Three-Dimensional Silicon-Based Photonic Crystals Fabricated byElectrochemical Etching

S. Matthias, F. Muller, R. Hillebrand, J. Schilling and U. Goselegoesele@mpi-halle.mpg.de

Max Planck Institute of Microstructure PhysicsWeinberg 2, D-06120 Halle, Germany

Abstract- We show a general concept to structurestandard silicon wafers with an almost perfect three-dimensional shape, which is versatile, accurate and fast.For characterisation we grow photonic crystals with acomplete photonic bandgap.

1 Introduction

Large scale, highly periodic structures have gained consider-able interest in a number of areas in modern physics servingas photonic crystals [3, 17], sensors [9, 4] or as massivelyparallel Brownian ratchets [11]. Recently photonic bandgapmaterials became increasingly important in which three-dimensional periodic variations of the dielectric constant con-trollably prohibit electromagnetic propagation throughout aspecific frequency range, inhibiting spontaneous emission orallowing loss-less waveguiding [17, 1]. It requires perfectlystructured dielectric material on the lengthscale of the wave-length of light to realize the theoretically proposed unusualelectromagnetic properties.

Such artificial structures were successfully fabricated mai-nly using self-assembly techniques [16, 2] and layer-by-layermethods [10, 13]. Structures fabricated by a layer-by-layerprocedure are based on an elaborate lithography and a numberof polishing and dry etching processes, which limit the num-ber of lattice constants in growth direction. Self-assemblytechniques using colloidal spheres, which were sintered in aface centered cubic lattice, combined with an inversion pro-cedure allow for almost perfect single crystals of silicon in-verted opals on a 100µm scale [2]. Within their approachit is difficult to introduce defects in a controlled manner andto avoid disorder or stacking faults. Alternative fabricationmethods for an extended photonic crystal as well as three-dimensional structures for other applications are highly de-sirable. It has been proposed by Leonard [8] that not only thefcc-arrangement of air spheres in silicon possesses a completephotonic bandgap but that also a simple cubic lattice of over-lapping air spheres in silicon prohibit light propagation in afrequency range of more than 4%.

This report is focussed on the electrochemical fabricationof three-dimensional microstructures with nanometer preci-sion for photonic crystal applications. The manufacturingprocess is based on the well-established macroporous siliconetching process developed by Lehmann [5] and described indetail in the following section. This method implies certainlimitations concerning the pore shape, which inhibit the fabri-cation of the proposed Leonard-structure [8]. We concentrate

on the significant improvement of the etching process. Theformer restrictions will be overcome and the resulting porescan be converted into a simple cubic three-dimensional net-work in silicon. The optical properties are characterized insection 3.

2 Electrochemical Etching

An excellent method to structure a whole silicon wafer withan arbitrary - lithographically predefined - arrangement ofcylindrical air-pores, called macroporous silicon, was demon-strated by Lehmann [6, 5]. The resulting structures act asan ideal model system for two-dimensional photonic crystalsover a wide wavelength range of 6 to 1.5 micrometer depend-ing on the lattice constant. This process with all its advan-tages can be extended to fabricate three-dimensional struc-tures in silicon.

Macroporous silicon is grown in a photo-electrochemicaletching process. An n-type (100) oriented silicon wafer isprepatterned by standard photolithography. Subsequent alka-line etching forms inverted pyramids acting as initial pores.Under anodic bias and backside illumination the wafer is thenetched in hydrofluoric acid. The photo-generated holes dif-fuse through the whole wafer. The silicon-electrolyte contactreminds of a Schottky-contact, where a space charge regionwithin the silicon evolves. The applied potential enlargesthe width of the space-charge region (SCR) in the silicon.The SCR acts on the electronic holes and concentrate themmainly on the pore tips, promotes the dissolution of siliconand results in a pore growth straight along the〈100〉 direc-tion. The effect of the applied voltage for steady-state con-ditions is found to be negligible. Because a n-type siliconwafer is used, the current-voltage characteristic of the silicon-electrolyte junction depends thus on the backside illumina-tion, which controls the number of minority carriers. The ap-plied voltage and the etch current can be independently cho-sen. The diameter of the resulting air-pores is approximatelyproportional to the etch-current and can be varied during thegrowth by changing the intensity of the applied backside il-lumination [7]. Modulation of the illumination intensity witha triangular profile lead to a sinusoidal pore diameter varia-tion [14]. With an asymmetric current density profile also aratchet-type pore shape is possible [11, 12]. However, thisprocess has restricted the resulting pore shapes to smooth si-nusoidal or ratchet-type ones with small variations in diam-eter so far. As a rule of thumb, the shorter the length of themodulation the lower are the variations of the diameter [15]

Figure I: Scanning electron micrographs of cleaved modu-lated macroporous silicon wafersa: The macropores obtainedby current modulated etching are arranged in a quadratic lat-tice with a pitch of 2µm. A defect plane was grown by miss-ing one modulation.b: Close up of the cavity of fig. 1a.c: Macropores by current-voltage modulated etching. Sharpedges and large diameter variations on the lengthscale of theinterpore distance can be grown.d: Bird’s eye view of thetop lithographic defined square lattice and the etched squarelattice. After homogeneous widening of the pores a simplecubic lattice of overlapping airspheres remains.

which can be realized (fig. Ia, b).Strong variations in diameter on a distance less than the

lateral lattice constant as well as pore shapes with sharp edgesare a challenge but required for the fabrication of a simple-cubic photonic crystal of overlapping air spheres in silicon.The observed smoothing of the pore shape can be signifi-cantly reduced by increasing the applied voltage. In partic-ular, for a constant anodic bias of the order of the break-down potential and a periodic varying backside illuminationthe necessary large and sharp modulated pore shapes canbe etched. However, this etching process is rather unstable.Some pores branch and others die, because the high appliedvoltage generates some defect electrons directly by tunnelingand drives the system out of the stable growth regime. Toovercome this instability, both the backside illumination andthe applied voltage are modulated.

The space charge region can thus be continuously adaptedto optimize the focussing effect for the holes during the etch-ing process and the growth follows more direct the currentprofile. The high voltage on the order of the breakdown po-tential is only applied in combination with a low current den-sity. This interplay allows to drill a very fine channel at thebottom of each modulation and works in the transition re-gion of normal pore growth and breakdown. After this fine

1000 2000 3000 40001E-3

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Figure II: Transmittance of a current-modulated sample. Thetransmission was measured along the growth direction with amicroscope FTIR (quadratic spot size of side length 150µm)and air served as a background. The bandgaps are highlightedin grey as guide to the eye.

pore has grown about 0.3µm, the voltage is reduced to returnto the stable regime and the current density is gradually in-creased to enlarge the diameter near the pore tips. The highminority current is not only consumed at the pore tip, but alsoto some extent on the sidewalls of the thin pore section and inthe transition region to the previous modulation. This effectsmears out formerly etched regions and increases the diam-eter of the fine pore enormously. However with a carefullyadjusted current-voltage profile sharp edges and large diame-ter variations can be grown (fig. Ic). Up to 100 modulationshave been realized so far and more are feasible. Although thegrowth velocity decreases with the depth of the pore due tothe limited diffusion, it is about 0.6µm/s and thus one modu-lation is etched in one step in less than 3 minutes.

To obtain the cubic symmetry and the optimum porosityfurther post-processing of the porous sample is required. Ina homogeneous and isotropic widening step the pore diame-ter is increased. First, the samples are annealed at 900◦C for150 minutes to grow a silicon oxide on the silicon surface. Ina second step the oxide is removed by a hydrofluoric etchingstep. The widening may be repeated several times to preciselyadjust the filling factor. Finally, this uniform erosion leads tointerconnected pores also in the plane perpendicular to thepore axis (fig. Id). Although starting from a columnar struc-ture, the geometry obtained is very close to cubic overlappingair spheres in silicon. The modulation length of the resultingstructure in growth direction is equal to the lithographicallydefined square lattice constant. The samples has nearly cubicsymmetry. The introduction of line defects can be achievedby leaving out a line of pores or even single pores during thelithography step. Combined with an etched defect layer thisprocedure allows to create point defects as well.

3 Characterization

The obtained samples were characterized with a MicroscopeFourier Transform Infrared Spectrometer (FTIR) along vari-ous crystal axes. Figure II shows the transmission of a cur-rent modulated sample, similar to one of fig. Ia without adefect plane along the growth direction. Air served as back-ground here. The transmission through the photonic crystal isreduced by more than 2 orders of magnitude within the fun-damental and the first higher order bandgap. Also the thirdorder gap can be seen. In addition Fabry-Perot-Resonancesresulting from the multiple reflection at the boundaries indi-cate a good quality crystal.

4 Conclusion

The well-established photo-electrochemical etching processby Lehmann, was significantly improved to allow the man-ufacturing of perfect three-dimensional microstructures. Asimple cubic lattice of overlapping air-spheres results by ahomogeneous widening of a strongly modulated samples withsharp edges. Moreover, this process allows a precise controlof the resulting shape with a resolution in nanometer range.Compared to other fabrication of three-dimensional photoniccrystals is this concept fast and versatile.

Acknowledgement R. B. Wehrspohn is thanked for dis-cussions and support by the wafer supply.

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