Simple Superlattices

Figure A2.5.18. Body-centred cubic arrangement of (3-brass (CiiZn) at low temperature showing two interpenetrating simple cubic superlattices, one all Cu, the other all Zn, and a single lattice of randomly distributed atoms at high temperature. Reproduced from Hildebrand J H and Scott R L 1950 The Solubility of Nonelectrolytes 3rd edn (New York Reinliold) p 342.

So it is essential to relate the LEED pattern to the surface structure itself As mentioned earlier, the diffraction pattern does not indicate relative atomic positions within the structural unit cell, but only the size and shape of that unit cell. However, since experiments are mostly perfonned on surfaces of materials with a known crystallographic bulk structure, it is often a good starting point to assume an ideally tenuinated bulk lattice the actual surface structure will often be related to that ideal structure in a simple maimer, e.g. tluough the creation of a superlattice that is directly related to the bulk lattice. 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

Because the appearance of a superlattice is usually well characterized qualitatively in terms of an interaction parameter w which has nothing to do, in the usual treatments, with the melting of the parent solid solution, one does not expect to find a simple relationship between the critical temperature for disordering of the superlattice, and Ts, the solidus temperature of the corresponding solid... 

The purpose of this work is to demonstrate that the techniques of quantum control, which were developed originally to study atoms and molecules, can be applied to the solid state. Previous work considered a simple example, the asymmetric double quantum well (ADQW). Results for this system showed that both the wave paeket dynamics and the THz emission can be controlled with simple, experimentally feasible laser pulses. This work extends the previous results to superlattices and chirped superlattices. These systems are considerably more complicated, because their dynamic phase space is much larger. They also have potential applications as solid-state devices, such as ultrafast switches or detectors. 

In summary, this work has shown that superlattices are promising systems for investigation of quantum control in the solid state. The examples presented here show that the dynamics of charge carriers can be controlled using relatively simple, experimentally laser fields. Superlattices are ideal candidates for quantum control precisely because their complexity does not allow for simple, intuition-guided experiments, and because their dynamics are largely unknown. 

In addition, the measurements are rapid and simple, and are now even used in 100% inspection for quality control of multiple-layer semiconductors. An example is shown in Figure 1.6. This is a GaAs substrate with a ternary layer and a thin cap. The mismatch between the layer and the substrate is obtained immediately from the separation between the peaks, and more subtle details may be interpreted with the aid of computer simulation of the rocking curve. This curve can be obtained in a matter of minutes. Routine analysis of such curves gives the composition of ternary epilayers, periods of superlattices and thicknesses of layers, whilst more advanced analysis can give a complete strain and composition profile as a lunction of depth. 

In Chapter 3 we went as far as we could in the interpretation of rocking curves of epitaxial layers directly from the features in the curves themselves. At the end of the chapter we noted the limitations of this straightforward, and largely geometrical, analysis. When interlayer interference effects dominate, as in very thin layers, closely matched layers or superlattices, the simple theory is quite inadequate. We must use a method theory based on the dynamical X-ray scattering theory, which was outlined in the previous chapter. In principle that formrrlation contains all that we need, since we now have the concepts and formtrlae for Bloch wave amplitude and propagatiorr, the matching at interfaces and the interference effects. 

Two common notations are used to relate superlattices to substrate lattices, one of these notations being a simplification of the other for simple cases. Let the substrate... 

SAMs are ordered molecular assemblies formed by the adsorption (qv) of an active surfactant on a solid surface (Fig. 6). This simple process makes SAMs inherently manufacturable and thus technologically attractive for building superlattices and for surface engineering. The order in these two-dimensional systems is produced by a spontaneous chemical synthesis at the interface, as the system approaches equilibrium. Although the area is not limited to long-chain molecules (112), SAMs of functionalized long-chain hydrocarbons are most frequently used as building blocks of supermolecular structures. 

Luther et al. (1996) conducted a systematic study of the occurrence of the simple lattice and superlattice across the vertebrate kingdom. Superlattices are present in the muscles of all the higher vertebrates, namely, in mammals (including humans), in amphibians, in birds, in reptiles, and in some muscles of cartilaginous fish. Simple lattices occur in all the teleost (bony fish) muscles so far studied, in some muscles of cartilaginous fish, and also in some primitive fish such as sturgeons and bowfin. 

The A-band lattices in different kinds of striated muscles have distinct arrangements. As shown in Fig. 3 and reproduced in simpler form in Fig. 10A and B, vertebrate striated muscle A-bands have actin filaments at the trigonal points of the hexagonal myosin filament array. As discussed prevously, this array also occurs in two types, the simple lattice and superlattice. The ratio of actin filaments to myosin filaments in each unit cell is 2 1. In both cases the center-to-center distance between adjacent myosin filaments is 70 A, but this varies as a function of overlap, becoming smaller as the sarcomere lengthens, giving an almost constant volume to the sarcomere (April et al, 1971). 

Fig. 24. M-band structure from electron microscopy of both simple lattice and superlattice muscles. (A) 3D Reconstruction of fish muscle M-band. Three distinct layers were observed in the reconstruction, at each of the M-bridge levels M4, Ml, and M4 (M and B label the myosin filaments and M-bridges, respectively.) The observed 32-point group symmetry has been imposed on the 3D map. (B) Part of the M-band as modeled by Luther and Squire (1978). Ml and M4 bridges are seen connecting adjacent myosin filaments. Halfway along the M-bridges and running parallel to the myosin filaments are the M-filaments. M3 marks a further level of secondary Y-shaped bridges. (C) A slice...

In iron bearing clays the time law of the luminescence decay of Ru(byp)3 + is multiexponential (29). In the long time limit (>1 /is) the decay approaches an exponential law, but at shorter time ( 300 ns), a more complex decay has been observed. The decay mechanism has been explained by a simple localized model based on the assumption that on each particle the quenching process can be described as occurring in an ensemble of small independent subsystems. Each subsystem is composed of an excited probe system (with a very reduced mobility) and of the nearest lattice sites of the solid which may be occupied by the quencher ions. For the sake of simplicity, it has been assumed that the adsorbed probe molecules occupy the sites of a superlattice which matches the lattice containing randomly distributed quenchers (Fe, for instance)... 

Periodic structures containing alternating layers of different ferroelectric and non-ferroelectric materials - superlattices (SLs) - have received increased attention. High-quality ferroelectric SLs with nearly atomically sharp interfaces in various perovskite systems have been synthesized and investigated [14, 24—27, 49-56], and also studied theoretically [44, 57-64]. Properties of such structures are not just a simple combination of the properties known for constituent bulk materials, as they are affected by both mechanical (lattice-mismatch-induced strain) and electrostatic boundary conditions at multiple interfaces located within close proximity to each other. Strain engineering is one of the most appealing ways to... 

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