9 Si Nanopowder for Photoluminescence and Hydrogen Generation Materials
365
dn e
1
dt
= −
k r
1
+ k nr
1
t,
(9.5)
where k nr is the rate constant for non-radiative transition. Since the PL lifetime is
inversely proportional to the total rate constant, we have
4.9 : 0.62 =
1
k r
0 + k nr
0
:
1
k r
1 + k nr
1
.
(9.6)
Considering the quantum efficiency of 0.42 and 0.45 for PL in the absence and
presence of Si nanopowder, respectively, we have
k r
0
k r
0 + k nr
0
= 0.42,
(9.7)
k r
1
k r
1 + k nr
1
= 0.45.
(9.8)
Using Eqs. (9.6), (9.7), and (9.8), we have
k r
1
= 8.5k r
0 .
(9.9)
Therefore, using Eq. (9.3), n e
1 is given by
n e
1
= 7.1 × 10
3 n e
0 .
(9.10)
The above consideration can lead to the following conclusion. The PL intensity
is increased by adsorption on Si nanopowder for the following two reasons: (i) an
increase in the number of electrons in the electronic excited-state (∼7100 times
enhancement) and (ii) an increase in the rate constant for radiative transition (∼8.5
times enhancement). The increased number of electrons in the excited-state results
from the increased transition probability which in turn results from a great increase
in the dynamic dipole moment by adsorption and/or enhancement of wave function
of DMA by adsorption, i.e., surface resonance state [25].
Photoluminescence Mechanism
The excitation spectra with the PL energies lower than 3.12 eV clearly possess
vibronic bands (Fig. 9.13), indicating that adsorbed DMA molecules are directly
excited. In the excitation spectra for the PL energies higher than 3.29 eV, on the
other hand, a broad structure is dominant. The peak energy of the broad structure
shifts in the higher energy direction with the PL energy. It should be noted that
for excitation with energies higher than 3.76 eV, the PL vibronic bands from
vibrational excited-states are observed (cf. Fig. 9.12). This result demonstrates
that for PL emission from vibrational excited-states, incident light is absorbed
365
dn e
1
dt
= −
k r
1
+ k nr
1
t,
(9.5)
where k nr is the rate constant for non-radiative transition. Since the PL lifetime is
inversely proportional to the total rate constant, we have
4.9 : 0.62 =
1
k r
0 + k nr
0
:
1
k r
1 + k nr
1
.
(9.6)
Considering the quantum efficiency of 0.42 and 0.45 for PL in the absence and
presence of Si nanopowder, respectively, we have
k r
0
k r
0 + k nr
0
= 0.42,
(9.7)
k r
1
k r
1 + k nr
1
= 0.45.
(9.8)
Using Eqs. (9.6), (9.7), and (9.8), we have
k r
1
= 8.5k r
0 .
(9.9)
Therefore, using Eq. (9.3), n e
1 is given by
n e
1
= 7.1 × 10
3 n e
0 .
(9.10)
The above consideration can lead to the following conclusion. The PL intensity
is increased by adsorption on Si nanopowder for the following two reasons: (i) an
increase in the number of electrons in the electronic excited-state (∼7100 times
enhancement) and (ii) an increase in the rate constant for radiative transition (∼8.5
times enhancement). The increased number of electrons in the excited-state results
from the increased transition probability which in turn results from a great increase
in the dynamic dipole moment by adsorption and/or enhancement of wave function
of DMA by adsorption, i.e., surface resonance state [25].
Photoluminescence Mechanism
The excitation spectra with the PL energies lower than 3.12 eV clearly possess
vibronic bands (Fig. 9.13), indicating that adsorbed DMA molecules are directly
excited. In the excitation spectra for the PL energies higher than 3.29 eV, on the
other hand, a broad structure is dominant. The peak energy of the broad structure
shifts in the higher energy direction with the PL energy. It should be noted that
for excitation with energies higher than 3.76 eV, the PL vibronic bands from
vibrational excited-states are observed (cf. Fig. 9.12). This result demonstrates
that for PL emission from vibrational excited-states, incident light is absorbed