Sheath Dynamics & Ion Bombardment Simulator

Advanced modeling of plasma sheath formation, ion acceleration, and energy/angular distributions. Simulate Child-Langmuir sheath voltage, Bohm criterion, RF modulation effects, and ion trajectory dynamics critical for anisotropic etching.

Key Physics

The plasma sheath is a thin boundary layer with strong electric fields that accelerates ions toward the wafer surface. The ion energy distribution function (IEDF) and angular distribution determine etch anisotropy, selectivity, and damage. RF bias creates time-varying sheath voltages crucial for directionality control.

Running
1.0×

Sheath & Bias Parameters

Sheath Voltage

-245
V

Ion Energy (Mean)

245
eV

Ion Flux

3.2e16
cm⁻²s⁻¹

Sheath Thickness

1.8
mm

Bohm Velocity

2.3e5
cm/s

Angular Spread

2.1
degrees

3D Ion Trajectory Simulation

Theoretical Background

Bohm Criterion

Ions must enter the sheath with minimum velocity (Bohm velocity) for stable sheath formation:

u_B = √(k_B T_e / M_i) where T_e is electron temperature and M_i is ion mass

Child-Langmuir Sheath Voltage

The sheath voltage drop is governed by space-charge limited current:

V_sheath ≈ -0.5 k_B T_e [ln(M_i / (2π m_e)) + 1] For collisionless sheath (typical: 3-5 T_e)

Sheath Thickness

The Debye length scaled sheath thickness:

s = λ_D · (2V_sheath / T_e)^(3/4) where λ_D = √(ε₀ k_B T_e / (n_e e²)) is the Debye length

Ion Energy Distribution Function (IEDF)

For collisionless sheath, ions gain energy from sheath voltage:

E_ion = e·V_sheath + (1/2)M_i·u_B² For RF bias, IEDF shows bimodal structure due to time-varying sheath

RF Sheath Modulation

Time-dependent sheath voltage for capacitively coupled RF:

V_sheath(t) = V_DC + V_RF·cos(ωt) where V_RF = √(2P·Z_plasma) and ω = 2πf

Ion Angular Distribution

Angular spread due to lateral ion temperature and collisions:

θ_rms = √(k_B T_i / E_ion) Collisional scattering adds: Δθ ∝ (p·s) / √E_ion

Ion Flux to Surface

The ion saturation current density:

J_i = 0.61 · e · n_e · u_B Flux: Γ_i = J_i / e = 0.61 · n_e · √(k_B T_e / M_i)

Presheath Formation

The quasi-neutral presheath accelerates ions to Bohm velocity:

Presheath potential drop: ΔV_pre ≈ 0.5 k_B T_e / e Total potential drop: V_total = V_sheath + ΔV_pre