118
S. Yanagisawa and I. Hamada
4.2.3 Theoretical Determination of the Ionization Energy
and Electron Affinity
Energies of the valence and conduction band edges relative to the vacuum level
of an organic molecular solid give the ionization energy (IE) and electron affinity
(EA), quantities of primary importance leading to the energy levels of the injected
or transported electron/hole at the organic-(in)organic heterojunction or inside the
organic layer. Essentially, IE and EA are defined as follows:
IE = vac − H , EA = vac − L ,
(4.7)
where vac is the vacuum level and H ( L ) is the edge of the highest (lowest)
occupied (unoccupied) energy level. Although the definition is straightforward for
a molecule in a gas phase, there are physical effects to take into account in case of a
molecular solid. The energy of the charge injected into the solid is renormalized: the
particle is stabilized by the surrounding polarization clouds with opposite charge.
The reduction in energy relative to the gas phase is referred to as polarization energy
[158]. The polarization energy is formally described as
P
+
= IE g − IE s , P
−
= EA s − EA g ,
(4.8)
where subscripts s and g denote solid and gas phases, respectively, and P + (P − )
is the polarization energy upon injection of hole (electron). P + corresponds to
increase in energy of the electron in a solid, leading to reduction in IE relative
to that in a gas phase, and vice versa in case of the polarization energy upon
electron (P − ), resulting in the increased EA. Measurement or quantification of the
polarization energy in organic solids dates back to the paper published by Sato, Seki,
and Inokuchi in 1981, which was based on the comparison of the photoelectron
spectroscopy data between the solid phase and the gas phase [158]. The measured
polarization energies upon the injected hole in the solids (P + ) were reported to
be in the range 0.9–3.0 eV [158]. The sum of the polarization energies P + + P − ,
corresponding to renormalization of the fundamental gap, becomes significant.
The reduced gap in the solid, inherently dielectric response event, may be
captured with the theoretical methodologies such as the GW approximation,
which describes the screened Coulomb potential based on the frequency-dependent
microscopic dielectric function [112, 159]. The weak intermolecular interaction in
organic solids may lead us to insights into the electronic nature described by a
single molecule surrounded by a dielectric medium of the other molecules. Actually,
treatment of a single molecule in the polarizable continuum model (PCM) or the
quantum mechanics (QM)/molecular mechanics (MM) treatment gave reasonable
estimation of IE and EA as total energy difference between neutral and charged
systems obtained at the DFT-GGA level of theory [160, 161].
In photoemission measurements, the energy of the particles injected or extracted
at the surface is measured, which is affected by the morphology or the molecular
S. Yanagisawa and I. Hamada
4.2.3 Theoretical Determination of the Ionization Energy
and Electron Affinity
Energies of the valence and conduction band edges relative to the vacuum level
of an organic molecular solid give the ionization energy (IE) and electron affinity
(EA), quantities of primary importance leading to the energy levels of the injected
or transported electron/hole at the organic-(in)organic heterojunction or inside the
organic layer. Essentially, IE and EA are defined as follows:
IE = vac − H , EA = vac − L ,
(4.7)
where vac is the vacuum level and H ( L ) is the edge of the highest (lowest)
occupied (unoccupied) energy level. Although the definition is straightforward for
a molecule in a gas phase, there are physical effects to take into account in case of a
molecular solid. The energy of the charge injected into the solid is renormalized: the
particle is stabilized by the surrounding polarization clouds with opposite charge.
The reduction in energy relative to the gas phase is referred to as polarization energy
[158]. The polarization energy is formally described as
P
+
= IE g − IE s , P
−
= EA s − EA g ,
(4.8)
where subscripts s and g denote solid and gas phases, respectively, and P + (P − )
is the polarization energy upon injection of hole (electron). P + corresponds to
increase in energy of the electron in a solid, leading to reduction in IE relative
to that in a gas phase, and vice versa in case of the polarization energy upon
electron (P − ), resulting in the increased EA. Measurement or quantification of the
polarization energy in organic solids dates back to the paper published by Sato, Seki,
and Inokuchi in 1981, which was based on the comparison of the photoelectron
spectroscopy data between the solid phase and the gas phase [158]. The measured
polarization energies upon the injected hole in the solids (P + ) were reported to
be in the range 0.9–3.0 eV [158]. The sum of the polarization energies P + + P − ,
corresponding to renormalization of the fundamental gap, becomes significant.
The reduced gap in the solid, inherently dielectric response event, may be
captured with the theoretical methodologies such as the GW approximation,
which describes the screened Coulomb potential based on the frequency-dependent
microscopic dielectric function [112, 159]. The weak intermolecular interaction in
organic solids may lead us to insights into the electronic nature described by a
single molecule surrounded by a dielectric medium of the other molecules. Actually,
treatment of a single molecule in the polarizable continuum model (PCM) or the
quantum mechanics (QM)/molecular mechanics (MM) treatment gave reasonable
estimation of IE and EA as total energy difference between neutral and charged
systems obtained at the DFT-GGA level of theory [160, 161].
In photoemission measurements, the energy of the particles injected or extracted
at the surface is measured, which is affected by the morphology or the molecular