56
M. Senami and A. Fukushima
This treatment is adopted in some groups and accurate enough for some purpose
of researches. However, if quantum property of photon is important for analyses,
quantum field theory should inevitably be used. The unified picture of the photon,
the electron, and their interactions are only described in quantum field theory.
As a result, we believe that response properties of nanosize devices to electromagnetic fields should be analyzed by using physical quantities based on quantum
field theory. For this purpose, local physical quantities based on quantum field
theory have been proposed for dielectric constant, conductivity, and spin torque [14–
16]. Local quantities for dielectric responses are the topic explained in this article.
For conductivity, two types of local conductivity are defined as local counterpart
of ordinary conductivity. One is the response to external electric field for a local
region, and the other is the response to internal electric field in a local region.
These two definitions of local conductivity are mentioned in the next section. Local
conductivity is demonstrated in computational approach for nanowire materials
and benzenedithiol and its derivatives [13, 17, 18]. By using GaN and silicon
nanowire models, internal and external conductivities have been studied [17, 18].
Importance of π -bonding has been studied in comparison between benzenedithiol
and its derivatives [13]. For spin torque, the equation of motion of the electron spin
is introduced based on quantum field theory, and local description of spin torque is
given in this formulation as shown in Fig. 3.1. In local description, in addition to the
local counterpart of the ordinary spin torque, new torque term for the electron spin
is introduced. This new torque describes a local effect, and this term gives zero if
integrated over the whole region. However, this effect is considered to be important.
Even for spin steady states, local spin torque does not vanish Heisenberg equation in
quantum mechanics, while the equation of motion of the electron spin in quantum
field theory gives zero torque state by the cancellation between the spin torque and
new torque term even in a local region. This is confirmed in numerical methods
for many molecules [19–21]. Hence, quantum field theory should be used for the
correct local description of spin torque.
The study of this local physical quantity in quantum field theory started recently,
and many things remain to be studied. In this article, we show the formalism
of the local dielectric constant and the local polarizability and introduce knowledge derived by recent works. This article is organized as follows. In the next
section, definitions of the local dielectric constant and the local polarizability are
explained, and some related formulae are introduced, such as the relation with local
conductivity tensors. In Sect. 3.3, we explain the internal distribution of the local
polarizability in simple molecules, XH n (X=C, N, O, F, Si, P, S, Cl, Ge, As, Se,
and Br). These molecules are typical examples of molecules with covalent bond.
It will be seen which electrons in molecules responds to external electric field. In
Sect. 3.4, we review the dielectric property of metal oxide for the purpose of the
study of hafnium dioxide (HfO 2 ). Hafnium dioxide has high permittivity (high-k)
and hence is often studied for a viewpoint of gate dielectric thin film as insulator
in semiconductor devices. In this section, four models are compared and discussed.
Four models are two different structures, monoclinic and cubic, of HfO 2 , La 2 O 3
model, and HfLaO x model. The HfLaO x model is investigated for the effect of the
M. Senami and A. Fukushima
This treatment is adopted in some groups and accurate enough for some purpose
of researches. However, if quantum property of photon is important for analyses,
quantum field theory should inevitably be used. The unified picture of the photon,
the electron, and their interactions are only described in quantum field theory.
As a result, we believe that response properties of nanosize devices to electromagnetic fields should be analyzed by using physical quantities based on quantum
field theory. For this purpose, local physical quantities based on quantum field
theory have been proposed for dielectric constant, conductivity, and spin torque [14–
16]. Local quantities for dielectric responses are the topic explained in this article.
For conductivity, two types of local conductivity are defined as local counterpart
of ordinary conductivity. One is the response to external electric field for a local
region, and the other is the response to internal electric field in a local region.
These two definitions of local conductivity are mentioned in the next section. Local
conductivity is demonstrated in computational approach for nanowire materials
and benzenedithiol and its derivatives [13, 17, 18]. By using GaN and silicon
nanowire models, internal and external conductivities have been studied [17, 18].
Importance of π -bonding has been studied in comparison between benzenedithiol
and its derivatives [13]. For spin torque, the equation of motion of the electron spin
is introduced based on quantum field theory, and local description of spin torque is
given in this formulation as shown in Fig. 3.1. In local description, in addition to the
local counterpart of the ordinary spin torque, new torque term for the electron spin
is introduced. This new torque describes a local effect, and this term gives zero if
integrated over the whole region. However, this effect is considered to be important.
Even for spin steady states, local spin torque does not vanish Heisenberg equation in
quantum mechanics, while the equation of motion of the electron spin in quantum
field theory gives zero torque state by the cancellation between the spin torque and
new torque term even in a local region. This is confirmed in numerical methods
for many molecules [19–21]. Hence, quantum field theory should be used for the
correct local description of spin torque.
The study of this local physical quantity in quantum field theory started recently,
and many things remain to be studied. In this article, we show the formalism
of the local dielectric constant and the local polarizability and introduce knowledge derived by recent works. This article is organized as follows. In the next
section, definitions of the local dielectric constant and the local polarizability are
explained, and some related formulae are introduced, such as the relation with local
conductivity tensors. In Sect. 3.3, we explain the internal distribution of the local
polarizability in simple molecules, XH n (X=C, N, O, F, Si, P, S, Cl, Ge, As, Se,
and Br). These molecules are typical examples of molecules with covalent bond.
It will be seen which electrons in molecules responds to external electric field. In
Sect. 3.4, we review the dielectric property of metal oxide for the purpose of the
study of hafnium dioxide (HfO 2 ). Hafnium dioxide has high permittivity (high-k)
and hence is often studied for a viewpoint of gate dielectric thin film as insulator
in semiconductor devices. In this section, four models are compared and discussed.
Four models are two different structures, monoclinic and cubic, of HfO 2 , La 2 O 3
model, and HfLaO x model. The HfLaO x model is investigated for the effect of the