conducting nanocrystals. The blue-shift in the band gap reveals the formation of
nanocrystals. In conjunction with more accurate approaches to calculate the band
gap as a function of the size available these days, it is possible to obtain reliable
estimates of the size from the measure of the band gap shift. Also, one can get an
estimate of the size distribution from the sharpness of the absorption peak. Fluorescence properties of the nanocrystals can be tuned to obtain emissions at various
energies, thus making possible the tunability of the emitted light for a number of
applications.
The electronic structure calculation methods discussed here give an overview of
the different methods used to study the size dependent electronic properties. The
single band IP-EMA method is a simple approach to understand the band gap
variation of nanocrystals with size. As the method overestimates the band gap for
small sized nanocrystals, improvements in the form of FP-EMA and MBEM have
been suggested to get a better agreement between the theoretical results and the
experimental data. The pseudopotential techniques provide a very good description
of the experimental results. The tight binding methods have found the widest applications in the description of the properties of nanocrystals because of their ease
of use. Also, they are computationally less expensive than other methods for large
sized nanocrystals. It is found that the sp
3 d
5 model with next nearest neighbor
interactions included gives the best description of the variation of band gap with
size in the case of II–VI semiconductors.
Valence band spectroscopic studies performed on the semiconducting nanocrystals give valuable information about the electronic structure of these materials. The
band edges vary with varying nanocrystal size and these can be quantified with the
help of the theoretical techniques. The shape of the density of states obtained from
the photoemission experiments also changes with the size of the nanocrystals.
This has been correlated with the sp
3 d
5 -NNN tight binding model, exhibiting an
excellent agreement between theory and experiment.
References
1 A. D. Yoffe, Adv. Phys., 50, 1, 2001.
2 A. P. Alivisatos, J. Phys. Chem., 100,
13226, 1996.
3 A. D. Yoffe, Adv. Phys., 42, 173, 1993.
4 H. Weller, Angew. Chem. Int. Ed.
Engl., 32, 41, 1993.
5 A. Hagfeldt, M. Gratzel, Chem. Rev.,
95, 49, 1995.
6 Y. Wang, N. Herron, J. Phys. Chem.,
95, 525, 1991.
7 C. B. Murray, C. R. Kagan, M. G.
Bawendi, Annu. Rev. Mater. Sci., 30,
545, 2000.
8 J. Nanda, B. A. Kuruvilla, K. V. P.
Shafi et al., in Physics of
Semiconducting Nanostructures, ed.
K. P. Jain, Narosa Publishers, New
Delhi, 1997, p. 25.
9 A. N. Goldstein, C. M. Echerand,
A. P. Alivisatos, Science, 256, 1425,
1992.
10 B. O. Dabbousi, J. Rodriguez-Viejo,
F. V. Mikulec et al., J. Phys. Chem. B,
101, 9463, 1997.
11 J. Nanda, Ph.D. Thesis, Bangalore,
2000.
12 J. Nanda, S. Sapra, D. D. Sarma et al.,
Chem. Mater., 12, 1018, 2000.
13 J. K. Furdyna, J. Appl. Phys., 64, R29,
1988.
11 Electronic Structure and Spectroscopy of Semiconductor Nanocrystals
402
nanocrystals. In conjunction with more accurate approaches to calculate the band
gap as a function of the size available these days, it is possible to obtain reliable
estimates of the size from the measure of the band gap shift. Also, one can get an
estimate of the size distribution from the sharpness of the absorption peak. Fluorescence properties of the nanocrystals can be tuned to obtain emissions at various
energies, thus making possible the tunability of the emitted light for a number of
applications.
The electronic structure calculation methods discussed here give an overview of
the different methods used to study the size dependent electronic properties. The
single band IP-EMA method is a simple approach to understand the band gap
variation of nanocrystals with size. As the method overestimates the band gap for
small sized nanocrystals, improvements in the form of FP-EMA and MBEM have
been suggested to get a better agreement between the theoretical results and the
experimental data. The pseudopotential techniques provide a very good description
of the experimental results. The tight binding methods have found the widest applications in the description of the properties of nanocrystals because of their ease
of use. Also, they are computationally less expensive than other methods for large
sized nanocrystals. It is found that the sp
3 d
5 model with next nearest neighbor
interactions included gives the best description of the variation of band gap with
size in the case of II–VI semiconductors.
Valence band spectroscopic studies performed on the semiconducting nanocrystals give valuable information about the electronic structure of these materials. The
band edges vary with varying nanocrystal size and these can be quantified with the
help of the theoretical techniques. The shape of the density of states obtained from
the photoemission experiments also changes with the size of the nanocrystals.
This has been correlated with the sp
3 d
5 -NNN tight binding model, exhibiting an
excellent agreement between theory and experiment.
References
1 A. D. Yoffe, Adv. Phys., 50, 1, 2001.
2 A. P. Alivisatos, J. Phys. Chem., 100,
13226, 1996.
3 A. D. Yoffe, Adv. Phys., 42, 173, 1993.
4 H. Weller, Angew. Chem. Int. Ed.
Engl., 32, 41, 1993.
5 A. Hagfeldt, M. Gratzel, Chem. Rev.,
95, 49, 1995.
6 Y. Wang, N. Herron, J. Phys. Chem.,
95, 525, 1991.
7 C. B. Murray, C. R. Kagan, M. G.
Bawendi, Annu. Rev. Mater. Sci., 30,
545, 2000.
8 J. Nanda, B. A. Kuruvilla, K. V. P.
Shafi et al., in Physics of
Semiconducting Nanostructures, ed.
K. P. Jain, Narosa Publishers, New
Delhi, 1997, p. 25.
9 A. N. Goldstein, C. M. Echerand,
A. P. Alivisatos, Science, 256, 1425,
1992.
10 B. O. Dabbousi, J. Rodriguez-Viejo,
F. V. Mikulec et al., J. Phys. Chem. B,
101, 9463, 1997.
11 J. Nanda, Ph.D. Thesis, Bangalore,
2000.
12 J. Nanda, S. Sapra, D. D. Sarma et al.,
Chem. Mater., 12, 1018, 2000.
13 J. K. Furdyna, J. Appl. Phys., 64, R29,
1988.
11 Electronic Structure and Spectroscopy of Semiconductor Nanocrystals
402