Etching, Ion Implantation, Diffusion & Annealing

Transferring patterns and placing dopants. Learn wet etching (isotropic, selectivity, undercut, anisotropic KOH for MEMS), dry etching (plasma, reactive-ion etching, high-aspect-ratio etching, ALE), selectivity, anisotropy, etch rate, loading and endpoint detection; then doping: thermal diffusion (predeposition and drive-in, Fick's laws, Gaussian and erfc profiles), ion implantation (energy and projected range, dose, straggle, channelling, damage), junction depth and sheet resistance, activation annealing (furnace, RTP, spike, laser/flash) and dopant diffusion control — with Python computing implanted Gaussian profiles, junction depth, drive-in diffusion, sheet resistance and etch times.

After lithography, etching removes material where the resist doesn't protect it, and implantation or diffusion introduces dopants into exposed regions. Together they sculpt and dope the device.

Modern devices need nanometre-accurate, vertical etches and ultra-shallow junctions activated without letting dopants spread.

An analogy

Etching is carving through a stencil — wet etching is like dissolving with water that also seeps under the edges, plasma etching is like sandblasting straight down. Ion implantation is like firing tiny projectiles to a chosen depth; annealing lets them settle into their places.

Etching figures of merit

What engineers specify:

Diffusion

Dopants move by vacancy and interstitial mechanisms; D rises exponentially with temperature (Arrhenius). Predeposition from a constant surface source gives an erfc profile; drive-in of a fixed dose gives a Gaussian. Effects such as transient enhanced diffusion (implant damage boosts boron diffusion), oxidation-enhanced diffusion and concentration-dependent diffusivity complicate real profiles — simulated with process TCAD.

Ion implantation

Ions are accelerated (0.2 keV–MeV), mass-selected and scanned across the wafer; dose is measured precisely by integrating beam current (10¹¹–10¹⁶ cm⁻²). Range depends on energy and ion mass; tilt (7°) reduces channelling along crystal axes. Implants amorphise the lattice at high doses; annealing recrystallises and activates dopants. Special implants: halos/pockets, retrograde wells, SOI Smart Cut (hydrogen), high-energy implants for power devices, and hot implants for SiC.

Annealing

Furnace anneals (minutes–hours) are too diffusive for modern shallow junctions. Rapid thermal processing (seconds), spike anneals (~1 s at peak) and millisecond flash/laser anneals activate dopants beyond equilibrium solubility with minimal diffusion. SiC requires ~1700 °C activation anneals with surface protection.

Formulas

Worked example: Peak concentration

Given: Q 5 × 10¹³, ΔR_p 50 nm

Find: N_peak.

Answer: ≈ 4 × 10¹⁸ cm⁻³

Worked example: Diffusion length

Given: D 10⁻¹³ cm²/s, 1 h

Find: 2√(Dt).

Answer: ≈ 380 nm

Worked example: Undercut

Given: Isotropic wet etch, 1 µm deep

Find: Undercut per side.

Answer: ≈ 1 µm

Wet vs dry etching profiles

  Wet (isotropic)          RIE (anisotropic)         KOH on (100) Si
   ▓▓ resist ▓▓   ▓▓        ▓▓ resist ▓▓   ▓▓          ▓▓ mask ▓▓   ▓▓
    ╲___________╱            │           │               ╲         ╱  54.7° (111) walls
   undercut ≈ depth          vertical walls              anisotropic by crystal orientation
  Plasma: ions (directional) + radicals (chemical) → vertical, selective etch; endpoint by optical emission

Wet etchants attack equally in all directions, undercutting the mask — acceptable for large features. Reactive-ion etching combines chemical radicals with vertically accelerated ions and sidewall passivation for straight walls at nanometre dimensions. Crystal-orientation-dependent wet etches (KOH, TMAH) are used in MEMS.

Implant profile, drive-in, sheet resistance and etch time

import math
# Ion implantation Gaussian profile, junction depth, and drive-in diffusion
Q, Rp, dRp, Nb = 1e15, 0.10e-4, 0.035e-4, 1e16          # dose cm^-2, range 100 nm, straggle 35 nm, background
peak = Q / (math.sqrt(2 * math.pi) * dRp)
xj = Rp + dRp * math.sqrt(2 * math.log(peak / Nb))
print(f"as-implanted: peak {peak:.2e} cm^-3 at {Rp*1e7:.0f} nm; junction depth {xj*1e7:.0f} nm (background 1e16)")
D = 1.5e-14                                                 # boron at ~1000 C (cm^2/s), illustrative
for t_min in (10, 60):
    Dt = D * t_min * 60
    xj2 = math.sqrt(4 * Dt * math.log(Q / (math.sqrt(math.pi * Dt) * Nb)))
    print(f"drive-in {t_min:2d} min: diffusion length 2*sqrt(Dt) = {2*math.sqrt(Dt)*1e7:.0f} nm, xj ~ {xj2*1e7:.0f} nm")
Rs = 1 / (1.602e-19 * 60 * Q)                               # sheet resistance with mobility ~60 cm^2/Vs (heavy doping)
print(f"sheet resistance of the activated layer ~ {Rs:.0f} ohm/sq")
etch_rate, film, over = 200.0, 400.0, 0.3                    # nm/min, nm, 30% over-etch
print(f"etch 400 nm at 200 nm/min with 30% over-etch: {film/etch_rate*(1+over):.1f} min; with selectivity 20:1 underlayer loss {film*over/20:.0f} nm")
# as-implanted: peak 1.14e+20 cm^-3 at 100 nm; junction depth 251 nm (background 1e16)
# drive-in 10 min: diffusion length 2*sqrt(Dt) = 60 nm, xj ~ 188 nm
# drive-in 60 min: diffusion length 2*sqrt(Dt) = 147 nm, xj ~ 440 nm
# sheet resistance of the activated layer ~ 104 ohm/sq
# etch 400 nm at 200 nm/min with 30% over-etch: 2.6 min; with selectivity 20:1 underlayer loss 6 nm

A 10¹⁵ cm⁻² boron implant peaking at 100 nm reaches 1.1 × 10²⁰ cm⁻³ and forms a junction ~250 nm deep in 10¹⁶ background. Drive-in diffusion spreads the dopant: after an hour at ~1000 °C the junction is ~440 nm — so modern processes use millisecond anneals to activate without diffusion. The activated layer's sheet resistance is ~100 Ω/□. A 30% over-etch with 20:1 selectivity removes only 6 nm of the underlying layer.

Common mistakes

Applications

Key takeaways

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