Thermal reversible breakdown and resistivity switching in hafnium dioxide

We present a model of thermal reversible breakdown via conductive filaments (CFs) in hafnium dioxide (HfO2). These CFs appear as a result of electrical pretreatment of a metal/HfO ₂/metal (semiconductor) nanostructure (MIM(S)). The model is based on an assumption that the thermal reversible breakdown of a CF is due to of Joule heating displaying an exponential dependence of conductivity on temperature. The corresponding current-voltage characteristic and temperature of a CF in its middle and at the interface with an electrode are calculated taking into account the heat conduction equation and boundary conditions with heat dissipation via electrodes. It is found that the current-voltage characteristic of a CF has three specific regions. The initial and final regions have turned out to be linear with respect to the current and display different slopes, while the middle region is characterized by both the S-shaped and ultralinear dependences which are affected by the ambient temperature and nanostructure parameters. The switching potential from the high resistivity state (HRS) to the low resistivity state (LRS) was shown to decrease with the ambient temperature and with worsening of heat dissipation conditions.