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.
Use this form to calculate either oxidation time given final oxide thickness, or thickness given time.
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.
- 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.
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.
Calculation detailsDuring 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/molUsing these, we can calculate the molar volumes...
MO = 15.9994 g/mol
MSiO₂ = MSi + 2 × MO = 60.0843 g/molNSi = MSi / ρSi = 12.0590 cm³/mol...and the final result:
NSiO₂ = MSiO₂ / ρSiO₂ = 27.3608 cm³/mol%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.