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or
where
and
At relatively long times, i.e.,
and also
Eq. (3.18a) becomes
which is the well-known parabolic oxidation law for relatively long times. At the other
extreme, for relatively short oxidation times, i.e.,
Eq. (3.18a) reduces to
which is a linear law.
The rate of thermal oxidation of silicon is orientation dependent. 105,510,911 Under
typical conditions the initial oxidation rates follow the order
(110)>(111)>(311)>(511)>(100)
The order changes within the first 25 nm of the oxide to (111) > (110) with the other
orientations remaining in the same order. A qualitative correlation appears to exist
between the order of the initial rates and the density of the atoms of the planes.
The kinetics of thermal oxide growth depends on the type of oxidation, whether
using dry oxygen, wet oxygen, or steam as the oxidation agent. 510 The growth rate in
wet oxygen can be much higher, by as much as a factor of five, than that in dry oxygen.
The reaction occurs at the interface and the growth rate is dominated by the
inward diffusion of the oxidizing species for oxide films more than 40 Å thick for dry
oxidation and 1000 Å thick for wet oxidation. 115,316,377,562 There is a difference between
wet and dry oxidation in terms of the involved oxidizing species. The wet oxidation by
has faster kinetics than the dry oxidation by
due to the much larger solubility
of
in
about
than that of
about
even though
the diffusivity of
in the temperature range for thermal oxidation is about an order
562
of magnitude smaller than that of
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