• superlattices
• silicon
• germanium
• heterostructures

Since the invention of the first transistors, silicon and germanium have been of fundamental importance in the development of electronic devices. Silicon in particular, due to its great availability and cheapness, is the uncontested leader in the field of microelectronics and integrated circuits. Complementary metal oxide semiconductor (CMOS) architectures, which dominate electronic circuit implementations, are totally or almost totally silicon based.

Strain engineering of the band structures of semiconductors, made accessible by the introduction of epitactic deposition techniques, such as Molecular Beam Epitaxy (MBE) or chemical vapor deposition (CVD), has opened a new field of development of heterostructure devices.

Heterostructures made of different SiGe alloys, have been thoroughly investigated by several authors. A special type of heterostructures, Si/Ge superlattices, are obtained by alternating n atomic layers of silicon with m layers of germanium. The strong interface effects due to the lattice mismatch between materials of different chemical composition introduce a great variety of new properties. Among them is the possibility to use a single silicon-based device for both electronic and optical purposes. However, the indirect gap of both silicon and germanium represents an obstacle to the achievement of this goal.

Recently, a new type of silicon multilayer structure has been proposed, fabricated by deposition of quantum dots on thin silicon membranes. The obtained structure was composed of alternating unstrained silicon layers and strained silicon layers, i. e. a superlattice with unit cells made of the same material but under different strain conditions. Such a structure has features similar to two-component superlattices, but with interface effects depending only on the different strain conditions. The potential of this new material has been inspected by Z. Liu and co-workers by means of an ab initio framework.

The present work investigates the properties of these single-element strained superlattices, exploiting the atomistic semi-empirical tight-binding (TB) model. The TB model has been first proposed by F. Bloch in 1928, and implemented by J. C. Slater and G. F. Koster. The TB model consists in expanding the crystal states in linear combinations of atomic-like orbitals. In the semi-empirical approach, the expectation value of the one-electron hamiltonian on this set of orbitals is given in terms of an appropriate set of parameters. The values of the parameters are determined from the requirement that the computed band structure matches the energy band structures obtained by experiments. Considerations on the number of interacting centers and on the number of orbitals strongly influence the possibility to reproduce reliable physical results. TB studies on electronic and optical properties of group-IV semiconductors which exploit the parametrization of reference have shown to reproduce a large number of measured properties.

In the present work, an application of the TB model to single-element strain superlattices of silicon and germanium has been proposed. The inspected crystal structures have been generated by repeating periodically a cell composed of a variable number of atomic layers of a given material. Strain has been applied to half the layers of the cell along the crystal growth direction, which is chosen along the (001) direction. The behaviour of the band structures has been investigated varying the number of layers and the magnitude of the applied strain.

Electronic properties in semiconductors depend on the electronic (hole) states in the lowest conduction (topmost valence) band. The energy of the extrema of these bands are strongly influenced by strain. For silicon bulk structures, the minima of the lowest conduction band along the growth direction and the orthogonal directions split, with the energy difference depending on the type of strain. Splitting also occurs in the topmost valence bands, as a consquence of the interplay between strain and spin-orbit coupling.

In germanium bulk structures, no splitting of the minima of the conduction band occurs. However, under tensile strain along the (001) direction, the shape of the lowest conduction band changes, changing the position of its minimum. For large tensile strain, the minimum may occur at the same point in momentum space as the maximum of the topmost valence point (the origin of the Brillouin zone) and the typical indirect gap of group-IV semiconductors may become direct.

The present TB calculations performed on silicon and germanium single-element strained superlattices give an accurate description of their electronic band structure, showing some important features. It has been shown that not only the strain conditions, but also the cell size strongly influences the behaviour of the near gap region bands. For instance, in silicon strained superlattices, for long cells and tensile strain along the growth direction, the energy of the minima along the same direction becomes lower than the energy of the orthogonal minima, while, from analyses of the bulk structure, the opposite behaviour is expected. Explanations in terms of confinements and effective masses have been used to properly justify these differences. Some particular interesting strain-size configuration has been deeper investigated, as for example, large silicon superlattices cells under compressive (001)-strain, candidates for direct gap materials. The predicted direct gap has been obtained, but it has been shown that the minimum of the lowest conduction band folds in the origin of the Brillouin zone as a consequence of the geometry of the primitive cell. This folding effect may lead to small first-order optical transitions and computation of the optical matrix elements is necessary to determine the effective magnitude of optical gain.

The most important result of this work concerns the possibility to obtain a direct gap in germanium strained superlattices. As expected from anlyses of the bulk structure, a direct gap occurs in tensile (001)-strained cells. As in the case of silicon, the size of the cell plays a fundamental role and only large tensile strained cells show the desired behaviour. However, the direct gap in germanium, on the contrary of silicon, is genuine, i. e. not a consequence of folding effects, and optical gain is shown to be relevant. Thus, these cells have been further investigated, describing their properties, as for example the gap width, which determines the energy of the radiation involved in optical transitions.

The results of the present work, especially for large germanium single-element tensile strained superlattices, show the potential of these new structures for applications in optoelectronics.