(a) The lattice constant of GaAs is 5.65 Å. Determine the number of Ga atoms andAs atoms per cm 3 .

( b ) Determine the volume density of germanium atoms in a germa-nium semiconductor. The lattice constant of germanium is 5.65 Å.

a) Number of atoms per unit cell for Ga = 4 atoms per unit cell

Number of atoms per unit cell for As = 4 atoms per unit cell

b) Volume density of Germanium in its unit cell = 4.35 × 10²² /cm³

Explanation:

GaAs has a number density of 4.42 x 10²² atoms/cm³ from literature.

Since GaAs is known to contain almost equal amounts of Ga and As.

Number density of Ga = Number density of As = 2.21 × 10²² atoms/cm³

Number density = Number of atoms in a unit cell/volume of the unit cell

Number of atoms in the unit cell = ?

Volume of the unit cell = (lattice parameter)³ = (5.65 × 10⁻⁸)³ = 1.804 × 10⁻²² cm³

Number of atoms per unit cell for Ga and As = number density × volume of unit cell = 2.21 × 10²² × 1.804 × 10⁻²² = 4 atoms/unit cell

b) Volume density = Number of atoms per unit cell/volume of unit cell

Germanium has 8 atoms per unit cell (from literature),

Volume of unit cell = (lattice parameter)³ = (5.65 × 10⁻⁸)³ = 1.804 × 10⁻²² cm³

Volume density = 8/(1.804 × 10⁻²²) = 4.35 × 10²² /cm³

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