Quantum tunnelling in hafnia-based metal-insulator-metal diodes: atomistic-to-continuum modelling approach and experimental validation

In this work, we present a metal-insulator-metal (MIM) diode, based on quantum tunnelling phenomena. Its model is based on a multilevel modelling approach consisting of atomistic and continuum simulations, fully validated by extensive measurements. The MIM structure comprises a hafnium oxide (or hafnia, HfO2) dielectric layer, less than 4 nm thick and a square contact area of only 4 μm2, placed between two metallic electrodes, namely platinum as the source and titanium as the drain. The current–voltage (I–V) curve has been estimated by Density Functional Theory (DFT) calculations through an optimisation of the interfaces between metals and monoclinic HfO2. The dielectric parameters arising from ab initio computations have then been used as inputs for the successive circuit and electromagnetic simulations. Finally, the multilevel model has been validated with great accuracy, first measuring the I–V characteristics by applying a drain-source voltage between −1 V and +1 V, and then extracting the scattering parameters up to 40 GHz, thus demonstrating that DFT and circuit/electromagnetic simulations match almost perfectly the experimental ones. These outcomes represent the first study of such nanoscale devices investigated by means of a rigorous atomistic-to-continuum approach, providing invaluable information in order to improve fabrication and correctly assess the macroscale performance of nanoelectronics systems.