Full text of DOI:10.1557/mrs2001.156

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is observed with pores in the range of
2–100 nm. For highly resistive crystalline
and amorphous p-type silicon, macropore
formation (0.4–10 ꢃm in diameter) is ob-
served below a thin layer of nanopores.13,14
Previously, macropore formation in low-
doped Si had been reported in anhydrous
electrolyte.15,16 The wall thickness is about
two times the space-charge region, whereas
the interpore distance is governed by the
properties of the silicon–electrolyte inter-
face, the resistivities of the silicon wafer,
Electrochemically
Prepared Pore
Arrays for Photonic-
and the properties of the electrolyte.17,18
A
detailed description of macroporous sili-
con formation in n-type Si can be found in
References 7 and 19. Since in n-type silicon
holes are minority carriers, the holes have
to be generated by back-side illumination.
Then they diffuse to the etch front through
the wafer. This technique puts high de-
mands on the minority carrier diffusion
length, so normally float-zone (FZ) wafers
are used. Since in this technique the holes
move by diffusion and not by drift as in
the p-type case, the strong boundary con-
dition is relaxed and thicker walls can
be obtained—up to 10 times the space-
charge region width.20 To obtain ordered
arrangements of pores, an n-type silicon
wafer with ꢀ100ꢁ orientation is first pre-
patterned by standard photolithography.
Subsequent alkaline etching produces in-
verted pyramids acting as initial pores.
Under anodic bias and back-side illumina-
tion, the wafer is then etched in hydro-
fluoric acid. The electronic holes generated
by the illumination near the back surface
diffuse through the whole wafer and pro-
mote the dissolution of silicon mainly
at the pore tips. As a result, pores grow
straight along the [100] direction with
very high aspect ratios. The arrangement
of these pores can be controlled by the
lithographic mask, and the pore diameter
can be controlled by the illumination in-
tensity. By controlling these parameters,
variations of the pore diameter with depth
can be made negligible. Figure 1 shows a
scanning electron microscope (SEM) image
of a porous Si sample, which was etched
on 0.5 ꢄ cm n-type FZ silicon substrates
having a photolithographically defined
hexagonal pore arrangement. The pores
have a center-to-center distance of 1.5 ꢃm
and a depth of 100 ꢃm. The pore diameter
after electrochemical etching is 0.9 ꢃm. By
subsequent oxidation/etching steps, the
pore diameter is increased to up to 1.36 ꢃm.
The beveled edge in Figure 1 shows the
very good depth homogeneity of the pore
diameter.
Crystal Applications
R.B.Wehrspohn and J. Schilling
Introduction
In the last few years, photonic crystals
monodomain porous alumina structures
with sizes in the micrometer range.
have gained considerable interest due to
their ability to “mold the flow of light.”1
Photonic crystals are physically based on
Bragg reflections of electromagnetic waves.
In simple terms, a one-dimensional (1D)
photonic crystal is a periodic stack of thin
dielectric films with two different refrac-
tive indices, n1 and n2. The two important
geometrical parameters determining the
wavelength of the photonic bandgap are
the lattice constant, a ꢀ d1(n1) ꢀ d2(n2), and
the ratio of d1 to a (where d1 is the thickness
of the layer with refractive index n1, and d2
is the thickness of layer n2). For a simple
quarter-wavelength stack, the center wave-
length ꢁ of the 1D photonic crystal would
be simply ꢁ ꢀ 2n1d1 ꢀ 2n2d2. In the case
of 2D photonic crystals, the concept is
extended to either airholes in a dielectric
medium or dielectric rods in air. There-
fore, ordered porous dielectric materials
like porous silicon or porous alumina are
intrinsically 2D photonic crystals.
Electrochemically grown pores in metals
and semiconductors2,3 have been studied
for about 50 years. However, only in the
last 10 years have intense research efforts
enabled the preparation of ordered arrays
of pores with pore diameters in the range
of a few nanometers to some tens of micro-
meters. The most studied materials are
porous alumina and macroporous silicon.
Porous alumina has been known for more
than a century, but only in 1995 was it first
observed that ordered arrays of porous
alumina could be achieved.4 This ordering
was initially by self-organization, and the
ordered domains were in the micrometer
range. However, electron-beam lithogra-
phy5 and a related new technique, nano-
indentation,6 allowed the preparation of
Macroporous silicon was pioneered in
the early 1990s by Lehmann and Föll.7
Very regular pore arrays in the microme-
ter range have been obtained by photo-
lithographic prepatterning. These pores
were called macropores (in contrast to
microporous silicon, which is a sponge-
like nanostructured material with photo-
luminescent properties that was also
intensively studied in the early 1990s).8
Moreover, recently a few other semi-
conductors like InP, GaAs, and GaP have
been shown to exhibit micrometer-sized
pores.9,10 Whereas standard nanostructur-
ing techniques are limited to small pore
aspect ratios (h/d ꢂ 40), and resolutions
are limited by lithographic tools, electro-
chemically prepared pores exhibit high
aspect ratios of 100–10,000 and inherent
short-range order. In the following, two
materials will be discussed in detail: macro-
porous silicon and porous alumina. Due
to the regular pore arrangements, these
materials are extremely well suited as
photonic crystals.
Macroporous Silicon
Porous silicon formed by the anodiza-
tion of p-type silicon in hydrofluoric acid
has been studied by numerous groups.
A current state-of-the-art summary is
given by Allongue.11 Three different pore-
formation regimes have been observed
experimentally as a function of the dopant
concentration. For degenerately doped
p-type silicon, a special type of mesopore
observed experimentally has been attrib-
uted to tunneling of holes through the
space-charge region.12 For moderately
doped p-type silicon, nanopore formation
Porous Alumina
Aluminum is electrochemically oxidized
to alumina (Al2O3) under positive polari-
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Electrochemically Prepared Pore Arrays for Photonic-Crystal Applications
traveling perpendicular to the pores.26
Transmission measurements on such bars
for samples with a fixed lattice constant
a ꢀ 1.5 ꢃm but varying pore diameters
were made for different polarizations and
directions. From these data, the bandgap
edges were determined as a function of
r/a (radius/lattice constant) for a range
of wavelengths; they are indicated in
Figure 3. For comparison, the theoretical
predictions obtained by solving Maxwell’s
equations by a plane-wave expansion
method are shown as solid lines.27 There is
very good agreement between theory and
experiment. The 2D silicon photonic crys-
tal exhibits a complete photonic bandgap
for both polarizations, transverse mag-
netic (TM) and transverse electric (TE), and
all in-plane directions. A maximum gap-
width to midgap frequency ratio of 17%
is obtained for r/a of 0.48. To obtain
bandgaps in the optoelectronically inter-
esting region around 1.3–1.55 ꢃm, it is
necessary to scale down the previously
described triangular pore lattice. Recently,
we have shown for the first time that it is
possible to fabricate pores with a pitch of
a ꢀ 0.5 ꢃm.28 The pores fabricated had a
radius r ꢀ 0.215 ꢃm, resulting in an r/a
ratio of 0.43 and a pore depth of 100 ꢃm.
Figure 4 shows a summary of data ob-
tained by various authors on the bandgap-
center wavelength for porous silicon and
porous alumina, as a function of lattice
constant a. For macroporous silicon, the
obtained interpore spacings range from
500 nm to 8 ꢃm,29–32 leading to photonic
bandgaps in the region from 1 ꢃm to
20 ꢃm. The electronic bandgap of silicon
is at 1.1 ꢃm, so for bandgaps below this
wavelength, absorption occurs.
creases, one should end up with a single
domain since this state represents the total
energy minimum of the system. Note that
this assumes a monocrystalline aluminum
substrate. However, both approaches seem
to be quite impractical. Therefore, a third
strategy is used. Knowing the optimum
potential U for a certain interpore distance
a, the aluminum substrate can be litho-
graphically prepatterned. Since the fea-
ture sizes are in the range of 50 nm,
electron-beam lithography prepatterning
is applied.5 Figure 2 shows a SEM image
of a hexagonally ordered pore array in
alumina prepared from an electron-beam
lithography prepatterned substrate. The
pattern has 200-nm interpore spacing, and
the anodic voltage was adjusted to 85 V,
based on the relationship between the
interpore distance a and the potential U.
The inset in Figure 2 shows the Fourier
transform of the image. Very recently,
Masuda et al. have shown that in addition
to the hexagonal lattice, the square and
honeycomb lattices can also be obtained
by appropriate prepatterning, resulting in
square or triangular pore shapes.25
Figure 1. Scanning electron microscope
(SEM) image of a perpendicular cut
(right side) and beveled cut (left side)
in a triangular macroporous silicon
array obtained by plasma etching
and subsequent polishing. Lattice
constant is 1.5 ꢃm. The pore diameter
is constant throughout the entire
100-ꢃm pore length.
zation. For certain electrolytes, which
weakly dissolve the alumina, the growth
of disordered pore arrangements has been
observed and studied for a century now.
A unique relationship between anodiza-
tion voltage U and interpore distance a
was found: a ꢀ d ꢀ 2ꢅU, where d is the di-
ameter of the pores and ꢅ ꢂ 1.2 V/nm.3,21
In 1995, Masuda and Fukuda4 first discov-
ered that after long anodization times, self-
ordered porous alumina films arranged in
a hexagonal pattern can be obtained at the
growth front. They have obtained ordered
pore arrays with lattice constants of
60 nm,22 100 nm,4 and 500 nm,6 depending
on the anodization conditions. The size of
the pore domains increases with time and
can reach micrometer size.23 Domains
touching each other have typically dif-
ferent orientations.24 Mechanical stress
between neighboring pores due to the vol-
ume expansion of alumina with respect
to the aluminum substrate has been pro-
posed as a mechanism for the self-
ordering. For example, it is observed that
the volume expansion for optimal pore
growth is in the range of 1.2–1.4, that is,
there is an incorporation yield of 60–70%
aluminum in the alumina film.5
Application to Photonic Crystals
In the following, we will briefly discuss
the optical properties of macroporous sili-
con and porous alumina photonic crystals.
Macroporous Silicon
The processed macroporous Si samples
shown in Figure 1 are very well suited to
investigate the optical properties of light
Figure 3. Bandgap edges in porous
Si photonic crystals determined from
transmission measurements as a
function of radius/lattice constant (r/a)
for a range of wavelengths. Data are
shown for transverse magnetic (TM, ꢀ)
and transverse electric (TE, ꢀ)
polarizations. The lattice constant was
a ꢀ 1.5 ꢃm. Calculated values for TM
(solid lines) show very good agreement
with the experimental data.27
Figure 2. SEM top view of
To obtain monodomain pore arrays,
three strategies are possible. First, if one
starts with a single-crystal seed, that is, a
single pore, one would expect the other
pores to arrange themselves hexagonally
around it due to repulsive forces. The sec-
ond strategy is based on the observation
of Li et al.23 As the anodization time in-
monocrystalline pore arrays in
ordered porous alumina prepared
with prepattern-guided anodization.
The prepattern with a pitch (lattice
constant) of 200 nm was induced by
using electron-beam lithography. The
inset shows the Fourier transform of
the image.5
624
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Electrochemically Prepared Pore Arrays for Photonic-Crystal Applications
Figure 4). Fabrication of more complicated
integrated-optics structures seems to be
difficult because lithographically defined
defects (missing pores) cannot be protected
during etching, as is the case for silicon.38
Summary
In the last 10 years, ordered pore arrays
with high aspect ratios have been studied
extensively. Ordered porous dielectric ma-
terials are intrinsically 2D photonic crys-
tals. Although there are a large variety of
materials exhibiting pores, to date only
silicon and alumina exhibit the extremely
high pore quality required in photonic-
crystal applications. Over the last five years,
the potential of macroporous silicon as an
infrared photonic crystal has been described
in numerous publications. Porous alumina
is a favorable candidate for photonic crys-
tals operating in the visible range.
Figure 4. Summary of experimentally
measured bandgap-center wavelengths
for porous alumina (TE gap) and porous
silicon (complete gap) as a function
of the lattice constant. (From
References 28–32, 36, and 37.)
Figure 5. Top-view SEM image of a
macroporous silicon photonic crystal
with a lattice constant of 500 nm
and an integrated two-dimensional
Mach-Zehnder interferometer structure.
The surface of the waveguide exhibits a
small surface roughness.
Defects can be made in the regular porous
Si structure by designing the proper litho-
graphic mask. In this way, specific etch
pits in the regular pattern are removed.
Electronic holes generated at the back side
by illumination are consumed by the
neighboring pores without great influence
on the position of these neighboring pores.
The result is a relatively perfect structure
with missing pores at predefined posi-
tions. These missing pores disturb the
translational symmetry and lead to local-
ized states in the forbidden spectral region.
Arranging such defects in a line creates
defect modes with transmission bands
inside the forbidden gap. As propagation
is forbidden in the surrounding medium,
waveguides with very sharp bends should
be possible, according to theory.33 In the
past, different defect structures have been
analyzed: linear34 and bent waveguide,
Y-branch, and microresonator.27 A 2D
Acknowledgments
The authors are indebted to Dr. F. Müller,
Dr. A. Birner, Dr. A.P. Li, K. Nielsch,
S. Matthias, Dr. K. Busch (Universität
Karlsruhe) and Prof. W. Hergert (Martin-
Luther-Universität, Halle) for collabo-
ration and discussions in the area of
photonic crystals. Concerning the experi-
mental realization and characterization of
the samples, the authors are grateful to
Infineon Technologies and the Universities
of Kiel, Konstanz, and Toronto. Special
thanks go to Dr. R. Hillebrand for fruitful
discussions and calculation of the bandgap
map for porous alumina (Figure 6) and
Prof. U. Gösele for substantially support-
ing the photonic-crystal activity.
Figure 6. Bandgap map of porous
alumina photonic crystals. The
maximum gap for TE polarization is at
r/a ꢀ 0.385 (11% gap midgap ratio).
There is no gap for TM polarization in
the triangular lattice. (Plane-wave
expansion with 271 plane waves,
ꢆ ꢀ 2.92.)
References
1. For a comprehensive introduction, see J.D.
Joannopoulos, R.D. Meade, and J.N. Winn,
Photonic Crystals (Princeton University Press,
New Jersey, 1995).
Mach-Zehnder interferometer with
a
500-nm interpore spacing is shown in
Figure 5. This device is designed to filter
wavelengths based on the interference of
two beams. In addition, by modulating
the pore diameter, either embedded wave-
guides or 3D photonic crystals with a
hexagonal symmetry can be obtained.35
2. A. Uhlir, Bell Sys. Tech. J. 35 (1956) p. 333.
3. F. Keller, M.S. Hunter, and D.L. Robinson,
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can be obtained is between 60 nm and
500 nm, leading to theoretical photonic
bandgaps centered at wavelengths between
200 nm and 1300 nm, depending on the
spacing. Note that the bandgap of alu-
mina (corundum) is around 10 eV, while
porous alumina has a lower bandgap due
to its amorphous nature. Experimentally,
however, absorption for wavelengths above
400 nm is negligible over the size of a pho-
tonic crystal. Masuda’s group has recently
shown transmission measurements through
porous alumina photonic crystals with
200-nm and 500-nm interpore distances
exhibiting photonic bandgaps around
600 nm36 and 1300 nm37 (see data points in
Porous Alumina
The feasibility of using monodomain
porous alumina as a 2D photonic-bandgap
material has been predicted theoretically.
Calculations show that perfectly hexago-
nal ordered porous alumina exhibits only
a photonic bandgap for TE polarized light
due to the low refractive index (n ꢃ 1.7).
Figure 6 shows the calculated gap frequency
range (hatched area) as a function of r/a.
A maximum gap-width midgap frequency
ratio of 11% is found for r/a ꢀ 0.385. For
porous alumina, the interpore spacing that
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