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5. Modeling of Oxidation

Thermal oxidation of silicon is one of the most important steps in fabrication of highly integrated electronic circuits, being mainly used for efficient insulation of adjacent devices. Those parts of silicon which shall not be oxidized are masked by a layer structure of silicon nitride that is not effected by an oxidation. Exposed parts of already existing silicon oxide are penetrated by the oxidant (oxygen diffusion), which reacts finally at the interface of silicon and silicon dioxide to form new dioxide. This chemical reaction consumes silicon, and due to the increased volume of the newly generated dioxide the old dioxide layer is lifted up.

From the mathematical point of view the problem can be described by a coupled system of partial differential equations:

During the last decades several approaches for simulation of two-dimensional local oxidation of silicon have been published. They are all based on the fundamental work of Deal and Grove [Dea65] who described the phenomenon in one dimension (see also Chapter 2). The common feature of all approaches is that they decouple the diffusion and displacement problem into a sequence of quasi-stationary time steps. The calculated results of the diffusion are used to extract the necessary conditions for the free boundary problem. The displacement computation yields the geometry of the newly generated silicon dioxide range for the next time step.

All published approaches can be classified essentially into three groups:

Moreover, none of the published approaches seems to be able to treat problems where not only the geometry but also the topology of the silicon dioxide range changes.




next up previous
Next: 5.1 Mechanical Models Up: PhD - Mustafa Radi Previous: 4.8.4 Three-Dimensional Temperature Distribution
Mustafa Radi
1998-12-11