First-Principles Study of Dielectric Properties of Amorphous High-k Materials

Abstract

The dielectric properties of amorphous alumina (a-Al2O3), hafnia (a-HfO2), and hafnium aluminate (a-HfAlO) having a Hf/(Al+Hf) ratio of 20% have been studied by the first-principles calculation. The calculated dielectric constants of amorphous model structures increase with increasing Hf/(Al+Hf) ratio in terms of both electronic and lattice polarization contributions. The lattice polarization contribution to the dielectric constants is larger than the electronic one. The calculated dielectric functions of the amorphous models show a negligible frequency dispersion at the operation frequencies of current complementary metal–oxide–semiconductor (CMOS) transistors. However, the dielectric functions of the amorphous models have high peaks at much lower frequencies from about 1 THz than those of α-alumina (α-Al2O3) and monoclinic hafnia (m-HfO2) crystals.

Local Dielectric Property of Cubic, Tetragonal, and Monoclinic Hafnium Oxides

“…The electronic contribution to macroscopic dielectric constant of HfO 2 are reported to be about 5, almost independent of the structure of crystal. 5,25,26) Hence, the values of the hydrogen termination models are worse compared to those of the point charge models. This smallness of the dielectric constant confirms that the termination with hydrogen atoms is not suitable for HfO 2 .…”

“…It is well known that the lattice oscillation contribution dominates over the electronic one and is more sensitive to the structure of the material. 4,5,25,26) One of the purposes of this work is to clarify the electronic contribution to the local dielectric response before we include the lattice contribution, and to establish the local dielectric response analysis, since the electronic contribution is easy to handle and its calculations have less ambiguity than the lattice contribution.…”

Local Dielectric Property of Hafnium and Lanthanum Atoms in HfLaOx

“…This similarity is due to the similarity of the bonding states of lanthanum and hafnium. In the computational works, 14,15,40) the electronic contributions of dielectric constant of the monoclinic structure of the hafnia are reported as about 5. The dielectric constant around bond regions is much less than this value.…”

“…Of course, it is known that the lattice contribution to the dielectric constant dominates over the electronic contribution and depends on the model structure compared to the electronic contribution. 14,15) Nevertheless, the effect of the electronic polarization is worth investigating, since the calculations of the electronic contribution have less ambiguity than the lattice contribution and are easy to handle, before we study the lattice contribution.…”

Structural, vibrational and transport properties of liquid and amorphous alumina: A molecular dynamics simulation study

“…Regarding liquid alumina, Jahn and Madden (2008) calculated frequency-dependent viscosity, and self-diffusion coefficient from the zero frequency limit of the vibrational spectrum, despite the fact that this value was usually determined by the slope of the mean squared displacement ( Van Hoang, 2004;Van Hoang andOh, 2004, 2005;Hung et al, 2006). In addition, for amorphous alumina, the vibrational (Gutiérrez et al, 2010;Sergio and Gonzalo, 2011), and dielectric properties (Momida et al, 2006;Momida et al, 2007a) were explored using the first-principles calculation. So far, only Vashishta et al (2008) provided a relatively comprehensive study on the dynamical properties of the liquid and amorphous alumina with different densities, including the vibrational density of states, specific heat, and frequency-dependent ionic conductivity.…”