Final answer:
The thickness of silicon consumed during thermal oxidation is 0.44 times the thickness of SiO₂ formed. This is determined by comparing the volumes calculated from the densities and molecular weights of Si and SiO₂, showing that the volume ratio of consumed Si to formed SiO₂ is about 0.44.
Step-by-step explanation:
The thickness of silicon consumed during the thermal oxidation process to form SiO₂ is linked to the volume consumed and the conversion ratio into SiO₂. To prove that the thickness of silicon consumed is 0.44 times the thickness of SiO₂, consider the volume of silicon that would be converted into SiO₂. When silicon is oxidized, it gains oxygen atoms from the reaction with O₂ to form SiO₂. The increase in volume is due to the incorporation of oxygen atoms, which have their own volume.
In this scenario, the volume ratio between SiO₂ and Si can be deduced from their respective densities and molecular weights. Density is mass per unit volume, so using the density of Si and SiO₂ along with their molecular weights, we can establish the ratio of volumes consumed to volumes formed.
To demonstrate this, we know the density (ρ) is mass (m) over volume (V), or ρ = m/V. Silicon has a density of 2.33 g/cm³ and a molar mass of 28.09 g/mol, while SiO₂ has a density of 2.21 g/cm³ and a molar mass of 60.08 g/mol. Given that one mole of Si will produce one mole of SiO₂, we can set up the equation:
(molecular weight of Si) / (density of Si) = V_Si
(molecular weight of SiO₂) / (density of SiO₂) = V_SiO₂
For silicon: 28.09 g/mol / 2.33 g/cm³ = 12.05 cm³/mol
For SiO₂: 60.08 g/mol / 2.21 g/cm³ = 27.18 cm³/mol
Finally, we find the ratio of Si consumed to SiO₂ formed as:
V_Si / V_SiO₂ = 12.05 cm³/mol / 27.18 cm³/mol = 0.443, or approximately 0.44.
This means the volume (and thus the thickness) of silicon consumed is 0.44 times the volume (or thickness) of the SiO₂ layer that is grown.