A 900 -nm oxide is grown on (100) Si in wet oxygen at 1100^∘ C (see Appendix VI). How long does

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A 900 -nm oxide is grown on (100) Si in wet oxygen at 1100^∘...

A 900 -nm oxide is grown on (100) Si in wet oxygen at $1100^{\circ} \mathrm{C}$ (see Appendix VI). How long does it take to grow the first $200 \mathrm{~nm}$, the next $300 \mathrm{~nm}$, and the final $400 \mathrm{~nm} ?$ A square window $(1 \mathrm{~mm} \times 1 \mathrm{~mm})$ is etched in this oxide, and the wafer is reoxidized at $1150^{\circ} \mathrm{C}$ in wet oxygen such that the oxide thickness outside of the window region increases to $2000 \mathrm{~nm}$. Draw a cross section of the wafer and mark off all the thicknesses, dimensions, and oxide-Si interfaces relative to the original Si surface. Calculate the step heights in $\mathrm{Si}$ and in the oxide at the edge of the window.

A 900 -nm oxide is grown on (100) Si in wet oxygen at $1100^{\circ} \mathrm{C}$ (see Appendix VI). How long does it take to grow the first $200 \mathrm{~nm}$, the next $300 \mathrm{~nm}$, and the final $400 \mathrm{~nm} ?$
A square window $(1 \mathrm{~mm} \times 1 \mathrm{~mm})$ is etched in this oxide, and the wafer is reoxidized at $1150^{\circ} \mathrm{C}$ in wet oxygen such that the oxide thickness outside of the window region increases to $2000 \mathrm{~nm}$. Draw a cross section of the wafer and mark off all the thicknesses, dimensions, and oxide-Si interfaces relative to the original Si surface. Calculate the step heights in $\mathrm{Si}$ and in the oxide at the edge of the window.

Key Concepts

Step Height Formation at Oxide-Silicon Interfaces

When a patterned oxide undergoes subsequent oxidation, the differing oxidation rates in exposed versus covered areas lead to step formation at the oxide-silicon interface. Calculating the step height involves understanding the oxide consumption from the silicon during oxidation and the additional oxide growth, which creates a topographical change that is critical for device performance and alignment in integrated circuits.

Diffusion Through Oxide Layers

Diffusion of the oxidizing species (such as oxygen or water vapor in wet oxidation) through the already grown oxide is a key factor that limits the oxidation rate in the parabolic regime. The rate at which these species transport through the dielectric determines how quickly further oxidation can occur, making it a central aspect of thorough oxidation kinetics analysis.

Selective Etching and Reoxidation Processes

In microfabrication, patterning the oxide layer via etching and then subjecting the wafer to a secondary oxidation step (reoxidation) is common. This process results in differential oxide growth where regions of bare silicon oxidize at a different rate compared to areas already covered by oxide. Understanding these mechanisms is essential for predicting changes in oxide thickness and for controlling device geometries.

Deal?Grove Oxidation Model

This model provides a fundamental framework for understanding thermal oxidation of silicon. It describes how the oxide thickness grows as a function of time, temperature, and oxidizing ambient by combining both reaction-rate and diffusion-limited processes. The model separates oxidation into a linear (reaction-rate limited) regime at very thin oxide thicknesses and a parabolic (diffusion limited) regime at larger thicknesses, tying the kinetics directly to the governing physical parameters.

Linear and Parabolic Growth Regimes

The linear regime describes oxidation kinetics when the oxide is very thin and the interface reaction at silicon is the rate?limiting step, while the parabolic regime occurs for thicker oxides when the diffusion of oxidizing species through the existing oxide layer limits the growth rate. These regimes are critical for predicting and calculating the time required to produce specific oxide thicknesses during thermal oxidation processes.

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