Basic Crystal Structures

Before we discuss the semiconductor crystal, let us consider three crystal structures and determine some of the basic characteristics of these crystals. Figure 1.5 shows the simple cubic, body-centered cubic, and face-centered cubic structures. For these simple structures, we may choose unit cells such that the general vectors a, 6, and 7 are perpendicular to each other and the leneths are equal. The simple cubic (sc) structure has an atorn located at each corner: the hod?-centered cubic (bcc) structure has an additional atom at the center of the cube; and the face-centred cubic(fcc) structure has additional atoms on each face plane. By knowing the crystal structure of a material and its lattice dimensions, we can determine several characteristics of the crystal. For example, we can determine the volume density of atoms. Figure
To find the volume density of atoms in a crystal.
Consider a single-crystal material that is a body-centered cubic with a lattice constant
a = 5 A⁰ = 5 x10^-8 cm. A corner atom is shared by eight unit cells which meet at each corner
so that each comer atom effectively contributes one-eighth of its volume to each unit cell. The
eight comer atoms then contribute an equivalent of one atom to the unit cell. If we add the body centered
atom to the comer atoms. each unit cell contains an equivalent of two atoms

Solution
The volume density of atoms is then found as

Comment
'Thc volume density of atoms just calculated represents the order of magnitude of density for
most materials. The actual density is a function of the crystal type and crystal structure since
the packing density-number of atoms per unit cell-depends on crystal structure.

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