Chemistry Reference
In-Depth Information
smaller pores are formed. This generalization is also applicable to the formation of
porous structures on semiconductors other than silicon.
Formation of Uniformly Spaced Pore Array.
Lehmann and Foll
763
in 1990
reported the formation of straight, smooth, and well-spaced macropore arrays on
n
-Si
using back-side illumination and surface patterning. The major difference between
back-side illumination and that in the dark is that the current is conducted through hole
diffusion from the back under illumination whereas it is by electron tunneling (or break-
down) from the front surface in the dark. Also, unlike in the dark, the current and the
potential under illumination can be independently controlled and thus a specific current
can be obtained at different potentials. Using such a separated current and potential
control plus surface patterning to define the number and spacing of the pores proved
to be a versatile method for fabrication of deep pore arrays of well-defined pore diam-
eters and interpore spacings.
763,770,1093
Among other morphological features, Lehmann
and Foll found that as with the macropores generated in the dark the diameter of pores
generated under backside illumination is closely correlated to the width of the space
charge layer of the silicon material.
In further investigations Lehmann
12,850
found that the pores propagate at similar
rates at different applied current densities. It was then postulated that all pore tips are
limited by mass transfer in the electrolyte defined by (see Fig. 5.1) in the steady-
state condition. It was further proposed that the relative rates of carrier transport in the
silicon semiconductor and mass transport in the electrolyte determine the PS morphol-
ogy of
n
-Si. At low current densities the reaction rate is limited by the transport of
carrier to the pore tips and there is no accumulation of holes so that dissolution occurs
only at pore tips while the pore walls do not dissolve because of the depletion of holes.
At high current densities the reaction at pore tips is mass transport limited and holes
accumulate at the pore tips and some of them move to the walls resulting in the disso-
lution of walls and larger pore diameters. When the concentration of holes in the walls
is close to that at the pore tips, the condition for the preferential dissolution at pore tips
disappears and PS ceases to form.
The rate of growth of macropores observed on
n
-Si is independent of current
density when the current density at the tip equals The pore diameter was related by
Lehmann
12
to the ratio of actual current density to peak current density
where
p
is the spacing between two pores. Assuming an orthogonal pattern the wall
thickness is then given as
The above equations were found to be in good agreement with experimental data gen-
erated under back-side illumination and surface patterning. However, they are only phe-
nomenological correlations of pore diameter and interpore spacing with current density,
HF concentration (embedded in
J
1
), and doping concentration (embedded in
p
) under
the specific condition. Equations (8.6) and (8.7) describe the pore diameter and spacing
