Chemistry Reference
In-Depth Information
dissolution through the formation and dissolution of oxide is insensitive to the surface
geometrical factors. Formation of an oxide film masks the semiconductor properties of
silicon.
The fundamental reason for the formation of pores is that the rate of electro-
chemical reactions on a semiconductor is sensitive to the radius of curvature of the
surface. This sensitivity can either be associated with the width of the space charge
layer or the resistance of the substrate. Thus, when the rate of the dissolution reactions
depends on the width of the space charge layer, formation of pores can in principle
occur in a semiconductor electrode, not just on silicon. The specific porous structures
are governed by the relative significance in spatial and temporal scales among the geo-
metric dimensions, reactions and their rates, physical regions of the current path, and
so on. Because different dimensions, rates, regions, and so on may be significant in the
formation process, the mechanistic details for the formation of each specific type of PS
morphology vary with situations. As a global generalization, the conceptual analysis
for the mechanisms involved in the formation of PS can be called the curvature-
relativity model.
The types of PS can be categorized into three groups according to this model: (1)
Space charge layer controlled; this includes all PS except for the macro PS formed on
p-
Si The diameter of the pores in this group is comparable to the width of the space
charge layer. (2) Substrate resistance controlled; this includes the macro PS formed on
lowly doped
p
-Si and possibly on lowly doped
n-
Si (a prediction). (3) Photocarrier con-
trolled; this includes two-layer PS (micro PS for > SCL and macro PS for
< SCL) and the micro PS structures resulting from photocorrosion.
Figure 8.75 summarizes PS features according to the formation conditions
defined by the kinetics relative to current and HF concentration. The lines defining the
regions are determined by the nature of the reactions and are independent of the doping
type and concentration (see Fig. 8.5). One important factor governing the change of
one region to another shown in Fig. 8.75 is the formation and coverage of an anodic
oxide film on the surface. The coverage of oxide on the surface increases from zero in
PS region A to only at pore tips in PS region B to part of the surface in the transition
region to full coverage in the electropolishing region. The actual size of the pores under
a given anodization condition is primarily determined by doping concentration. Most
of the other morphological features can be phenomenologically correlated with pore
diameter as illustrated in Fig. 8.56. The mechanisms responsible for these features are
determined by the various factors involved in the formation processes discussed in
Section 8.6.2. The characteristics of fundamental reaction processes and the rate-
limiting steps in these reactions are given in Table 5.8.
A quantitative description of the diverse morphological features of PS
requires the integration of the aspects discussed above as well as the fundamental
reaction processes involved in silicon/electrolyte interface structure, anodic dissolution,
and anodic oxide formation and dissolution as detailed in Chapters 2-5. Any mathe-
matical formulation for the mechanisms of PS formation without such a global inte-
gration would be limited in the scope of its validity and in the power to explain details.
In addition, a globally and microscopically accurate model would also require the full
characterization of all of the morphological features of PS in relation to all of the
