Abstract
A little bit of crystallography... The concepts of the direct and reciprocal lattice, point and space groups, unit and elementary cells and the Wigner–Seitz cell are laid out. The important crystal structures for semiconductors (diamond, sphalerite, wurtzite, chalcopyrite,...) are discussed in some detail. Also alloys and ordering are covered.
La science cristallographique ne consiste donc point à décrire scrupuleusement tous les accidens des formes cristallines; mais à spécifier, en décrivant ces formes, les rapports plus ou moins immédiats qu’elles ont entre elles.
Crystallographic science does not consist in the scrupulous description of all the accidents of crystalline form, but in specifying, by the description of these forms, the more or less close relationship they have with each other.
J.-B. Romé de l’Isle, 1783 [165]
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Notes
- 1.
5-fold periodic symmetry is geometrically impossible. However, quasicrystals with aperiodic five-fold symmetry exist [167, 168], some of them possibly being semiconducting [169, 170].
- 2.
\(2_1\), \(3_1\), \(3_2\), \(4_1\), \(4_2\), \(4_3\), \(6_1\), \(6_2\), \(6_3\), \(6_4\), \(6_5\).
- 3.
One should in particular consider the pitfalls pointed out in Appendix 10 of this reference.
- 4.
Zincblende technically means the material ZnS which occurs in sphalerite (cubic) and wurtzite (hexagonal) phase. However, in the literature the term ‘zincblende’ for the sphalerite structure is common and used throughout this book.
- 5.
The dot product \(\mathbf{a} \cdot \mathbf{b}\) of two vectors shall also be denoted as \(\mathbf{a} \mathbf{b}\).
- 6.
The CuAu-I structure has tetragonal symmetry. There exists also the CuAu-II structure that is orthorhombic.
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Grundmann, M. (2016). Crystals. In: The Physics of Semiconductors. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-23880-7_3
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DOI: https://doi.org/10.1007/978-3-319-23880-7_3
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