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

See Also:   What is a semiconductor? IC ManufacturingSi, Ge, GaAs Properties