Size quantisation effects

The use of nanoscale constructs has given a further major boost to solar photon conversion. The scale of nanosized materials such as quantum dots and nanotubes, conventionally taken to lie in the range 1-100 nm, produces very interesting size quantisation effects in optoelectronic and other properties bandgaps shift to the blue, carrier lifetimes increase, potent catalytic properties emerge and constructs with very high surface-to-volume ratios can be made. Incorporation of nanoscale structures in photovoltaic devices allows these unique properties to be exploited, with conversion efficiencies above the detailed balance limit becoming possible in principle. 

A few reports in the last two decades have described exciton confinement in small TiOi particles. Anpo and co-workers (1987) prepared particles of titania with sizes (diameters) ranging from 55 A to 2000 A for rutile, and from 38 A to 530 A for the anatase form of TiOi, and noted that these crystallites display size quantisation in optical properties and in the photocatalytic hydrogenation of methylacetylene, even for such large sizes. For a 120 A rutile particle the bandgap increased by 67 meV relative to the bulk rutile bandgap Eg 3.03 eV) for anatase Eg increased by 156 meV (from the bulk Eg of -3.18 eV). Moreover, quantum yields of photocatalytic activity of TiOi appeared to increase with the magnitude of the blue shift of the effective bandgap. Kormann et at. (1988) indicated that small particles of TiOi, prepared by the arrested hydrolysis of either TiCU or Ti(i-PrO)4, showed size... 

There has been intense interest in nanoparticles in the scientific community in recent years due to their potential for incorporation into functional structures such as single electron transistors, nanoscale switching devices or photonic materials. Nanoparticles exhibit novel optical and electronic properties due to their structure and size, which in the limit leads to electronic quantisation effects. Of particular interest is the interaction of these properties with other nanoparticles and/or other entities to produce nanoscale devices, for example, a nanometre-scale electronic switch. ... 

For semiconductor materials on the macroscale the valence and conduction bands have band widths associated with the continuum of orbitals. However, on going from the macroscale to nanometre (nm) dimensions two effects occur due to the removal of atoms (and hence orbitals) firstly, the bands cease to be a continuum and individual orbitals, and hence quantised energy levels are observed (hence the term quantum dot) secondly, orbitals are removed from the edges of the valence and/or conduction bands, which increases the band gap. The size of the quantum dot dictates the absorption and emission characteristics the smaller the quantum dot, the larger the band gap, and hence the more blue-shifted (shorter wavelength) the emission (Fig. 4.1) [7]. 

Fig. 4.1 Schematic representation of the effect of size on semiconductor properties, i.e. changes on going from the macro-scale (continuum of energy levels) to the nano-scale (quantised energy levels). The average energy position of the bands do not change (represented by the lines dissecting the relevant bands and orbitals) however, the band gap increases with decreasing size as extreme energy levels are removed. Figure adapted from Ref. [8]...

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