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6. The formation of a silicon oxide (SiO2) thin film on a silicon (Si) wafer surface is an important step in the fabrication of solid-state microelectronic devices. A thin film of SiO2 serves as a barrier to dopant diffusion or as a dielectric insulator to isolate various devices being formed on the wafer. In one common process, silicon is oxidized by exposure to oxygen (O2) gas at temperatures above 700°C through this very fast chemical reaction: Si(s) + O2(g) \rightarrow SiO2(s). z = 0 100% O2 gas (constant concentration along outer surface) z = \delta(t) SiO2 Si L Molecular O2 dissolves into the SiO2 solid, diffuses through the SiO2 film, and then reacts with Si at the Si/SiO2 interface as shown in the figure above. Assume that the diffusion of O2 through the SiO2 film limits the oxidation process. Use the quasi-steady state assumption to develop a model to predict the thickness of the SiO2 layer ($\delta$) as a function of time at 1000°C. The density of solid SiO2 ($\rho_B$) is 2.27 g/cm³, and the molecular weight of SiO2 ($M_B$) is 60 g/mol. The molecular diffusion coefficient of O2 in SiO2 ($D_{AB}$) is 2.7 x $10^{-9}$ cm²/s at 1000°C. The maximum solubility of O2 in SiO2 ($C_{AS}$) is 9.6 x $10^{-8}$ mol O2/cm³ solid at 1000°C and 1 atm O2 partial pressure. What is the thickness of the film, $\delta$, at 10 hours?

          6. The formation of a silicon oxide (SiO2) thin film on a silicon (Si) wafer surface is an important step in the fabrication of solid-state microelectronic devices. A thin film of SiO2 serves as a barrier to dopant diffusion or as a dielectric insulator to isolate various devices being formed on the wafer. In one common process, silicon is oxidized by exposure to oxygen (O2) gas at temperatures above 700°C through this very fast chemical reaction: Si(s) + O2(g) \rightarrow SiO2(s).
z = 0
100% O2 gas
(constant concentration along outer surface)
z = \delta(t)
SiO2
Si
L
Molecular O2 dissolves into the SiO2 solid, diffuses through the SiO2 film, and then reacts with Si at the Si/SiO2 interface as shown in the figure above. Assume that the diffusion of O2 through the SiO2 film limits the oxidation process. Use the quasi-steady state assumption to develop a model to predict the thickness of the SiO2 layer ($\delta$) as a function of time at 1000°C. The density of solid SiO2 ($\rho_B$) is 2.27 g/cm³, and the molecular weight of SiO2 ($M_B$) is 60 g/mol. The molecular diffusion coefficient of O2 in SiO2 ($D_{AB}$) is 2.7 x $10^{-9}$ cm²/s at 1000°C. The maximum solubility of O2 in SiO2 ($C_{AS}$) is 9.6 x $10^{-8}$ mol O2/cm³ solid at 1000°C and 1 atm O2 partial pressure.
What is the thickness of the film, $\delta$, at 10 hours?

6. The formation of a silicon oxide (SiO2) thin film on a silicon (Si) wafer surface is an important step in the fabrication of solid-state microelectronic devices. A thin film of SiO2 serves as a barrier to dopant diffusion or as a dielectric insulator to isolate various devices being formed on the wafer. In one common process, silicon is oxidized by exposure to oxygen (O2) gas at temperatures above 700°C through this very fast chemical reaction: Si(s) + O2(g) →SiO2(s).
z = 0
100% O2 gas
(constant concentration along outer surface)
z = δ(t)
SiO2
Si
L
Molecular O2 dissolves into the SiO2 solid, diffuses through the SiO2 film, and then reacts with Si at the Si/SiO2 interface as shown in the figure above. Assume that the diffusion of O2 through the SiO2 film limits the oxidation process. Use the quasi-steady state assumption to develop a model to predict the thickness of the SiO2 layer (δ) as a function of time at 1000°C. The density of solid SiO2 () is 2.27 g/cm³, and the molecular weight of SiO2 (MB) is 60 g/mol. The molecular diffusion coefficient of O2 in SiO2 (DAB) is 2.7 x 10^-9 cm²/s at 1000°C. The maximum solubility of O2 in SiO2 (CAS) is 9.6 x 10^-8 mol O2/cm³ solid at 1000°C and 1 atm O2 partial pressure.
What is the thickness of the film, δ, at 10 hours?

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