Silicon thermal oxidation calculator

Calculate silicon oxide thickness or oxidation time.

This calculator uses the Deal–Grove or Massoud models for thermal oxidation of silicon. Choose the oxidation process parameters (wet/dry, oxidation temperature, Si crystal orientation, etc.), and the calculator will return either the oxide thickness given oxidation time or the oxidation time given thickness, with a plot of results.

Calculator

Use this form to calculate either oxidation time given final oxide thickness, or thickness given time.

atm
Å
°C
Å
hr
min
s

Instructions

Select the desired oxidation process parameters in the above form and click Submit; the oxidation time and thickness are displayed, along with a plot of the oxide thickness vs. time for the duration of the process. Additional comments on the various process parameters follow.

Ambient
Choose Wet or Dry, depending on whether the gaseous oxidising species in the furnace is water vapour or oxygen, respectively. Wet oxidation is much faster than dry oxidation due to the much higher solubility of H₂O (compared with O₂) in SiO₂, yielding a higher concentration of oxidant within the oxide. The Deal–Grove model can be used for both wet and dry oxidation, whereas the Massoud model is limited to dry oxidation only.
Partial pressure
Enter the partial pressure of the oxidising species, in atm. Higher partial pressures of the oxidising species will yield higher oxidation rates. The default for wet oxidation is 0.92 atm, corresponding to the industry standard for wet oxidation using pyrogenic steam; this value may not be accurate for flash vaporisation or bubbler systems. The default for dry oxidation is 1.00 atm (100% oxygen ambient). This value can also be adjusted to account for local differences in atmospheric pressure due to altitude. In this calculator, choosing the Massoud model fixes the oxygen partial pressure at 1.00 atm.
Model
Choose Deal–Grove or Massoud. The phenomenological Deal–Grove model works well for wet and dry oxidation of thicker oxide films, but performs poorly for dry oxidation of thin oxides (less than ~500 Å), where the experimental oxidation rate is faster than predicted by this model. For such thin, dry oxides, the Massoud model is more accurate, particularly in the 800–1000 °C temperature range.
Crystal orientation
Choose (100), (111), or (110), depending on the crystal orientation of the Si surface being oxidised. Oxidation is fastest for (111) Si and slowest for (100); Deal and Grove hypothesised that this difference is due to the variation in atomic surface density (available oxidation sites) for these orientations.
Initial oxide thickness
Enter the thickness of the initial oxide present on the wafers prior to the oxidation process, in Å. In general, the oxidation process is non-linear: the oxidation rate decreases with time as the process transitions from being surface-reaction rate limited to being limited by diffusion of the oxidant through the SiO₂. As such, sequential oxidation steps should be handled by using the final oxide thickness after one step as the initial oxide for the next step (e.g., to model a dry–wet–dry sequence).
Temperature
Enter the temperature at which the oxidation reaction is taking place, in °C (limited to 700–1200 °C). The oxidation process is highly temperature dependent, due to the Arrhenius-like (exponential) behaviour of the oxidant diffusivities and surface reaction rates. The Massoud model is most accurate in the 800–1000 °C temperature range for which it was developed; use outside of this range should be done with caution, though a result will still be returned by the calculator.
Final oxide thickness
Select this option and enter a desired final oxide thickness (including initial oxide), in Å, to solve for the oxidation time.
Oxidation time
Select this option and enter a total oxidation time, in HH:MM:SS, to solve for the final oxide thickness (including initial oxide).

Results

The following results are provided when the form is submitted:

Oxidation time
Total oxidation time, in HH:MM:SS format and in minutes.
Oxide thickness
Total oxide thickness, including any initial oxide, in Å.
Si thickness consumed
Total thickness of Si consumed during oxidation, including any initial oxide (also assumed to be grown via thermal oxidation), in Å.
During thermal oxidation, silicon is replaced by roughly twice its volume of silicon dioxide. That is, for a final oxide thickness of D, the thickness of silicon consumed is 0.4407D. This value can be calculated from the densities (ρ) and molar masses (M) of Si and SiO₂, taken from CRC Handbook of Chemistry and Physics, 77th ed. (CRC Press, Boca Raton, 1996).
ρSi = 2.329 g/cm³ (crystalline)
ρSiO₂ = 2.196 g/cm³ (amorphous)
MSi = 28.0855 g/mol
MO = 15.9994 g/mol
MSiO₂ = MSi + 2 × MO = 60.0843 g/mol
Using these, we can calculate the molar volumes...
NSi = MSi / ρSi = 12.0590 cm³/mol
NSiO₂ = MSiO₂ / ρSiO₂ = 27.3608 cm³/mol
...and the final result:
%Si consumed = NSi / NSiO₂ = 0.4407.
Thickness vs. time plot
A plot of oxide thickness in Å as a function of oxidation time in minutes. Mouse-over the plot to view individual datapoints.
Please send bug reports or feature requests for this page to Aaron Hryciw.