A model for the growth of a conducting filament in metal-to-metal amorphous-silicon antifuses is presented. The transition from a high-resistance state to a low-resistance one is initiated by the formation of a localized hot spot. The growth of the filament occurs by melting the surrounding amorphous silicon. The latent heat required for filament growth is provided by the power dissipation in the melt. As the filament grows, power dissipation drops rapidly and the growth slows. For a given set of programming conditions and at a certain value of the melt radius, the power dissipation in the filament is no longer sufficient to provide the energy needed for the growth process. This condition leads to ending the filament growth. The thermal model presented here predicts several characteristics of the ON state, such as the dependence of the final filament radius rfil on the programming voltage Vpp and the series resistance Rser. It also predicts that the ON resistance is inversely related to the programming voltage Vpp. The model predictions agree with experimental results. © 1998 American Institute of Physics.