Etch Selectivity Simulator
Real-time simulation of multi-material etch selectivity based on ion energy distribution, reactive species sticking coefficients, and surface chemistry. Model differential etching rates between Si, SiO₂, Si₃N₄, and photoresist materials.
Selectivity Physics & Equations
Ion-Enhanced Etching Model
The etch rate for each material combines spontaneous chemical etching and ion-enhanced physical sputtering:
ER(material) = Y_chem(material) · Γ_neutral · γ(material, T) + Y_phys(material, E_ion) · Γ_ion
where:
Y_chem = chemical etch yield (reactions per incident neutral)
Y_phys = physical sputter yield (atoms removed per ion)
Γ_neutral = neutral radical flux (cm⁻²s⁻¹)
Γ_ion = ion flux (cm⁻²s⁻¹)
γ = temperature-dependent sticking coefficient
Chemical Etch Yield (Langmuir-Hinshelwood)
Surface reaction kinetics following Langmuir-Hinshelwood mechanism:
Y_chem = (k_rxn · θ_F · θ_site) / (1 + K_ads · P_F)
where:
k_rxn = surface reaction rate constant = k₀ · exp(-E_a / kT)
θ_F = fluorine coverage = K_ads · P_F / (1 + K_ads · P_F)
θ_site = available surface site fraction
K_ads = adsorption equilibrium constant
E_a = activation energy (material-dependent)
Material-specific activation energies:
Si: E_a = 0.15 eV (highly reactive with F)
SiO₂: E_a = 0.45 eV (requires ion activation)
Si₃N₄: E_a = 0.35 eV (intermediate)
PR: E_a = 0.25 eV (organic polymer)
Physical Sputter Yield (Sigmund Model)
Ion-induced physical sputtering described by Sigmund theory:
Y_phys(E) = 0 for E < E_th
Y_phys(E) = K · (E - E_th) / U₀ for E ≥ E_th
where:
K = material-dependent constant (function of mass ratio)
E_th = sputtering threshold energy
U₀ = surface binding energy
Threshold energies:
Si: E_th = 20 eV, U₀ = 4.7 eV
SiO₂: E_th = 35 eV, U₀ = 7.2 eV
Si₃N₄: E_th = 30 eV, U₀ = 6.5 eV
PR: E_th = 15 eV, U₀ = 3.2 eV
Sticking Coefficient Temperature Dependence
Arrhenius-type temperature dependence of reactive sticking:
γ(T) = γ₀ · exp(-E_des / kT) · [1 - exp(-E_ads / kT)]
where:
γ₀ = intrinsic sticking probability (0.1 - 0.8)
E_des = desorption activation energy
E_ads = adsorption activation energy
Si with F radicals: γ₀ = 0.65, E_des = 0.08 eV
SiO₂ with F radicals: γ₀ = 0.25, E_des = 0.22 eV
Selectivity Definition
Etch selectivity is the ratio of etch rates:
S(A:B) = ER(A) / ER(B)
High selectivity (S > 20): Ion energy at threshold, high chemical component
Low selectivity (S < 5): High ion energy, physical sputtering dominant
Infinite selectivity: ER(B) → 0 (perfect etch stop)
Practical target for Si:SiO₂ in contact etching: S > 50:1
Ion Energy Distribution Function
Ions arrive with a distribution of energies from the plasma sheath:
f(E) = (1 / √(2π σ²)) · exp(-(E - E_peak)² / (2σ²))
where:
E_peak = eV_dc + eV_rf · cos(ωt)
σ = energy spread ≈ 0.1 · E_peak (collisional broadening)
Effective etch yield integrates over IEDF:
Y_eff = ∫ Y(E) · f(E) dE
Surface Coverage Dynamics
Time evolution of surface coverage by reactive species:
dθ_F/dt = γ · Γ_F · (1 - θ_F - θ_prod) - k_rxn · θ_F - k_des · θ_F
dθ_prod/dt = k_rxn · θ_F - Y_phys · Γ_ion · θ_prod
Steady-state solution (dθ/dt = 0) gives coverage for etch rate calculation