Silicon micromachined periodic structures for optical applications at

APPLIED PHYSICS LETTERS 89, 151110 共2006兲
Silicon micromachined periodic structures for optical applications
at ␭ = 1.55 ␮m
G. Barillaroa兲 and A. Diligenti
Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, Telecomunicazioni,
Università di Pisa, Via G. Caruso 16, 56126 Pisa, Italy
M. Benedetti and S. Merlo
Dipartimento di Elettronica, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy
共Received 8 May 2006; accepted 22 August 2006; published online 10 October 2006兲
In this letter, the authors report the design, fabrication, and characterization of a silicon
micromachined periodic structure for optical applications at ␭c = 1.55 ␮m. The microstructure,
which can be envisioned as a one-dimensional photonic crystal, is composed of a periodic array of
1-␮m-thick silicon walls and 2-␮m-wide air gaps, each one corresponding to a different odd
number of quarter wavelength at ␭c 共hybrid quarter wavelength兲. The fabrication is based on the
electrochemical etching of silicon, yielding parallel trenches with depths up to 100 ␮m. Preliminary
reflectivity measurements show the presence of a band gap at ␭c = 1.55 ␮m, as theoretically
expected. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2358323兴
In the past years, there has been a lot of interest in the
development of materials and concepts with increased optical functionality for a variety of applications. Photonic band
gap 共PBG兲 materials, also known as photonic crystals 共PCs兲,
are artificial periodic structures showing band gaps for photon propagation, which may play an important role in this
development.
One-dimensional photonic crystals 共1D-PCs兲 consist of a
periodic structure of two alternating dielectric materials with
thicknesses d1 and d2 and refractive indices n1 and n2, respectively. The periodic variation of the refractive index
gives rise to a photonic band gap, which is a forbidden gap in
the electromagnetic dispersion relation, at least for the radiation propagating in a direction normal to the layers; since the
propagation of electromagnetic radiation at wavelengths in
the gap is forbidden, these structures are very interesting as
ideal reflectors. The simplest kind of 1D-PC is the quarterwavelength stack, composed of quarter-wavelength layers,
for which the center wavelength ␭c of the PBG depends on
the thickness and refractive index of the different layers according to the relationship
␭c = 4n1d1 = 4n2d2 .
共1兲
A quarter-wavelength stack can also be considered a
Bragg grating, for which the Bragg condition p = 共␭c / 2neff兲
on the period or pitch p = d1 + d2 of the grating holds with
neff = 2n1n2 / 共n1 + n2兲. Usually, in Bragg gratings the index
step ⌬n = 兩n1 − n2兩 Ⰶ n1, n2, so that high reflectivity at ␭c is
obtained only with a high number of layers.
1D-PCs are commonly fabricated by thin-film coating
technology1 or by electrochemical conversion of a crystalline
silicon substrate into porous silicon layers.2 These structures
are designed to control the light propagation in a direction
normal to the substrate. However, in view of the fabrication
of all-optical networks, vertical 1D-PCs able to condition the
light flow parallel to the surface are required. Moreover,
structures with a photonic band gap centered at ␭c
= 1.55 ␮m would be of great interest for designing devices to
be used for communications in the third transmission wina兲
Electronic mail: [email protected]
dow of optical fibers. To obtain such a gap in a quarterwavelength structure using crystalline silicon as higher index
material 共n1 = 3.48兲 and air 共n2 = 1兲, silicon layers with thickness d1 = ␭c / 4n1 = 111 nm should be fabricated in a periodic
structure with period p = d1 + d2 = 499 nm. Since ⌬n = 兩n1
− n2兩 = 2.48, high reflectivity at ␭c is ensured by just a few
periods.
It is possible to calculate the reflectivity of this kind of
structure as a function of the wavelength by using, for
example, the characteristic matrix method.3 In Fig. 1, the
continuous trace corresponds to the reflectivity spectrum,
relative to normal incidence, for a silicon-air quarterwavelength structure formed by ten silicon-air layers, with
d1 = 111 nm and d2 = 388 nm.
For the fabrication of such a structure by silicon micromachining, an advanced lithographic tool, with a resolution
of 0.11 ␮m, close to the minimum geometry of lastgeneration integrated circuits, would be necessary. Moreover,
the typical error in the definition of dimensions in the horizontal plane, due to the etching process used to deeply remove silicon, could be as low as ±10 nm and would yield a
FIG. 1. 共Color online兲 Comparison between calculated reflectivity spectra of
a standard quarter-wavelength 共solid trace兲 and a hybrid quarter-wavelength
共dotted trace兲 1D-PC designed for applications at ␭c = 1.55 ␮m.
0003-6951/2006/89共15兲/151110/3/$23.00
89, 151110-1
© 2006 American Institute of Physics
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151110-2
Appl. Phys. Lett. 89, 151110 共2006兲
Barillaro et al.
significant relative error of about 10% on the designed thickness, thus strongly affecting the optical characteristics of the
structure.
An additional problem could limit the exploitation of
100-nm-thick silicon walls. As previously mentioned, vertical 1D-PCs could be interesting as building blocks of optical
devices used in all-optical networks, thanks to their omnidirectional high reflectivity,4 at least in the horizontal plane.
Silicon walls as high as 100 ␮m would then be necessary to
avoid excessive optical losses and the resulting structures
would have a very high aspect ratio 共up to 1000兲, which
could limit the mechanical stability of the device. The aspect
ratio is by definition h / d, where h is the height and d the
width of the walls.
To overcome this problem, the thickness of each layer
might be increased as long as the following condition is
satisfied:
␭c = 4n1d1/N = 4n2d2/M .
共2兲
In Eq. 共2兲, N and M are independent parameters, which
can only assume odd integer values, and represent the number of quarter wavelength ␭c / 4 within the high and low
refractive index layers of the stack. Equation 共2兲 reduces to
Eq. 共1兲 for N = M = 1, while for N = M = m ⫽ 1 we obtain an
mth order grating5–7 for which the Bragg condition becomes
p = m 共␭c / 2neff兲 with neff = 2n1n2 / 共n1 + n2兲 as defined earlier.
However, the choice N = M may not be the best one
when considering fabrication constraints. Starting with technologically reasonable values for the thicknesses d̃1 and d̃2,
the numbers Ñ and M̃ can be determined by using Eq. 共2兲,
thus yielding
Ñ = 4n1d̃1/␭c ,
M̃ = 4n2d̃2/␭c .
共3兲
Once N and M are determined by rounding Ñ and M̃ to
the closest odd integer, the effective thicknesses d1 and d2 to
be used for the 1D-PC fabrication are given by
d1 = ␭cN/4n1 ,
d2 = ␭cM/4n2 .
共4兲
For example, if d̃1 = 1 ␮m and d̃2 = 2 ␮m, Eqs. 共3兲, with
␭c = 1.55 ␮m, n1 = 3.48, and n2 = 1, yield Ñ = 8.98 and
M̃ = 5.16 and thus N = 9 and M = 5, so that, from Eqs. 共4兲,
d1 = 1.002 ␮m and d2 = 1.937 ␮m. In this case, since the
rounding error is small, one has d1 ⬇ d̃1 = 1 ␮m and
d2 ⬇ d̃2 = 2 ␮m. In Fig. 1, the calculated reflectivity versus ␭
of such a hybrid silicon/air quarter wavelength is shown
共dotted trace兲, compared to the previously mentioned spectrum of the standard quarter-wavelength structure. It is evident that with the hybrid structure, the stop band containing
␭c = 1.55 ␮m has a reduced width, though larger than
100 nm, and additional band gaps appear in the near-infrared
region. Both features do not represent a limitation for the
development of interesting devices for optical networks.
The theoretical relation for constructive interference in
reflection p = m 共␭c / 2neff兲 holds in this hybrid case with
m = 共N + M兲 / 2 and neff = Dn2 + 共1 − D兲n1, where D = d2 / 共d1
+ d2兲 is the material porosity. Usually, this hybrid design
approach is not experimentally exploited. Moreover, the proposed approach based on the definition of the layer thicknesses d1 and d2 gives the designer an additional degree of
freedom, for a better matching of the constraints imposed by
the available lithographic tool and by the fabrication process,
without affecting the multilayer behavior at the given wavelength.
Recently, it has been shown that vertical 1D-PCs can be
fabricated by trenching the silicon substrate using micromachining techniques.8 In Ref. 8, a periodic array of trenches
grooved in a 共110兲 oriented silicon substrate by using an
anisotropic etch has been proposed as a vertical silicon/air
1D-PC for IR range applications.
In this letter, we report the fabrication of hybrid, vertical
1D-PCs by means of electrochemical micromachining
共ECM兲 of 共100兲 n-type silicon in a HF-based solution. The
ECM exploits the photoelectrochemical etching of a n-type
silicon substrate, a well known technique for fabricating twodimensional 共2D兲- and three dimensional 共3D兲-PC,9–11 to
form high aspect ratio silicon microstructures.12 This process
allows the fabrication of structures with a maximum depth of
hundreds micrometers, with extremely limited underetching
共almost ideal anisotropy兲 and high lateral and vertical uniformity. An important feature of the technique is the possibility
of adjusting the silicon thickness, which is the parameter d1
of the designed structure, by controlling the etching current.
The main advantage of the electrochemical micromachining
for PC fabrication, with respect to standard micromachining
techniques,8 consists in the independence of the etching process from crystal directions for 共100兲 oriented Si substrates.
In fact, silicon PC fabrication by using standard anisotropic
wet etching is limited to 1D-PCs on 共110兲 substrates, due to
the dependence of standard etching on the orientation. Moreover, for a 共110兲 substrate, vertical trenches for 1D-PCs can
be only etched along the 关110兴 direction. On the contrary,
ECM allows the fabrication of 1D-, 2D-, and 3D-PCs without limitations due to the orientation. Other advantages are:
共1兲 the possibility of using 共100兲 substrate that are cheaper
and more widely used than 共110兲 substrates and 共2兲 the absence of underetching even for etching depth of hundreds of
microns. A limitation of ECM for the fabrication of 1.55 ␮m
photonic crystals can be related to the minimum distance
between two adjacent etched structures once the substrate
resistivity is chosen. In fact, the minimum distance 共in micrometers兲 is roughly equal to the square root of the substrate
resistivity 共in ⍀ cm兲, that is, about 2 ␮m for a 4 ⍀ cm resistivity. The value d2 = 2 ␮m was then chosen to comply with
this constraint. The value d1 = 1 ␮m was selected as a compromise between the opposite needs of a large value, useful
for the silicon wall robustness, and a value as close as possible to the quarter-wavelength thickness which gives a sufficiently wide band gap around ␭c.
The main steps of the fabrication process are summarized in the following. The starting material was a
550-␮m-thick n-doped silicon wafer, 共100兲 oriented and with
a 2.4– 4 ⍀ cm resistivity. A silicon dioxide layer 共100 nm
thick兲 was thermally grown on the sample. A standard photolithographic process was used for pattern definition. Arrays
of 2-mm-long straight lines, with width of 1 ␮m and pitch of
3 ␮m, were defined on the sample, covering a 2 mm2 area. A
BHF etch followed by a KOH etch were used to transfer the
pattern in the silicon dioxide and the silicon substrate, respectively. The KOH etch time was long enough to obtain
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151110-3
Appl. Phys. Lett. 89, 151110 共2006兲
Barillaro et al.
FIG. 2. SEM cross section of a 100 ␮m deep hybrid 1D-PC composed of
1-␮m-thick silicon walls and 2-␮m-wide air gaps.
full V grooves, thus forming the initial seeds for the following step. Electrochemical micromachining in a HF-based solution was then used to fabricate deep regular trenches in the
patterned substrate, as detailed elsewhere.12,13 The samples
were finally cleaved to allow scanning electron microscope
共SEM兲 observation of the cross section and to expose the
front access of the photonic crystal for reflectivity measurements. A typical result is reported in Fig. 2, which shows a
SEM cross section of a 1D-PC about 100 ␮m deep.
As preliminary optical characterization, the reflectivity
spectrum 共orthogonal incidence兲 in the wavelength range of
1.0– 1.7 ␮m was measured. Radiation from a white light
source was launched into a multimode fiber-optic Y coupler.
The output fiber 共the single branch of the Y coupler兲 was
cleaved with a 7° angle to minimize the back reflection from
the glass-air interface, and aligned in front of the device
under test, which was mounted on a mechanical xyz translator stage equipped with micrometers. For direct alignment
monitoring through a personal computer we used a 1 / 2 in.
digital camera, with an 8⫻ telecentric lens. In order to simplify the initial placement, we used red light from a He–Ne
laser, so that the light spot was clearly visible. Then, we
optimized the coupling of the broad-spectrum radiation reflected by the silicon device into the fiber by acting on the
xyz and tilt controls of the fiber holder and using a power
meter for monitoring the output power from the free end of
the fiber-optic coupler. The spectrum of the reflected optical
power was finally collected by means of a commercial optical spectrum analyzer. Measurements were performed also
using a wide-aperture focusing lens placed between the output fiber tip and the device, yielding similar results. In Fig. 3,
data acquired on 100 ␮m deep device, with 3 ␮m period and
porosity D = d2 / 共d1 + d2兲 = 0.666 共both as design parameters兲,
are compared to the calculated reflectivity, best fitted to the
measured values with a 2.98 ␮m period. We have plotted the
experimental data as normalized reflectivity, with respect to
the peak output power, to highlight that the wavelength dependence of the measured reflected power is in good agreement with the theoretically expected behavior. Whereas the
stop band at ␭ = 1.55 ␮m has been clearly demonstrated, the
theoretical gaps at 1.2 and 1.34 ␮m are not resolved in the
experimental spectrum, where they collapse into a single
large gap. It is worth to note that while in principle highorder gaps are a common feature of photonic crystals, their
FIG. 3. 共Color online兲 Comparison between measured reflectivity spectra,
acquired on a 100 ␮m deep hybrid 1D-PC with 3 ␮m period and porosity
D = d2 / 共d1 + d2兲 = 0.666, and calculated spectra, best fitted with a 2.98 ␮m
period and D = 0.666.
observation requires the fabrication of structures with a high
degree of perfection.5–7 We also measured the absolute reflectivity at ␭ = 1.55 ␮m using a semiconductor laser, focused on the device with incidence angles in the range of
5°–30°, and a power meter with a large area sensor, and
found results of the order of 70%–80%, which are quite
promising. Future work will include measurements of reflectivity at different incidence angles with linearly polarized
radiation TE and TM.
In conclusion, a simple process was developed and employed to fabricate one-dimensional photonic crystals on
silicon substrates. The validity of the design criterion, based
on the hybrid quarter wavelength, was verified by means
of reflectivity measurements, which demonstrated that the
structure strongly reflects in the wavelength range of
1.45– 1.65 ␮m. It seems thus suitable for applications in the
field of optical communications as building block of standalone micro-optic components for reflecting, deflecting, or redirecting collimated optical beams traveling in free space as
well as of sections of silicon optical benches, in which active
and passive devices are integrated as hybrid components.
Two of the authors 共S.M.兲 and 共M.B.兲 wish to thank V.
Annovazzi-Lodi for his scientific guidance throughout the
course of their research work.
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