Plasma Chemistry Simulator

Advanced electron kinetics and reactive species generation modeling for plasma etching processes. Solve the Boltzmann equation to predict electron energy distribution functions (EEDF), ionization rates, and radical production in various gas chemistries.

Key Physics

This simulator models the fundamental electron-neutral interactions that govern plasma chemistry. The electron energy distribution function (EEDF) determines ionization rates, radical generation, and power absorption through electron-impact collisions with gas molecules.

Running
1.0×

Plasma Parameters

Ionization Rate

2.4e15
cm⁻³s⁻¹

Radical Density

8.3e14
cm⁻³

Mean Electron Energy

4.2
eV

Power Absorption

425
W

Collision Frequency

3.2e9
Hz

Plasma Impedance

42
Ω

3D Species Concentration Distribution

Theoretical Background

Boltzmann Equation

The electron energy distribution function f(ε) is governed by the Boltzmann equation:

∂f/∂t + v·∇f + (e/m)(E + v×B)·∇ᵥf = (∂f/∂t)_coll

In steady-state, this reduces to a balance between field acceleration and collisional losses.

Electron Energy Distribution Function (EEDF)

For a Maxwellian distribution:

f(ε) = (2/π^(1/2)) · n_e · ε^(1/2) / (k_B T_e)^(3/2) · exp(-ε / k_B T_e)

Where ε is electron energy, n_e is electron density, and T_e is electron temperature.

Ionization Rate Calculation

The ionization rate coefficient k_iz is calculated by integrating the product of the EEDF and ionization cross-section:

k_iz = ∫ σ_iz(ε) · v(ε) · f(ε) dε where v(ε) = √(2ε/m_e) is the electron velocity

Townsend Coefficients

The first Townsend coefficient α represents ionization per unit length:

α/p = A · exp(-B·p/(E/p)) For CF₄: A ≈ 15 cm⁻¹Torr⁻¹, B ≈ 350 V·cm⁻¹·Torr⁻¹

Radical Generation

Fluorine radical generation from CF₄ dissociation:

e + CF₄ → CF₃ + F + e (k_diss ≈ 2×10⁻⁸ cm³/s at T_e = 3 eV) e + CF₄ → CF₂ + 2F + e (threshold: 12.5 eV)

Collision Cross Sections

Elastic scattering cross-section (momentum transfer):

σ_m(ε) = σ_0 · (1 - α·ε) for ε < ε_threshold Ionization cross-section (semi-empirical): σ_iz(ε) = a · (ε - ε_iz) / (ε · ε_iz) for ε > ε_iz

Power Absorption

Ohmic heating from electron-neutral collisions:

P_abs = (1/2) · n_e · e² · E₀² · ν_m / (m_e · (ω² + ν_m²)) where ν_m is the momentum transfer collision frequency

Plasma Impedance

The complex plasma impedance for capacitively coupled plasma:

Z_plasma = R_plasma + jX_plasma R_plasma = V_rf² · ν_m / (2·P_abs) X_plasma = -1/(ω·C_sheath) where C_sheath = ε₀·A/s