semiconductor and insulator)

semiconductor and insulator)

1. Semiconductor — Small Gap (~0.5–3 eV)

Semiconductor: band gap $E_g$ small (Si $1.12$ eV, Ge $0.66$ eV, GaAs $1.42$ eV). At $0$ K, valence full, conduction empty ⇒ insulator-like. At room $T$, thermal energy $kT≈0.026$ eV excites some electrons across gap:

⇒ $n_i∼10^{16}$ m⁻³ Si at 300K (vs $10^{28}$ metal) — conductivity between.

• Resistivity: $10^{-3}$ to $10^{3}$ Ω·m, decreases with $T$ (more carriers excited, opposite to metal).
• Band diagram: $E_F$ mid-gap for intrinsic; tunable by doping (next).

2. Insulator — Large Gap (>3–6 eV)

Insulator: $E_g$ large (diamond $5.5$ eV, SiO₂ $∼9$ eV, glass $∼4$ eV). Even at 300K, $e^{-E_g/2kT}$ negligible ⇒ $n∼0$, no conduction ($ρ∼10^{8}$–$10^{16}$ Ω·m).

• Band diagram: valence full, conduction empty, huge gap ⇒ $E_F$ mid-gap but no thermal crossing.
• Needs breakdown field ($∼MV/cm$) to force.

3. Comparison Table (exam must-draw)

Type	Gap $E_g$	$E_F$ Location	Carriers at 300K	$ρ$ at 300K	Example
Metal	0 (overlapped)	inside band	$10^{28}$ (all)	$10^{-8}$ Ω·m, ↑ with $T$	Cu, Al
Semiconductor	0.5–3 eV	mid-gap (intrinsic)	$10^{16}$ (excited)	$10^{-3}$–$10^{3}$, ↓ with $T$	Si, Ge, GaAs
Insulator	>3 eV	mid-gap	~0	$10^{8}$–$10^{16}$	Glass, diamond, SiO₂

4. Why $E_g$ Determines Type

Photon/thermal $kT$ must be comparable to $E_g$ to excite. Visible light $1.5$–$3$ eV can excite semiconductor but not insulator (transparent).

5. Exam Points

• Draw three band diagrams side-by-side with $E_F$ — 7 marks, almost certain (the classic question).
• State $E_g$ values (Si 1.12, Ge 0.66, diamond 5.5) — 3-5 marks, frequent.
• Explain $ρ$ vs $T$ opposite for metal vs semiconductor — 5 marks, very frequent.