  A promising candidate for universal memory, which would involve combining the
most favourable properties of both high-speed dynamic random access memory
(DRAM) and non-volatile flash memory, is resistive random access memory
(ReRAM). ReRAM is based on switching back and forth from a high-resistance
state (HRS) to a low-resistance state (LRS). ReRAM cells are small, allowing
for the creation of memory on the scale of terabits. One of the most promising
materials for use as the active medium in resistive memory is hafnia (HfO$_2$).
  However, an unresolved physics is the nature of defects and traps that are
responsible for the charge transport in HRS state of resistive memory.
  In this study, we demonstrated experimentally and theoretically that oxygen
vacancies are responsible for the HRS charge transport in resistive memory
elements based on HfO$_2$. We also demonstrated that LRS transport occurs
through a mechanism described according to percolation theory.
  Based on the model of multiphonon tunneling between traps, and assuming that
the electron traps are oxygen vacancies, good quantitative agreement between
the experimental and theoretical data of current-voltage characteristics were
achieved. The thermal excitation energy of the traps in hafnia was determined
based on the excitation spectrum and luminescence of the oxygen vacancies.
  The findings of this study demonstrate that in resistive memory elements
using hafnia, the oxygen vacancies in hafnia play a key role in creating
defects in HRS charge transport.
