COMPROBACIÓN DE LA HIPÓTESIS

2.5 1.5 0.5 2.12 2.13 2.14 2.15 2.16 PHOTON ENERGY

Figure 4.1 9. Optical absorption spectrum of hydrogen-like transitions of excitons in [Adapted from P. W. Baumeister, Phys. Rev. 121, 359

shifted to higher energy as the particle size decreases. Since the absorption edge is due to the band gap, this means that the band gap increases as particle size decreases. Notice also that the intensity of the absorption increases as the particle size is reduced. The higher energy peaks are associated with the exciton, and they shift to higher energies with the decrease in particle size. These effects are a result of

I

I CdSe

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 0

ENERGY

Figure 4.20. Optical absorption spectrum of CdSe for two nanoparticles having sizes 20A and respectively. [Adapted from D. M. Mittleman, Phys. Rev. B49, 14435

the confinement of the exciton that was discussed above. Essentially, as the particle size is reduced, the hole and the electron are forced closer together, and the separation between the energy levels changes. This subject will be discussed in greater detail in Chapter 9.

4.3.2. Photofragmentation

It has been observed that nanoparticles of silicon and germanium can undergo fragmentation when subjected to laser light from a Q-switched laser. The products depend on the size of the cluster, the intensity of the laser light, and the wavelength. Figure 4.21 shows the dependence of the cross section for

mentation (a measure of the probability for breakup of the cluster) with 532 nm laser light, versus the size of a Si fragment. One can see that certain sized fragments are more likely to dissociate than others. Some of the fissions that have been observed are

Si,,

+

+

+

+

Figure 4.21. Photodissociation cross section of silicon nanoparticles versus number of atoms in particle. [Adapted from L. Bloomfield et al., Rev. Lett. 54, 2266

4.3. SEMICONDUCTING

where hv is a photon of light energy. Similar results have been obtained for ger- manium nanoparticles. When the cluster size is greater than 30 atoms, the fragmen- tation has been observed to occur explosively.

4.3.3. Coulombic Explosion

Multiple ionization of clusters causes them to become unstable, resulting in very rapid high-energy dissociation or explosion. The fragment velocities from this pro- cess are very high. The phenomena is called Coulombic explosion. Multiple ioniza- tions of a cluster cause a rapid redistribution of the charges on the atoms of the cluster, making each atom more positive. If the strength of the electrostatic repulsion between the atoms is greater than the binding energy between the atoms, the atoms will rapidly fly apart from each other with high velocities. The minimum number of atoms N required for a cluster of charge Q to be stable depends on the kinds of

atoms, and the nature of the bonding between the atoms of the cluster. Table 4.2

gives the smallest size that is stable for doubly charged clusters of different types of atoms and molecules. The table also shows that larger clusters are more readily stabilized at higher degrees of ionizations. Clusters of inert gases tend to be larger because their atoms have closed shells that are held together by much weaker forces called van der Waals forces.

The attractive forces between the atoms of the cluster can be overcome by the electrostatic repulsion between the atoms when they become positively charged as a result of photoionization. One of the most dramatic manifestations of Coulombic explosion reported in the journal Nature is the observation of nuclear in deuterium clusters subjected to femtosecond laser pulses. A femtosecond is seconds. The clusters were made in the usual way described above, and then subjected to a high-intensity femtosecond laser pulse. The fragments of the dissociation have energies up to one million electron volts (MeV). When the

Table 4.2. Some examples of the smallest obtainable multiply charged clusters of different kinds (smaller clusters will explode)

Charge Atom

deuterium fragments collide, they have sufficient energy to undergo nuclear fusion by the following reaction:

D

+

+

This reaction releases a neutron of 2.54 MeV energy. Evidence for the occurrence of fusion is the detection of the neutrons using neutron scintillation detectors coupled to photomultiplier tubes.

4.4. RARE GAS AND MOLECULAR CLUSTERS

4.4.1. Inert-Gas Clusters

Table 4.2 lists a number of different kinds of nanoparticles. Besides metal atoms and semiconducting atoms, nanoparticles can be assembled from rare gases such as krypton and xenon, and molecules such as water. Xenon clusters are formed by adiabatic expansion of a supersonic jet of the gas through a small capillary into a vacuum. The gas is then collected by a mass spectrometer, where it is ionized by an electron beam, and its mass : charge ratio measured. As in the case of metals, there are magic numbers, meaning that clusters having a certain number of atoms are more stable than others. For the case of xenon, the most stable clusters occur at particles having 13, 19, 25, 55, 71, 87, and 147 atoms. Argon clusters have similar structural magic numbers. Since the inert-gas atoms have filled electronic shells, their magic numbers are structural magic numbers as discussed in Chapter 2. The forces that bond inert-gas atoms into clusters are weaker than those that bond metals and semiconducting atoms. Even though inert-gas atoms have filled electron shells, because of the movement of the electrons about the atoms, they can have an instantaneous electric dipole moment, An electric dipole moment occurs when a positive charge and a negative charge are separated by some distance. This dipole produces an electric field at another atom a distance R away. This, in induces a dipole moment, on the second atom, where is called the

electronic polarizability. Thus inert-gas atoms will have an attractive potential

This is known as the van der Waals potential, and it is effective at relatively large separations of the atoms. As the two atoms get much closer together, there will be repulsion between the electronic cores of each atom. Experimentally this has been shown to have the form Thus the overall interaction potential between two inert-gas atoms has the form

B C

4.4. RARE GAS AND MOLECULAR CLUSTERS