Calculator Inputs
Enter furnace, film, and model settings. Results appear above this form after submission.
Formula Used
The calculator uses the Deal Grove oxide growth equation:
Where:
- x is final oxide thickness in micrometers.
- B is the parabolic rate constant.
- B/A is the linear rate constant.
- A = B / (B/A).
- τ = (xᵢ² + Axᵢ) / B accounts for initial oxide.
The solved form is:
How to Use This Calculator
- Select dry oxygen or wet steam oxidation.
- Enter the furnace temperature and process time.
- Add initial oxide thickness, including native oxide if needed.
- Choose the silicon orientation and correction factors.
- Use custom constants when you have furnace calibration data.
- Press calculate and review the result above the form.
- Download CSV for spreadsheet work or PDF for reporting.
Example Data Table
| Case | Ambient | Temperature | Time | Initial Oxide | Typical Use |
|---|---|---|---|---|---|
| Gate oxide planning | Dry oxygen | 950 °C | 25 minutes | 2 nm | Thin dense oxide estimate |
| Field oxide planning | Wet steam | 1000 °C | 90 minutes | 10 nm | Faster thick oxide growth |
| Calibration check | Custom | 1050 °C | 45 minutes | 20 nm | Compare measured wafer data |
Thermal Oxide Growth Guide
Thermal Oxide Growth Basics
Thermal oxidation grows silicon dioxide on silicon. The wafer sits in a hot furnace. Oxygen or steam reacts with silicon at the oxide interface. The film becomes thicker as oxidant moves through the existing oxide. Early growth is often fast. Later growth slows because diffusion takes more time.
Why Growth Modeling Matters
A small oxide error can change capacitance, threshold voltage, leakage, and mask behavior. Engineers therefore estimate thickness before running a furnace recipe. This calculator uses the Deal Grove approach. It links time, temperature, ambient, and starting oxide thickness. It also lets you tune constants when your furnace has measured calibration data.
Dry And Wet Oxidation
Dry oxidation uses oxygen. It is slower, but it can form dense and high quality films. Wet oxidation uses steam. It usually grows faster, especially for thick field oxide layers. Real growth also depends on crystal orientation, pressure, chlorine chemistry, loading, ramp time, and furnace history. The optional correction fields help you test those effects.
Reading The Results
The final thickness shows the total oxide after the selected run. Added growth shows only new oxide. Average rate gives a simple process speed. The linear and parabolic terms show which part of the model dominates. A small thickness is more linear-rate controlled. A thick oxide is more diffusion controlled. The target estimate reverses the formula and predicts the time needed for a chosen thickness.
Using The Chart
The chart plots predicted oxide thickness across the run. It helps you see the curve shape. A nearly straight curve means surface reaction is important. A bending curve means diffusion resistance is rising. Export the table when you need spreadsheet records. Export the report when you need a quick process note.
Practical Limits
The model is a planning tool. It is not a replacement for ellipsometry, furnace qualification, or process control. Thin native oxides, very short runs, doped silicon, high pressure tools, and rapid thermal systems can need special constants. Use measured wafers to calibrate B and B over A values for production decisions. Always compare predictions with monitor wafers before freezing final recipes. Record measured runs for future tuning and audits.
FAQs
1. What does this calculator estimate?
It estimates silicon dioxide thickness after thermal oxidation. It uses time, temperature, ambient, initial oxide, and model constants to predict final growth.
2. What model is used?
The calculator uses the Deal Grove equation. It combines a linear surface reaction term and a parabolic diffusion term.
3. Is wet oxidation faster than dry oxidation?
Usually yes. Wet steam oxidation often grows oxide faster than dry oxygen. Dry oxide is often preferred when dense thin films matter.
4. Why include initial oxide thickness?
Existing oxide changes the effective starting point. The calculator adds a time shift so the model begins from the entered initial thickness.
5. What are B and B/A?
B is the parabolic rate constant. B/A is the linear rate constant. Together they define the speed and shape of oxide growth.
6. Should I use custom constants?
Use custom constants when you have measured furnace data. Production tools can vary because of flow, pressure, loading, and calibration history.
7. Can this replace wafer measurement?
No. It is a planning estimate. Use ellipsometry or another qualified method before releasing important semiconductor process recipes.
8. What does the chart show?
The chart shows oxide thickness versus process time. It helps reveal whether growth is nearly linear, mixed, or diffusion controlled.