Drift

Drift

1. What Drift Is

Drift = directed motion of carriers due to electric field $E$, superimposed on random thermal motion.

• Electron drift velocity:

(negative because electron $-e$ moves opposite $E$)

• Hole drift velocity:

where $μ_n, μ_p$ are electron/hole mobilities (m²/V·s, positive numbers; Si: $μ_n≈0.14$, $μ_p≈0.05$ m²/V·s).

2. Drift Current Density

Conventional current from drift:

with conductivity

and resistivity

This is Ohm's law $J=σE$ microscopically. Total current = drift + diffusion:

etc., with $D$ from Einstein.

3. Velocity Saturation (note)

At high $E$ (>10⁴ V/cm), $v_d$ saturates ~ $10^5$ m/s in Si due to scattering — Ohm's law fails.

4. Worked Examples

(a) n-type Si N_D=1e22, n≈1e22, p negligible: σ=1.6e-19·1e22·0.14≈224 S/m, ρ≈4.46e-3 Ω·m, for E=1e3 V/m, J=2.24e5 A/m², v_n=-140 m/s ✓

(b) Intrinsic Si n=p=1e16: σ=1.6e-19·1e16·(0.14+0.05)=0.304e-3 S/m much lower ✓

(c) J=1 A through 1 mm² wire: J=1e6 A/m² ⇒ E=J/σ; for n-type above E≈4460 V/m (small) ✓

(d) Hall vs drift: drift sets current for given E; Hall transverse E balances magnetic deflection.

5. Contrast with Diffusion

Drift	Diffusion
Due to $E$ field	Due to $dn/dx$ gradient
$J∝E$	$J∝dn/dx$
Direction set by $E$ polarity	Down gradient regardless of $E$
Dominates in resistive region	Dominates at junctions where gradient large

6. Exam Points

• Define drift velocity $v_d=μE$ and $J_{drift}=e(nμ_n+pμ_p)E$ — 5 marks, very frequent.
• Give $μ_n, μ_p$ values for Si — 3 marks.
• Show $J=σE$, $σ=e(nμ_n+pμ_p)$ — 3-5 marks, frequent.
• Distinguish drift vs diffusion — 5 marks, very frequent.