Defects in the $\beta$-Ga$_2$O$_3$($\bar201$)/HfO$_2$ MOS system and the effect of thermal treatments
We have investigated the properties of the $\beta$-Ga$_2$O$_3$($\bar201$)/HfO$_2$/Cr/Au MOS (metal-oxide-semiconductor) system after annealing (450$^\circ$C) in different ambient conditions (forming gas, N$_2$ and O$_2$). Defect properties have been analyzed using an approach combining experimental impedance measurements with physics-based simulations of the capacitance-voltage (C-V) and conductance-voltage (G-V) characteristics of $\beta$-Ga$_2$O$_3$/HfO$_2$ MOS capacitors. This approach enabled us to detect two defect bands in HfO$_2$ characterized by thermal ionization energies of ~1.1eV (acceptor-like) and ~2eV (donor-like) attributed to a polaronic self-trapping state and an oxygen vacancy in HfO$_2$, respectively. This study demonstrates how thermal treatments affect the energy distributions and densities of the observed defects. The adopted methodology also enabled the extraction of the spatial distribution of defects across the HfO$_2$ thickness and Cr/HfO$_2$ interface. The high concentration of oxygen vacancies close to the Cr/HfO$_2$ interface extracted from experimental and simulated electrical data is confirmed by in-situ XPS analysis which shows how Cr is scavenging oxygen from the HfO$_2$ and creating the donor band confined near the Cr/HfO$_2$ interface. This donor band density is observed to be reduced after annealing as per simulation and unchanged for different annealing conditions. We speculate this may be due to the formation of dense films and polyforms of HfO$_2$ under different ambient as revealed by high-resolution TEM images.