Energy Bands In Intrinsic and Extrinsic Silicon

Semiconductor Materials

• The term conductor is applied to any material that will support a generous flow of charge when a voltage source of limited magnitude is applied across its terminals.
• An insulator is a material that offers a very low level of conductivity under pressure from an applied voltage source.
• A semiconductor, therefore, is a material that has a conductivity level somewhere between the extremes of an insulator and conductor.

Band Theory

A bonding of atoms, strengthened by the sharing of electrons, is called covalent bonding. In the crystal, closely spaced energy levels form a band called as energy band. Each orbit has a separate energy band. A band of energy levels associated with valence shells is called as valence band. Electrons from other bands cannot be removed but electrons from valence band can be removed by supplying a little energy. The conduction band is generally empty. The valence band and conduction band are separated by a gap called forbidden energy gap.

Compound Semiconductors: Such as Gallium Arsenide (GaAs), Cadmium Sulphide (CdS), Gallium Arsenide Phosphide (GaAsP), Gallium Nitride (GaN) are constructed by two or more semiconductor materials of different atomic structures are called compound semiconductors.

Properties of Semiconductor Materials: Various materials are classified based on the width of forbidden energy gap. In metal, there is no forbidden gap and valence and conduction band are overlapped. In insulator, the forbidden gap is very large upto 7eV while in semiconductors it is upto 1eV. The silicon and germanium are widely used semiconductors. Intrinsic materials are those semiconductor that have been carefully refined to reduce the impurities to a very level-essentially' as pure as can be made available through modern technology.

• The conductivity of intrinsic semiconductor is very less. The properties like conductivity can be changed by adding impurity to the intrinsic semiconductor. The process of adding impurity is called doping.
• A semiconductor doped with trivalent impurity atoms forms p-type material. It is called acceptor impurity with concentration N_A atoms per unit volume.
• A semiconductor doped with pentavalent impurity atoms forms n-type material. It is called donor impurity with concentration N_D atoms per unit volume.
• In p-type, holes are majority carriers and in n-type electrons are majority carriers.
• When a material is subjected to electric field, electrons move in a particular direction with steady speed called drift speed and current drift current.

Negative Temperature Coefficient: Those parameters decreasing with the temperature have negative temperature coefficient, e.g., energy gap (E_g).

where, constant β₀ = 2.2 × 10^–4 (for Ge)

= 3.6 × 10^–4 (for Si)

Mobility (μ), μ ∝ T^–m

Positive Temperature Coefficient: Those parameters increasing with temperature have positive temperature coefficient.

Important terms:

• Drift velocity V_d = μE
• Current density J = nq μE
• Conductivity σ = nq μ
• Concentration of free electrons per unit volume 
• Semiconductor conductivity σ = (nμ_n + pμ_p)q
• In intrinsic semiconductor, n = p = n_i Hence, conductivity σ_i = n_i (μ_n + μ_p)q Intrinsic concentration 
• In extrinsic semiconductor, the conductivity is given by, For n-type, σ_n = (n_nμ_n + p_nμ_p)q For p-type, σ_n = (n_pμ_n + p_pμ_p)q But in n-type p_n < < n_n   N_D = Concentration of donor impurity   N_A = Concentration of acceptor impurity   n_p = Number of electrons (concentration) in p-type   P_p = Number of holes (concentration) in p-type and n_n ≅ N_D while in p-type   n_p < < p_p and p_p ≅ N_A Hence, conductivity can be calculated as,   σ_n = N_Dμ_nq and σ_p = N_Aμ_pq
• Mass-action law np = 

In n-type, n_np_n = , hence 

In p-type, p_pn_p = , hence