Chemistry Reference
In-Depth Information
flat surface. For
n
-Si under anodic potentials the current conduction is by electron tun-
neling from the surface into the conduction band. Note that the steep band bending due
to decreasing radius of curvature increases the number of energy levels for electron
tunneling. In the case shown in Fig. 8.64 the available energy range for tunneling at
a tunneling distance of 40 Å is about 180mV for a flat surface whereas it is about
470mV for a curved surface with a radius of curvature of
Similar analysis can be made for other types of materials. Thus, as a generaliza-
tion, the curvature of a surface causes field intensification, which results in a higher
current than that on a flat surface. Although the detailed current flow mechanism can
be different for different types of materials under different potential and illumination
conditions, the effect of surface curvature on the field intensification at local areas is
the same. The important point is that the order of magnitude for the radius of curva-
ture that can cause a significant effect on field intensification is different for substrates
having different widths of the space charge layer. Surface curvature determines the
vector of the field, that is, magnitude and direction of the field near the surface and is
a principal factor determining the dimensions of the pores.
Potential Drop in the Substrate.
For a moderately or highly doped material the
potential drop due to ohmic resistance in the substrate is very small. For example, for
a substrate with a resistivity of the potential drop in the 0.1 mm
thick substrate at a current density of is 0.01mV, which is insignificant
relative to a potential in the millivolt range that is required to significantly affect the
rate of charge transfer process at the interface. However, when the resistivity is on the
or larger the potential drop inside the substrate is in
order of
the millivolt range and starts to affect the distribution of the change of potential in the
current path.
For a solid between two spherical surfaces shown in Fig. 8.65, the resistance can
be described by
