3 Local Dielectric Constant Density Analysis of High-k Dielectric Nanomaterial
73
Fig. 3.12 Peak positions in Fig. 3.11 over internuclear length. Horizontal axis means the group of
X atom
3.4 Local Dielectric Property of HfLaO x
In this section, we show local dielectric properties of metal oxides used in new
insulators for transistors. Among many materials, we focused on hafnium dioxide
(HfO 2 ), which has high permittivity. HfO 2 has two different structures, including
monoclinic and cubic. Cubic HfO 2 (c-HfO 2 ) has a larger dielectric constant than
that of monoclinic HfO 2 (m-HfO 2 ). However, the c-HfO 2 is unstable. Yamamoto
et al. [57] reported that the crystal structure changes into the cubic phase by doping
La atoms into m-HfO 2 . Based on this report, in this study, we employed a HfLaO x
model to analyze the effect of the La atom on the dielectric properties. The details
of our work are in Refs. [22–24].
To clarify the effect of La atoms on the dielectric properties, four different
models were used, as shown in Fig. 3.15. Red spheres represent O atoms, green
spheres represent La atoms, and yellow spheres represent Hf atoms. Figure 3.15a is
a m-HfO 2 model, Fig. 3.15b is a La 2 O 3 model, Fig. 3.15c is a c-HfO 2 model, and
Fig. 3.15d is a HfLaO x model. All models were rendered by VESTA [58]. These
models are made based on their crystal structures. The La 2 O 3 has hexagonal unit
cell, the m-HfO 2 has a monoclinic unit cell, and the c-HfO 2 has a cubic unit cell. O
73
Fig. 3.12 Peak positions in Fig. 3.11 over internuclear length. Horizontal axis means the group of
X atom
3.4 Local Dielectric Property of HfLaO x
In this section, we show local dielectric properties of metal oxides used in new
insulators for transistors. Among many materials, we focused on hafnium dioxide
(HfO 2 ), which has high permittivity. HfO 2 has two different structures, including
monoclinic and cubic. Cubic HfO 2 (c-HfO 2 ) has a larger dielectric constant than
that of monoclinic HfO 2 (m-HfO 2 ). However, the c-HfO 2 is unstable. Yamamoto
et al. [57] reported that the crystal structure changes into the cubic phase by doping
La atoms into m-HfO 2 . Based on this report, in this study, we employed a HfLaO x
model to analyze the effect of the La atom on the dielectric properties. The details
of our work are in Refs. [22–24].
To clarify the effect of La atoms on the dielectric properties, four different
models were used, as shown in Fig. 3.15. Red spheres represent O atoms, green
spheres represent La atoms, and yellow spheres represent Hf atoms. Figure 3.15a is
a m-HfO 2 model, Fig. 3.15b is a La 2 O 3 model, Fig. 3.15c is a c-HfO 2 model, and
Fig. 3.15d is a HfLaO x model. All models were rendered by VESTA [58]. These
models are made based on their crystal structures. The La 2 O 3 has hexagonal unit
cell, the m-HfO 2 has a monoclinic unit cell, and the c-HfO 2 has a cubic unit cell. O