Lattice parameters strained layers

Find the unit cell of layer material in the fully relaxed (i.e. bulk) condition from materials databases. For alloys of more than one material, Vegard s law is applied to the lattice parameters, Poisson ratios and stmcture factors. Find the susceptibility of the layers (the extremely small change in susceptibility when a layer is strained may be ignored). 

Calculate the strains and that would be applied if the lattice parameters in the interface plane of the layer were forced to conform to the substrate (full coherent epitaxy). Multiply these by (1-i ) where R is the (fractional) relaxation of the layer. (See the discussion of measurement of relaxation in Chapters.)... 

The rapid developments in the microelectronics industry over the last three decades have motivated extensive studies in thin-film semiconductor materials and their implementation in electronic and optoelectronic devices. Semiconductor devices are made by depositing thin single-crystal layers of semiconductor material on the surface of single-crystal substrates. For instance, a common method of manufacturing an MOS (metal-oxide semiconductor) transistor involves the steps of forming a silicon nitride film on a central portion of a P-type silicon substrate. When the film and substrate lattice parameters differ by more than a trivial amount (1 to 2%), the mismatch can be accommodated by elastic strain in the layer as it grows. This is the basis of strained layer heteroepitaxy. 

A model system to study the effects of tensile strain is Cu on Ru(0001). Cu has a 5.5% smaller lattice parameter than Ru. Each Cu layer grown on Ru(0001) presents a specific pattern of surface reconstruction due to the layer-dependent relaxation of the strain [69]. The first Cu layer is pseu-domorphic with Ru(0001) [70], e.g. it is laterally expanded by 5.5% from a nearest neighbor distance (nnd) of 2.55 A in Cu(lll) to 2.70 A. The Cu atoms occupy hep sites (i.e. the continuation of the Ru lattice) with a Cu-Ru distance at the interface of 2.10 A as determined by LEED [71]. 

The compositions of the ternary layers were evaluated from the lattice parameters measured using X-ray diffraction (see Datareview A1.2) and from the positions of the photoluminescence peaks. Both methods gave the same results, if the bowing parameters of 3.2 eV and 0.1 eV, for InGaN and AlGaN, respectively, were used (as proposed by Takeuchi et al [25] for strained layers on relaxed GaN on sapphire). 

The strain properties of these materials have been investigated by high resolution XRD. Studies involving samples that span a wide range of concentrations show fully strained (tensile and compressively strained), as well as relaxed Si-Ge-Sn films are obtained on strain-free Ge-Sn buffer layers. These results show that strain engineering can be achieved in Si-Ge-Sn heterostructures and multilayers by tuning the lattice parameter of the Ge-Sn buffer layer. 

Recent transport measurements have been carried out on nanocrystalline thin films - either as single layers on an inert substrate or as multilayers - and in these cases the interfaces were more well-defined than in compacted samples. The examination of interfaces using TEM is also simpler to interpret, as the samples are generally more uniform. However, there is normally a lattice mismatch between the film and the substrate, or between alternating layers, such that the degree of mismatch may be large and lead to disorder and strain in the interface. The nature of the interface is therefore very dependent on the lattice parameters of the layers and the preparation conditions. These points must be borne in mind when discussing the transport results. 

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