Intrinsic and extrinsic semiconductors

Intrinsic and extrinsic semiconductors

1. Intrinsic — Pure Semiconductor

Intrinsic semiconductor = undoped, chemically pure (Si, Ge). At $T=0$, no carriers → insulator-like. At $T>0$, thermal generation creates electron-hole pairs:

• Electron concentration $n$ in conduction band, hole concentration $p$ in valence ($p$ = missing electron, $+e$ charge, mobile).
• Mass action law:

always (even when doped, if equilibrium).

Si $n_i≈1×10^{16}$ m⁻³ at 300K (Ge higher due to smaller $E_g$). Conductivity

low, $σ$ ↑ with $T$ (more $n_i$).

Fermi level $E_{F,i}$ near mid-gap (intrinsic):

≈ mid.

2. Extrinsic — Doped Semiconductor

Extrinsic = doped with impurity atoms to intentionally increase $n$ or $p$ by orders of magnitude, making n-type or p-type (next topic).

• Donor doping (group V in Si: P, As) adds extra electron → $n$-type.
• Acceptor doping (group III: B, Al) adds hole → $p$-type.

Doping concentration $N_D, N_A ∼10^{21}$–$10^{24}$ m⁻³ ≫ $n_i$ ⇒ $σ$ increases dramatically, can be tuned. At high doping, extrinsic dominates intrinsic beyond certain $T$ (freeze-out at low $T$, intrinsic at high $T$).

Conservation:

still holds in equilibrium; so if $n≈N_D$ (n-type), then

minority suppressed.

3. Worked Illustration

Si intrinsic 300K: n_i≈1e16 m⁻³ ⇒ σ=1.6e-19·(1e16·0.14 +1e16·0.05)=0.3e-3 S/m (high resistivity)
Doped N_D=1e22 m⁻³ (n-type): n≈1e22, p≈1e10 ⇒ σ≈ e·1e22·0.14=0.22e3 S/m ⇒ 10⁶× higher ✓

4. Exam Points

• Define intrinsic ($n=p=n_i$) and extrinsic (doped) — 3-5 marks, very frequent.
• $n·p=n_i²$ — 3 marks, frequent.
• Show $σ$ with $n,p,μ$ — 5 marks, frequent.
• Mention $n_i∝ e^{-E_g/2kT}$ — 3 marks.
• Diagram of bands with $E_F$ mid-gap (intrinsic) — 5 marks, frequent (next topics shift $E_F$).