Structural study of oxygen vacancy in CaO stabilized cubic-$HfO_2$ using density functional theory

Density Functional Theory를 이용한 CaO 안정화 Cubic-$HfO_2$의 산소 공공 구조연구

CaO stabilized cubic-$HfO_2$ is studied by using Density Functional Theory with GGA. When a Ca atom is substituted for a Hf atom, an oxygen vacancy is produced to satisfy the charge neutrality condition. When the oxygen vacancy is located at the first nearest site from the Ca atom, the total energy of $HfO_2$ is the most favorable. We calculate the energy barriers for the oxygen vacancy migration. The energy barriers between the first and the second nearest sites, the second and the third nearest sites, and the third and fourth nearest sites are 0.2, 0.5, 0.24 eV, respectively. The oxygen vacancies at the third and fourth nearest sites from the Ca atom represent the oxygen vacancies in undoped $HfO_2$. Therefore, the energy barrier for oxygen migration in $HfO_2$ gate dielectricis is 0.24eV, which can explain a leakage origin of gate dielectric.