Quantum confinement effects

Figure C2.17.11. Exciton energy as a function of particle size. The Bms fonnula is used to calculate the energy shift of the exciton state as a function of nanocrystal radius, for several different direct-gap semiconductors. These estimates demonstrate the size below which quantum confinement effects become significant.

The first electrodeposition of a compound superlattice appears to have been by Rajeshwar et al. [219], where layers of CdSe and ZnSe were alternately formed using codeposition in a flow system. That study was proof of concept, but resulted in a superlattice with a period significantly greater then would be expected to display quantum confinement effects. There have since been several reports of very thin superlattices formed using EC-ALE [152, 154, 163, 186], Surface enhanced Raman (SERS) was used to characterize a lattice formed from alternated layers of CdS and CdSe [163]. Photoelectrochemistry was used to characterize CdS/ZnS lattices [154, 186]. These EC-ALE formed superlattices were deposited by hand, the cycles involving manually dipping or rinsing the substrate in a sequence of solutions. 

At what small dimensions do quantum-confinement effects begin to have manifestations in NMR, quite apart from the higher surface areas expected for smaller nanoparticles ... 

The magnetic moments of the Ni clusters are dominated by the contribution from surface atoms.48,69 The analysis of Wan et al. indicates that the orbital and spin local moments of cluster atoms with atomic coordination 8 or larger are similar to those in the bulk (p spin 0.55 and orb 0.05 pB) 73 that is, the orbital moment is almost quenched for internal cluster atoms. In contrast, there is a large enhancement of the spin and orbital moments for atoms with coordination less than 8. This enhancement increases with the coordination deficit, and it is larger for the orbital moment. Wan et al.48 also analyzed the quantum confinement effect proposed by Fujima and Yamaguchi,56 i.e., the... 

Colloidal CdS particles 2-7 nm in diameter exhibit a blue shift in their absorption and luminescence characteristics due to quantum confinement effects [45,46]. It is known that particle size has a pronounced effect on semiconductor spectral properties when their size becomes comparable with that of an exciton. This so called quantum size effect occurs when R < as (R = particle radius, ub = Bohr radius see Chapter 4, coinciding with a gradual change in the energy bands of a semiconductor into a set of discrete electronic levels. The observation of a discrete excitonic transition in the absorption and luminescence spectra of such particles, so called Q-particles, requires samples of very narrow size distribution and well-defined crystal structure [47,48]. Semiconductor nanocrystals, or... 

A particularly interesting property of this mesostructured cubic Ge framework is the substantial blue-shift in optical absorption at 1.42 eV relative to 0.66 eV of bulk Ge. This large blue-shift can be understood by considering the change in the density of the electronic energy states caused by the substantial dimensional reduction of the Ge structure from the bulk Ge (infinity wall thickness) to an 1 nm. Similar large blue-shifted band gaps by 0.76 eV are also observed in Ge nanocrystals of 4 nm in diameter, which is a consequence of quantum confinement effects [42], Whether... 

The exact absorption threshold of the absorption spectra was determined from the intercept of (crhv)2 versus hv plots (where absorption coefficient) for the direct band gap and was found to be 2.82-2.86 eV regardless of size. From a relationship between Eg and particle size of Agl after Meisel et al. (36), we found that the size of these particles was 6-7 nm. For the smallest particles, sample I, there is no peak in the spectra. Other than this finding, there is no apparent quantum confinement effect such as peak shift in the sample whose sizes are larger than 5 nm. 

There are two very broad, general conclusions resulting from the above review. The first is that MoS2-type nanoparticles are very different than other types of semiconductor nanoparticles. Nanoparticles of several different types of semiconductors, such as CdSe, CdS, and InP, have been extensively studied. Experimental and theoretical studies have elucidated much of their spectroscopy, photophysics, and dynamics. The results reviewed above are, in many places, in sharp contrast with those obtained on other types of quantum dots. This does not come as a surprise. The properties of the bulk semiconductor are reflected in those of the nanoparticle, and properties of layered semiconductors are vastly different from those of semiconductors having three-dimensional crystal structures. Although the electronic and spectroscopic properties of nanoparticles are strongly influenced by quantum confinement effects, the differences in the semiconductors cause there to be few generalizations about semiconductor quantum dots that can be made. 

Indeed we study the two-dimensional systems in Section 5. In this section we will analyze the structural, electronic and, in particular, the optical properties of Si and Ge based nanofilms (Section 5.1), of Si superlattices and multiple quantum wells where CalQ and SiC>2 are the barrier mediums (Sections 5.2 and 5.3). The quantum confinement effect and the role of symmetry will be considered, changing the slab thickness and orientation, and also the role of interface O vacancies will be discussed. 

Concerning the electronic minimum gap (which is direct or quasi-direct in all the studied wires, see Ref. [121,122,149,154] for details) at the DFT level (see Table 9) we find that it decreases monotonically with the wire diameter. The calculated values are larger than the electronic bulk indirect gap, thus reflecting the quantum confinement effect. This effect, which has been recently confirmed in STM experiments [37,143], is related to the fact that carriers are confined in two directions, being free to move only along the axis of the quantum wires. Clearly we expect that, increasing the diameter of the wire, such an effect becomes less relevant and the electronic gap will eventually approach the bulk value. 

Another aspect that is interesting to note concerns the dependence of the DFT gap on the orientation of the wire, indeed, for each wire size the following relation holds g[100] > g[lll] > Eg [110]. As has been pointed out in Ref. [121], this is related to the different geometrical structure of the wires in the [100], [111] and [110] directions. Indeed the [100], [111] wires appear as a collection of small clusters connected along the axis, while the [110] wires resemble a linear chain. So we expect that quantum confinement effects are much bigger in the [100], [111] wires, due to their quasi zero-dimensionality, with respect to the [110] wires. Further, the orientation anisotropy reduces with the wire width and it is expected to disappear for very large wires, where the band gap approaches that of the bulk material. 

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