CHEM01200604009 Sreejith Kaniyankandy - Homi Bhabha ...

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correction factor in small nanocrystal. This interacting electron hole pair is now called an
exciton. When a semiconductor radius decreases from infinite to confined solid where mean
free path is close to radius, coulomb interaction has a significant role to play. Theoretically
this interplay between confinement energy and coulomb interaction leads to three different
confinement regimes. Before going into effects of degree of confinement we define the mean
free path of the exciton ( a
B
, also called Bohr Radius of the exciton) as
a B
2
(1.17)
2
e
Based on a B
and attractive coulomb interaction we can define three kinds of weak (r> a B
),
intermediate confinement (r~ a B
) and strong confinement (r< a B
) [1.16]
Weak Confinement Regime: In this regime confinement energy is less than coulomb
interaction or Exciton binding energy. The band gap in this case can be given as
2 2
EQD EB Ec
2( m m ) a
e
h
2
(1.18)
Intermediate Confinement Regime: In this size regime confinement will be set in the
carrier with smaller effective mass. Very often electrons have a low
er effective mass; therefore in such a size regime electron levels will exhibit discreteness
while the hole levels will be continuous. Therefore the system may be approximated as a
donor type exciton with electron governing quantization behavior.
Strong Confinement Regime: In this size regime, exciton as a whole experiences
confinement leading to quantization of exciton levels.