Thermal oxide thickness calculator (Deal-Grove model)
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KEY POINTS
Thermal oxide thickness on silicon follows the Deal-Grove model, x² + Ax = B(t + τ). Thin films grow linearly with time (linear law) and thick films with the square root of time (parabolic law). Wet oxidation is 5 to 10 times faster than dry; on a (100) surface at 1000 °C for one hour, dry oxidation gives about 40 nm and wet about 400 nm.
Inputs
Coefficients are Deal and Grove's (1965) values for 1 atm and lightly doped substrates. Rates change with heavily doped substrates, chlorine addition (HCl oxidation), high-pressure oxidation and the H₂/O₂ ratio of pyrogenic oxidation, so calibration against measurements on each furnace is assumed.
Thickness by temperature and time
| Temperature | 30 min | 1 h | 2 h | 4 h |
|---|---|---|---|---|
| 900 °C | 5 nm | 9 nm | 18 nm | 35 nm |
| 1000 °C | 21 nm | 38 nm | 69 nm | 119 nm |
| 1100 °C | 59 nm | 99 nm | 158 nm | 245 nm |
| 1200 °C | 116 nm | 178 nm | 268 nm | 395 nm |
How the Deal-Grove model works
In thermal oxidation, the oxidant (O₂ or H₂O) diffuses through the oxide already formed, reaches the Si interface and reacts there to grow the film. While the film is thin, the interface reaction limits growth and thickness increases linearly with time (linear law, coefficient B/A). Once it is thick, diffusion through the film limits growth and thickness increases with the square root of time (parabolic law, coefficient B). The Deal-Grove model combines both into a single equation, x² + Ax = B(t + τ).
H₂O is about three orders of magnitude more soluble in SiO₂ than O₂, so wet oxidation grows 5 to 10 times faster than dry oxidation at the same temperature. That is why thick films such as isolation and field oxides use wet oxidation, while gate oxides and thin pad oxides, where film quality matters, use dry oxidation.
FAQ
How much silicon does thermal oxidation consume?
About 0.44 of the oxide thickness. Growing 100 nm of oxide consumes about 44 nm of silicon.
Is the Deal-Grove model accurate for gate oxides?
Not below about 30 nm in dry oxidation. Real growth is faster in that range (initial enhanced oxidation), so the model underestimates thin gate oxides.
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Last updated: October 23, 2026