Chemistry Reference
In-Depth Information
As shown in Fig. 7.40, in general, the dissolution of a silicon surface involves
three essential species: A, etching species such as in the electrolyte; active
silicon atoms on the surface; and h, charge carriers from the semiconductor. The etch
rate of the surface can then be expressed as
where
k,
a, b, c, are constants. In KOH, the dissolution is of chemical nature, meaning
the etching is independent of [h]. Equation (7.21) is reduced to
On the other hand, in HF solutions the dissolution reaction strongly depends on
carrier concentration and the etch rate is described by Eq. (7.21). The reason that the
planar etching rate in HF is isotropic can be attributed to the fact that the etched
surface in HF is rough at an atomic scale. Therefore, the density of active silicon
atoms on such a rough surface is similar for different orientations. In the electro-
polishing region, where the dissolution proceeds through oxide formation and dissolu-
tion, the etching is isotropic due to the fact that amorphous anodic oxide is identical
on surfaces of different orientations. The etching in this region is intrinsically
isotropic.
Thus, the mechanistic model described above is consistent with the characteris-
tics of the anisotropic etching of silicon in alkaline solutions as well as the isotropic
planar etching in HF solutions. It is also a useful simple model for explanation of the
etched features and surface roughness as will described in the following sections.
7.6.3. Basic Features of Anisotropically Etched Surfaces
Anisotropic dissolution of crystal surface results in the formation of surface
contour whose geometric features depend on the crystal orientation.
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During steady-
state etching the etched surface profile exhibits a characteristic shape—either convex
or concave.
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A convex surface will be bounded by fast etching planes whereas a
concave surface will be bounded by slow etching planes. As shown in Fig. 7.42(a), two
planes intersecting in a concave configuration constitute a stable configuration if there
is no other plane with lower etching rate lying between them. In such a case, the etch
rate as a function of orientation must exhibit a maximum at the intersection of these
planes. On the other hand, the intersection of two planes in a convex configuration is
stable if there is no other plane with higher etching rate lying between them as shown
in Fig. 7.42(b).
Etching of a sphere, which is a convex surface, will result in a polyhedron
bounded by faces that exhibit high etch rates, and vertices corresponding to minima in
etch rates.
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Because the fast etching planes vary with solution composition, the faces
and vertices of etched polyhedron also vary. For example, in KOH solutions the poly-
hedron has six 4-sided <100> vertices and eight 6-sided <111> ones, defining 24 {320}
fast etching planes.
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In CsOH solution the polyhedron has eight 3-sided <111> ver-
tices and six 4-sided <100> giving 12 {110} fast etching planes. A sphere etched in
