The majority of crystalline materials do not have a structure that fits into the one atom per site simple Bravais lattice. A number of other important crystal structures are found, however, only a few of these crystal structures are those of which occur for the elemental and compound semiconductors and the majority of these are derived from fcc or hcp lattices. Each structural type is generally defined by an archetype, a material (often a naturally occurring mineral) which has the structure in question and to which all the similar materials are related. With regard to commonly used elemental and compound semiconductors the important structures are diamond, zinc blende, Wurtzite, and to a lesser extent chalcopyrite. However, rock salt, β-tin, cinnabar and cesium chloride are observed as high pressure or high temperature phases and are therefore also discussed. The following provides a summary of these structures. Details of the full range of solid-state structures are given elsewhere.
Diamond Cubic
The diamond cubic structure consists of
two interpenetrating face-centered cubic lattices, with one offset 1/4 of a
cube along the cube diagonal. It may also be described as face centered cubic
lattice in which half of the tetrahedral sites are filled while all the
octahedral sites remain vacant. The diamond cubic unit cell is shown in
Figure 7.1.87.1.8. Each of the atoms (e.g., C) is four
coordinate, and the shortest interatomic distance (C-C) may be determined from
the unit cell parameter (a).
C−C = a3–√4≈ 0.422a(7.1.1)(7.1.1)C−C = a34≈ 0.422a
Figure 7.1.8 Unit cell structure of a diamond cubic lattice showing the two
interpenetrating face-centered cubic lattices.
Zinc Blende
This is a binary phase (ME) and is named
after its archetype, a common mineral form of zinc sulfide (ZnS). As with the
diamond lattice, zinc blende consists of the two interpenetrating fcc lattices.
However, in zinc blende one lattice consists of one of the types of atoms (Zn
in ZnS), and the other lattice is of the second type of atom (S in ZnS). It may
also be described as face centered cubic lattice of S atoms in which half of
the tetrahedral sites are filled with Zn atoms. All the atoms in a zinc blende
structure are 4-coordinate. The zinc blende unit cell is shown in Figure 7.1.97.1.9. A number of inter-atomic distances may be calculated for any material
with a zinc blende unit cell using the lattice parameter (a).
Zn−S = a3–√4≈ 0.422a(7.1.2)(7.1.2)Zn−S = a34≈ 0.422a
Zn−Zn = S−S =a2–√≈0.707 a(7.1.3)(7.1.3)Zn−Zn = S−S =a2≈0.707 a
Figure 7.1.9 Unit cell structure of a zinc blende (ZnS) lattice. Zinc atoms
are shown in green (small), sulfur atoms shown in red (large), and the dashed
lines show the unit cell.
Chalcopyrite
The mineral chalcopyrite CuFeS2 is the
archetype of this structure. The structure is tetragonal (a = b ≠ c, α = β = γ
= 90°, and is essentially a superlattice on that of zinc blende. Thus, is
easiest to imagine that the chalcopyrite lattice is made-up of a lattice of
sulfur atoms in which the tetrahedral sites are filled in layers,
...FeCuCuFe..., etc. (Figure 7.1.10. In such an idealized
structure c = 2a, however, this is not true of all materials with chalcopyrite
structures.
Figure 7.1.10 Unit cell structure of a chalcopyrite lattice. Copper atoms are
shown in blue, iron atoms are shown in green and sulfur atoms are shown in
yellow. The dashed lines show the unit cell.
Rock Salt
As its name implies the archetypal rock
salt structure is NaCl (table salt). In common with the zinc blende structure, rock
salt consists of two interpenetrating face-centered cubic lattices. However,
the second lattice is offset 1/2a along the unit cell axis. It may also be
described as face centered cubic lattice in which all of the octahedral sites
are filled, while all the tetrahedral sites remain vacant, and thus each of the
atoms in the rock salt structure are 6-coordinate. The rock salt unit cell is
shown in Figure 7.1.11. A number of
inter-atomic distances may be calculated for any material with a rock salt
structure using the lattice parameter (a).
Na−Cl = a2≈0.5a(7.1.4)(7.1.4)Na−Cl = a2≈0.5a
Na−Na = Cl−Cl = a2–√≈0.707 a(7.1.5)(7.1.5)Na−Na = Cl−Cl = a2≈0.707 a
Figure 7.1.11 Unit cell structure of a rock salt lattice. Sodium ions are
shown in purple (small spheres) and chloride ions are shown in red (large
spheres).
Cinnabar
Cinnabar, named after the archetype
mercury sulfide, HgS, is a distorted rock salt structure in which the resulting
cell is rhombohedral (trigonal) with each atom having a coordination number of
six.
Wurtzite
This is a hexagonal form of the zinc
sulfide. It is identical in the number of and types of atoms, but it is built
from two interpenetrating hcp lattices as opposed to the fcc lattices in zinc
blende. As with zinc blende all the atoms in a wurtzite structure are
4-coordinate. The wurtzite unit cell is shown in Figure 7.1.12. A number of inter atomic distances may be calculated for any material
with a wurtzite cell using the lattice parameter (a).
Zn−S = a3/8−−−√ = 0.612 a =3c8 = 0.375 c(7.1.6)
(7.1.6)Zn−S = a3/8 = 0.612 a =3c8 = 0.375 c
Zn−Zn = S−S = a = 1.632 c(7.1.7)(7.1.7)Zn−Zn = S−S = a = 1.632 c
However, it should be noted that these
formulae do not necessarily apply when the ratio a/c is different from the
ideal value of 1.632.
Figure 7.1.12 Unit cell structure of a wurtzite lattice. Zinc atoms are shown
in green (small spheres), sulfur atoms shown in red (large spheres), and the
dashed lines show the unit cell.
Cesium Chloride
The cesium chloride structure is found
in materials with large cations and relatively small anions. It has a simple
(primitive) cubic cell (Figure 7.1.137.1.13) with a chloride ion
at the corners of the cube and the cesium ion at the body center. The
coordination numbers of both Cs+ and Cl-, with the inner atomic distances
determined from the cell lattice constant (a).
Cs−Cl = a3–√2≈0.866a(7.1.8)(7.1.8)Cs−Cl = a32≈0.866a
Cs−Cs = Cl−Cl =a(7.1.9)(7.1.9)Cs−Cs = Cl−Cl =a
β-Tin
The room temperature allotrope of tin is
β-tin or white tin. It has a tetragonal structure, in which each tin atom has
four nearest neighbors (Sn-Sn = 3.016 Å) arranged in a very flattened
tetrahedron, and two next nearest neighbors (Sn-Sn = 3.175 Å). The overall
structure of β-tin consists of fused hexagons, each being linked to its
neighbor via a four-membered Sn4 ring.
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