Biomedical Engineering Reference
In-Depth Information
is inversely related to the simulation time, a long runtime is required to obtain
an acceptable resolution, and the disadvantage in terms of computation time
can be severe.
7.2 One-Dimensional PhC Biosensors
7.2.1 Preparation and Selected Properties of Porous Silicon
One-dimensional PhC biosensors have been made using porous silicon (PSi).
PSi is obtained by the electrochemical etching of a crystalline silicon wafer
in a hydrofluoric acid (HF) solution [4]. The properties of PSi, including the
thickness of the porous layer, its porosity, the average pore diameter, and
the pore nanomorphology, can be controlled precisely. As a result, the optical
properties of PSi can be tuned widely, which makes it a very flexible material
for optical biosensors. The internal surface of PSi is very large, ranging from
a few to hundreds of square meters per gram, which makes PSi very suitable
for capturing biological targets.
The dissolution of silicon requires the presence of fluorine ions (F
−
)and
holes (h
+
). The pore initiation and growth mechanisms are qualitatively un-
derstood. Pore growth can be explained by several models [5-7]. If the sili-
con/electrolyte interface becomes rough shortly after etching starts, the sur-
face fluctuations of the Si/electrolyte interface either grow (PSi formation) or
disappear (electropolishing). In forward bias for p-type substrates, the holes
can still reach the Si/electrolyte interface as the electric field lines are focused
at the tip of the pores. Thus, holes preferentially reach the Si/electrolyte in-
terface deep in the pores, where etching can proceed rapidly (Fig. 7.7). In
contrast, no holes reach the end of the Si rods, effectively stopping the etch-
ing there. In addition to this electrostatic effect, the random walk of the holes
toward the Si/electrolyte interface makes it more likely that they reach it at
or near the pore's tip, also resulting in preferential etching at the pore's tip.
When an
n
-type substrate is used, porous silicon formation takes place in
reverse bias. Another important mechanism becomes predominant if the Si
rods are narrow enough (typically much less than 10 nm). In this size regime,
the electronic states start to be affected by quantum confinement. When the
motion of carriers is restricted in one or more dimensions, the hole states in
the valence band are pushed to lower energy by quantum confinement, which
produces a potential barrier to hole transport from the wafer to the Si rods.
The holes can no longer drift or diffuse into the Si rods and further etching
stops except at the pore's tip.
When the current density decreases, the number of holes at the pore tips
drops, which produces smaller pores. Thus, the porosity (defined as the per-
centage of void space in the material) can be precisely controlled by the etching
current density. Figure 7.8 shows the dependence of the porosity on current
