Chemistry Reference
In-Depth Information
where is the ionic current, the anionic concentration in the oxide,
q
the anionic
charge, the anionic mobility,
E
the electric field,
d
(
t
) the thickness of the oxide film,
and
V
the voltage across the oxide.
The analytical solution gives
where is the number of anions per unit volume of the silicon dioxide.
The electronic current is assumed to be due to electron injection by tunneling
from the states in the electrolyte into the conduction band of
It is limited by the
space charge electronic current density described by
where is the velocity of electrons due to applied voltage across the thin film of thick-
ness
d
(
t
). The solution of the electronic current density has the form
where
A, B,
and
are constants. The results calculated from Eqs. (3.21) to (3.26)
were found by Ghowsi and Gale
201
C
to be in good agreement with experimental
data.
It is interesting that Eq. (3.23), describing the growth of an anodic oxide, is in
its mathematical form identical to the growth of a thermal oxide by Eq. (3.19), that is,
the thickness of oxide increases parabolically with oxidation time. It is reasonable in
terms of the conditions and assumptions of the two models: (1) both are under constant
driving forces—the anodic anodization is under a constant potential and the thermal
oxidation is under a concentration gradient—and (2) both assume a linear dependence
of the inward transport of the oxidants on the driving force.
3.5. PROPERTIES
Compared to thermal oxides, there is much less systematic information on the
properties of anodic oxides. Table 3.2 shows that the properties of anodic oxides vary
in a wide range. Several remarks may be made on comparing the properties of anodic
and thermal oxides: (1) the density of anodic oxides is lower; (2) the anodic oxide is
nonstoichiometric and is silicon deficient; (3) the electrical resistance is much lower
although the breakdown field strength may be similar; (4) the dielectric constant is
higher; and (5) anodic oxides have higher charge and interface state densities. Figure
3.22, using the data from Table 3.2, illustrates the ratios of anodic oxides to thermal
