Calculated Results
The result block appears above the calculator after submission.
Calculator Inputs
Example Data Table
These example cases help benchmark dry and wet oxidation behavior under common thermal process conditions.
| Case | Ambient | Temperature | Time | Pressure | Orientation | Initial Oxide | Typical Use |
|---|---|---|---|---|---|---|---|
| 1 | Dry O2 | 950 °C | 45 min | 1.0 atm | <100> | 10 nm | Thin gate oxide planning |
| 2 | Dry O2 | 1050 °C | 90 min | 1.0 atm | <111> | 20 nm | Higher-temperature dry growth review |
| 3 | Wet H2O | 1000 °C | 60 min | 1.0 atm | <100> | 25 nm | Field oxide pre-estimation |
| 4 | Wet H2O | 1100 °C | 120 min | 1.2 atm | <110> | 40 nm | Fast thick-oxide screening |
Formula Used
This calculator uses a linear–parabolic thermal oxidation model commonly associated with Deal–Grove silicon oxidation behavior. It estimates final oxide thickness from process time, ambient, temperature, pressure, wafer orientation, and correction factors.
Core growth relation
x² + A·x = B·(t + τ)
Final oxide thickness
x = [-A + √(A² + 4B(t + τ))] / 2
Virtual time for initial oxide
τ = (x₀² + A·x₀) / B
Linear constant relation A = B / (B/A)
Parameter meaning
- x = final oxide thickness
- x₀ = starting oxide thickness
- t = oxidation time
- A = linear length constant
- B = parabolic rate constant
- τ = equivalent time offset caused by existing oxide
Temperature scaling is handled with Arrhenius-style factors. Pressure, crystal orientation, doping, and recipe calibration apply practical multipliers. Real furnaces vary, so measured ellipsometry remains the final validation step.
How to Use This Calculator
- Select the oxidation ambient, either dry oxygen or wet steam.
- Enter process temperature and choose the correct temperature unit.
- Enter oxidation time and choose seconds, minutes, or hours.
- Set operating pressure in atmospheres.
- Choose wafer orientation for the silicon surface.
- Provide the initial oxide thickness before the new growth step.
- Adjust doping and calibration factors if plant data supports them.
- Choose the output unit and press the calculation button.
- Review the result cards, summary table, and thickness trend graph.
- Download the result package as CSV or PDF for documentation.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates thermal silicon oxide thickness after an oxidation step. It uses process inputs like ambient, temperature, pressure, time, starting oxide, and correction factors.
2. Why are dry and wet oxidation different?
Dry oxygen usually creates denser, thinner oxides with slower growth. Wet oxidation grows faster and is often preferred when thicker oxide layers are needed quickly.
3. Why does initial oxide thickness matter?
A pre-existing oxide changes the virtual starting point of the reaction. The calculator converts that starting thickness into an equivalent time shift using τ.
4. What is the calibration factor for?
It lets you tune predictions to match measured plant data. That helps compensate for furnace-specific conditions, gas purity, loading, and metrology differences.
5. Is this suitable for gate oxide design?
It can support early planning and sensitivity checks. Final device work still needs measured thickness, uniformity, and electrical verification from your actual fabrication flow.
6. What does the A constant represent?
A is the linear length constant. It reflects the early interface-reaction controlled region and helps describe faster growth behavior for very thin oxides.
7. Why is the graph useful?
The graph shows how thickness evolves over process time. It makes recipe comparisons easier and highlights how growth slows as oxide becomes thicker.
8. Can I use this for materials other than silicon oxidation?
Not directly. The built-in assumptions target silicon thermal oxidation. Other materials often require different kinetics, constants, and process-specific empirical models.