JOURNAL OF APPLIED PHYSICSVOLUME 91, NUMBER 10

15 MAY 2002

Dichroic behavior of multilayer structures based on anisotropicallynanostructured silicon
J. Diener,a) N. Künzner, D. Kovalev, E. Gross, and F. Koch
Physik-Department E16, Technische Universität München, D-85747 Garching, Germany

M. Fujii
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657-8501, Japan

共Received 17 December 2001; accepted for publication 27 February 2002兲
Multilayer structures of anisotropically nanostructured 共birefringent兲 silicon have been fabricatedand studied by polarization-resolved reflection and transmission measurements. We demonstrate thatstacks of birefringent porous silicon layers with alternating refractive indices and thicknesses act asdichroic Bragg reflectors or dichroic microcavities with a transmission/reflection dependent on thepolarization direction of the incident light. The possibility of separate fine tuning of two
orthogonally polarized transmission/reflection bands and their spectral splitting is demonstrated.
© 2002 American Institute of Physics. 关DOI: 10.1063/1.1471581兴

I. INTRODUCTION

During recent years, nanostructuring of semiconductors
has been considered as an alternative way to search for new
materials. Material properties, especially optical ones, can be
modified by reducing the dimensions or by proper engineering of macroscopic structures on the nanometer scale. A key
idea is the introduction of optical anisotropy due to the reduction of the symmetry of bulk crystals via ordered nanostructuring. The simplest approach based on drilling holes insemiconductors has proven to be an effective strategy for avariety of optical applications.1– 4 However, not all photonic
applications require a strictly ordered distribution of holes. A
quasiuniform distribution will be sufficient for specific applications under conditions when the dimensions of both holes
and skeleton fragments are much smaller than the wavelength of the propagating light. Under these conditions thelayers are optically homogeneous media where light propagates without internal scattering. The random spatial distribution of holes implies simply a reduced refractive index of
the layers. Its value is defined by the fraction of empty spaceinside the layers.5 The easiest approach leading to dielectricnanostructuring is electrochemical etching of bulk semiconductor substrates resulting in their porous structures.
The porous modification of silicon 关porous silicon 共PSi兲兴
consists of a sponge-like network of interconnected silicon
共Si兲 nanocrystals. Due to the reduced size of Si nanocrystals
and voids, in the range of a few nm, PSi is a quasicontinuous
optical medium for the visible and infrared spectral range.
Another important property of porous silicon is the simplicity of controlling the mean refractive index of the layers
and their thickness via variations of the etching current density and the time of etching, respectively.5,6 This enables
modification of their dielectric properties in a controlledmanner and production of a stack of alternating layers witha兲

Electronic mail: jdiener@physik.tu-muenchen.de

0021-8979/2002/91(10)/6704/6/$19.00

6704

different refractive indices and thicknesses. A variety of PSibased one-dimensional photonic structures like distributed
Bragg reflectors 共DBRs兲,7,8 microcavity resonators,9–11 antireflection coatings,12 and waveguides13 have been realized so
far on the basis of this approach.
All these devices have been prepared from 共100兲 oriented Si wafers. For this surface pores propagate preferentially along the direction of the current flow and the remaining Si nanocrystals are aligned along the 关100兴 direction
共perpendicular to the surface of the specimen兲.5,14 Consequently, PSi layers prepared from 共100兲 Si wafers exhibit adielectric in-plane isotropy.
A dielectric in-plane anisotropy can be achieved bychanging the surface orientation of the Si wafer. The rate ofpore propagation under electrochemical etching varies fordifferent crystallographic orientations of Si wafers.5 Therefore a macroscopic alignment of the pores and remnant
nanocrystals in a certain direction15 can be realized. Si due toits cubic lattice is not an anisotropic crystal but if the poresare formed to some extent ordered, the symmetry of thespecimen can be changed and its porous modification becomes highly optically anisotropic due to anisotropic dielectric nanostructuring. For instance, PSi layers produced from共110兲 oriented Si wafers exhibit nanocrystal and pore elongation in the 关 11̄0 兴 surface plane direction.16 This macroscopic pore alignment has a very important implication forthe optical properties of the layers. According to effective
medium predictions this leads to a uniaxial surface symmetry
with a refractive index n 关 11¯ 0 兴 being different from n 关 001兴 ,where subscripts denote the polarization direction of the incident light. Indeed, as it has been demonstrated in Ref. 16
the value of the optical anisotropy achieved n 关 11¯ 0 兴 ⫺n 关 001兴
⫽0.25 exceeds that of natural birefringent crystals.
We found the optical anisotropy of porous Si layers to be
crucial for nonlinear wave interactions. The anisotropy levelis high enough to compensate the normal dispersion of bulk
Si and to achieve phase matching conditions for nonlinear© 2002 American Institute of Physics

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002

optical wave interactions.17 However, an ideal structure fornonlinear optical applications has to exhibit additionally light
localization properties for the fundamental and higher harmonics of the propagating wave. For instance, a microcavity,
consisting of a ␭/2 layer placed between two distributed
Bragg reflectors made from pairs of alternating ␭/4 layers ofhigh and low refractive indices acts as a multipass cell confining radiation and causing field enhancement inside. Therefore optical devices based on a stack of PSi layers acting asa microcavity 共PSM兲 with each layer exhibiting an in-planebirefringence level which is high enough to achieve phasematching conditions 共i.e., having variation of the refractive
index in three dimensions兲 seem to be almost ideal candidates for nonlinear optical interactions.
These structures yield optical effects which are difficult
to achieve with conventional stacks of isotropic dielectrics.
For instance, DBRs from anisotropically nanostructured
共110兲 silicon have two distinct reflection bands depending on
the polarization of the incident linearly polarized light.18 We
study the optical properties of multiple in-plane optically anisotropic PSi layers in detail and demonstrate that porous
silicon-based polarization-dependent dichroic Bragg reflectors and microcavities are promising for photonic applications of nanostructured Si in the visible and infrared spectral
range.
This article is structured as follows: Section II deals withthe sample preparation procedure and experimental details.
Optical parameters of single optically anisotropic PSi layers
and modeling of their optical properties are discussed in Sec.
III. The possibility of fine spectral tuning of two orthogonally polarized reflection/transmission bands and their relative separation for DBRs is demonstrated in Sec. IV. Opticalinvestigations of a dichroic 共110兲 porous silicon microcavity
are described in Sec. V.
II. EXPERIMENTAL DETAILSPSi multilayer structures have been produced by electrochemical etching 共in the dark兲 of 共110兲 oriented p-type 共Boron兲 doped Si wafers with a resistivity of 1.5 m⍀ cm. The
etching solution was a 1:1 共by volume兲 mixture of C2 H5 OH
and concentrated aqueous HF acid 共50%兲. For the preparation of the stacks two current densities were used: 22
mA/cm2 (⫽J 1 ) and 70 mA/cm2 (⫽J 2 ). To characterize
single layer optical parameters separate layers etched with J 1
and J 2 have been prepared. Multilayer structures 共ten J 1 /J 2
cycles兲 were grown using etching at alternating low and highcurrent densities 共computer controlled current source兲 asschematically depicted in the upper left part of Fig. 1. A
temporal variation of the etching current density results in adielectric stack consisting of porous silicon layers having
different thicknesses and average porosities. Actually, theetching procedure is identical to that one for PSi multilayersgrown from 共100兲 oriented Si wafers.19 In the upper rightside of Fig. 1 we show the basic geometrical arrangement 共inreflection geometry兲 and the crystallographic frame used.
The surface of the sample is illuminated under almost normal
incidence by unpolarized light from a halogen lamp.
Reflected/transmitted light is analyzed by a Glan–Thomson

Diener et al.

6705

FIG. 1. The upper left part depicts the formation of multilayer structuresfrom anisotropically nanostructured silicon. During the electrochemical
etching of 共110兲 oriented silicon wafers the etching current is periodicallyvaried in time between low (J 1 ⫽22 mA/cm2 ) and high (J 2 ⫽70 mA/cm2 )current density. This results in a dielectric stack with porous layers etched at
J 1 共thickness d 1 兲 and J 2 共thickness d 2 兲. The upper right side illustrates thegeometrical arrangement 共in reflection geometry兲 and the used crystallographic frame. 共a兲 and 共b兲 The spectrally and polarization-resolved reflectionof the same 共110兲 distributed Bragg reflector 共d 1 ⫽95 nm, d 2 ⫽217 nm兲. In
共a兲 关共b兲兴 the polarization vector of the reflected light 共E兲 is parallel to the关001兴 关 11̄0 兴 crystallographic directions in the 共110兲 surface plane 共solidlines兲. The dashed lines are results of calculations.

prism with polarization vector 共E兲 aligned either parallel tothe 关001兴 or to the 关 11̄0 兴 crystallographic direction in the
共110兲 surface plane. The polarized light was dispersed with amonochromator and detected with a charge coupled device
共CCD兲. All spectra are normalized to the intensity of theincident light. Transmission measurements were performed
with free-standing samples detached from the Si substrate by
an electropolishing step. The specimens were fixed on a copper holder with a small pinhole 共2 mm diameter兲. No noticeable difference has been observed when illuminating thespecimen from the front or the back surface.
III. MEASURED AND CALCULATED OPTICAL
PARAMETERS OF A SINGLE OPTICALLYANISOTROPIC PSi LAYER

From spectrally and polarization-resolved measurementsof reflection of linearly polarized light from a single 共110兲
PSi layer prepared via etching with current densities J 1 or J 2
the corresponding refractive indices 共n 关 11¯ 0 兴 and n 关 001兴 兲 andtheir anisotropy (⌬n⫽n 关 11¯ 0 兴 ⫺n 关 001兴 ) were evaluated. Theirvalues are given in Table I. The in-plane optical anisotropyof the layers is evident: the refractive index for the electricfield vector parallel to the 关 11̄0 兴 crystallographic direction issubstantially larger. As seen in the table, ⌬n varies for dif-

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

6706

Diener et al.

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002
TABLE I. n 关 011兴 and n 关 11¯ 0 兴 denote the measured refractive indices for single layers of 共110兲 PSi etched withcurrent densities J 1 and J 2 for different directions of E with respect to the crystalline 关001兴 and 关 11̄0 兴
directions. F 关 001兴 and F 关 11¯ 0 兴 are the corresponding calculated Si volume filling factors 共Bruggeman effective
medium theory兲.

J1J2n 关 001兴(E储 关 001兴 )n 关 11¯ 0 兴(E储 关 11̄0 兴 )⌬n(n 关 11¯ 0 兴 ⫺n 关 001兴 )F 关 001兴
共from n 关 001兴 兲

F 关 11¯ 0 兴共from n 关 11¯ 0 兴 兲

2.39
1.55

2.55
1.75

0.16
0.2

42.2%
70.5%

36.8%
63.4%

ferent current densities 共J 1 and J 2 兲. This difference can becaused by the geometrical specifics of the standard etchinggeometry for 共110兲 oriented Si wafers: the direction of theetching current flow is always normal to the 共110兲 Si surface.
While the etching in the 关001兴 crystallographic direction isperpendicular to the current flow, the equivalent 关010兴 and关100兴 directions have components parallel to the direction of
the current. The etching rates parallel and perpendicular tothe current direction are not equal and depend on the doping
level of the substrate and the current density. Therefore theoverall morphology of 共110兲 PSi layers and consequently ⌬ndepends on these two parameters. This is similar to the wellstudied microstructure formation of conventional 共100兲
layers.5,6 This is in our opinion the reason for the difference
between ⌬n values for 共110兲 oriented PSi layers etched with
J 1 and J 2 .
To correlate the porosities of the PSi layers and theirrefractive index values for 共100兲 PSi layers the Bruggeman
effective medium approximation has been successfully
used.20,21 We found that similar to 共100兲 PSi layers the absolute gravimetrically measured porosity 共␳兲 rises with increasing current density. However, for 共110兲 PSi layers ␳ is anaverage value and does not allow one to describe their anisotropic morphology.
A detailed description of the optical anisotropy parameters of a single PSi layer is crucial for the understanding of
the overall spectral and polarization-dependent response of
the multilayer structures. Therefore contrary to the ordinary
Bruggeman model describing an isotropic medium, different
volume filling factors F 共volume fraction of empty spaceinside the layer兲 have been assumed to account for thepolarization-dependent refractive index values. We used thesimplified assumption that the 共110兲 porous layers consist of
dielectric spheres having different F for the two principal
in-plane directions. Solving the equation:21

冉

⑀ ⫺⑀

冊

i
av
⫽0,
兺i F i ⑀ i ⫹2
⑀ av

共1兲

with F i being the volume fraction of the ith medium 共either
Si or air兲, ⑀ i their dielectric constant, and ⑀ av the mean dielectric constant of the mixture, the two principal F values
are calculated and given in the table. The spectral dispersionof the dielectric function of bulk Si leads to wavelength dependent values of n 关 11¯ 0 兴 , n 关 001兴 , and ⌬n. Therefore the Fvalues are evaluated in the near infrared region 共at 1240 nm兲
where the refractive index of Si is almost dispersionless. For
the calculation of the optical properties of 共110兲 PSi single
and multilayer systems in the visible spectral range the dis-persion of the dielectric function of Si has been taken into
account. Transmission and reflection spectra of the DBRs
and PSMs are calculated applying the 2⫻2 transfer matrix
method.22 The two principal values of the dielectric constantof 共110兲 PSi at a given wavelength are determined with the
Bruggeman formula 关Eq. 共1兲兴 based on two different F values.
IV. DICHROIC BRAGG REFLECTORS

Figure 1 shows the spectra of the polarization-resolved
reflection of a 共110兲 DBR. Part 共a兲 shows the spectrum of thereflected light being polarized parallel to the 关001兴 crystallographic direction. In part 共b兲 the polarization direction isalong the 关 11̄0 兴 crystallographic direction. A DBR exhibits ahigh reflectivity band with the Bragg wavelength (␭ Bragg)
approximately at its center. ␭ Bragg depends on the thicknessof the layers (d 1 ,d 2 ) and the corresponding refractive indices (n 1 ,n 2 ). The mth order of the Bragg peak is given by:23m␭ Bragg⫽2 共 d 1 n 1 ⫹d 2 n 2 兲 .
Contrary to 共100兲 porous silicon DBRs8 the spectral position of m␭ Bragg depends on the polarization direction of theincident light. For E储 关 001兴 the first order Bragg band is centered around 1060 nm 关Fig. 1共a兲兴 while it is significantly
shifted towards longer wavelength 共⬃1170 nm兲 for E储 关 11̄0 兴
关Fig. 1共b兲兴. For high quality dichroic structures it is essentialthat both reflection bands do not overlap what is not the casefor the first order Bragg reflection bands in Fig. 1. However,the second order bands in the visible spectral range are fully
spectrally separated. The second order bands are twice narrower, as expected. The dispersion of the dielectric functionof bulk Si leads to their spectral positions which are notexactly a half of the first order.
Dashed lines show reflectance spectra calculated on thebasis of experimentally measured optical parameters of
single layers. We found that for exact coincidence between
the experimentally measured and calculated reflectance spectra a 10% correction of the filling factors towards higher
values is required for thin layers etched with J 1 (d⬍150 nm). This indicates that optical parameters of a thinsingle layer and those in a stack are slightly different. We
believe that the reason for this is a very short etching time
共shorter than 1 s兲 used to produce thin layers and a relatively
slow response of the electrochemical reaction on the steplike switching of the current. After this correction the wavelength and the width of the first and second order Braggbands are well reproduced by the calculations for both polar-

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

Diener et al.

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002

FIG. 2. The polarization-resolved reflection spectrum of two 共110兲 distributed Bragg reflectors, having different spectral separation of the two orthogonally polarized reflection bands 共solid lines兲. The reflection maximum
at the high 共low兲 energy side in 共a兲 and 共b兲 corresponds to the polarization
vector of the reflected light parallel to the 关001兴 ( 关 11̄0 兴 ) crystallographic
directions in the 共110兲 surface plane. d 1 (d 2 ) denotes the thickness of thelayer etched with current density J 1 (J 2 ). Dashed lines are results of calculations.

ization directions 共dashed lines in Fig. 1兲. The thicknesses
used for the calculations (d j 1 ⫽95 nm,d J 2 ⫽217 nm) arewithin the range of estimates based on the etching time 共approximately 90 and 200 nm兲.
The separation of the second order Bragg bands in Fig. 1
is 57 nm 共618 nm for E储 关 11̄0 兴 and 561 nm for E储 关 001兴 兲 andis defined by the birefringence level (⌬n) of each layer. The
large variation of ⌬n, here around 20%, allows one to adjust
the separation of the two reflection bands. By growing the
thick layers with larger ⌬n 共here at current density J 2 兲 andthin layers with lower ⌬n the separation of the Bragg bands
can be increased and vice versa.
Figure 2 shows two extreme cases. The relative thicknesses of the multilayers were intentionally chosen toachieve the appearance of the second order Bragg peaks inthe same spectral range for both cases. In part 共a兲 the layerswith larger ⌬n are very thick and the separation from thesecond order Bragg bands is around 75 nm 共668 nm forE储 关 11̄0 兴 and 593 nm for E储 关 001兴 兲. Part 共b兲 of the same
figure shows an example of a 共110兲 DBR with the thicklayers having low ⌬n. The corresponding wavelength difference between the reflection maxima is 38 nm 共618 nm forE储 关 11̄0 兴 and 580 nm for E储 关 001兴 兲. The spectral separationof the Bragg bands is well reproduced by the calculations
共dashed lines in Fig. 2兲. The estimated thicknesses (d J 1 /d J 2 )were 25 nm/310 nm 关Fig. 2共a兲兴 and 200 nm/15 nm 关Fig. 2共b兲兴
which are similar to the values used in the calculations 共30
nm/322 nm and 209 nm/17 nm兲.
Figure 3 shows the polarization resolved reflection spectra of two 共110兲 DBRs having nearly the same spectral separation but different spectral positions. The difference in the

6707

FIG. 3. Polarization-resolved reflection spectrum of two distinct 共110兲 distributed Bragg reflectors having similar spectral separation of their two orthogonally polarized reflection bands but different wavelength positions
共solid lines兲. The reflection maximum at the high 共low兲 energy side in 共a兲
and 共b兲 corresponds to the polarization vector of the reflected light parallelto the 关001兴 ( 关 11̄0 兴 ) crystallographic directions in the 共110兲 surface plane.
d 1 (d 2 ) denotes the thickness of the layer etched at current density J 1 (J 2 ).
Dashed lines are calculated reflection spectra.

spectral position of the reflection bands is about 20 nm 关Figs.
3共a兲 and 3共b兲兴 while the separation of 40 nm 关Fig. 3共a兲, 599
nm for E储 关 11̄0 兴 and 559 nm for E储 关 001兴 兴 and 38 nm 关Fig.
3共b兲, 618 nm for E储 关 11̄0 兴 and 580 nm for E储 关 001兴 兴 arealmost equal. It is clear that for a larger spectral shift 共withthe same separation interval兲 the thicknesses of both types oflayers have to be carefully chosen taking into account thedispersion relation of bulk Si. Again, the predicted opticalresponse 共dashed lines兲 is in good agreement with experimental results.
As it follows from Figs. 2 and 3 with a proper choice ofthe thickness ratio and value of ⌬n it is possible to tune
spectrally two orthogonally polarized reflection/transmission
bands and adjust their spectral splitting separately. This is anadditional degree of freedom and important for practical applications of dichroic photonic structures.

V. DICHROIC MICROCAVITIESAnother specific type of PSi multilayers are microcavities 共PSMs兲 grown via electrochemical etching of Si wafers.
PSMs are realized by inserting a layer with nd equal to␭ PSM/2 between two symmetric Bragg mirrors each one assembled from alternative layers having high and low refractive indices with d 1 n 1 ⫽d 2 n 2 ⫽m␭ PSM/4. The interference ofthe reflected waves of the two DBRs leads to a transmission
maximum at ␭ PSM within the spectral region of the high reflection 共stop兲 band. Microcavities are of special interest for
nonlinear or laser applications since the electric field of thelight inside the central layer can be significantly enhanced.

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

6708

Diener et al.

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002

FIG. 4. Spectrally and polarization-resolved transmission through a 共110兲
distributed Bragg reflector 共dashed lines兲 and the corresponding 共110兲 microcavity 共thick solid lines兲. In 共a兲 the polarization vector of the transmitted
light 共E兲 is parallel to the 关001兴 crystallographic directions in the 共110兲
surface plane. 共b兲 The same measurements for E parallel to the 关 11̄0 兴 crystallographic directions in the 共110兲 surface plane. Thin solid lines show
calculated transmittance.

only 4% of the light polarized along the 关001兴 crystallographic direction. The intensity of the transmitted light islimited by self-absorption in the PSi layers in this spectral
range. For 共100兲 mesoporous Si having 50% porosity theabsorption coefficient at 660 nm is about 950 cm⫺1 共⬃1500
cm⫺1 at 600 nm兲.24,25 For a given thickness of the PSM
structure 共⬃3–3.5 ␮m兲 with an average porosity of ⬃50%
up to 30% of the light is absorbed at 660 nm 共⬃40% at 600
nm兲.
Thin solid lines in Fig. 4 show the calculated transmittance for the PSM having thicknesses of 66 nm/99 nm. The
position, the width, and the depth of the stop band, and thewavelength position of the cavity mode and its magnitude
共especially for light polarized in the 关 11̄0 兴 crystallographic
direction兲 are well reproduced by the fit. The field enhancement at 660 nm in the central layer of the 共110兲 PSM forlight polarized along the 关 11̄0 兴 crystallographic direction isestimated to be around 3. This value can be significantly
enlarged by an increase of the dielectric contrast between thelayers. Therefore thin 共110兲 PSi layers having a larger variation of their average porosity and smaller interface roughness
are desired and the preparation procedure still has to be improved. We note that all degrees of freedom for tuning thespectral position and the polarization state of the cavity mode
are identical to those demonstrated for the DBRs.
VI. CONCLUSIONSThe basic requirement for PSMs are high quality DBRs.
Figure 4 shows the transmission spectra of a free standing
共110兲 DBR grown with 20 J 1 /J 2 cycles 共with thicknesses of
60 nm/90 nm兲 for the two principal polarization directions of
the transmitted light 共dashed lines兲. Since the suppression of
the transmitted light for the first order Bragg peak is on theorder of 99% and the edges of the stop bands are well pronounced the optical performance of the DBR is high.
A ␭ PSM/2 layer has been introduced in an identical dielectric stack of layers by doubling of the etching time of thecentral layer. The thick solid lines in Fig. 4 show the polarization resolved transmission spectra of a 共110兲 PSM. For
both polarization directions a sharp cavity mode approximately in the center of the stop band can be seen. The finesseF̂ of a microcavity 共or Fabry–Pèrot filter兲 is defined as the
wavelength position of ␭ PSM divided by the full width at half
maximum of the cavity mode ⌬␭.22 For the PSM in Fig. 4 F̂for light polarized in the 关 11̄0 兴 direction is ␭ PSM /⌬␭
⫽661 nm/7 nm⫽94.4, which satisfies the requirements for
optical grade quality. Due to the difference in ⌬n for different current densities the best performance of the DBRs canbe achieved for one polarization direction only. To get thebest optical quality DBRs usually d 1 n 1 is chosen to be equal
to d 2 n 2 with a value of m␭ PSM/4. However, for 共110兲 DBRs
⌬n is not the same for J 1 and J 2 共see Table I兲. Therefore thiscondition can only be fulfilled for one polarization direction.
Since the PSM has been optimized for light polarized in the关 11̄0 兴 direction, F̂ for light polarized in the 关001兴 direction
is smaller (600 nm/7 nm⫽85.7). The intensities of the transmitted light differ as well. For the 关 11̄0 兴 polarization direction 22% of the initial light intensity is transmitted while it is

We demonstrate that stacks of 共110兲 PSi layers, witheach single layer having strong in-plane birefringence, canact as dichroic Bragg reflectors and microcavities. Due to thespecifics of the crystallographic direction-selective etchingprocess the strength of the birefringence depends strongly on
the etching current density. This offers additional opportunities for the design of polarization-dependent optical PSibased multilayered structures. We show that it is possible totune spectrally two orthogonally polarized reflection/transmission bands of the PSi-based structures and adjust
their spectral splitting separately. 共110兲 PSi dichroic microcavities have been manufactured. Because the in-plane birefringence level is high enough to achieve phase-matchingconditions for nonlinear wave interactions, microcavities
prepared from 共110兲 Si substrate seem to be promising candidates for a novel type of nonlinear optical media.
ACKNOWLEDGMENTS

The authors would like to acknowledge Deutsche Forschungsgemeinschaft for the support of this work. M. Fujii isgrateful to the Alexander von Humboldt Foundation for financial support.
E. Yablonovitch, Phys. Rev. Lett. 58, 2059 共1987兲.
E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 共1989兲.
3
U. Grüning, V. Lehmann, and C. M. Engelhardt, Appl. Phys. Lett. 66,
3254 共1995兲.
4
F. Genereux, S. W. Leonhard, H. M. van Driel, A. Birner, and U. Gösele,
Phys. Rev. B 63, 161101共R兲 共2001兲.
5
A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909
共1997兲.
6
V. Lehmann, R. Stengl, and A. Luigart, Mater. Sci. Eng., B 69–70, 11
共2000兲.
1
2

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002
G. Vincent, Appl. Phys. Lett. 64, 2367 共1994兲.
M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Munder,
W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 共1994兲.
9
M. Araki, H. Koyama, and N. Koshida, Appl. Phys. Lett. 69, 2956 共1996兲.
10C. Mazzoleni and L. Pavesi, Appl. Phys. Lett. 67, 2983 共1996兲.
11
V. Mulloni and L. Pavesi, Appl. Phys. Lett. 76, 2523 共2000兲.
12P. Menna, G. Di Francia, and V. La Ferrara, Sol. Energy Mater. Sol. Cells
37, 13 共1995兲.
13
H. F. Arrand, T. M. Benson, A. Loni, M. G. Krueger, M. Thönissen, and H.
Lüth, Electron. Lett. 33, 1724 共1997兲.
14
M. Christophersen, J. Carstensen, and H. Föll, Phys. Status Solidi A 182,
103 共2000兲.
15
M. Christophersen, J. Carstensen, A. Feuerhake, and H. Föll, Mater. Sci.
Eng., B 69–70, 194 共2000兲.
16
N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G.
Polisski, F. Koch, and M. Fujii, Opt. Lett. 26, 1265 共2001兲.
17
L. A. Golovan, V. Yu. Timoshenko, A. B. Fedotov, L. P. Kuznetzova, D. A.
7
8Diener et al.

6709

Sidorov-Biryukov, P. K. Kashkarov, A. M. Zheltikov, D. Kovalev, N. Künzner, J. Diener, G. Polisski, and F. Koch, Appl. Phys. B: Lasers Opt. 73, 31
共2001兲.
18
J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G.
Polisski, and F. Koch, Appl. Phys. Lett. 78, 3887 共2001兲.
19
O. Bisi, S. Ossicini, and L. Pavesi, Surf. Sci. Rep. 38, 1 共2000兲.
20
D. A. G. Bruggeman, Ann. Phys. 共Paris兲 24, 636 共1935兲.
21
P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, J. Appl.
Phys. 86, 1781 共1999兲.
22
P. Yeh, Optical Waves in Layered Media 共Wiley, New York, 1988兲, p. 102.
23
G. Björg, Y. Yamamoto, and H. Heitman, Confined Electrons and Photons
共Plenum, New York, 1995兲, p. 481.
24
D. Kovalev, G. Polisski, M. Ben-Chorin, J. Diener, and F. Koch, J. Appl.
Phys. 80, 5978 共1996兲.
25
D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B
215, 871 共1999兲.

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp