9 Si Nanopowder for Photoluminescence and Hydrogen Generation Materials
367
state. Immediately after a hole is captured, electronic transition of the electron in
the electronic excited-state occurs, resulting in PL emission. Because of lowering
of the potential energy for the temporary captured electron (i.e., the potential of the
excited-state), the PL energy decreases, in contrast to the case where a hole transfers
to DMA first. The above consideration clearly shows that the PL energy for case a in
Fig. 9.15 increases by solvation, while that for case b decreases. This consideration
is verified by observation of two (0, 0) bands (or one (0,0) band and one (n, n) band)
separated by 0.11 eV. Each solvation energy is likely to be approximately a half of
the energy difference of the two (0, 0) bands, i.e., ∼55 meV.
The (0, 0) PL band for case a and the (n, n) band for case b are located at 3.10
and 3.21 eV, respectively. The (0, 0) band in the absorption spectra is observed at
3.15 eV, i.e., the average energy between the (0, 0) and (n, n) PL bands. In the
case of light absorption, both the initial and final states are in neutral charge states,
and therefore, solvation doesn’t occur. Therefore, the transition energy is between
that for the ground-state-stabilized case (case a) and the excited-state-stabilized case
(case b).
The intensity ratios of the PL peaks due to transitions from the vibrational
ground-states, i.e., (0, 0), (0, 1), (0, 2), and (0, 3) bands, are nearly independent on
the excitation energy. This is because after complete internal relaxation, transition
from the vibrational ground-state proceeds, and in this case, the PL intensity is
determined by the individual Franck-Condon factors which don’t depend on the
excitation energy. On the other hand, the intensity ratios of the PL peaks due
to transitions from the vibrational excited-states strongly depend on the incident
photon energy. To explain this phenomenon, we consider the case where an electron
enters the x-th vibrational state of the electronic excited-state. The n-th PL band
contains various transitions, (l, m), which satisfy the following equation:
l − m = n.
(9.11)
The transition rate, R l, m , is given by the product of the transition probability,
P l, m , and the number of electrons in the l-th vibrational state, N l :
R l,m = P l,m N l .
(9.12)
N l is given by
N l = N x (1 − a x ) (1 − a x−1 ) · · · · · · · · (1 − a l+1 ) = N x
l+1
x
(1 − a x ) ,
(9.13)
where N x is the number of electrons transferred from Si nanopowder to the xth vibrational state of the electronic excited-state, and a j expresses the transition
probability from the j-th vibrational states to various vibrational states of the
electronic ground-state which probability is proportional to the sum of the FranckCondon factors:
367
state. Immediately after a hole is captured, electronic transition of the electron in
the electronic excited-state occurs, resulting in PL emission. Because of lowering
of the potential energy for the temporary captured electron (i.e., the potential of the
excited-state), the PL energy decreases, in contrast to the case where a hole transfers
to DMA first. The above consideration clearly shows that the PL energy for case a in
Fig. 9.15 increases by solvation, while that for case b decreases. This consideration
is verified by observation of two (0, 0) bands (or one (0,0) band and one (n, n) band)
separated by 0.11 eV. Each solvation energy is likely to be approximately a half of
the energy difference of the two (0, 0) bands, i.e., ∼55 meV.
The (0, 0) PL band for case a and the (n, n) band for case b are located at 3.10
and 3.21 eV, respectively. The (0, 0) band in the absorption spectra is observed at
3.15 eV, i.e., the average energy between the (0, 0) and (n, n) PL bands. In the
case of light absorption, both the initial and final states are in neutral charge states,
and therefore, solvation doesn’t occur. Therefore, the transition energy is between
that for the ground-state-stabilized case (case a) and the excited-state-stabilized case
(case b).
The intensity ratios of the PL peaks due to transitions from the vibrational
ground-states, i.e., (0, 0), (0, 1), (0, 2), and (0, 3) bands, are nearly independent on
the excitation energy. This is because after complete internal relaxation, transition
from the vibrational ground-state proceeds, and in this case, the PL intensity is
determined by the individual Franck-Condon factors which don’t depend on the
excitation energy. On the other hand, the intensity ratios of the PL peaks due
to transitions from the vibrational excited-states strongly depend on the incident
photon energy. To explain this phenomenon, we consider the case where an electron
enters the x-th vibrational state of the electronic excited-state. The n-th PL band
contains various transitions, (l, m), which satisfy the following equation:
l − m = n.
(9.11)
The transition rate, R l, m , is given by the product of the transition probability,
P l, m , and the number of electrons in the l-th vibrational state, N l :
R l,m = P l,m N l .
(9.12)
N l is given by
N l = N x (1 − a x ) (1 − a x−1 ) · · · · · · · · (1 − a l+1 ) = N x
l+1
x
(1 − a x ) ,
(9.13)
where N x is the number of electrons transferred from Si nanopowder to the xth vibrational state of the electronic excited-state, and a j expresses the transition
probability from the j-th vibrational states to various vibrational states of the
electronic ground-state which probability is proportional to the sum of the FranckCondon factors: