Chapter 3
Local Dielectric Constant Density
Analysis of High-k Dielectric
Nanomaterial
Masato Senami and Akinori Fukushima
Abstract This article reviews progress of recently proposed local dielectric constant and polarizability. Local dielectric constant and polarizability are defined only
in the formalism of quantum field theory. These quantities are expected to be good
tool to the numerical analysis of nanosize materials. Basis set dependence of these
quantities is explained with examples, an atom and a cation. The distribution of local
polarizability in molecules is explained for covalent molecules, XH n (X=C, N, O,
F, Si, P, S, Cl, Ge, As, Se, and Br). Particularly, the relation between chemical bond
and dielectric property is discussed. Application to practical nanosize materials is
introduced for hafnium dioxide, which is the leading candidate for next-generation
gate dielectric thin film. Particularly, HfLaO x model is studied for the purpose of the
clarification of the effect of the incorporation of La atoms to HfO 2 on the dielectric
properties.
Keywords Quantum field theory · Local polarizability · Local dielectric
constant · Hafnium dioxide
3.1 Introduction
The notion of nanotechnology has been started from the lecture by Richard P.
Feynman in 1959 [1]. Then technology has been progressed extremely for several
decades. In an industrial aspect, some electronic devices are designed and manufactured in a nanometer scale. In laboratory level, molecular computer is studied hard
in computational and experimental methods. Properties of these extremely small
devices are often dominated by definite local regions in devices: for example, as a
M. Senami ()
Department of Micro Engineering, Kyoto University, Kyoto, Japan
e-mail: senami@me.kyoto-u.ac.jp
A. Fukushima
Faculty of Engineering, University of Fukui, Fukui, Japan
e-mail: akinori@u-fukui.ac.jp
© Springer Nature Singapore Pte Ltd. 2020
T. Onishi (ed.), Theoretical Chemistry for Advanced Nanomaterials,
https://doi.org/10.1007/978-981-15-0006-0_3
53
Local Dielectric Constant Density
Analysis of High-k Dielectric
Nanomaterial
Masato Senami and Akinori Fukushima
Abstract This article reviews progress of recently proposed local dielectric constant and polarizability. Local dielectric constant and polarizability are defined only
in the formalism of quantum field theory. These quantities are expected to be good
tool to the numerical analysis of nanosize materials. Basis set dependence of these
quantities is explained with examples, an atom and a cation. The distribution of local
polarizability in molecules is explained for covalent molecules, XH n (X=C, N, O,
F, Si, P, S, Cl, Ge, As, Se, and Br). Particularly, the relation between chemical bond
and dielectric property is discussed. Application to practical nanosize materials is
introduced for hafnium dioxide, which is the leading candidate for next-generation
gate dielectric thin film. Particularly, HfLaO x model is studied for the purpose of the
clarification of the effect of the incorporation of La atoms to HfO 2 on the dielectric
properties.
Keywords Quantum field theory · Local polarizability · Local dielectric
constant · Hafnium dioxide
3.1 Introduction
The notion of nanotechnology has been started from the lecture by Richard P.
Feynman in 1959 [1]. Then technology has been progressed extremely for several
decades. In an industrial aspect, some electronic devices are designed and manufactured in a nanometer scale. In laboratory level, molecular computer is studied hard
in computational and experimental methods. Properties of these extremely small
devices are often dominated by definite local regions in devices: for example, as a
M. Senami ()
Department of Micro Engineering, Kyoto University, Kyoto, Japan
e-mail: senami@me.kyoto-u.ac.jp
A. Fukushima
Faculty of Engineering, University of Fukui, Fukui, Japan
e-mail: akinori@u-fukui.ac.jp
© Springer Nature Singapore Pte Ltd. 2020
T. Onishi (ed.), Theoretical Chemistry for Advanced Nanomaterials,
https://doi.org/10.1007/978-981-15-0006-0_3
53