duction band, leaving behind a valence band hole. Once promotion has occurred,
the conduction band electron quickly relaxes into the lowest energy conduction
band state while the hole moves to the top of the valence band. Holes accumulate
in the highest valence band states so that the valence band electrons can cascade
down into the lower energy valence states. Photoluminescence arises from the recombination of the conduction band electron with the valence band hole where
energy is released in the form of a photon. In the process, the conduction band
electron and valence band hole are annihilated. In terms of solid-state physics, it
is convenient to refer to this coupled electron–hole pair as a single entity, since
one cannot exist without the other if charge neutrality is to be maintained. This
pseudoparticle is known as an exciton [8]. In fact, the previous discussion about
the electronic properties should be viewed in the light of this pseudoparticle rather
than the conduction and valence band electrons only. For simplicity the holes
are neglected in the discussion. Since the exciton is composed of an electron and
a hole that have opposite charges, a strong coulomb attraction causes them to
remain relatively localized within a nanometer-sized crystal. The exciton volume
can be calculated for a given material, and quantum confinement occurs when the
dimensions of the nanocrystal approach the exciton’s Bo ¨hr radius.
Although all semiconductors undergo absorption processes, there is a large difference in the luminescence behavior depending on the semiconductor type. Only
direct band gap semiconductors exhibit band edge photoluminescence with high
quantum efficiencies [26]. This is because in the recombination process both energy and momentum must be conserved. As a result, the following relations must
be obeyed:
E conduction À E valence ¼ hn and hk valence þ hk photon ¼ hk conduction
Because the photon momentum is negligible compared to the electron crystal
momentum, the momentum conservation requirement simplifies to:
hk valence A hk conduction
The result is that optical transitions occur as vertical transitions from the conduction band to the valence band. Examining the E–k diagram for direct versus indirect band gap materials, one can see that a direct band gap material will accumulate electrons and holes in the region with nearly identical crystal momenta.
Conversely, an indirect material will accumulate electrons and holes with a large
difference in crystal momentum that cannot be compensated by the emission of a
photon. Therefore, the optical transition must be accompanied by the simultaneous release of a lattice phonon in order to conserve momentum. These two particle
processes are statistically much less probable than a single particle process, and
consequently direct band gap materials such as CdSe are extremely efficient (theoretically 100%) in light emission. By comparison, indirect band gap materials, like
silicon, have band edge photoluminescence quantum yields that are 3 to 4 orders
of magnitude lower than direct band gap materials. For this reason, optoelectronic
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406
the conduction band electron quickly relaxes into the lowest energy conduction
band state while the hole moves to the top of the valence band. Holes accumulate
in the highest valence band states so that the valence band electrons can cascade
down into the lower energy valence states. Photoluminescence arises from the recombination of the conduction band electron with the valence band hole where
energy is released in the form of a photon. In the process, the conduction band
electron and valence band hole are annihilated. In terms of solid-state physics, it
is convenient to refer to this coupled electron–hole pair as a single entity, since
one cannot exist without the other if charge neutrality is to be maintained. This
pseudoparticle is known as an exciton [8]. In fact, the previous discussion about
the electronic properties should be viewed in the light of this pseudoparticle rather
than the conduction and valence band electrons only. For simplicity the holes
are neglected in the discussion. Since the exciton is composed of an electron and
a hole that have opposite charges, a strong coulomb attraction causes them to
remain relatively localized within a nanometer-sized crystal. The exciton volume
can be calculated for a given material, and quantum confinement occurs when the
dimensions of the nanocrystal approach the exciton’s Bo ¨hr radius.
Although all semiconductors undergo absorption processes, there is a large difference in the luminescence behavior depending on the semiconductor type. Only
direct band gap semiconductors exhibit band edge photoluminescence with high
quantum efficiencies [26]. This is because in the recombination process both energy and momentum must be conserved. As a result, the following relations must
be obeyed:
E conduction À E valence ¼ hn and hk valence þ hk photon ¼ hk conduction
Because the photon momentum is negligible compared to the electron crystal
momentum, the momentum conservation requirement simplifies to:
hk valence A hk conduction
The result is that optical transitions occur as vertical transitions from the conduction band to the valence band. Examining the E–k diagram for direct versus indirect band gap materials, one can see that a direct band gap material will accumulate electrons and holes in the region with nearly identical crystal momenta.
Conversely, an indirect material will accumulate electrons and holes with a large
difference in crystal momentum that cannot be compensated by the emission of a
photon. Therefore, the optical transition must be accompanied by the simultaneous release of a lattice phonon in order to conserve momentum. These two particle
processes are statistically much less probable than a single particle process, and
consequently direct band gap materials such as CdSe are extremely efficient (theoretically 100%) in light emission. By comparison, indirect band gap materials, like
silicon, have band edge photoluminescence quantum yields that are 3 to 4 orders
of magnitude lower than direct band gap materials. For this reason, optoelectronic
12 Core–Shell Semiconductor Nanocrystals for Biological Labeling
406