Dielectric response of high-κ hafnium oxide under finite electric field: nonlinearities from ab initio and experimental points of view

Abstract

Herein, we report on the dielectric-voltage nonlinearities under a constant electric field in metal insulator metal (MIM) capacitor-based hafnium oxide (HfO₂) with respect to the frequency range. Via the Schottky emission mechanism obtained from the current–voltage characteristic (I–V), we calculated the optical dielectric constant ε_r,opt for different external DC bias values. The extracted ε_r,opt revealed a quadratic dependence on the applied external field. This confirmed that such dependence is a common feature of high-κ oxides in the low and high frequency ranges. The results were correlated with the ab initio calculations using the finite field (FF) method as implemented in the CRYSTAL 17 code. Good agreement between the results from the FF method, I–V plots, as well as the UV-visible spectrometry is observed. To assess any change in the dielectric constant upon the application of an external electric field, several parameters such as exchange–correlation functional, basis sets (BSs), as well as supercell expansion factor (N) were tested. The corresponding parameters have a great influence on the macroscopic electron density and voltage along the field direction and thus on the optical response. For N > 2 and rich basis sets, the hybrid functional B3LYP revealed good agreement with the experimental results as compared to other Hamiltonian's forms such as LDA, PW-GGA and HF.