THE QUANTUM-MECHANICS OF LARGER SEMICONDUCTOR CLUSTERS (QUANTUM DOTS)

We have reviewed the electronic quantum size effect in nanometer-scale fragments of inorganic tetrahedral semiconductors. The effect is a consequence of strong chemical bonding. We have described the nodal patterns and energies of discrete, size dependent crystallite molecular orbitals. Molecular orbital effects, along with Coulombic attraction between the electron and hole, can be incorporated into an effective mass Hamiltonian. The resulting discrete eigenspectrum of crystallite excited states shows a rich structure. Electron-hole correlation, and a continuous band structure, develop gradually with increasing size. Large crystallites, of diameter several times the bulk exciton Bohr radius, are predicted to have giant oscillator strengths and large resonant optical nonlinearities. The calculated discrete electronic spectra may need modification to incorporate ultrafast excited state internal conversion processes. Quantitative calculations will require improvement beyond the effective mass approximation. The atomic nature and structure of intrinsic surface states, and the general question of possible surface electronic bands and reconstruction, remain largely unexplored. The dephasing of physically large, yet correlated electron-hole bound states needs to be addressed. Experiments on CdSe crystallites clearly demonstrate the reality of the electronic quantum size effect. Detailed interpretations are partially hindered by averaging over inhomogeneous distributions of size, shape, and surface composition.