⚛️ Unit 5 – Part A (2-Mark Q&A)

1) Direct vs Indirect bandgap semiconductors

• Direct: CB minimum and VB maximum at same k. Efficient radiative recombination ⇒ good for LEDs/lasers (e.g., GaAs, InP).
• Indirect: CB min and VB max at different k; needs phonon for momentum change ⇒ weak light emission (e.g., Si, Ge).

E_g = E_c − E_v (direct: vertical in E–k).

2) Drift current vs Diffusion current

• Drift: Due to applied electric field E (carriers “pulled”). J_drift = q(nμ_n + pμ_p)E
• Diffusion: Due to concentration gradient (carriers “spread”). J_diff = qD_n∇n − qD_p∇p

D/μ = k_BT/q (Einstein relation).

3) Schottky diode vs Ohmic contact

• Schottky (metal–lightly doped semi): Forms barrier Φ_B ⇒ rectifying I–V, fast switching, low forward drop.
• Ohmic (metal–heavily doped semi): Negligible barrier ⇒ linear I–V (Ohm’s law), bidirectional conduction.

I = I_S(e^{qV/ηkT} − 1)

4) Hall effect & Hall voltage

Current I along x, magnetic field B along z ⇒ transverse voltage along y due to Lorentz force. Used to find type (n/p), carrier density, and mobility.

V_H = (R_H I B)/t, R_H = 1/(q n) (n-type ⇒ negative sign), μ = σR_H.

5) Why prefer extrinsic over intrinsic?

Extrinsic (doped) semiconductors provide much higher, controllable conductivity by adding donors/acceptors; enable n/p regions for diodes, BJTs, MOSFETs. Intrinsic has low σ and strong T-dependence.

σ = q(nμ_n + pμ_p)

6) Intrinsic vs Extrinsic semiconductor

Aspect	Intrinsic	Extrinsic
Purity	Pure; n = p = ni	Doped (donor/acceptor)
Fermi level	Mid-gap	Towards CB (n) / VB (p)
Conductivity	Low, T-sensitive	High, engineered
Examples	Pure Si, Ge	n-Si (P), p-Si (B)

7) Hole concentration in p-type (valence band)

For full ionization and light doping: p ≈ N_A.

General (from F-D stats): p = N_v exp\{−(E_F − E_v)/(k_BT)\}

Mass-action law: np = n_i².

8) Given an extrinsic sample — identify n-type or p-type

Use Hall effect: measure polarity of Hall voltage.

• R_H < 0 ⇒ majority electrons ⇒ n-type.
• R_H > 0 ⇒ majority holes ⇒ p-type.

Optional cross-checks: Seebeck sign, hot-probe test.

9) Energy band diagram of intrinsic semiconductor (T > 0 K)

1. Valence band (VB) filled; conduction band (CB) nearly empty.
2. Forbidden gap E_g = E_c − E_v.
3. Equal electron–hole pairs thermally generated (n = p = n_i).
4. Fermi level at mid-gap: E_F ≈ (E_c + E_v)/2.

10) Elemental vs Compound semiconductors (with examples)

• Elemental (Group IV): Single element; typically indirect gap. Examples: Si, Ge.
• Compound (III–V / II–VI): Tunable bandgaps; many direct gap ⇒ optoelectronics. Examples: GaAs, InP, GaN, CdS.

Advantages of compounds: high electron mobility, direct E_g, lattice/ band-engineering (heterostructures).