Optical properties of 3D macroporous silicon structures

Materials Science and Engineering B 149 (2008) 275–280

Optical properties of 3D macroporous silicon structures M. Gar´ın a , T. Trifonov a,∗ , A. Rodr´ıguez a , L.F. Marsal b , R. Alcubilla a a

Departament d’Enginyeria Electr`onica, Universitat Polit`ecnica de Catalunya, Campus Nord C4, Jordi Girona 1-3, 08034 Barcelona, Spain b Departament d’Enginyeria Electr` onica, El`ectrica i Autom`atica, Universitat Rovira i Virgili, Pa¨ısos Catalans 26, 43007 Tarragona, Spain Received 2 July 2007; accepted 16 August 2007

Abstract We study the optical properties of three-dimensional (3D) microstructures fabricated by electrochemical etching of macroporous silicon with modulated pore diameter. Optical measurements along the pore axis reveal photonic band gaps which are also confirmed by calculations of photonic band dispersion. We investigate numerically and experimentally the evolution of these gaps as a function of pore diameter modulation. In addition, a subsequent anisotropic etching of macroporous silicon in alkaline solutions allows to achieve pores with new shapes of modulation. We compare the optical characteristics of 3D macroporous structures with and without such anisotropic treatment. © 2007 Elsevier B.V. All rights reserved. Keywords: Macroporous silicon; Three-dimensional structures; Photonic crystals; Electrochemical etching; Alkaline etching

1. Introduction Significant efforts have been undertaken up to now to fabricate micro- and nano-structures that meet the requirements for 3D photonic crystals [1], namely: periodicity in all three dimensions, high dielectric contrast and very good uniformity. Macroporous silicon, produced by electrochemical etching of silicon in hydrofluoric acid (HF) solutions [2], has proved to meet these requirements and has turned out to be an excellent system to study the optical properties of 2D and 3D photonic crystals [3–5]. Because of its outstanding structural properties, macroporous silicon has also become attractive for applications in microfluidics [6,7], biotechnology [8,9], optical filtering [10], betavoltaics [11] and many other fields of modern technology and material science. Large scale periodic macroporous structures are commonly produced by photo-assisted electrochemical etching of lightly doped n-type silicon [2]. In this method, 2D periodic arrangement of the pores is achieved by structuring the wafer surface prior to the etching using standard lithographic techniques. The diameter of growing pores is controlled by adjusting the intensity of backside illumination. Periodicity in third dimension,

∗

Corresponding author. Tel.: +34 93 4017488; fax: +34 93 4016756. E-mail address: [email protected] (T. Trifonov).

0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.08.006

i.e., along the pores axis, can therefore be introduced by modulating the pore diameter and can be independently controlled from the in-plane periodicity defined by the initial lithographic pattern. This is a remarkable feature of the electrochemical etching because it offers large freedom concerning the shape of pore diameter modulation. For example, pores with a symmetric sine-wave modulation [4], asymmetric sawtooth-like profile [8], as well as sharply modulated diameter [5] can be realized by a proper design of the light intensity profile used for the etching. In this paper, we report on the fabrication and optical characterization of 3D photonic structures based on macroporous silicon with modulated pore diameter. Two concepts are addressed. First, we study the influence of periodicity on the dispersion characteristics for light propagating along the pore axis. Samples with fixed in-plane periodicity but with different periods of pore diameter modulation were fabricated and characterized numerically by simulations of photonic band dispersion and optically by reflectance and transmission measurements at normal incidence. Second, we investigate how the shape of modulation, instead of periodicity, affects the optical properties of these structures. Macroporous silicon samples with identically modulated pores were etched in different alkaline solutions. The strong anisotropy of alkaline etching causes important changes in the shape of pore modulation. This anisotropy depends on the etchant composition and can be modified, allowing

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the realization of pore shapes that cannot be attained by the electrochemical etching only. We show that this treatment can also be applied to connect laterally the neighboring pores and thus, to obtain a fully 3D structure consisting of overlapping voids in silicon. We compare the optical properties of such 3D structures with those without an anisotropic post-treatment. 2. Experimental 2.1. Fabrication of 3D macroporous silicon A thorough description of the electrochemical etching process and macropore formation has been published elsewhere [2,4,5]. We shall briefly summarize here the process sequence and etching conditions. The substrate was n-type (1 0 0) silicon wafer with a resistivity of 2–6  cm. The wafer front side was pre-structured by oxidation, lithography and tetramethyl ammonium hydroxide (TMAH) etching. This creates a pattern of inverted pyramids, which define the positions where the pores should grow. The formed pattern consists of a square lattice with 4 ␮m pitch. An n+ -layer was ion-implanted on the wafer backside to form a transparent ohmic contact. The electrochemical etching was then carried out in 5 wt.% aqueous HF solution at 15 ◦ C and under backside illumination. The applied anodic potential was 2 V. A small amount (0.1 mM) of the non-ionic surfactant Triton X-100 was added to the electrolyte as a wetting agent. Periodic modulation of pore diameter is achieved by varying the intensity of backside illumination and thus, the etching current while pores grow into the substrate. Applying a sawtooth-like current profile produces sinusoidal modulation of pore diameter in depth [4,5]. The period of pore diameter modulation can be modified by properly adjusting the frequency of the etching current variations. The HF concentration decreases toward the pore tips due to a limited diffusion inside the narrow pores. This effect should be taken into account because it leads to a decrease of the etching rate with increasing pore depth. The frequency of the current modulation must therefore be reduced accordingly in order to produce equidistant changes of pore diameter in depth. 2.2. Anisotropic alkaline etching Some of the fabricated 3D macroporous samples with modulated pores were subjected to post-etching treatment in alkaline TMAH solutions. Prior to the alkaline etching, the pores were opened from the backside by etching off the remaining silicon in order to obtain a macroporous membrane. Membranes are required to avoid concentrations gradients of the etchant, which would arise in closed pores due to a limited diffusion. Details on the preparation of macroporous silicon membranes can be found elsewhere [12]. Experiments were conducted in two different TMAH solutions, as follows: (i) 25 wt.% TMAH, 6 ◦ C, 65 min and (ii) 1 wt.% TMAH with 10 wt.% IPA addition, 5 ◦ C, 160 min. For both experiments the same starting structure has been used, namely a macroporous silicon membrane with 130 ␮m thick-

ness, 3.95 ␮m modulation period, and 4 ␮m pitch of the in-plane square periodicity. 2.3. Optical characterization The fabricated samples were characterized by measuring reflectance and transmission spectra in the mid-IR region with a Fourier transform infrared (FTIR) spectrometer (Bruker Vertex 70, DTGS detector, KBr beam splitter) at a spectral resolution of 4 cm−1 . Measurements were done in a direction parallel to the pore axis. A gold mirror was used as a reference for the reflection measurements, while transmission data was normalized to the open beam spectrum. 3. Results and discussion 3.1. 3D macroporous silicon with sinusoidally modulated pores As shown by Schilling et al. [4], macroporous silicon with modulated pores arranged in a hexagonal lattice exhibits a band gap in the transmission spectrum for light propagating along the pore direction. Here, we show that pores arranged also in a square lattice have similar optical behavior, which infers that the in-plane periodicity has a little effect on the photonic dispersion in that direction. To study this, we have fabricated four samples with different periods of pore modulation: 3, 4, 5, and 6 ␮m, respectively. All samples have 21 crystal periods. The periodicity in the xy-plane is constant and corresponds to a square lattice with a pitch of 4 ␮m. SEM images (in cross-section) of the fabricated samples are shown in Fig. 1 a and b. The resulting periodicities derived from the SEM micrographs are very near to the targeted ones. However, the pore diameter variation is reduced for shorter modulation periods. This effect is due to limitations of the used etching model. When the applied etching current varies too suddenly, the pore growth mechanism changes, leading to deviations between designed and etched pore profiles. The band dispersion of the corresponding 3D photonic crystal was calculated using a freely available MIT photonic package [13]. It implements a fully-vectorial iterative eigensolver to compute the eigenstates and eigenmodes of Maxwell’s equations in a planewave basis [14]. Simplified 3D model used for the calculations assumes pores with circular cross-section and sine-wave modulation of pore radius r of the form r = r0 − r sin(2πz/az ), where az is the periodicity along the pore axis (ax = ay = a being the periodicity in the xy-plane). Fig. 2 shows the calculated band structure together with the measured transmission spectrum in z-direction. Wave vectors along the M– Γ –X path of the irreducible Brillouin zone correspond to waves propagating in the xy-plane perpendicular to the pore axis. The dispersion relation along M– Γ –X is therefore similar (at least, for the long wavelength range) to the band structure of a square 2D photonic crystal with non-modulated pores. In z-direction, which corresponds to the Γ –A path (Fig. 1c), the dispersion relation results from the periodic pore modulation and exhibits a stop gap between the first and second photonic bands. Consequently,

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Fig. 1. (a) SEM micrographs of four 3D macroporous silicon samples with different periods of modulation. The periodicity in the xy-plane is a = 4 ␮m. (b) A bird-eye’s image of the sample with 4 ␮m modulation period and 21 periods, revealing the square arrangement of the pores. (c) Brillouin zone of the 3D square lattice used for the numerical simulations.

a spectral region of zero transmission (also, total reflection) is expected for light propagating along the pore axis. Indeed, transmission is almost zero for wavelengths between 20.91 and 22.74 ␮m, which agrees well with the predicted bandgap position (20.65–22.78 ␮m). This is also confirmed in the reflection measurements (Fig. 3 , spectrum corresponding to az = 4 ␮m), where reflectivity of 100% is found in the spectral region of photonic band gap. Vanishing transmission (high reflectivity) may however be observed not only in spectral regions corresponding to forbidden gaps, but also in spectral regions where the excitation of photonic bands is inefficient or not allowed [16]. That is what happens for wavelengths around 11.7 ␮m, where

Fig. 2. Left: Transmission along Γ –A direction of 3D macroporous structure with 4 ␮m modulation period. Right: Calculated band structure for sine-wave modulated pores with az /a = 0.99, r0 /a = 0.32 and r/a = 0.08. Gray-shaded region indicates the photonic gap along Γ –A direction.

Fig. 3. Reflectance spectra of 3D macroporous samples with different periodicities along the pore axis. The regions of high reflectivity, which correspond to band gaps along the Γ –A direction, shift toward longer wavelength with increasing the modulation period az . For az = 5 and 6 ␮m, the first-order band gap falls outside of the detection range.

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Fig. 4. Positions (gap map) of the first and second-order band gaps as a function of the periodicity az along the pore axis. Experimental values (symbols) determined from the reflectance spectra show very good agreement with the simulation. The in-plane square periodicity is a = 4 ␮m.

the observed zero transmission is caused by non-coupling bands along Γ –A direction. The influence of modulation period on the dispersion characteristics along Γ –A direction can be understood from Figs. 3 and 4 . Fig. 3 shows reflectance spectra taken from samples with different periods of pore diameter modulation. Unfortunately, for periods az = 5 and 6 ␮m the first-order (fundamental) band gap falls outside of the detection range of our equipment. Nevertheless, the overall behavior can be clearly seen. All spectra have similar features which shift to longer wavelengths as the modulation period increases. Increasing the period leads to opening of a new second-order band gap located at shorter wavelengths. We note that for az = 4 ␮m this gap overlaps with a non-coupling band along Γ –A direction, which gives rise to high reflection peaks observed in the spectral region around 11.7 ␮m. At longer wavelengths, the periodicity along the pore axis can be efficiently approximated by an 1D photonic crystal of several layers with different refractive indexes. The refractive index of each layer is found applying Maxwell–Garnet effective medium approximation [15]. Layers with the highest and lowest effective refractive indexes will therefore correspond to sections of minimal and maximal pore diameters, respectively. As predicted by the theory of 1D photonic crystals [1], forbidden gaps are opened between every two photonic bands and can be classified as odd- or even-order gaps if they lie at the edge or center of the Brillouin zone, respectively. According to this classification the fundamental stop gap opened between the first and second bands at the A symmetry point would be an odd-order gap. Alternatively, the new gap observed in the reflectance spectra for periodicities of 5 and 6 ␮m would be an even-order one because it opens at the Γ point between the second and third photonic bands. Even-order gaps are usually narrower than odd-order ones and thus, are more sensitive to structural inhomogeneities present in the sample. This could account for a measured reflectivity below 100% in the spectral region of the second gap.

The discussed above simple 1D model is no longer valid if the modulation period is equal or less than the in-plane periodicity, i.e., az ≤ a. In this case, the band dispersion along Γ –A direction does not resemble anymore an 1D band structure. This has been already seen in Fig. 2 and can also be easily deduced from Fig. 4, where the calculated and experimentally determined spectral positions of the forbidden gaps are plotted as functions of modulation period. Simulations were performed taking into account the reduction of pore diameter variation with decreasing modulation period, discussed at the beginning of this section. As can be seen, there is a good agreement between the measured gap positions for different periods and the calculated gap map. The second stop gap disappears for periods below az = 4.3 ␮m (az /a = 1.08), while the fundamental one closes at az = 2.2 ␮m (az /a = 0.55). We would like to point out that our results are very similar to those reported by Schilling et al. [4,15], although the authors have studied 3D hexagonal photonic crystal with modulated pores. Fundamental and second-order gaps were reported to vanish for modulation periods of az /a = 0.55 and az /a = 1.13, respectively. Similarities can also be found in the reported spectral positions and gap widths. This close resemblance between the results for hexagonal and square 3D structures of modulated pores indicates that the effect of inplane periodicity on light propagation along the pore axis could be neglected as long as az > a. 3.2. 3D macroporous silicon with anisotropic treatment Having discussed the effect of modulation period on the dispersion characteristics, we turn now to study how the shape of modulation affects the light propagation. As was mentioned before, the anisotropic properties of TMAH etching can be exploited to obtain new pore shapes that cannot be attained by the electrochemical etching alone. The TMAH is an organic alkaline etchant with anisotropic etching properties similar to those of potassium hydroxide (KOH). The (1 1 1) crystal plane has always the slowest etching rate. However, the etching rates of (1 1 0) and (1 0 0) planes depend on the temperature and etchant composition [17]. At high TMAH concentrations (25 wt.%), the (1 1 0) plane is etched faster, i.e., ν1 1 0 > ν1 0 0 . For lower concentrations (below 10 wt.%), the above etch rate relation becomes reversed, that is, ν1 1 0 < ν1 0 0 . Addition of an alcohol, for instance isopropyl alcohol (IPA), is known to further enhance the etching rate of (1 0 0) planes with respect to (1 1 0) ones. Higher index planes are also found to be affected by the specific etchant composition but their etch-rate dependences are less known. Fig. 5 shows SEM micrographs of a 3D macroporous sample after etching in different TMAH solutions. The initial sine-wave shape of pore modulation is modified but the period of modulation along the pore axis remains unchanged (az ≈ 4 ␮m). Adjacent pores have also become connected in-plane due to the erosion of pore walls first at the position of diameter maxima. However, the resulting shapes of opened windows are completely different because of the specific anisotropy of each TMAH solution. The intersections between the pores when the sample is subjected to TMAH 25% solution resemble more less

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Fig. 5. SEM micrographs of 3D macroporous silicon with sinusoidally modulated pores after post-etching treatment in TMAH solutions, as follows: (a) 25 wt.% TMAH, 6 ◦ C, 65 min and (b) 1 wt.% TMAH + 10 wt.% IPA, 5 ◦ C, 160 min. For both experiments the same starting structure (Fig. 1b) has been used. Pores are connected laterally due to erosion of pore walls at the positions of diameter maxima.

octagons (Fig. 5a), whereas those for TMAH 1% with IPA addition are rectangles (Fig. 5b). Cusps formed by the remaining pore walls are no longer smooth as in the initial structure (Fig. 1a) but have sharp edges. The shown micrographs indicate that the formed structures are complete 3D networks of interconnected voids in silicon. Their optical response along the pore axis would be different because of the strong refractive index variation in z-direction. To test the optical properties, we carried out reflection and transmission measurements of the samples before and after TMAH anisotropic treatment. Measured reflection and transmission spectra are shown in Figs. 6 and 7 , respectively. The optical response before the TMAH etching (top spectra) is similar to that already presented in the previous section. In this case, however, the sample is a membrane with through-wafer pores which is required to allow free flow of the TMAH and thereby to avoid inhomogeneous etching. This explains the slight differences, observed particularly in the fundamental gap position and in the overall transmission of the sample. After TMAH treatment, the optical response changes. In general, spectral regions of high

reflectivity are broadened and shifted to lower wavelengths. For the 25% TMAH case, the octagonal intersections between the pores (Fig. 5a) suggest that the structure could be modelled by considering overlapping air polyhedrons, i.e., solid bodies having many sides. However, in the long wavelength limit a good approximation is the 3D square lattice formed of overlapping air spheres since light does not see the fine faceting of the pore walls. If we use spheres with radius of r = 0.581a, the numerical simulations predict a forbidden gap in 11.47–16.43 ␮m spectral range which coincides fairly well with the measured band gap position. For the second structure obtained after etching in 1% TMAH (Fig. 5b), we were unable to find a reasonable model that could substantiate the obtained reflectance and transmission spectra. The analysis is complicated by the fact that the structure is strongly asymmetric. For example, formed cusps between neighbor pores have smaller size and different shapes than the cusps along the pore axis. Furthermore, it is possible that the structure suffers from non-uniformities which induces high scattering losses. Unambiguous and detailed information about

Fig. 6. Reflectance spectra along Γ –A (pore axis) direction of 3D macroporous silicon samples without and with TMAH anisotropic treatments. Periodicity along the pore axis is similar to the in-plane periodicity (az ≈ a = 4 ␮m).

Fig. 7. Transmission spectra along Γ –A (pore axis) direction of 3D macroporous silicon samples without and with TMAH anisotropic treatments. Periodicity along the pore axis is similar to the in-plane periodicity (az ≈ a = 4 ␮m).

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the uniformity of the structure and the exact pore shape at different depths is therefore needed and can be acquired, for instance, by polishing the sample under certain angles with respect to the surface. Further studies on the development of a 3D model are currently underway.

de la Cierva fellowship. This work has been partly financed by the Spanish Commission of Science and Technology (CICYT) through grants TEC2005-02716 and TEC2006-06531.

4. Conclusions

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Three-dimensional macroporous silicon structures were fabricated by modulating the pore diameter along the growth direction. Optical measurements in this direction reveal the existence of photonic gaps which agree very well with the simulated photonic band structure. Spectral positions of these forbidden gaps depend mainly on pore modulation period and are not affected by the in-plane periodicity as long as the period is greater than the in-plane periodicity constant. For such periods, the structure can be efficiently approximated with a 1D photonic crystal. In contrast, the shape of pore modulation has indeed a strong influence on the optical properties. This shape is additionally modified by exploiting the anisotropic properties of alkaline solutions. Unusual pore shapes can be attained by changing the composition and temperature of alkaline etchant. This possibility to control the anisotropy of alkaline etching when combined with the freedom to modulate the pore diameter in depth can enable the realization of many and new 3D geometries. Acknowledgements M.G. acknowledges fellowship support from DURSI of Catalonia’s Government and from the European Social Fund. T.T. acknowledges support from the Spanish Government for a Juan

References