62
METHODS OF MEASURING PROPERTIES
270
280
290
300 310 320
Raman shift (cm-1)
1
bL 8 9 10 1 1
radius R (nm)
Figure 3.26. Histogram of the distribution of Ge nanocrystal particle sizes (lower figure) around
the mean radius 6.5 nm, used to simulate (solid line) the Raman spectrum (dotted line) depicted
at the top. The size distribution was obtained by transmission electron microscopy. [From C. E.
Bottani, C. Mantini, P. Milani, M. Manfredini, A. Stella, P. Tognini, P. Cheyssac, and R. Kofman,
Appl. Phys. Left. 69, 2409 (1996).]
provides a narrow range of size distributions, so optical spectra of the type shown in
Fig. 3.27 can accurately determine the dependence of the gap on the average particle
radius and this dependence is shown in Fig. 3.28 for CdSe. We see that the energy
gap data for the colloidal samples plotted on this figure agree with the gaps evaluated
from optical spectra of CdSe nanoparticle glass samples. The solid line in the figure
is a theoretical plot made using a parabolic band model for the vibrational potential,
and the measured energy is asymptotic to the bulk value for large particle sizes. The
increase in the gap for small nanoparticle radii is due to quantum confinement
effects.
3.4.2. Photoemission and X-Ray Spectroscopy
Photoemission spectroscopy (PES) measures the energy distribution of electrons
emitted by atoms and molecules in various charge and energy states. A material
METHODS OF MEASURING PROPERTIES
270
280
290
300 310 320
Raman shift (cm-1)
1
bL 8 9 10 1 1
radius R (nm)
Figure 3.26. Histogram of the distribution of Ge nanocrystal particle sizes (lower figure) around
the mean radius 6.5 nm, used to simulate (solid line) the Raman spectrum (dotted line) depicted
at the top. The size distribution was obtained by transmission electron microscopy. [From C. E.
Bottani, C. Mantini, P. Milani, M. Manfredini, A. Stella, P. Tognini, P. Cheyssac, and R. Kofman,
Appl. Phys. Left. 69, 2409 (1996).]
provides a narrow range of size distributions, so optical spectra of the type shown in
Fig. 3.27 can accurately determine the dependence of the gap on the average particle
radius and this dependence is shown in Fig. 3.28 for CdSe. We see that the energy
gap data for the colloidal samples plotted on this figure agree with the gaps evaluated
from optical spectra of CdSe nanoparticle glass samples. The solid line in the figure
is a theoretical plot made using a parabolic band model for the vibrational potential,
and the measured energy is asymptotic to the bulk value for large particle sizes. The
increase in the gap for small nanoparticle radii is due to quantum confinement
effects.
3.4.2. Photoemission and X-Ray Spectroscopy
Photoemission spectroscopy (PES) measures the energy distribution of electrons
emitted by atoms and molecules in various charge and energy states. A material