Crystal Structures and Lattice Constants of Semiconductors and Other Materials

Lattice Constants

A crystal is a material that has an orderly and periodic arrangement of atoms in three-dimensional space. The manner in which the atoms are arranged in a crystal is known as its crystal structure. A crystal structure is composed of a motif, a set of atoms arranged in a particular way, and a lattice. Motifs are located upon the points of a lattice, which is an infinite periodic array of points in space.

A volume in the lattice that is representative of the entire lattice and repeated regularly throughout the crystal is called a unit cell. While the smallest parallelepiped that satisfies this definition is usually chosen as the unit cell, it is sometimes useful to specify a unit cell of larger volume. Note that since the lattice is infinite in extent, there is also an infinite number of ways to specify a unit cell.

The crystal structure of the unit cell is always the same as that of a bigger chunk of the crystal, so a given bulk of crystal may be studied using just a small representative sample thereof.

Six lattice constants are generally required to define the shape and size of a unit cell. These are its axial lengths (lengths of the edges of the unit cell along its major axes), which are usually denoted as a, b, and c, and its inter-axial angles, which are usually denoted by alpha (α), beta (β), and gamma (γ). In some crystal structures, however, the edge lengths along all axes are equal (a=b=c), so only one lattice constant is used for its dimensional description, a.

Lattice constant values and knowledge of crystal structure are needed to calculate distances between neighboring atoms in a crystal, as well as in determining some of the crystal's important physical and electrical properties. Note that, depending on the crystal structure, the distance between two neighboring atoms in a lattice may be less than the lattice constant. Table 1 shows the crystal structures and lattice constants of some semiconductors.

Table 1. Lattice Constants and Crystal Structures of

some Semiconductors and Other Materials

Element or Compound	Type	Name	Crystal Structure	Lattice Constant at 300 K (Å)
C	Element	Carbon (Diamond)	Diamond	3.56683
Ge	Element	Germanium	Diamond	5.64613
Si	Element	Silicon	Diamond	5.43095
Sn	Element	Grey Tin	Diamond	6.48920
SiC	IV-IV	Silicon carbide	Wurtzite	a=3.086; c=15.117
AlAs	III-V	Aluminum arsenide	Zincblende	5.6605
AlP	III-V	Aluminum phosphide	Zincblende	5.4510
AlSb	III-V	Aluminum antimonide	Zincblende	6.1355
BN	III-V	Boron nitride	Zincblende	3.6150
BP	III-V	Boron phosphide	Zincblende	4.5380
GaAs	III-V	Gallium arsenide	Zincblende	5.6533
GaN	III-V	Gallium nitride	Wurtzite	a=3.189; c=5.185
GaP	III-V	Gallium phosphide	Zincblende	5.4512
GaSb	III-V	Gallium antimonide	Zincblende	6.0959
InAs	III-V	Indium arsenide	Zincblende	6.0584
InP	III-V	Indium phosphide	Zincblende	5.8686
InSb	III-V	Indium antimonide	Zincblende	6.4794
CdS	II-VI	Cadmium sulfide	Zincblende	5.8320
CdS	II-VI	Cadmium sulfide	Wurtzite	a=4.160; c=6.756
CdSe	II-VI	Cadmium selenide	Zincblende	6.050
CdTe	II-VI	Cadmium telluride	Zincblende	6.482
ZnO	II-VI	Zinc oxide	Rock Salt	4.580
ZnS	II-VI	Zinc sulfide	Zincblende	5.420
ZnS	II-VI	Zinc sulfide	Wurtzite	a=3.82; c=6.26
PbS	IV-VI	Lead sulfide	Rock Salt	5.9362
PbTe	IV-VI	Lead telluride	Rock Salt	6.4620

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