Thin quantum-well states

Lin X, Nilius N, Freund HJ, et al. Quantum well states in two-dimensional gold clusters on MgO thin films. Phys Rev Lett. 2009 102 206801 (I 4). 

J.J. Paggel, T. Miller, T. C. Chiang Quantum-well states as Fabry-Perot modes in a thin-film electron interferometer. Science 283,1709-1711 (1999)... 

R., and Beauvillain, P. (1997a). Second harmonic generation study of quantum well states in thin noble metal overlayer films. Surf.Sci., 377 409 - 413. 

Fig. 1 Schematic drawing to show the concept of system dimensionality (a) bulk semiconductors, 3D (b) thin film, layer structure, quantum well, 2D (c) linear chain structure, quantum wire, ID (d) cluster, colloid, nanocrystal, quantum dot, OD. In the bottom, it is shown the corresponding density of states [A( )] versus energy (E) diagram (for ideal cases).

Figure 3.4 Energy levels of (a) multiple quantum wells and (b) superlattices. When the barriers are thick, the wells are isolated, there is no inter-well electronic coupling, and the quantised states are narrow. When the barriers are thin (<4 nm), inter-well electronic coupling occurs, the quantised states broaden, minibands form and electron delocalisation and transport can occur. Source Nozik and Memming (1996).

Whereas quantum wells provide 1-D confinement of electrons to dimensions such that their individual quantum states become significant, it is possible to form thin (<100 nm) bars or strips of semiconductors called quantum wires that provide 2-D confinement, and nano-sized particles called quantum dots (QD) that provide 3-D confinement. 

A thin, undoped, narrow-gap quantum well layer, usually a few atomic layers across, separates the doped layers. The quantum well ideally collects and traps all of the injected carriers of both types, producing an inverted population in which a large number of electrons occupy high-energy states while a large number of holes occupy low energy states. In practice, over 90% of the injected carriers can be induced to recombine in the well. 

Figure 1. Quantum-mechanical (thick lines) and mean-field-trajectory (thin lines) calculations obtained for Model 1 describing the S2 — Si internal-conversion process in pyrazine. Shown are the time-dependent population probabilities Pf t) and Pf (t) of the initially prepared adiabatic and diabatic electronic state, respectively, as well as the mean momenta pi (t) and P2 t) of the two totally symmetric modes Vi and V( of the model.

Both the absorption and the resonant tunneling experiments find quantization effects for layer thicknesses of 50 A or less. It is, however, not immediately obvious why the quantum states should be observed even in these thin layers. The discussion of the transport in Chapter 7 concludes that the inelastic mean free path length is about 10-15 A at the mobility edge. The rapid loss of phase coherence of the wavefunction should prevent the observation of quantum states even in a 50 A well, but there are some factors that may explain the observations. The mean free path increases at energies above the... 

The Matsuura method (57) compares the photolysis result of a solution actinometer with that of a thin crystalline film of equal surface area after exposure. Thus, evaporation of a solution containing the photoreactive substrate results in a thin crystalline film on the glass wall of a test tube, which is subsequently exposed to actinic radiation in a merry-go-round type photolysis apparatus. To test for complete absorption of the incident photons within the crystalline film, the evaporation process is carried out at various concentrations of the substrate, which leads to films of different thickness. If the yield of photoproduct after a certain exposure time is independent of the concentration of the original solution before evaporation, complete absorption of all actinic photons is established. The quantity of the photons absorbed by the crystalline film is then estimated by parallel photolysis of a 0.1 M solution of 2,4,6-triisopropylbenzophenone in methanol solution, which has a well-established quantum yield of 0 = 0.52 (58). The volume of this actinometer solution in the test tube is adjusted so that the crystalline film and the solution exhibit irradiated surfaces of identical size. In summary, this method provides approximate estimates of solid-state quantum yields however, differences in the reflection of the... 

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