The proposed mechanisms is roughly classified into two groups: (1) electronic redistribution around the interface and (2) redistribution of ions across the interface. The second one, proposed by Kita and Toriumi  has gained popular support because of its applicability to a wide range of high-k materials. The model states that the interface dipole is formed by the movement of negatively charged O ions from higher oxygen-density side to a lower side. This model is referred to as “oxygen-density difference accommodation,” hereafter.
The picture of oxygen-density difference accommodation model was well reproduced in our MD simulation (Fig.1) of Al2O3/SiO2 system [3-5], which employs a simple two-body ionic interaction model of the Born-Mayer-Huggins potential. A dipole layer is formed by the migration of O ions from the Al2O3 side to the SiO2 side (Fig.2). The direction and magnitude of the dipole coincides well with experimental results. The driving force of the O- ions migration is found to be the short-range repulsion between ionic cores. The repulsive force becomes larger in the higher oxygen density materials, so that the O- ions is pushed into the lower oxygen density side (Fig.3).
In my previous talk in this conference held in 2014 , I discussed that an imbalance of multipole potentials between both oxide layer is a possible origin of the O- ion migration. However, the subsequent analysis  clarified that the dominant force acting on O- ions in near the interface is not originated from the charge-to-charge interaction, so that my previous hypothesis was denied nowadays.
Furthermore, the author’s group succeeded in reproducing the direction of dipoles at MgO/SiO2 and SrO/SiO2 interfaces (Fig.2) , which is opposite to that of the Al2O3/SiO2 system. The MgO/SiO2 system is an irregular case of the oxygen-density difference accommodation model, because the oxygen density of MgO is higher than that of SiO2, but the experimentally observed dipole is opposed to the direction of the density gradient of O ions. In spite of the fact, our MD simulation can correctly reproduce the direction of the dipole at the MgO/SiO2 interface. The dipoles at the MgO/SiO2 and SrO/SiO2 interfaces are formed by a preferential migration of metal cations from the high-k oxide toward the SiO2 layer, and silicate layers are formed at these interfaces.
In conclusion, the dipole formation at high-k/SiO2 interfaces can be explained by the ion redistribution model, as shown in Fig.4. The negative dipoles at the MgO/SiO2 and SrO/SiO2 interfaces are formed by a preferential migration of metal cations from the high-k oxide toward the SiO2 layer during the formation of a stable silicate phase. Thus, the migration of metal cations as well as the migration of oxygen ions must be taken into account when considering the mechanics of the dipole layer formation.
This work was supported by JST-CREST and a Grant-in-Aid for Scientiﬁc Research (B) (15H03979) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.
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