Limitations of Poole–Frenkel Conduction in Bilayer HfO₂/SiO₂ MOS Devices

The gate leakage current of metaloxidesemiconductors (MOSs) composed of hafnium oxide $(\hbox{HfO}-{2})$ exhibits temperature dependence, which is usually attributed to the standard PooleFrenkel (PF) transport model. However, the reported magnitudes of the trap barrier height vary significantly. This paper explores the fundamental challenges associated with applying the PF model to describe transport in $\hbox{HfO}-{2}/ \hbox{SiO}-{2}$ bilayers in n/p MOS field-effect transistors composed of 3- and 5-nm $\hbox{HfO}-{2}$ on 1.1-nm $ \hbox{SiO}-{2}$ dielectric stacks. The extracted PF trap barrier height is shown to be dependent on several variables including the following: the temperature range, method of calculating the electric field, electric-field range considered, and $\hbox{HfO}-{2}$ thickness. PF conduction provides a consistent description of the gate leakage current only within a limited range of the current values while failing to explain the temperature dependence of the 3-nm $\hbox{HfO}-{2}$ stacks for gate voltages of less than 1 V, leaving other possible temperature-dependent mechanisms to be explored.