Deal-Grove Thickness Calculator
Solve the zero-initial-thickness Deal-Grove relation x² + A·x = B·t for thermal oxide thickness.
Description
Calculate thermal silicon oxide thickness from Deal–Grove linear and parabolic rate constants and oxidation time.
The Deal–Grove linear-parabolic model connects thermal oxidation time to silicon dioxide thickness. This calculator solves x² + A·x = B·t for growth from zero initial oxide and reports the positive thickness root.
When to use Deal–Grove Oxide Thickness Calculator
- Estimate thermal oxide thickness from fitted A and B constants
- Compare reaction-limited and diffusion-limited oxidation regimes
- Check a hand calculation of the zero-initial-thickness Deal–Grove relation
How the calculation works
At thin oxide, the A·x term makes growth approximately linear; at thick oxide, x² dominates and thickness approaches √(B·t). The implementation uses a rationalized root to retain thin-growth precision.1
x = 2B·t / (√(A² + 4B·t) + A) Interpreting the result
A and B must use the displayed nm and hour units. Published constants in micrometers or minutes must be converted before entry.
Assumptions and limitations
- The model assumes zero starting oxide; a nonzero initial oxide requires the Deal–Grove time shift τ.
- A and B depend on temperature, oxidant, pressure, crystal orientation, and process conditions.
- Classic Deal–Grove behavior can be inaccurate for very thin dry oxides, so process data remains necessary.
References
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Process and Device Simulation of Atomic Layer Deposition — Stanford University