Nondiffusive Thermal Transport Increases Temperature Rise in RRAM Filaments

Thermal transport in resistive random-access memory (RRAM) is modeled in the set state, where the conductive filament (CF) is approximated by an infinitely long cylinder embedded in crystalline rutile TiO
₂
, a prototypical RRAM material. Determination of the phonon mean free path (MFP) spectrum in TiO
₂
shows that MFPs are similar to the CF radius, indicating that thermal transport is nondiffusive. We develop an analytical solution to the Boltzmann transport equation (BTE) to model the nondiffusive thermal transport in TiO
₂
and find that the surface temperature rise of the CF predicted by the BTE is larger than that predicted by the heat diffusion equation (e.g., 4x larger for a 1 nm CF radius in a device operating at a temperature of 300 K). We propose a suppressed, effective TiO
₂
thermal conductivity to more accurately predict the CF temperature rise with the heat diffusion equation.