P-type and N-type semiconductors

P-type and N-type semiconductors

1. N-Type — Donor Doped

N-type: Si doped with group V (P, As, Sb) — 5 valence electrons, 4 used in bonding, 1 donor electron weakly bound ($E_d≈0.045$ eV below $E_c$ for P in Si).

• At room $T$, donor ionization:

⇒ majority electrons $n≈N_D$, minority holes $p≈n_i²/N_D$.

• Fermi level $E_F$ moves up toward $E_c$:

( ближе to conduction).

Band diagram: donor level $E_d$ just below $E_c$.

2. P-Type — Acceptor Doped

P-type: Si doped with group III (B, Al, Ga) — 3 valence electrons, missing one ⇒ acceptor level $E_a≈0.045$ eV above $E_v$, captures electron from valence ⇒ creates hole.

• Ionization:

⇒ majority holes $p≈N_A$, minority electrons $n≈n_i²/N_A$.

• $E_F$ moves down toward $E_v$:

3. Comparison Table (exam must-draw)

Type	Dopant	Level	Majority	Minority	$E_F$ Shift	Conductivity Type
N-type	donor (P,As) group V	$E_d$ near $E_c$	electrons $n≈N_D$	holes $p=n_i²/N_D$	up to $E_c$	electrons negative
P-type	acceptor (B,Al) group III	$E_a$ near $E_v$	holes $p≈N_A$	electrons $n=n_i²/N_A$	down to $E_v$	holes positive

4. Worked Illustration

Si doped N_D=1e22 m⁻³: n≈1e22, p≈1e16²/1e22=1e10 ⇒ electrons dominate 10¹²× ; EF ≈ Ec -0.21 eV (since kT ln(Nc/ND) small)

P-type N_A=1e22: p≈1e22, n≈1e10, EF near Ev.

5. Compensation and Heavily Doped

If both donors and acceptors present, net $N_D-N_A$ determines type (compensated). At high doping, bands merge (degenerate semiconductor, Fermi enters band like metal).

6. Exam Points

• Define donor/acceptor, $n≈N_D$, $p≈N_A$ — 5 marks, very frequent.
• Draw band diagram with $E_d$ near $E_c$ and $E_a$ near $E_v$ and $E_F$ shift — 7 marks, very frequent (almost certain to ask diagram).
• Show $n·p=n_i²$ still holds — 3 marks.
• Give examples: P donor, B acceptor — 3 marks.