Semiconductor Materials: Intrinsic and extrinsic semiconductor types

Semiconductor Materials: Intrinsic and extrinsic semiconductor types

1. What Semiconductors Are (recap — same as earlier physics but for electronics)

Semiconductor = material with conductivity between metal and insulator, band gap $E_g$ ~0.5–3 eV, whose carriers can be controlled by doping, $T$, light, field — basis for diodes, transistors, ICs.

2. Intrinsic (Pure)

Intrinsic semiconductor = undoped pure crystal (Si: 4 valence electrons, diamond lattice; Ge similar). At $0$ K, no free carriers (valence full, conduction empty) ⇒ insulator-like. At $T>0$, thermal generation: electron excited across $E_g$ ⇒ creates electron ($n$) in conduction + hole ($p$) in valence, with

~ $1×10^{16}$ m⁻³ for Si, $2×10^{19}$ for Ge at 300K (Ge smaller $E_g$ ⇒ larger $n_i$).

• Fermi level mid-gap, conductivity

low.

3. Extrinsic (Doped)

Extrinsic = doped with impurity to increase $n$ or $p$ intentionally:

• N-type: donor (group V P,As) adds extra electron $E_d$ just below $E_c$ ⇒ $n≈N_D$, $p=n_i²/N_D$ minority, $E_F$ up toward $E_c$.
• P-type: acceptor (group III B,Al) adds hole $E_a$ just above $E_v$ ⇒ $p≈N_A$, $n=n_i²/N_A$, $E_F$ down toward $E_v$.

Doping $N_D,N_A$ $10^{21}$–$10^{24}$ m⁻³ ≫ $n_i$ ⇒ conductivity tunable over 10⁶×.

4. Why Types Matter for Devices

All p-n junctions, BJTs, MOSFETs rely on p vs n regions; type determines carrier polarity and Fermi level alignment (built-in potential $V_{bi}= (kT/e) ln(N_A N_D/n_i²)$).

5. Worked Illustration

Si intrinsic: n_i=1e16 ⇒ σ≈0.3 mS/m
Doped N_D=1e22 (n-type): n≈1e22, p≈1e10 ⇒ σ≈224 S/m (10⁶× higher) ✓

6. Exam Points

• Define intrinsic ($n=p=n_i$) and extrinsic (doped, n-type donor, p-type acceptor) — 5 marks, very frequent (almost certain).
• Show $n_i$ formula and $n·p=n_i²$ — 3-5 marks, frequent.
• Give donor (P) and acceptor (B) examples — 3 marks.
• Draw band diagram with $E_F$ mid-gap vs near $E_c$/$E_v$ — 7 marks, frequent (common diagram).