244
A. V. Pomogaeva and A. Y. Timoshkin
belong to E symmetry of C 3v point group and have p-nature. States of the valence
band have the main contribution from N atoms, and states of the conduction band
have the main contribution from Ga atoms. Similar conclusions about the nature of
valence and conductive bands were made on the basis of PBC computations of the
band structure of Ga-N nanowires with diameters of 0.9−2.8 nm [167].
It is interesting that the band gap of the [HGaNH] 3∞ polymer is clearly indirect,
with the bottom of the conduction band laying near (but not exactly at) the edge
of BZ with k = π/a. Contributions of individual atomic orbitals to the lowest
unoccupied delocalized MO of [HGaNH] 115 consistently change sign from one unit
cell to another. The bulk Ga-N is a direct band gap semiconductor. However, it
is known that stress applied to a unit cell of a bulk material via doping or strain
applied to the one-dimensional nanostructures [185, 186] can cause a switching
from direct to indirect band gap. Recent research of GaAs nanowires grown in the
[0001] direction [187] demonstrated the phenomenon of transition from direct to
indirect band gap when the diameter of the GaAs nanowire becomes smaller than
~28 Å. Obviously, the same effect takes place in the case of Ga-N nanowires. While
wider Ga-N nanowires have the direct band gap [167], the thinnest [HGaNH] 3n+1
rod-shaped polymer has a conduction band with minimum shifted from the point
toward the edge of BZ with k = π/a.
The band gap of the [HGaNH] 3∞ polymer is found to be about 7.0 eV, that
is, significantly larger than 3.4 eV of the band gap of bulk Ga-N or the band
gaps 3–4 eV, obtained for Ga-N nanowires with diameters of 0.9−2.8 nm by
pseudopotential DFT computations with PBC [167]. However, the actual energy
gap of the finite [HGaNH] 3n+1 oligomer is defined by localized states situated in the
band gap rather than in the top of valence and in the bottom of conductive bands. It
is interesting that elongation of the [HGaNH] 3n+1 does not lead to delocalization of
HOMOs and LUMOs over the oligomer. Thus, [HGaNH] 3n+1 oligomers differ from
the similar rods of group 14 elements [119, 188], unsaturated (BN) 3n rods [184], and
model nitrogen nanoneedles [182]. In Fig. 6.24, HOMOs and LUMOs are shown
for closed and open oligomers. The structure with n = 9 is chosen to compare the
orbitals of hydrogen- and methyl-substituted oligomers that will be discussed later.
Elongation up to n = 38 of the hydrogen-substituted oligomers does not reduce
the degree of localization of the MOs. In case of the closed [HGaNH] 115 oligomer,
about 92% of the electronic density of HOMO is distributed over the two unit cells
of the oligomer near the Ga-capped edge (Fig. 6.24a). LUMO of this oligomer is
about 91% localized on the unit cell near the N-capped edge (Fig. 6.24b).
MOs which are localized in the real space cannot be localized in the reciprocal
space of the BZ. Thus, energy positions of HOMO, LUMO, and other edgelocalized MOs of the [HGaNH] 115 oligomer are shown by the dashed lines in Fig.
6.23a. Most of these states are located in the band gap near the top of valence band
and near the bottom of the conduction band. Similar to states of valence band of the
[HGaNH] 3∞ polymer, HOMO of the [HGaNH] 115 oligomer is doubly degenerate,
with a major contribution of p orbitals of N atoms, with some contributions from
s orbitals of H atoms. LUMO is formed mainly by s orbitals of Ga atoms. The
presence of the localized states in the spectrum of the finite oligomer reduces the
A. V. Pomogaeva and A. Y. Timoshkin
belong to E symmetry of C 3v point group and have p-nature. States of the valence
band have the main contribution from N atoms, and states of the conduction band
have the main contribution from Ga atoms. Similar conclusions about the nature of
valence and conductive bands were made on the basis of PBC computations of the
band structure of Ga-N nanowires with diameters of 0.9−2.8 nm [167].
It is interesting that the band gap of the [HGaNH] 3∞ polymer is clearly indirect,
with the bottom of the conduction band laying near (but not exactly at) the edge
of BZ with k = π/a. Contributions of individual atomic orbitals to the lowest
unoccupied delocalized MO of [HGaNH] 115 consistently change sign from one unit
cell to another. The bulk Ga-N is a direct band gap semiconductor. However, it
is known that stress applied to a unit cell of a bulk material via doping or strain
applied to the one-dimensional nanostructures [185, 186] can cause a switching
from direct to indirect band gap. Recent research of GaAs nanowires grown in the
[0001] direction [187] demonstrated the phenomenon of transition from direct to
indirect band gap when the diameter of the GaAs nanowire becomes smaller than
~28 Å. Obviously, the same effect takes place in the case of Ga-N nanowires. While
wider Ga-N nanowires have the direct band gap [167], the thinnest [HGaNH] 3n+1
rod-shaped polymer has a conduction band with minimum shifted from the point
toward the edge of BZ with k = π/a.
The band gap of the [HGaNH] 3∞ polymer is found to be about 7.0 eV, that
is, significantly larger than 3.4 eV of the band gap of bulk Ga-N or the band
gaps 3–4 eV, obtained for Ga-N nanowires with diameters of 0.9−2.8 nm by
pseudopotential DFT computations with PBC [167]. However, the actual energy
gap of the finite [HGaNH] 3n+1 oligomer is defined by localized states situated in the
band gap rather than in the top of valence and in the bottom of conductive bands. It
is interesting that elongation of the [HGaNH] 3n+1 does not lead to delocalization of
HOMOs and LUMOs over the oligomer. Thus, [HGaNH] 3n+1 oligomers differ from
the similar rods of group 14 elements [119, 188], unsaturated (BN) 3n rods [184], and
model nitrogen nanoneedles [182]. In Fig. 6.24, HOMOs and LUMOs are shown
for closed and open oligomers. The structure with n = 9 is chosen to compare the
orbitals of hydrogen- and methyl-substituted oligomers that will be discussed later.
Elongation up to n = 38 of the hydrogen-substituted oligomers does not reduce
the degree of localization of the MOs. In case of the closed [HGaNH] 115 oligomer,
about 92% of the electronic density of HOMO is distributed over the two unit cells
of the oligomer near the Ga-capped edge (Fig. 6.24a). LUMO of this oligomer is
about 91% localized on the unit cell near the N-capped edge (Fig. 6.24b).
MOs which are localized in the real space cannot be localized in the reciprocal
space of the BZ. Thus, energy positions of HOMO, LUMO, and other edgelocalized MOs of the [HGaNH] 115 oligomer are shown by the dashed lines in Fig.
6.23a. Most of these states are located in the band gap near the top of valence band
and near the bottom of the conduction band. Similar to states of valence band of the
[HGaNH] 3∞ polymer, HOMO of the [HGaNH] 115 oligomer is doubly degenerate,
with a major contribution of p orbitals of N atoms, with some contributions from
s orbitals of H atoms. LUMO is formed mainly by s orbitals of Ga atoms. The
presence of the localized states in the spectrum of the finite oligomer reduces the