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PECVD Packing Density

Film packing density of PECVD Ge-doped SiO₂ (SiH₄ / N₂O / GeH₄) — from refractive index, density, or deposition conditions.

A. Refractive index (Lorentz–Lorentz)
B. Density ratio
C. Deposition conditions

Bulk index is the fused-SiO₂ / GeO₂ Sellmeier value (Fleck–Fleming) at λ, molar-averaged by x. Packing density solves the Lorentz–Lorentz relation for film vs. bulk molar refraction.

Bulk density interpolated between fused SiO₂ (2.20 g/cm³) and GeO₂ glass (3.65 g/cm³) by mol fraction. p = ρ_film / ρ_bulk.

Empirical model: densification increases with T (Arrhenius, E_a≈0.15 eV), with N₂O/SiH₄ oxidant ratio (fuller oxidation → fewer voids/Si–H), and with ion energy (∝ RF/P). Ge incorporation from GeH₄/(SiH₄+GeH₄) is reported for reference. Calibrate constants to your tool.

Packing density vs. the swept variable of the active method.

Equations

Lorentz–Lorentz:  (n²−1)/(n²+2) = p · (n_bulk²−1)/(n_bulk²+2)  ⟹  p = R_film / R_bulk
Density ratio:  p = ρ_film / ρ_bulk,  ρ_bulk(x) = (1−x)·2.20 + x·3.65  [g/cm³]
Deposition (empirical):  p = p₀ · f_T · f_ox · f_ion,  f_T = exp[−(E_a/k)(1/T − 1/T_ref)],  f_ox = 1 − A·exp(−r_ox/r₀),  r_ox = N₂O/SiH₄,  f_ion = 1 + B·ln(1 + (RF/P)/S₀)
Ge mol fraction (dep):  x_Ge ≈ η · GeH₄/(SiH₄+GeH₄),  η≈0.6 (incorporation efficiency)
packing_density.py PackingDensity.java