106
S. Yanagisawa and I. Hamada
width suggests distribution of the electronic charge density at the intermolecular
site, as indicated in Refs. [98–100].
Compared to the fundamental gap estimated with the experimental technique
such as photoconductivity, optical absorption, and inverse photoemission measurements [71–80], the theoretical band gap within G 0 W 0 is underestimated. The
band gap averaged over the k-points in the Brillouin zone was also slightly
underestimated, which is in line with Ref. [52]. To remove the starting point
dependence of the G 0 W 0 calculation [90–95], we took partially into account the
effect of self-consistency within the eigenvalue-only self-consistent GW (evGW )
treatment [88, 89]. As a result, the fundamental gap becomes slightly overestimated,
becoming closer to experiments (see Table 4.2) [13]. For pentacene, the gap is in
agreement with the recent experimental value measured with the low-energy inverse
photoemission spectroscopy (LEIPS) [80]. The band widths slightly increased by
the evGW calculation by at most 0.07 eV, independently of the k-point.
Figures 4.2b, 4.3b, 4.4b, and 4.5b display the calculated density of states
(DOS) in comparison to the experimental photoemission measurement, in which
the substrate temperature was kept at 150 K [81]. We calculated the DOS with
the Gaussian smearing with the width set to the imaginary part of the self-energy
obtained with the G 0 W 0 calculation, rather than a uniform broadening. The width or
the satellite peak structure of photoemission spectra is, in principle, the imaginary
part of the self-energy, i.e., spectral function. Notice that according to Ref. [101],
the structures of the organic thin films are similar to those of the single crystal
investigated in this study, implying that comparison of the theoretical electronic
structures of bulk organic crystals with the experimental photoemission spectra of
organic thin films is meaningful. The calculated peak positions of the valence bands
derived from HOMO, the next HOMO, the second next HOMO, and so forth, of the
constituent molecule, are in agreement with the experimental photoemission spectra
of the thin films on Ag(111) [81]. Some shoulder structures are found in the vicinity
of the valence band, for instance, H-1 and H-3 DOS peaks in tetracene, which are not
resolved in the experimental photoemission spectra. Although there is agreement
found between the theoretical DOS and the experiment, factors affecting the
experimental photoemission spectra of organic semiconductors such as broadening
by temperature effects, instrumental resolution, and other factors causing structural
disorder [102] should be taken into account. The incomplete charge screening at the
surface was taken into account, when the G 0 W 0 DOS of oligoacenes were compared
with the experimental data [52]. Furthermore, it was proposed that the electronphonon coupling and structural disorder should be taken into account to describe
the electronic structure of organic semiconductors at finite temperature [103].
As far as the DOS of the unoccupied states are concerned, the inverse photoemission data of 2–3 monolayers of the oligoacenes on Ag(111) were reported
[104]. The measured energy difference between the lowest and the second lowest
unoccupied π ∗ -derived peaks was 0.8, 1.1, and 1.7 eV for naphthalene, anthracene,
and tetracene, respectively [104]. The theoretical energy difference between the
corresponding DOS peaks with G 0 W 0 were 0.90, 1.39, and 1.73 eV, respectively,
in fair agreement with the experiment.
S. Yanagisawa and I. Hamada
width suggests distribution of the electronic charge density at the intermolecular
site, as indicated in Refs. [98–100].
Compared to the fundamental gap estimated with the experimental technique
such as photoconductivity, optical absorption, and inverse photoemission measurements [71–80], the theoretical band gap within G 0 W 0 is underestimated. The
band gap averaged over the k-points in the Brillouin zone was also slightly
underestimated, which is in line with Ref. [52]. To remove the starting point
dependence of the G 0 W 0 calculation [90–95], we took partially into account the
effect of self-consistency within the eigenvalue-only self-consistent GW (evGW )
treatment [88, 89]. As a result, the fundamental gap becomes slightly overestimated,
becoming closer to experiments (see Table 4.2) [13]. For pentacene, the gap is in
agreement with the recent experimental value measured with the low-energy inverse
photoemission spectroscopy (LEIPS) [80]. The band widths slightly increased by
the evGW calculation by at most 0.07 eV, independently of the k-point.
Figures 4.2b, 4.3b, 4.4b, and 4.5b display the calculated density of states
(DOS) in comparison to the experimental photoemission measurement, in which
the substrate temperature was kept at 150 K [81]. We calculated the DOS with
the Gaussian smearing with the width set to the imaginary part of the self-energy
obtained with the G 0 W 0 calculation, rather than a uniform broadening. The width or
the satellite peak structure of photoemission spectra is, in principle, the imaginary
part of the self-energy, i.e., spectral function. Notice that according to Ref. [101],
the structures of the organic thin films are similar to those of the single crystal
investigated in this study, implying that comparison of the theoretical electronic
structures of bulk organic crystals with the experimental photoemission spectra of
organic thin films is meaningful. The calculated peak positions of the valence bands
derived from HOMO, the next HOMO, the second next HOMO, and so forth, of the
constituent molecule, are in agreement with the experimental photoemission spectra
of the thin films on Ag(111) [81]. Some shoulder structures are found in the vicinity
of the valence band, for instance, H-1 and H-3 DOS peaks in tetracene, which are not
resolved in the experimental photoemission spectra. Although there is agreement
found between the theoretical DOS and the experiment, factors affecting the
experimental photoemission spectra of organic semiconductors such as broadening
by temperature effects, instrumental resolution, and other factors causing structural
disorder [102] should be taken into account. The incomplete charge screening at the
surface was taken into account, when the G 0 W 0 DOS of oligoacenes were compared
with the experimental data [52]. Furthermore, it was proposed that the electronphonon coupling and structural disorder should be taken into account to describe
the electronic structure of organic semiconductors at finite temperature [103].
As far as the DOS of the unoccupied states are concerned, the inverse photoemission data of 2–3 monolayers of the oligoacenes on Ag(111) were reported
[104]. The measured energy difference between the lowest and the second lowest
unoccupied π ∗ -derived peaks was 0.8, 1.1, and 1.7 eV for naphthalene, anthracene,
and tetracene, respectively [104]. The theoretical energy difference between the
corresponding DOS peaks with G 0 W 0 were 0.90, 1.39, and 1.73 eV, respectively,
in fair agreement with the experiment.