Finite element modeling of current-induced filaments in nanocrystalline silicon

Rapid, heat-induced phase transitions in amorphous (a-), nano-crystalline (nc-) or poly-crystalline semiconductors may lead to current percolation along a highly conductive preferred path, or filament, if the material becomes more conductive as it heats [1]. Increased conductivity with temperature leading to positive feedback and thermal runaway is observed in nano-crystalline silicon (nc-Si) as well as phase-change materials such as Ge₂Sb₂Te₅. Formation of filaments can lead to non-uniform heating and very high-density current conduction through only a small portion of the structure. Modeling filament behavior is critical for small scale devices like phase change memory (PCM) elements, which show resistance variations after SET operations due to partial crystallization of the material [2]. Partially crystallized materials have been modeled through networks of resistors statistically assigned to infinite or zero resistance, but these models assume contact between conductive grains, an assumption not valid in nanocrystalline semiconductors [3]. In this study, we use 2-D, finite element simulations to model the time dependent evolution of current-induced filaments in nc-Si wires using physical parameters for Si.