(Invited) Molecular Dynamics Simulation of Dipole Layer Formation at High-k/SiO2 Interfaces

Implementation of high-k/metal gate stack poses a challenge in controlling the threshold voltage (V_TH) of MOSFET devices. Recent studies have shown that an electric dipole layer formed at high-k/SiO₂ interface is responsible for anomalous V_THshifts. The origin of the dipole layer has been explained by several mechanisms, such as the areal density difference of O atoms [1], electronegativity difference [2], and contact induced gap state [3]. Among these models, the first model proposed by Kita and Toriumi [1] is noteworthy because of its simplicity and potential to be applicable to wide variety 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 one.

Recently, we performed molecular dynamics (MD) simulations of high-k/SiO₂ interfaces and succeeded in reproducing the O atom migration across the Al₂O₃/SiO₂ interface [4]. The O ion moves one-sidedly from Al₂O₃ side to SiO₂ one, but opposite movement never occurs. The simulation result implies that the O ion migration is induced by some drift forces, but not by a simple diffusion due to the O density gradient across the high-k/SiO₂. In this paper, we discuss the driving force of the O ion migration across the high-k/SiO₂ in terms of the multipole moment around oxide cation.

The MD simulation was performed by a commercial simulation package SCIGRESS ME from Fujitsu Ltd. Al₂O₃/SiO₂ interface model was constructed by sandwiching amorphous Al₂O₃ blocks in between amorphous SiO₂ blocks as shown in Fig.1. The hetero-oxide structure was annealed by the isothermal-isobaric MD calculation for 100 ps, thermostated at 1000 K by a velocity scaling with keeping the pressure at atmospheric pressure. The Born-Mayer-Huggins potential is employed in the MD simulation.

Figure 2(a) shows a charge density profile across the SiO₂/Al₂O₃ interface. Electric dipole layer appears at the interface, and it is directed from the SiO₂ side to Al₂O₃ side. Figure 2(b) shows the electric potential profile around the interface, which is obtained by solving one-dimensional Poisson’s equation. The built-in potential at SiO₂/Al₂O₃ interface is about 0.5 V, which matches the experimental value of the flat-band voltage shift [1]. Thus the direction and magnitude of the dipole moment in our model agrees with the experimental result. Figure 3 shows the magnified image of the SiO₂/Al₂O₃ interface, in which the O ions originated from Al₂O₃ are colored by green. It can be clearly seen that the O ion moves one-sidedly from Al₂O₃ side to SiO₂ one.

The simulation result indicates that the O ion is driven by some drift forces, but not by a simple diffusion due to the density difference at the interface. It is inferred that the O ions in Al₂O₃ are attracted to the strong positive charges of Si ions. The positive charges of Si ions must be canceled by the negative charges of O ions in SiO₂, but at very close distance, there is an appreciable octupole moment around the Si ion which is located at the center of SiO₄ tetrahedron (see Fig.4). On the other hand, there is an hexadecapole moment around the Al ion which located at the center of AlO₆octahedron. The electrostatic field induced by the octupole moment around the Si ion is stronger than that of the hexadecapole moment around the Al ion, and thus O ions in the vicinity of the interface can be attracted to Si ions in specific directions. Opposite dipole formation at SiO₂/Y₂O₃interface can also be explained by the difference in the multipole moments around Si and Y ions [4].

The multipole moment around an oxide cation is relevant to its electronegativity of the O density of the oxide. Therefore, our “multipole moment induced O migration model” can be regarded as the unified model of the O density [1] model and the electronegativity model [2].

Acknowledgement

This work is supported by JST-CREST, and a Grant-in-Aid for Scientific Research (B) from the MEXT Japan.

References

[1] K. Kita, and A. Toriumi, Appl. Phys. Lett. 94, 132902 (2009).

[2] K. Kakushima, K. Okamoto, M. Adachi, K. Tachi, P. Ahmet, K. Tsutsui, N. Sugii, T. Hattori, H. Iwai, Solid-State Electron. 52, 1280 (2008).

[3] X. Wang, K. Han, W. Wang, S. Chen, X. Ma, D. Chen, J. Zhan, J. Du, Y. Xiong,  and A. Huang,  Appl. Phys. Lett. 96, 152907 (2010).

[4] R. Kuriyama, M. Hashiguchi, R. Takahashi, A. Ogura, S. Satoh, T. Watanabe, JJAP, submitted.