration mass flux is mapped to a damage rate that continuously degrades the local electrical conductivity. Because material failure (burn-through) occurs within fractions of a second once a critical state is reached, the solver must handle extremely steep spatial and temporal gradients; direct solution often leads to numerical instability or requires non-physical artificial diffusion. To avoid this, we introduce a mathematical variable transformation within the PDE interface, z = -ln(1-D), where D denotes the physical damage bounded strictly between 0 (intact) and 1 (fully degraded). This transformation stabilises the time-dependent solver without spatial or temporal smoothing.

The simulation reproduces four degradation phases that qualitatively match the optical microscopy observations: (1) an incubation period with damage accumulation at the FIB defect, (2) slow lateral spreading of the degraded zone, (3) rapid, exponential lateral burn-through across the track (computationally within milliseconds), and (4) a post-burn-through saturation phase with a fully developed damage line. Grounded by experimental validation, this model demonstrates how custom PDE transformations can be combined with standard electro-thermal interfaces to handle highly nonlinear, moving-front degradation and provides a basis for future virtual design and lifetime prediction of MEMS IR emitters. The stabilization technique is highly transferable to other complex material degradation phenomena in COMSOL®.