Calculator Inputs
Defaults are editable engineering starting values. Use your measured fab constants for tighter process control.
Example Data Table
| Case | Oxidation | Temperature | Time | Initial Oxide | Estimated Final Oxide |
|---|---|---|---|---|---|
| Example 1 | Dry O₂ | 1000°C | 1.5 h | 20 nm | About 86 nm |
| Example 2 | Wet Oxidation | 1000°C | 1.0 h | 20 nm | About 420 nm |
| Example 3 | Dry O₂ | 1100°C | 2.0 h | 10 nm | About 180 nm |
Formula Used
This calculator uses the Deal-Grove thermal oxidation model. It estimates silicon dioxide growth on silicon wafers during dry or wet oxidation.
The main relation is:
x² + Ax = B(t + τ)
Here, x is final oxide thickness in micrometers. A is the linear constant. B is the parabolic constant. t is process time. τ is the equivalent time shift caused by initial oxide thickness.
The calculator first scales reference constants to the entered temperature with Arrhenius form:
B/A = (B/A)ref × exp[(-Eₗ/k)(1/T - 1/Tref)]
B = Bref × exp[(-Eₚ/k)(1/T - 1/Tref)]
It then applies pressure scaling, wafer orientation adjustment, and an empirical factor. Finally, it solves the quadratic expression for oxide thickness or rearranges the same model to solve for time.
This method is useful for process planning, furnace recipe comparison, and fast engineering studies. It should be calibrated with actual process data before production use.
How to Use This Calculator
- Select the calculation mode.
- Choose dry, wet, or custom oxidation.
- Enter wafer orientation and furnace temperature.
- For forward calculation, enter process time.
- For reverse calculation, enter target thickness.
- Enter initial oxide thickness, pressure, and exponent.
- Review or edit the reference Deal-Grove constants.
- Set the empirical factor if your fab data needs correction.
- Click the button to calculate the result.
- Download the result as CSV or PDF.
Silicon Thermal Oxide Thickness Guide
Why This Calculator Matters
A silicon thermal oxide thickness calculator helps process engineers estimate oxide growth before running a furnace recipe. It reduces guesswork. It also supports faster planning for gate oxide, field oxide, and masking layers. Small thickness errors can change device behavior. That makes a quick engineering estimate very useful.
How Oxide Growth Is Estimated
Thermal oxidation usually follows a linear and parabolic growth pattern. Thin oxides grow under a stronger interface reaction effect. Thick oxides grow under a stronger diffusion effect. The Deal-Grove model combines both behaviors in one practical equation. That is why it remains popular for semiconductor process estimation.
Inputs That Change the Result
Temperature has a strong effect on oxide thickness. A small furnace increase can raise the growth rate sharply. Process time matters too. Longer oxidation gives thicker oxide. Pressure can accelerate growth, especially when the pressure exponent is raised. Wafer orientation also influences the final estimate. Dry oxidation usually grows slower. Wet oxidation usually grows faster.
Why Editable Constants Help
No single coefficient set matches every furnace. Gas purity, tube history, loading, and measurement method can shift real results. That is why this page lets you adjust the reference linear rate, parabolic rate, activation energies, and empirical factor. You can begin with a reasonable estimate and then fit the model to measured ellipsometry data.
Best Engineering Use
Use this tool for recipe comparison, target planning, and process education. It is also useful during early design reviews. For production work, always compare the estimate with measured wafer data. Update the constants when your process drifts. That creates a more reliable thermal oxidation model and a better thickness forecast for future runs.
FAQs
1. What does this calculator estimate?
It estimates silicon dioxide thickness grown during thermal oxidation. It can also reverse the model and estimate the time needed to reach a target oxide thickness.
2. Which growth model is used?
It uses the Deal-Grove oxidation model. This model combines linear and parabolic growth behavior, which makes it useful for many engineering oxidation estimates.
3. Is dry oxidation slower than wet oxidation?
Yes. Dry oxidation usually grows thinner oxide in the same time. Wet oxidation usually grows faster and is often used when thicker oxide is required.
4. Why are the constants editable?
Real furnace behavior changes by equipment, gas purity, pressure, loading, and metrology. Editable constants let you tune the estimate to your own measured process data.
5. What is the empirical factor for?
It is a correction multiplier. Use it when your actual process grows slightly faster or slower than the current model constants predict.
6. Can I use this for production signoff?
Use it for planning and comparison first. Final production decisions should always be checked against measured oxide thickness from your real wafers.
7. Why does initial oxide thickness matter?
Initial oxide changes the equivalent time shift in the model. A wafer that already has oxide needs less additional process time to reach the same final thickness.
8. What output units are shown?
The calculator reports thickness in nanometers, angstroms, and micrometers. It also reports time in hours and minutes for convenient process review.