Parabolic Oxide Thickness Calculator
Compute diffusion-limited thermal oxide thickness in the parabolic regime as sqrt(B·t).
Description
Estimate diffusion-limited thermal oxide thickness as the square root of parabolic rate constant times oxidation time.
The parabolic approximation describes the thick-oxide regime of the Deal–Grove model, where oxidant diffusion through the existing oxide controls growth. It intentionally omits the linear reaction term.
When to use Parabolic Oxide Thickness Calculator
- Estimate thick thermal oxide growth when the parabolic regime applies
- Check the √time scaling of diffusion-limited oxidation
- Compare with the complete Deal–Grove result to judge whether the linear term matters
How the calculation works
Oxide thickness is √(B·t). Because B is entered in nm²/hour and time in hours, their product is nm² and its square root is nanometers.1
oxide thickness = √(parabolic rate constant B × oxidation time) Interpreting the result
Quadrupling time doubles predicted thickness. That square-root behavior is a key distinction from a constant deposition-rate model.
Assumptions and limitations
- Use this only when the linear term A·x is negligible compared with x².
- The calculation assumes zero effective initial oxide or time shift.
- B must be characterized for the actual oxidant, temperature, pressure, orientation, and units.
References
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Process and Device Simulation of Atomic Layer Deposition — Stanford University