3.30 Sspd_chapter 1_part 11_solid state of matter_continued_crystal  (Page 3/4)

Table.1.26.Properties of Elemental&Binary Compound Semiconductors at 300K.

^a I = Indirect, D = Direct;

^b The values are for drift mobilities obtained in the purest and the most perfect materials available to date;

^c Silicon Carbide crystallizes in the wurtzite structure.( Physics of Semiconductor Devices, S.M.Sze, 2 ^nd Edition, Wiley, New York, 1981.

1.11.6. BASIC CRYSTAL STRUCTURES.

The elemental semiconductors, Ge and Si, crystallize as diamond structure and most of the compound semiconductors crystallize as Zinc-Blende structure. These are variants of cubic structures.

We have three basic cubic structures: simple cube, body centered cube (bcc) and face centered cube (fcc). The side of a cube ‘a’ is known as lattice constant. The three parameters that characterize a cubic unit cell are : coordination number, the packing fraction and the nearest neighbor distance.

Polonium crystallizes as simple cube.

• Each lattice center is occupied by one atom.
• At each corner we have one atom and each corner atom is occupied by eight cubes. Hence unit cell has 8 corner atoms×(1/8)= 1 atom.
• Coordination number is the number of nearest neighbor lattice site.
• In simple cube it is 6. Four lattice sites lie in the same plane and two lie above and below the plane.
• Packing fraction is {[(1/8)(4/3)πR ³ ]×8}/a ³ . Here a ³ is the volume of an unit cell. If we assume that the atom spheres are touching one another then R=a/2 where R is the radius of the atom. Therefore packing fraction is π/6. The nearest neighbor distance is ‘a/2’.

Sodium and Tungsten crystallize as Body Centered Cube(bcc).

• This has one extra atom at the body center.
• This amounts to [8 corner atoms×(1/8) + 1] = 2 atoms per cell.
• The coordination number is 8 as the nearest neighbor atoms are the 8 body center atoms residing in the 8 unit cells surrounding each corner atom.
• Therefore nearest neighbor distance a√3/2.
• If we assume that the body center atom is touching the corner atom then the radius is R= a√3/4.
• Therefore packing factor = (volume of 2 atoms)/a ³ = [2×(4/3)πR ³ ]/a ³ = [2×(4/3)π(a√3/4) ³ ]/a ³ =π√3/8= 0.68.

Aluminum, copper, gold and platinum crystallize as Face Centered Cube(fcc) .

• Here there are no body centered atom. Instead there are 6 atoms at the center of the 6 faces of the cube.
• This amounts to [8 corner atoms×(1/8) + 6 face atoms×(1/2) ] = 4 atoms per unit cell.
• The corner atom lies at the intersection of 3 orthogonal planes. Each plane has four faces and each face has one atom at the center which is the nearest neighbor. Hence the coordination number is 12. Nearest neighbor distance is a√2/2 and the radius R = a√2/4. The packing factor is = (volume of 4 atoms)/a ³ = [4×(4/3)πR ³ ]/a ³ = [4×(4/3)π(a√2/4) ³ ]/a ³ = π√2/6= 0.74.