900 Fi it 1111 t 11 i i i i 111 i i t i i i i i i i ! i-0 50 100 150 200 250 300 DIAMETER (A)

Figure 4.18. Melting temperature of gold nanoparticles versus particle diameter (10A = 1 nm). [Adapted from J. P. Borel et al., Surface Sci. 106,1 (1981).]

4.3. SEMICONDUCTING NANOP ARTICLES 4.3.1. Optical Properties

Because of their role in quantum dots, nanoparticles made of the elements, which are normal constituents of semiconductors, have been the subject of much study, with particular emphasis on their electronic properties. The tide of this section, "semiconducting nanoparticles," is somewhat misleading. Nanoparticles made of cadmium, germanium, or silicon are not themselves semiconductors. A nanoparticle of Si„ can be made by laser evaporation of a Si substrate in die region of a helium gas pulse. The beam of neutral clusters is photo lyzed by a UV laser producing ionized clusters whose mass to charge ratio is then measured in a mass spectrometer. The most striking property of nanoparticles made of semiconducting elements is the pronounced changes in their optical properties compared to those of the bulk material. There is a significant shift in the optical absorption spectra toward die blue (shorter wavelength) as the particle size is reduced.

In a bulk semiconductor a bound electron-hole pair, called an exciton, can be produced by a photon having an energy greater than that of the band gap of the material. The band gap is the energy separation between die top filled energy level of the valence band and the nearest unfilled level in the conduction band above it The photon excites an electron from the filled band to the unfilled band above. The result is a hole in the otherwise filled valence band, which corresponds to an electron with an effective positive charge. Because of die Coulomb attraction between die positive hole and die negative electron, a bound pair, called an exciton, is formed that can move through the lattice. The separation between the hole and the electron is many lattice parameters. The existence of the exciton has a strong influence on the electronic properties of the semiconductor and its optical absorption. The exciton can be modeled as a hydrogen-like atom and has energy levels with relative spacings analogous to the energy levels of the hydrogen atom but with lower actual energies, as explained in Section 2.3.3. Light-induced transitions between these hydrogenlike energy levels produce a series of optical absorptions that can be labeled by the principal quantum numbers of the hydrogen energy levels. Figure 4.19 presents the optical absorption spectra of cuprous oxide (Cu20), showing the absorption spectra due to the exciton. We are particularly interested in what happens when the size of the nanoparticle becomes smaller than or comparable to the radius of the orbit of the electron-hole pair. There are two situations, called the weak-confinement and the strong-confinement regimes. In the weak regime the particle radius is larger than the radius of the electron-hole pair, but the range of motion of the exciton is limited, which causes a blue shift of the absorption spectrum When the radius of the particle is smaller than the orbital radius of the electron-hole pair, the motion of the electron and the hole become independent, and the exciton does not exist. The hole and the electron have their own set of energy levels. Here there is also a blue shift, and the emergence of a new set of absorption lines. Figure 4.20 shows the optical absorption spectra of a CdSe nanoparticle at two different sizes measured at 10 K. One can see that the lowest energy absorption region, referred to as the absorption edge, is

Figure 4.19. Optical absorption spectrum of hydrogen-like transitions of excitons in Cu20. [Adapted from P. W. Baumeister, Phys. Rev. 121, 359 (1961).]

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