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 ()

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

 

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