Effective Density of States in Conduction Band (Nc)
The effective density of states in the conduction band (Nc) is an important concept in semiconductor physics.
Formula
Nc = 2 × [(2Ï€ m* k T) / h²]3/2
- m* = effective mass of electrons
- k = Boltzmann constant
- T = temperature (Kelvin)
- h = Planck’s constant
Standard Values at 300 K
Silicon (Si)
- Nc ≈ 2.8 × 1019 cm-3
Gallium Arsenide (GaAs)
- Nc ≈ 4.7 × 1017 cm-3
Germanium (Ge)
- Nc ≈ 1.0 × 1019 cm-3
Indium Phosphide (InP)
- Nc ≈ 5.7 × 1017 cm-3
Gallium Nitride (GaN)
- Nc ≈ 2.3 × 1018 cm-3
- Silicon has higher Nc than GaAs
- Materials with higher effective mass → higher Nc
- Materials with lower effective mass → lower Nc
Comparison Table
| Material | Nc (300 K) |
|---|---|
| Silicon (Si) | 2.8 × 1019 cm-3 |
| Gallium Arsenide (GaAs) | 4.7 × 1017 cm-3 |
| Germanium (Ge) | 1.0 × 1019 cm-3 |
| Indium Phosphide (InP) | 5.7 × 1017 cm-3 |
| Gallium Nitride (GaN) | 2.3 × 1018 cm-3 |
Summary
Si = heavy electrons → more states → high Nc
GaAs = light electrons → fewer states → low Nc