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The gate defect of the ferroelectric HfO$_2$-based Si field-effect transistor(Si FeFET) plays a dominant role in its reliability issue. The first-principlescalculations are an effective method for the atomic-scale understanding of gatedefects. However, the first-principles study on the defects of FeFET gatestacks, i.e., metal/orthorhombic-Hf$_{0.5}$Zr$_{0.5}$O$_2$/SiO$_2$/Sistructure, has not been reported so far. The key challenge is the constructionof metal/orthorhombic-Hf$_{0.5}$Zr$_{0.5}$O$_2$/SiO$_2$/Si gate stack models.Here, we use the Hf$_{0.5}$Zr$_{0.5}$O$_2$(130) high-index crystal face as theorthorhombic ferroelectric layer and construct a robust atomic structure of theorthorhombic-Hf$_{0.5}$Zr$_{0.5}$O$_2$/SiO$_2$/Si gate stack without any gapstates. Its high structural stability is ascribed to the insulated interface.The calculated band offsets show that this gate structure is of the type-I bandalignment. Furthermore, the formation energies and charge transition levels(CTLs) of defects reveal that the oxygen vacancy defects are more favorable toform compared with other defects such as oxygen interstitial and Hf/Zr vacancy,and their CTLs are mainly localized near the Si conduction band minimum andvalence band maximum, in agreement with the reported experimental results. Theoxygen vacancy defects are responsible for charge trapping/de-trapping behaviorin Si FeFET. This work provides an insight into gate defects and paves the wayto carry out the first-principles study of ferroelectric HfO$_2$-based SiFeFET.

First-principles study of oxygen vacancy defects in orthorhombic Hf$_{0.5}$Zr$_{0.5}$O$_2$/SiO$_2$/Si gate stack