Chapter 3
Crystals
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
accidental crystalline forms, 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 [186]
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.
3.1 Introduction
The economically most important semiconductors have a relatively simple atomic arrangement and
are highly symmetric. The symmetry of the atomic arrangement is the basis for the classification of
the various crystal structures. Using group theory [187], basic and important conclusions can be drawn
about the physical properties of the crystal, such as its elastic and electronic properties. The presence of
highly symmetric planes is obvious from the crystal shape of the minerals and their cleavage behavior.
Polycrystalline semiconductors consist of grains of finite size that are structurally perfect but have
various orientations. The grain boundaries are a lattice defect (see also Sect. 4.4.3). Amorphous semiconductors are disordered on the atomic scale, see Sect. 3.3.7.
3.2 Crystal Structure
A crystal is built up by the (quasi-) infinite periodic repetition of identical building blocks. This
translation lattice [188–190] is generated by the three fundamental translation vectors a 1 , a 2 and a 3 .
These three vectors may not lie in a common plane. The lattice (Fig. 3.1) is the set of all points R
R = n 1 a 1 + n 2 a 2 + n 3 a 3 .
(3.1)
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_3
35
Crystals
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
accidental crystalline forms, 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 [186]
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.
3.1 Introduction
The economically most important semiconductors have a relatively simple atomic arrangement and
are highly symmetric. The symmetry of the atomic arrangement is the basis for the classification of
the various crystal structures. Using group theory [187], basic and important conclusions can be drawn
about the physical properties of the crystal, such as its elastic and electronic properties. The presence of
highly symmetric planes is obvious from the crystal shape of the minerals and their cleavage behavior.
Polycrystalline semiconductors consist of grains of finite size that are structurally perfect but have
various orientations. The grain boundaries are a lattice defect (see also Sect. 4.4.3). Amorphous semiconductors are disordered on the atomic scale, see Sect. 3.3.7.
3.2 Crystal Structure
A crystal is built up by the (quasi-) infinite periodic repetition of identical building blocks. This
translation lattice [188–190] is generated by the three fundamental translation vectors a 1 , a 2 and a 3 .
These three vectors may not lie in a common plane. The lattice (Fig. 3.1) is the set of all points R
R = n 1 a 1 + n 2 a 2 + n 3 a 3 .
(3.1)
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_3
35