The Atomic-scale Domain Wall Structure And Evolution In HfO₂-based Ferroelectrics:A First-principle Study

The Hf O₂-based ferroelectrics have aroused considerable attention due to their potential application in silicon process-compatible memory devices.However,there are very few studies on the ferroelectric domains（or domain walls）of Hf O₂-based ferroelectrics,although they are the core features of ferroelectric materials.The theoretical research on them is still in the blank stage.In this work,by performing density functional theory calculations,we systematically studied the domain wall structure and evolution based on the orthorhombic ferroelectric phase（Pca2₁）.From the perspective of the evolution of ferroelectric domain walls,the microscopic mechanism of polarization switching and ferroelectric activation of Hf O₂-based ferroelectrics are revealed,and the electronic structure and oxygen vacancy distribution of typical domain walls are analyzed.The specific research contents are as follows:（1）There are 6 different ferroelectric phase variants（regardless of the two opposite polarization directions）,when Hf O₂is cooled down from the high symmetry cubic phase to low symmetry orthorhombic ferroelectric phase.Based on these 6variants,10 types of non-equivalent domain walls（DWs）can be constructed,including 3 types of 180°DWs,3 types of polarization twisting 90°DWs and 4 types of polarization tilting 90°DWs.（2）By predicting and calculating the 180°DWs,the atomic structures of 3 types of 180°DWs were determined,and the DW energy of each structure was obtained,and the evolution of the DW was also simulated.Type-1 domain wall has the lowest DW energy-21.2 m J/m²,indicating that the type-1 DW is the most likely domain wall structure in the Hf O₂-based ferroelectric thin films.And the evolution of the type-1DW is probably the microscopic mechanism of 180°polarization reversal in the Hf O₂-based ferroelectric thin films.The energy barrier for the type-1 DW migration across one unit cell is 0.93 e V,which is about15 times larger than that of the Pb Ti O₃ferroelectric.Such larger energy barrier for the DW migration of Hf O₂should be the reason why the coercive electric field of Hf O₂-based ferroelectric film is 10 to 100times larger than that of perovskite ferroelectric films.（3）The 90°DWs are divided into two categories according to the relationship between the polarization directions of the two domains:polarization twisting 90°DWs and polarization tilting 90°DWs.Type-7 90°DW and its migration are believed to be the important microscopic mechanism for the ferroelectricity activation of Hf O₂-based ferroelectric filmunder the external electric field.This is because if the longest axis a is induced to be lying in-plane by the epitaxial tensile strain,the transformation between the two shorter axes b and c will be easy,which would substantially lower the DW migration barrier.（4）Electronic structure and defect distribution of typical domain walls.The electronic structure of type-1 180°DW and type-7 90°DW are studied.It is found that the valence band maximum of the type-7 90°domain wall is substantially enhance by the polarization,meaning that it is easy to form a hole-type conductive channel at the DW.In the type-1 180°DW,due to the displacements of the negatively charged oxygen atoms in the direction perpendicular to the domain wall,the lowest and highest points of the oxygen vacancy formation energy will appear on both sides of the domain wall.The lack of oxygen atoms causes a new defect level near the Fermi level.If a large number of electrons are accumulated,it will affect ferroelectric performance.