Semiconducting nanoparticles are the classic example of quantum confinement systems. A wonderful example of the behavior of semiconducting nanoparticles is that of lead sulfide (PbS). Depending on the particle size, the band gap
increases from 0.41 eV in bulk crystals up to a few electron volts in nanoparticles.
Therefore, bulk PbS absorbs throughout the visible range and hence appears
black. However, with decreasing crystal size, the color changes to dark brown,
while suspensions of PbS nanoparticles are clear and reddish. In this context,
interesting experimental results have been provided by Reisfeld [10], who
prepared nanosized semiconducting PbS particles in glasses by using the sol–
gel method. The optical properties of these materials are shown graphically in
Figure 9.15. Reisfeld demonstrated a blue shift of nanoparticles with decreasing
particle size; the absorbance of PbS nanoparticles as a function of the wavelength
for particle sizes 4.8, 5.4, and 6.0 nm are shown in Figure 9.15a. The blue shift of
the absorbance found with decreasing particle size is correlated to a widening of
the band gap.
Figure 9.15b displays a plot according to Eq. (9.9) to estimate the gap width. The
intersection of the extrapolation of the linear part of the graph with the abscissa at
(ahn)
2 ¼ 0 yields the band gap, which is seen clearly to widen, from 1.42 eV for the
6-nm particles to 1.92 eV for the 4.8-nm particles. A plot of the gap width versus
inverse particle size squared is shown in Figure 9.16, and this demonstrates the
validity of Eqs. (9.7) and (9.8). Clearly, the exponent À2 for the particle size is
perfectly valid, although a minor deviation may be caused by the particle size
distribution and experimental uncertainties. In any case, the validity of the simple
considerations leading to the exponent À2 is very well justified.
Figure 9.14 Tauc plot according to Eq. (9.9)
[8,9], using the absorption data for ZnO
nanoparticles with different sizes shown in
Figure 9.13. The intersection of the
extrapolation with the abscissa (ahn)
0.5 ! 0
gives the width of the optical band gap. In this
example, a gap width of 3.08 eV for the 3-nm
particles and 2.87 eV for the 12-nm particles
was determined.
218j 9 Optical Properties of Nanoparticles
increases from 0.41 eV in bulk crystals up to a few electron volts in nanoparticles.
Therefore, bulk PbS absorbs throughout the visible range and hence appears
black. However, with decreasing crystal size, the color changes to dark brown,
while suspensions of PbS nanoparticles are clear and reddish. In this context,
interesting experimental results have been provided by Reisfeld [10], who
prepared nanosized semiconducting PbS particles in glasses by using the sol–
gel method. The optical properties of these materials are shown graphically in
Figure 9.15. Reisfeld demonstrated a blue shift of nanoparticles with decreasing
particle size; the absorbance of PbS nanoparticles as a function of the wavelength
for particle sizes 4.8, 5.4, and 6.0 nm are shown in Figure 9.15a. The blue shift of
the absorbance found with decreasing particle size is correlated to a widening of
the band gap.
Figure 9.15b displays a plot according to Eq. (9.9) to estimate the gap width. The
intersection of the extrapolation of the linear part of the graph with the abscissa at
(ahn)
2 ¼ 0 yields the band gap, which is seen clearly to widen, from 1.42 eV for the
6-nm particles to 1.92 eV for the 4.8-nm particles. A plot of the gap width versus
inverse particle size squared is shown in Figure 9.16, and this demonstrates the
validity of Eqs. (9.7) and (9.8). Clearly, the exponent À2 for the particle size is
perfectly valid, although a minor deviation may be caused by the particle size
distribution and experimental uncertainties. In any case, the validity of the simple
considerations leading to the exponent À2 is very well justified.
Figure 9.14 Tauc plot according to Eq. (9.9)
[8,9], using the absorption data for ZnO
nanoparticles with different sizes shown in
Figure 9.13. The intersection of the
extrapolation with the abscissa (ahn)
0.5 ! 0
gives the width of the optical band gap. In this
example, a gap width of 3.08 eV for the 3-nm
particles and 2.87 eV for the 12-nm particles
was determined.
218j 9 Optical Properties of Nanoparticles