Diffusion

Diffusion

1. What Diffusion Current Is

Diffusion = flow of carriers from high concentration to low due to random thermal motion, down concentration gradient, independent of electric field.

• Electron diffusion current density:

? Actually conventional current direction? For electrons, particle flux $-D_n dn/dx$ ⇒ current

? Wait sign: electrons diffuse down gradient ⇒ particle flux $-D_n dn/dx$ (Fick's first law: flux = $-D dn/dx$); current = $-e × particle flux$? For electrons $q=-e$, careful:

? Let's use standard:

and

gives correct direction (holes diffuse down gradient gives current same direction as diffusion). Alternatively magnitude

.

Standard textbook forms:

(with $n,p$ concentrations).

Diffusion coefficient $D_n, D_p$ (m²/s) linked to mobility $μ$ by Einstein relation:

V at 300K.

2. When It Matters

• P-n junction: concentration gradient at junction drives diffusion of electrons p→n? Actually n-side high $n$, p-side low ⇒ electrons diffuse n→p, holes p→n, building depletion region and built-in field which later balances with drift.
• Non-uniform doping: any gradient ⇒ diffusion.
• In bipolar transistor base, minority diffusion is main transport.

3. Worked Estimate

D_n≈ 36 cm²/s? Actually Si: D_n≈36? Wait μ_n=1400 cm²/Vs ⇒ D_n=μ_n·kT/e≈36 cm²/s? Convert: 1400·0.026=36.4 cm²/s=3.64e-3 m²/s.
dn/dx ≈ (1e22-1e16)/1e-6 (gradient over 1 µm)≈1e28 m⁻⁴ ⇒ J_n≈1.6e-19·3.6e-3·1e28≈5.8e6 A/m² huge — hence small gradients give large diffusion in nanoscale.

4. Exam Points

• Define diffusion and Fick's law — 3-5 marks, frequent.
• Write $J_n=e D_n dn/dx$, $J_p=-e D_p dp/dx$ and $D/μ=kT/e$ — 5 marks, very frequent.
• Explain p-n junction diffusion vs drift balance — 5 marks, frequent.