This calculator determines the thickness of silicon dioxide (SiO2) thermally grown on a pure Silicon wafer in an oxidizing ambient.
The model for thermal oxidation of silicon was pioneered by Deal and Grove in the 1960's.  Since that time, other researchers have honed the physics to account for different perturbations or regimes not originally considered by the Deal-Grove Model.
Today, thermal oxidation is perhaps the most important and contolled step in the manufacture of silicon integrated circuits, forming the gate oxide in a field effect transistor, and the tunnel oxide in flash memory devices.
This calculator uses Deal-Grove as the backbone for the calculation, and incorporates the work of other research for more accurate prediction.
This subject generates the most questions about the calculation. For a dry oxidation, you should generally use 1.0 if your lab is at sea level. The only exceptions would be if:
For wet oxidation, the gas concentration is rarely ever 100% H20 vapor (steam).
|Altitude (feet)||Altitude (meter)||Correction factor for Altitude|
|1641 ft||500 m||0.94|
|3281 ft||1000 m||0.89|
|4922 ft||1500 m||0.83|
|6562 ft||2000 m||0.78|
|8203 ft||2500 m||0.74|
|9843 ft||3000 m||0.69|
For Example: a "default" wet oxidation in a lab located at 1000m elevation should used a partial pressure of 0.92 * 0.89 = 0.82. The first factor of 0.92 accounts for our (default wet) stoichiometry, and the 0.89 factor is from the table above to account for the higher than sea level location of our laboratory. We should enter 0.82 in the partial pressure box on the form for our wet oxidation example. A (default) dry oxidation would use 1.0 * 0.89 = 0.89. The 1.0 factor is for our (default) dry stoichiometry assuming pure oxygen, and the 0.89 factor is from the table, so we should enter 0.89 in the partial pressure box for our dry oxidation.
1 atm = 101325 Pa = 1.013 bar = 760 Torr = 29.92 in Hg = 14.696 pounds per square inch.
Rapid Thermal Oxidations (where the chamber is filled with gas before the temperature is ramped) are usually limited by transient temperature control.
B.E. Deal and A.S. Grove, J. Appl. Phys. 36, 3770 (1965).
H.Z. Massoud, et. al, J. Electrochem. Soc. 132, 2685 (1985).
B.E. Deal, J. Electrochem. Soc. 125, 576 (1978).
H. Sunami, J. Electrochem. Soc. 125, 892 (1978).
E. A. Irene, J. Electrochem. Soc. 120, 1613 (1974).
R. R. Razouk, J. Electrochem. Soc. 128, 2214 (1981).
B.E. Deal and M. Sklar, J. Electrochem. Soc. 112, 430 (1965).
H.Z. Massoud, Ph.D. Dissertation, Stanford Electronics Labs, Tech. Rep. No. G502-1, Stanford Univ., Stanford, CA (1983).
E. A. Irene, J. Electrochem. Soc. 125, 1708 (1978).
H. L. Tsai, et. al, J. Electrochem. Soc. 131, 411 (1984).
A.S. Grove, et. al., J. Appl. Phys. 35, 2629 (1964).Send comments or suggestions to Eric Perozziello (run the calculator to get my email).