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Angle-dependent laser diffraction in inverse opal photonic crystals
Superlattices and Microstructures 44 (2008) 626–632 www.elsevier.com/locate/superlattices
Angle-dependent laser diffraction in inverse opal photonic crystals Alexander Sinitskii a,∗ , Vera Abramova a , Tatyana Laptinskaya b , Yuri Tretyakov a a Department of Materials Science, M.V. Lomonosov Moscow State University, Lenin Hills, 119992 Moscow, Russia b Department of Physics, M.V. Lomonosov Moscow State University, Lenin Hills, 119992 Moscow, Russia
Available online 19 February 2008
Abstract We discuss the experimental data on laser diffraction in photonic crystal films with an inverse opal structure. Inverse opals based on tungsten, manganese and titanium oxides were prepared by replicating colloidal crystals made of 900 nm polystyrene microspheres. We scanned both colloidal crystals and inverse opals with a 532 nm laser beam and recorded symmetrical sixfold diffraction patterns for all samples studied. By using diffraction data we calculated the period of the photonic crystals and examined their crystalline quality; both parameters were found to be in good agreement with the scanning electron microscopy results. Thus, laser diffraction can be considered as a method to visualize the shrinkage of photonic crystal samples that occurs in their transformation from colloidal crystals to inverse opals in a replicating process. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Photonic crystals; Self-assembly; Inverse opals; Laser diffraction
1. Introduction Periodic dielectric structures have recently attracted considerable interest as photonic crystals, leading to novel optical phenomena and important technological applications [1]. Over the last decade, self-assembly of submicron colloidal particles has been demonstrated to be a suitable ∗ Corresponding author. Tel.: +7 495 939 4729; fax: +7 495 939 0998.
E-mail address: [email protected] (A. Sinitskii). c 2007 Elsevier Ltd. All rights reserved. 0749-6036/$ - see front matter doi:10.1016/j.spmi.2007.12.010
A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
627
platform for the preparation of photonic crystals [2–4]. The materials thus formed are usually referred to as colloidal crystals or artificial opals, since they resemble corresponding natural gemstones [5]. Due to the easy and low-cost fabrication process, colloidal crystals have been used as model objects in numerous studies of photonic crystals [3,4]. Nevertheless, opals are not expected to be employed in a wide range of commercial high-technology products since they do not meet several important requirements. In addition to inevitable structural defects in selfassembled systems, opals are typically made of low refractive index materials, such as silica or polymers, while the use of materials with high refractive index would result in a tremendous enhancement of photonic crystals’ optical properties [6]. An even more important restriction arises when a particular optoelectronic device demands photonic crystals, in which unique optical characteristics are combined with additional functional properties (magnetic, electrical, mechanic, etc.). Numerous recent studies have been focused on the preparation of inverse photonic crystals, which can be synthesized by filling the voids of opal templates with suitable structure-forming precursors and subsequent removal of the initial microspheres to leave three-dimensionally ordered macroporous materials. This templating technique is very flexible and can be applied to the preparation of inverse photonic crystals based on a huge variety of materials, such as metals, nonmetals, oxides, semiconductors and polymers [7]. Some of the thus synthesized inverse opals possess high refractive index contrast and exhibit tunable functional properties that are promising for optoelectronic applications [8–14]. However, the use of inverse opals is strongly limited due to the preparation complexity of their well-ordered samples. The replicating procedure typically results in the shrinkage of the photonic crystal framework, cracking, misalignment of different domains, etc. As a result, inverse opals are significantly less investigated than artificial opals. Typical tools for the structure analysis of inverse opals include scanning electron microscopy (SEM) and optical spectroscopy. In the present work we demonstrate that important structural information on inverse opal photonic crystals can be obtained using laser diffraction, which to date has typically been applied to colloidal crystals [15–20]. 2. Experimental details Monodisperse polystyrene microspheres with an average diameter of 900 nm and a relative standard deviation σ < 5% were synthesized by emulsifier-free emulsion polymerization of styrene using potassium persulfate as initiator [21]. Colloidal crystal films made of polystyrene microspheres were prepared using the vertical deposition method [22]. Glass microslides were thoroughly cleaned and immersed in an aqueous suspension of microspheres with a concentration ranging from 0.1 to 0.5 vol.%. The temperature of film growth was 50 ± 1 ◦ C. Tungsten oxide was introduced into the voids of the colloidal crystals as follows [12,23]. First, we prepared the dipping solution by dissolving metallic tungsten in a mixture of hydrogen peroxide (30%) and glacial acetic acid at 0 ◦ C for a few hours, filtering the solution and redissolving the sediment in absolute ethanol. Then, we infiltrated the colloidal crystal voids with the dipping solution and dried the sample in air for a few minutes. The resulting polystyrene–gel composite was heated up to 500 ◦ C at the rate of 1 ◦ C/min and annealed for 1 h to remove the polystyrene template. Inverse opals based on manganese oxide were synthesized by infiltrating colloidal crystal template with a water–alcohol solution of manganese acetate, drying the sample in air, heating the resulting composite at the rate of 1 ◦ C/min up to 500 ◦ C and annealing for 1 h.
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A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
Fig. 1. Scheme for laser diffraction experiment. The dashed line represents the normal to the surface of the sample; ϕ and θ are angles of incidence and diffraction, respectively. The setup was adjusted so that angles ϕ and θ are in the horizontal plane.
The reaction mixture for the synthesis of titania inverse opals was prepared by diluting titanium (IV) butoxide with heptane in a 1:1 ratio. Colloidal crystal films were infiltrated with the reaction mixture, dried in air, heated up to 500 ◦ C at the rate of 1 ◦ C/min and annealed it for 1 h. SEM images of the samples were recorded using a LEO Supra VP 50 instrument. Prior to imaging, the samples were coated with a thin gold layer to reduce surface charging. The phase composition of the samples was studied by X-ray powder diffraction (XPD) using a DRON-3M X-ray diffractometer with filtered Cu Kα radiation. The geometry of the experiments on laser diffraction is shown in Fig. 1. Laser diffraction patterns were recorded using a weakly focused frequency doubled Nd:YAG laser (λ = 532 nm). The diameter of the laser beam spot on the sample was 0.1 mm, corresponding to a spot area of 8000 µm2 . The photonic crystals were placed on a special stage allowing micrometer adjustment of the in-plane sample position with a precision of 10 µm. The setup allowed variation of the angle of incidence of the laser beam maintaining illumination of the same area of the sample. 3. Results and discussion All inverse opals prepared in this work were annealed at 500 ◦ C for 1 h. According to the XPD results (Fig. 2), titanium oxide inverse opal consists of crystalline anatase (PDF-2 file [21–2372]). Further annealing of the sample would result in a phase transition from anatase to rutile and simultaneous degradation of ordered microstructure of inverse opal [24]. The XPD pattern of tungsten oxide inverse opal can be attributed to a crystalline WO3 [71–131] (Fig. 2). The complex XPD spectrum of the manganese oxide sample can be interpreted as a mixture of peaks corresponding to crystalline Mn5 O8 [39–1289] and Mn3 O4 [18–803] phases. The representative areas of inverse opals based manganese, tungsten and titanium oxides are shown at the same magnification in Fig. 3a, b and c, respectively. Apparently, for each sample shown the average center-to-center distance d between spherical voids is less than the average size of the polystyrene microspheres used for template preparation (900 nm). The shrinkage of the samples takes place during their heating and annealing due to the removal of volatile components (mainly water and carbon oxides). However, this shrinkage makes the sizing of air voids ambiguous, because the voids undergo shape deformation and many of them are elliptical rather than spherical. The deformation of the voids is clearly seen, for instance, in Fig. 3e. The effect is different for different regions of the samples and becomes more evident for the voids near the edges of cracks and domain boundaries. Thus, since SEM is the method for local analysis of microstructure, the results of sizing of the voids may vary from point to point of the sample.
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Fig. 2. XPD patterns for inverse opals based on titanium, tungsten and manganese oxides. Here and later manganese oxide inverse opal is referred to as “MnOx ”.
The period of photonic crystals can be independently determined from the diffraction experiments. In contrast to the sizing of mesoscopic objects by SEM, laser diffraction provides an average size, integrated over a macroscale region of the sample. The angle at which the diffraction spots are observed can be analyzed by considering each layer within the photonic√crystal as a twodimensional diffraction grating [15]; the pitch of the grating D is equal to d 3/2. Following simple diffraction theory we can write λ , (1) D where λ is the laser wavelength, ϕ is the angle of incidence of the laser beam, and θ is the angle of diffraction (Fig. 1). In angle-dependent diffraction experiments we mounted a colloidal crystal or inverse opal film on a stage. Then, by in-plane moving of the sample, we scanned it with the laser beam until a sixfold diffraction pattern with no diffuse ring linking the spots was observed (see the inset of Fig. 4). Then, the sample was rotated around the axis of the laser beam to make two of the six diffraction spots horizontal, ensuring that the angles of incidence and diffraction were in the horizontal plane. Finally, we rotated the sample around the vertical axis and monitored the diffraction angle as a function of angle of incidence. It should be stressed that the sixfold diffraction pattern shown in the inset of Fig. 4 is typical of single crystals and indicates that the illuminated area of 8000 µm2 contains close-packed domains with the same crystallographic orientation [23]. Such patterns were recorded from numerous spots of both opal and inverse opal films, confirming that the well-ordered close-packed structure of colloidal crystals was preserved during the replicating process. The dependences of diffraction angle θ on the angle of incidence ϕ for the polystyrene colloidal crystal and inverse opals are shown in Fig. 4. According to Eq. (1), the plot of sin θ against sin ϕ is linear with a gradient of 1 and an intercept of λ/D. It should be noted that the laser diffraction data are in good agreement with the SEM results. The lowest linear fit sin θ = sin ϕ +
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A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
Fig. 3. SEM images of inverse opals based on manganese (a), tungsten (b) and titanium (c) oxides, taken at the same magnification; the scale bars are 5 µm. Low-magnification SEM images of inverse opals based on manganese (d) and titanium (e) oxides; the scale bars are 10 µm.
corresponds to the colloidal crystal, which obviously possesses the maximum lattice period of all four samples studied. The average size of colloidal microspheres calculated from the diffraction data is 899 nm, which is in good agreement with the SEM results. For the inverse opals based on manganese, tungsten and manganese oxides the average center-to-center distances between spherical voids are 882, 862 and 730 nm, respectively. As already mentioned, each of these values was obtained not for a few square micrometers area of the sample but for the macroscale spot, and thus they can be considered as average for the whole sample. Moreover, in contrast to SEM, which requires the use of vacuum and often employs coating the samples with conductive materials, this method to determine the period of photonic crystals is nondestructive. It should be stressed that laser diffraction can also be employed for constructing domain maps of photonic crystals, demonstrating for macroscale areas of the samples both regions where all domains have the same crystallographic orientation and disordered regions [23]. Another promising application of laser diffraction to photonic crystals relies on the monitoring of the intensity of diffraction spots as a function of laser beam angle of incidence; such a study provides information on layer stacking in self-assembled photonic crystals, which is inaccessible by conventional microscopy methods [15]. 4. Conclusions In the present work we demonstrate that the shrinkage that occurs in self-assembled photonic crystals during their transformation from colloidal crystals to inverse opals can be visualized by laser diffraction. Bright sixfold diffraction patterns recorded from numerous spots of inverse opal films testify to their high structural quality. By using angle-dependent laser diffraction
A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
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Fig. 4. Angle-dependent laser diffraction data for polystyrene colloidal crystal and inverse opals. The solid lines are linear fits to the data from which the photonic crystal lattice periods can be determined. The inset is a side view photograph of a diffraction experiment on WO3 inverse opal. The sample and the sample holder can be distinguished in the left bottom corner of the photograph.
data we calculated the periodicity for both colloidal crystals and inverse opals; in contrast to the sizing of mesoscopic objects by SEM, laser diffraction provides an average size, integrated over a macroscale region of the sample. This method of analysis takes on special significance for inverse photonic crystals, which are much less investigated than conventional opals. Since diffraction patterns can be recorded in a reflection mode, this method can also be applied for the study of bulk inverse photonic crystals. The significant limitation of this method is that the diffraction patterns can be observed only if the laser wavelength is less than the photonic crystal lattice period. Therefore, the method is difficult to apply to photonic crystals for the visible range, typically composed of structural units less than 300 nm in size. Acknowledgements The work was supported by the Russian Foundation for Basic Research (grants no. 0503-32778 and 07-03-92113), the Program for Fundamental Research of Russian Academy of Sciences and the Federal Target Science and Engineering Program. References [1] T.F. Krauss, R.M. De La Rue, Progress in Quantum Electronics 23 (1999) 51. [2] Y. Xia, B. Gates, Y. Yin, Y. Lu, Advanced Materials 12 (2000) 693. [3] V.N. Astratov, Yu.A. Vlasov, O.Z. Karimov, A.A. Kaplyanskii, Yu.G. Musikhin, N.A. Bert, V.N. Bogomolov, A.V. Prokofiev, Superlattices and Microstructures 22 (1997) 393.
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[4] C. L´opez, L. V´azquez, F. Meseguer, R. Mayoral, M. Oca˜na, H. Miguez, Superlattices and Microstructures 22 (1997) 399. [5] J.V. Sanders, Nature 204 (1964) 1151. [6] K. Busch, S. John, Physical Review E 58 (1998) 3896. [7] A. Stein, Microporous and Mesoporous Materials 44–45 (2001) 227. [8] A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. L´opez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, H.M. van Driel, Nature 405 (2000) 437. [9] J.E.G.J. Wijnhoven, W.L. Vos, Science 281 (1998) 802. [10] P.V. Braun, P. Wiltzius, Nature 402 (1999) 603. [11] S.L. Kuai, G. Bader, P.V. Ashrit, Applied Physics Letters 86 (2005) 221110. [12] K.S. Napolskii, A. Sinitskii, S.V. Grigoriev, N.A. Grigorieva, H. Eckerlebe, A.A. Eliseev, A.V. Lukashin, Y.D. Tretyakov, Physica B 397 (2007) 23. [13] M. Li, P. Zhang, J. Li, J. Zhou, A. Sinitskii, V. Abramova, S.O. Klimonsky, Y.D. Tretyakov, Applied Physics B 89 (2007) 251. [14] V. Abramova, A. Sinitskii, Yu. Tretyakov, Pis’ma v ZhETF 86 (2007) 370; English translation: JEPT Letters 86 (2007) 317. [15] R.M. Amos, J.G. Rarity, P.R. Tapster, T.J. Shepherd, S.C. Kitson, Physical Review E 61 (2000) 2929. [16] L.M. Goldenberg, J. Wagner, J. Stumpe, B.R. Paulke, E. G¨ornitz, Langmuir 18 (2002) 3319. [17] L.M. Goldenberg, J. Wagner, J. Stumpe, B.R. Paulke, E. G¨ornitz, Physica E 17 (2003) 433. [18] F. Garc´ıa-Santamar´ıa, J.F. Galisteo-L´opez, P.V. Braun, C. L´opez, Physical Review B 71 (2005) 195112. [19] B.G. Prevo, O.D. Velev, Langmuir 20 (2004) 2099. [20] A.S. Sinitskii, P.E. Khokhlov, V.V. Abramova, T.V. Laptinskaya, Y.D. Tretyakov, Mendeleev Communications 17 (2007) 4. [21] J.W. Goodwin, J. Hearn, C.C. Ho, R.H. Ottewill, Colloid and Polymer Science 252 (1974) 464. [22] P. Jiang, J.F. Bertone, K.S. Hwang, V. Colvin, Chemistry of Materials 11 (1999) 2132. [23] A. Sinitskii, V. Abramova, T. Laptinskaya, Y.D. Tretyakov, Physics Letters A 366 (2007) 516. [24] J.E.G.J. Wijnhoven, L. Bechger, W.L. Vos, Chemistry of Materials 13 (2001) 4486.
Angle-dependent laser diffraction in inverse opal photonic crystals Alexander Sinitskii a,∗ , Vera Abramova a , Tatyana Laptinskaya b , Yuri Tretyakov a a Department of Materials Science, M.V. Lomonosov Moscow State University, Lenin Hills, 119992 Moscow, Russia b Department of Physics, M.V. Lomonosov Moscow State University, Lenin Hills, 119992 Moscow, Russia
Available online 19 February 2008
Abstract We discuss the experimental data on laser diffraction in photonic crystal films with an inverse opal structure. Inverse opals based on tungsten, manganese and titanium oxides were prepared by replicating colloidal crystals made of 900 nm polystyrene microspheres. We scanned both colloidal crystals and inverse opals with a 532 nm laser beam and recorded symmetrical sixfold diffraction patterns for all samples studied. By using diffraction data we calculated the period of the photonic crystals and examined their crystalline quality; both parameters were found to be in good agreement with the scanning electron microscopy results. Thus, laser diffraction can be considered as a method to visualize the shrinkage of photonic crystal samples that occurs in their transformation from colloidal crystals to inverse opals in a replicating process. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Photonic crystals; Self-assembly; Inverse opals; Laser diffraction
1. Introduction Periodic dielectric structures have recently attracted considerable interest as photonic crystals, leading to novel optical phenomena and important technological applications [1]. Over the last decade, self-assembly of submicron colloidal particles has been demonstrated to be a suitable ∗ Corresponding author. Tel.: +7 495 939 4729; fax: +7 495 939 0998.
E-mail address: [email protected] (A. Sinitskii). c 2007 Elsevier Ltd. All rights reserved. 0749-6036/$ - see front matter doi:10.1016/j.spmi.2007.12.010
A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
627
platform for the preparation of photonic crystals [2–4]. The materials thus formed are usually referred to as colloidal crystals or artificial opals, since they resemble corresponding natural gemstones [5]. Due to the easy and low-cost fabrication process, colloidal crystals have been used as model objects in numerous studies of photonic crystals [3,4]. Nevertheless, opals are not expected to be employed in a wide range of commercial high-technology products since they do not meet several important requirements. In addition to inevitable structural defects in selfassembled systems, opals are typically made of low refractive index materials, such as silica or polymers, while the use of materials with high refractive index would result in a tremendous enhancement of photonic crystals’ optical properties [6]. An even more important restriction arises when a particular optoelectronic device demands photonic crystals, in which unique optical characteristics are combined with additional functional properties (magnetic, electrical, mechanic, etc.). Numerous recent studies have been focused on the preparation of inverse photonic crystals, which can be synthesized by filling the voids of opal templates with suitable structure-forming precursors and subsequent removal of the initial microspheres to leave three-dimensionally ordered macroporous materials. This templating technique is very flexible and can be applied to the preparation of inverse photonic crystals based on a huge variety of materials, such as metals, nonmetals, oxides, semiconductors and polymers [7]. Some of the thus synthesized inverse opals possess high refractive index contrast and exhibit tunable functional properties that are promising for optoelectronic applications [8–14]. However, the use of inverse opals is strongly limited due to the preparation complexity of their well-ordered samples. The replicating procedure typically results in the shrinkage of the photonic crystal framework, cracking, misalignment of different domains, etc. As a result, inverse opals are significantly less investigated than artificial opals. Typical tools for the structure analysis of inverse opals include scanning electron microscopy (SEM) and optical spectroscopy. In the present work we demonstrate that important structural information on inverse opal photonic crystals can be obtained using laser diffraction, which to date has typically been applied to colloidal crystals [15–20]. 2. Experimental details Monodisperse polystyrene microspheres with an average diameter of 900 nm and a relative standard deviation σ < 5% were synthesized by emulsifier-free emulsion polymerization of styrene using potassium persulfate as initiator [21]. Colloidal crystal films made of polystyrene microspheres were prepared using the vertical deposition method [22]. Glass microslides were thoroughly cleaned and immersed in an aqueous suspension of microspheres with a concentration ranging from 0.1 to 0.5 vol.%. The temperature of film growth was 50 ± 1 ◦ C. Tungsten oxide was introduced into the voids of the colloidal crystals as follows [12,23]. First, we prepared the dipping solution by dissolving metallic tungsten in a mixture of hydrogen peroxide (30%) and glacial acetic acid at 0 ◦ C for a few hours, filtering the solution and redissolving the sediment in absolute ethanol. Then, we infiltrated the colloidal crystal voids with the dipping solution and dried the sample in air for a few minutes. The resulting polystyrene–gel composite was heated up to 500 ◦ C at the rate of 1 ◦ C/min and annealed for 1 h to remove the polystyrene template. Inverse opals based on manganese oxide were synthesized by infiltrating colloidal crystal template with a water–alcohol solution of manganese acetate, drying the sample in air, heating the resulting composite at the rate of 1 ◦ C/min up to 500 ◦ C and annealing for 1 h.
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Fig. 1. Scheme for laser diffraction experiment. The dashed line represents the normal to the surface of the sample; ϕ and θ are angles of incidence and diffraction, respectively. The setup was adjusted so that angles ϕ and θ are in the horizontal plane.
The reaction mixture for the synthesis of titania inverse opals was prepared by diluting titanium (IV) butoxide with heptane in a 1:1 ratio. Colloidal crystal films were infiltrated with the reaction mixture, dried in air, heated up to 500 ◦ C at the rate of 1 ◦ C/min and annealed it for 1 h. SEM images of the samples were recorded using a LEO Supra VP 50 instrument. Prior to imaging, the samples were coated with a thin gold layer to reduce surface charging. The phase composition of the samples was studied by X-ray powder diffraction (XPD) using a DRON-3M X-ray diffractometer with filtered Cu Kα radiation. The geometry of the experiments on laser diffraction is shown in Fig. 1. Laser diffraction patterns were recorded using a weakly focused frequency doubled Nd:YAG laser (λ = 532 nm). The diameter of the laser beam spot on the sample was 0.1 mm, corresponding to a spot area of 8000 µm2 . The photonic crystals were placed on a special stage allowing micrometer adjustment of the in-plane sample position with a precision of 10 µm. The setup allowed variation of the angle of incidence of the laser beam maintaining illumination of the same area of the sample. 3. Results and discussion All inverse opals prepared in this work were annealed at 500 ◦ C for 1 h. According to the XPD results (Fig. 2), titanium oxide inverse opal consists of crystalline anatase (PDF-2 file [21–2372]). Further annealing of the sample would result in a phase transition from anatase to rutile and simultaneous degradation of ordered microstructure of inverse opal [24]. The XPD pattern of tungsten oxide inverse opal can be attributed to a crystalline WO3 [71–131] (Fig. 2). The complex XPD spectrum of the manganese oxide sample can be interpreted as a mixture of peaks corresponding to crystalline Mn5 O8 [39–1289] and Mn3 O4 [18–803] phases. The representative areas of inverse opals based manganese, tungsten and titanium oxides are shown at the same magnification in Fig. 3a, b and c, respectively. Apparently, for each sample shown the average center-to-center distance d between spherical voids is less than the average size of the polystyrene microspheres used for template preparation (900 nm). The shrinkage of the samples takes place during their heating and annealing due to the removal of volatile components (mainly water and carbon oxides). However, this shrinkage makes the sizing of air voids ambiguous, because the voids undergo shape deformation and many of them are elliptical rather than spherical. The deformation of the voids is clearly seen, for instance, in Fig. 3e. The effect is different for different regions of the samples and becomes more evident for the voids near the edges of cracks and domain boundaries. Thus, since SEM is the method for local analysis of microstructure, the results of sizing of the voids may vary from point to point of the sample.
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Fig. 2. XPD patterns for inverse opals based on titanium, tungsten and manganese oxides. Here and later manganese oxide inverse opal is referred to as “MnOx ”.
The period of photonic crystals can be independently determined from the diffraction experiments. In contrast to the sizing of mesoscopic objects by SEM, laser diffraction provides an average size, integrated over a macroscale region of the sample. The angle at which the diffraction spots are observed can be analyzed by considering each layer within the photonic√crystal as a twodimensional diffraction grating [15]; the pitch of the grating D is equal to d 3/2. Following simple diffraction theory we can write λ , (1) D where λ is the laser wavelength, ϕ is the angle of incidence of the laser beam, and θ is the angle of diffraction (Fig. 1). In angle-dependent diffraction experiments we mounted a colloidal crystal or inverse opal film on a stage. Then, by in-plane moving of the sample, we scanned it with the laser beam until a sixfold diffraction pattern with no diffuse ring linking the spots was observed (see the inset of Fig. 4). Then, the sample was rotated around the axis of the laser beam to make two of the six diffraction spots horizontal, ensuring that the angles of incidence and diffraction were in the horizontal plane. Finally, we rotated the sample around the vertical axis and monitored the diffraction angle as a function of angle of incidence. It should be stressed that the sixfold diffraction pattern shown in the inset of Fig. 4 is typical of single crystals and indicates that the illuminated area of 8000 µm2 contains close-packed domains with the same crystallographic orientation [23]. Such patterns were recorded from numerous spots of both opal and inverse opal films, confirming that the well-ordered close-packed structure of colloidal crystals was preserved during the replicating process. The dependences of diffraction angle θ on the angle of incidence ϕ for the polystyrene colloidal crystal and inverse opals are shown in Fig. 4. According to Eq. (1), the plot of sin θ against sin ϕ is linear with a gradient of 1 and an intercept of λ/D. It should be noted that the laser diffraction data are in good agreement with the SEM results. The lowest linear fit sin θ = sin ϕ +
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A. Sinitskii et al. / Superlattices and Microstructures 44 (2008) 626–632
Fig. 3. SEM images of inverse opals based on manganese (a), tungsten (b) and titanium (c) oxides, taken at the same magnification; the scale bars are 5 µm. Low-magnification SEM images of inverse opals based on manganese (d) and titanium (e) oxides; the scale bars are 10 µm.
corresponds to the colloidal crystal, which obviously possesses the maximum lattice period of all four samples studied. The average size of colloidal microspheres calculated from the diffraction data is 899 nm, which is in good agreement with the SEM results. For the inverse opals based on manganese, tungsten and manganese oxides the average center-to-center distances between spherical voids are 882, 862 and 730 nm, respectively. As already mentioned, each of these values was obtained not for a few square micrometers area of the sample but for the macroscale spot, and thus they can be considered as average for the whole sample. Moreover, in contrast to SEM, which requires the use of vacuum and often employs coating the samples with conductive materials, this method to determine the period of photonic crystals is nondestructive. It should be stressed that laser diffraction can also be employed for constructing domain maps of photonic crystals, demonstrating for macroscale areas of the samples both regions where all domains have the same crystallographic orientation and disordered regions [23]. Another promising application of laser diffraction to photonic crystals relies on the monitoring of the intensity of diffraction spots as a function of laser beam angle of incidence; such a study provides information on layer stacking in self-assembled photonic crystals, which is inaccessible by conventional microscopy methods [15]. 4. Conclusions In the present work we demonstrate that the shrinkage that occurs in self-assembled photonic crystals during their transformation from colloidal crystals to inverse opals can be visualized by laser diffraction. Bright sixfold diffraction patterns recorded from numerous spots of inverse opal films testify to their high structural quality. By using angle-dependent laser diffraction
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Fig. 4. Angle-dependent laser diffraction data for polystyrene colloidal crystal and inverse opals. The solid lines are linear fits to the data from which the photonic crystal lattice periods can be determined. The inset is a side view photograph of a diffraction experiment on WO3 inverse opal. The sample and the sample holder can be distinguished in the left bottom corner of the photograph.
data we calculated the periodicity for both colloidal crystals and inverse opals; in contrast to the sizing of mesoscopic objects by SEM, laser diffraction provides an average size, integrated over a macroscale region of the sample. This method of analysis takes on special significance for inverse photonic crystals, which are much less investigated than conventional opals. Since diffraction patterns can be recorded in a reflection mode, this method can also be applied for the study of bulk inverse photonic crystals. The significant limitation of this method is that the diffraction patterns can be observed only if the laser wavelength is less than the photonic crystal lattice period. Therefore, the method is difficult to apply to photonic crystals for the visible range, typically composed of structural units less than 300 nm in size. Acknowledgements The work was supported by the Russian Foundation for Basic Research (grants no. 0503-32778 and 07-03-92113), the Program for Fundamental Research of Russian Academy of Sciences and the Federal Target Science and Engineering Program. References [1] T.F. Krauss, R.M. De La Rue, Progress in Quantum Electronics 23 (1999) 51. [2] Y. Xia, B. Gates, Y. Yin, Y. Lu, Advanced Materials 12 (2000) 693. [3] V.N. Astratov, Yu.A. Vlasov, O.Z. Karimov, A.A. Kaplyanskii, Yu.G. Musikhin, N.A. Bert, V.N. Bogomolov, A.V. Prokofiev, Superlattices and Microstructures 22 (1997) 393.
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