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Fabrication of phononic crystals on free-standing silicon membranes
Microelectronic Engineering 149 (2016) 41–45
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Fabrication of phononic crystals on free-standing silicon membranes M. Sledzinska a,⁎, B. Graczykowski a, F. Alzina a, J. Santiso Lopez a, C.M. Sotomayor Torres a,b a b
ICN2 — Catalan Institute of Nanoscience and Nanotechnology, Campus UAB, Bellaterra, 08193 Barcelona, Spain Institucio Catalana de Recerca i Estudis Avancats (ICREA), 08010 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 27 April 2015 Received in revised form 27 July 2015 Accepted 8 September 2015 Available online 12 September 2015 Keywords: E-beam lithography Plasma etching Nanomembrane Phononics
a b s t r a c t Free-standing Si films have been and remain an excellent example to study experimentally the effect of the reduction of the characteristic size on the phonon dispersion relation. A step further in geometrical complexity and, therefore, in increasing the control and manipulation of phonons is achieved by introducing periodicity in the medium to form phononic crystals. Here we report on the development of the fabrication process of large-area, solid–air and solid–solid two-dimensional phononic crystals, directly on free-standing, single crystalline silicon membranes. The patterning of the membranes involved electron-beam lithography and reactive ion etching for holes or metal evaporation and lift-off for pillars. The fabrication was possible due to the external strain induced on the membrane in order to reduce the buckling, which is typically found in large area free-standing structures. As a result, we obtained 250 nm thick structured membranes with patterned areas up to 100 × 100 μm, feature size between 100 and 300 nm and periodicity between 300 and 500 nm. The changes in dispersion relations of hypersonic acoustic phonons due to nanopatterning in free-standing silicon membranes were measured by Brillouin light scattering and the results were compared with numerical calculations by finite elements method. Information on phonon dispersion relation combined with a reliable fabrication process for large-scale structures opens a way for phonon engineering in more complex devices. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Phononic crystals (PnCs) are in general periodic structures made of materials with different elastic properties, with lattice spacing comparable to the acoustic wavelength [1,2]. In analogy to photonic crystals, where propagation of certain electromagnetic waves is prohibited by creating a photonic band gap, a phononic band gap can appear in properly designed PnCs. Engineering of the phonon dispersion relation provides the means to impact on related properties of materials in a controlled manner. In this context, silicon nanomembranes, which are component parts in integrated photonic, plasmonic, mechanical and magnonic devices, appear as an excellent example to study the effect of the reduction of the characteristic size on the phonon dispersion relation and its influence on phonon propagation or material properties such as thermal transport [3–5]. The control and manipulation of phonons can be achieved by introducing periodicity in the elastic properties of the nanomembrane to form phononic crystals [6–8]. Alternatively, placing a periodic arrangement of an array of cylindrical resonators on the membrane can result in the appearance of hybrid slow phonons [9].
⁎ Corresponding author. E-mail address: [email protected] (M. Sledzinska).
http://dx.doi.org/10.1016/j.mee.2015.09.004 0167-9317/© 2015 Elsevier B.V. All rights reserved.
The fabrication of free-standing silicon PnCs-patterned membranes is typically based on processing of the silicon-on-insulator (SOI) wafer with a thin top silicon device layer. The device layer is patterned by means of lithography and reactive ion etching (RIE) and the buried oxide layer (BOX) is removed to obtain a suspended structure [3, 10–12]. However, this method has many disadvantages. First of all, the suspended area has to be relatively small to prevent from bending or collapsing of the structure after suspension. Second of all, etching of the BOX requires harsh chemicals, such as hydrofluoric acid, and critical point drying. Alternatively, focused ion beam (FIB) milling can be used to pattern holes, as it is often done in case of photonic crystals [13]. This approach allows fabrication of large scale PnCs with well controlled diameters, but is usually time consuming. Moreover, the profile of the holes is not perfectly straight: the top diameter is larger than the bottom one [14,15]. In this article we present a method to fabricate phononic crystals with dimensions of 100 × 100 μm, based on free-standing silicon membranes, which avoids the abovementioned problems. With the presented process the suspended areas can be larger than in case of fabrication with SOI wafers and the integration of Al fabricated structures like, for example, electrodes, plasmonic or phononic structures is easier. This fabrication process was already successfully realized using SiN membranes for holey phononic crystals [16].
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M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
First of all, we show that a thin layer of poly(methyl methacrylate) (PMMA) on top of the membrane induces enough strain to reduce the buckling, typical for thin, stress-free membranes. The exact profile of the membrane with and without the PMMA was obtained using optical profilometry. Then we present a fabrication process for obtaining large area PnCs, both holes and metallic pillars. Finally, we compare the Brillouin spectra of the plain and holey membrane and resolve the phonon modes using finite element method calculations (FEM). 2. Fabrication methods We have adapted the electron beam lithography (EBL) and RIE pattern transfer process in order to fabricate square-lattice, holey PnCs over large areas of a free-standing membrane. We have also performed EBL and, metal evaporation in order to achieve square-lattice of aluminium nanopillars on the membrane. In our process we used commercially available, single crystal silicon (100) membranes (Fig. 1 inset), with a window size of 3.2 × 3.2 mm2 and 250 nm thick (Norcada Inc.). These ultra-thin silicon membranes were slightly wrinkled due to the low stress and thickness of the membrane film. The buckling is typical for large free-standing membranes, unless external strain is applied [17,18]. In our approach we used a layer of PMMA, approximately 300 nm thick, on the sample, which induced enough strain in order to flatten the membrane. The membrane profile was measured using optical profilometry on both pristine and PMMA-covered membranes. The pristine membrane shows clear buckling, but after being covered with a thin polymer layer it becomes flat, as shown in Fig. 1. In both of the figures we show a part of the bulk membrane frame as a reference. The PMMA 950k (Allresist) was spun at 4000 rpm for one minute, followed by one hour bake at 100 °C in an oven. We designed PnCs with hole diameters between 100 and 250 nm with a constant period of 300 nm. The EBL (Raith 150-TWO) was performed at 20 kV acceleration voltage, with a different dose for each hole diameter (320–360 μC/cm2) in order to reduce the proximity effect. The writefield area was of 100 × 100 μm and this was the maximum size of the phononic structures. After development in 1:3 methyl isobutyl ketone:isopropanol (MIBK:IPA) the samples were post-baked for one minute at 80 °C on a hot plate. This step additionally hardened the PMMA mask before the RIE. The pattern was transferred to silicon using the Bosch process (Alcatel AMS-110DE). The source power was set to 500 W and the flow of SF6 and C4F8 gases was of 150 sccm and 100 sccm, respectively. The etching time varied between 30 and 60 s, depending on the hole diameter. Finally, after pattern transfer the samples were placed in a plasma system (PVA Tepla), and cleaned in 50 sccm O2 at 400 W for one minute. For the preparation of PnCs made of metal nanopillars the same spin-coating and EBL process as described previously were used, adjusting the exposure dose between 360 and 380 μC/cm2. The EBL was followed by metal evaporation of 5 nm Ti and 70 nm Al (ATC
Orion, Telemark). In this case we fabricated structures with the pitch of 400 and 500 nm and pillar diameter of 300 nm. Lift-off was done in acetone bath at 50 °C.
3. Experimental technique Measurements of the dispersion relations of phonons propagating both in pristine membranes and phononic crystal membranes were performed by means of Brillouin light scattering (BLS). Brillouin light scattering spectroscopy allows the investigation of thermally activated acoustic phonons in the GHz range of frequencies (0.2–250 GHz). BLS is a well-established technique commonly used in non-destructive testing of elastic properties and structural phase transitions in bulk materials [19–21]. BLS has been also found as an excellent tool to characterize phonon propagation in the nm-scale systems, such as ultra-thin free standing membranes [22] and phononic crystals [9]. BLS experiments provide information on the relative change in the frequency (Stokes and anti-Stokes components) of laser light undergoing inelastic coherent scattering by acoustic phonons. For opaque or semi-transparent materials, the main contribution to the scattered light comes from the surface ripple mechanism. Brillouin spectroscopy measurements were performed on a six-pass tandem type Fabry–Perot interferometer (JRS Scientific Instruments) in the p–p (incident and scattered light polarization parallel to the plane of incidence) backscattering geometry. The light source was an argon gas laser generating light at λ = 514.5 nm. For the backscattering geometry the angle of the laser beam incidence onto a given surface studied is equal to the scattering angle and denoted by θ. The magnitude of the scattering wave vector q is given by [19–21]: q ¼ 4π λsinθ : (1) For periodic structures such as phononic crystals, the scattering wave vector q is defined by momentum conservation:q = k + G , (2)where k denotes the wave vector of an acoustic phonon and G is a reciprocal lattice vector. To get a correct dispersion relation for the acoustic waves propagating in 2D phononic crystal membranes we use the FEM approach. The FEM calculations were performed using frequency domain module (COMSOL Metaphysics) and the silicon material properties are gathered in Table 1.
4. Results and discussion Using the above-described procedure we successfully fabricated free-standing holey PnCs with thickness of 250 nm and with a variety of filling factors (relation between hole area and unit cell area), ranging from 10% to 50%, as shown in Fig. 2. The largest filling factor corresponds to the hole diameter of 240 nm, which means that the walls between the holes are 60 nm thick. There is still room for improvement and achieving even larger filling factor, as the limit for standard nanofabrication is around 20 nm.
Fig. 1. Optical profilometry images of a) pristine and b) PMMA-covered membranes. Inset: photo of a Norcada chip indicating the studied area.
M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45 Table 1 Elastic constants Cij and mass density ρ of Si and Al used in FEM calculations [24]. Material
C11(GPa)
C12(GPa)
C44(GPa)
ρ(kg/m3)
Silicon (anisotropic) Aluminium (isotropic)
165.7 111.3
63.9 59.1
79.9 26.1
2331 2700
For all the holey structures we set the periodicity a to 300 nm. PnCs of this size can be used to control the propagation of hypersound and are convenient to perform experiments such as Brillouin light scattering because it allows probing both 1st and 2nd Brillouin zones. Moreover, simultaneous phononic and photonic bandgaps could be obtained with an appropriate design [25]. The SEM images in Fig. 2 show that both the diameter of the holes and periodicity are maintained within each structure. To verify the etching profile of the holes we performed focus ion beam cross-sections on two of the PnCs with holes of 200 and 220 nm (Zeiss 1560XB Cross Beam), and period 300 nm. The SEM image of the latter is shown in Fig. 2e) (FEI Magellan 400). In both of the cases the cut revealed etching profile of 90° and the roughness of the walls is approximately 8 nm (magnification 650,000×). The cuts also confirmed that the etching process is reproducible for different diameters of the holes. For both holey and nano-pillar PnCs it is possible to fabricate various structures on the same sample, as shown in Fig. 3a). For the latter case, we fabricated structures with pillar diameter of 300 nm and pitch of 400 and 500 nm. A pitch size in the range of hundreds of nanometers affects the propagation of the acoustic waves in the GHz range and at the same time can localize phonon modes in the pillars, which can result in sub-
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wavelength features like in metamaterials. It is important that all the pillars have uniform diameter, shape and height. SEM analysis of the structures confirms this uniformity, as shown in Fig. 3b) and the inset. The Brillouin light spectroscopy measurements were done in the [110] axis of the membrane, which corresponds to the Γ-X direction of the first Brillouin zone. For thin homogenous membranes breaking spatial continuity in one dimension results in a propagation of three families of Lamb waves, namely antisymmetric (A), symmetric (S) and shear horizontal (SH) [23]. Fig. 4a) shows the anti-Stokes component of a BLS spectrum obtained at q = 0.0122 nm− 1 for 250 nm thick plain Norcada membrane. After the position of the five peaks in the spectrum was obtained by a fitting procedure to Lorentzian functions, they were identified from the eigenmode FEM solutions (see Fig. 4b)) to belong to the antisymmetric (A) and symmetric (S) families of phonons. There are two fundamental modes A0 and S0 present at 8.15 GHz and 13.24 GHz, respectively and their higher harmonics A1, S1 and S2 at 17.3 GHz, 16.31 GHz and 28.09 GHz, respectively. Since for all SH modes the out-of-plane displacement is zero, therefore they are not present in BLS spectrum. This sample was measured as a reference for the BLS experiments performed on PnCs fabricated on the membranes with the same thickness and elastic properties. There is clear evidence that periodic PnC leads to the change in the phonon frequencies propagating in the membrane. As an example of the influence of a PnC on the propagating phonon modes we measured Si membrane with air inclusions of diameter of d = 170 nm and lattice constant a = 300 nm. It is clearly visible in Fig. 4c) that introducing a periodic modification of the membrane results is the presence of new spectral features for the same wave vector q. In this case we could fit
Fig. 2. SEM images of the nanopatterned Si membranes with 300 nm pitch and filling factors of a) 10%, b) 25%, c) 42%, and d) 50%. The scale bar corresponds to 300 nm. e) SEM image of the cross-section of a patterned membrane with hole diameter of 220 nm and pitch of 300 nm obtained by FIB. The scale bar corresponds to 300 nm. f) Schematic representation of the PnC on the Si membrane, where [110] and ½110 represent crystallographic orientation of the membrane. The unit cell with size a is colored pink and d is the hole diameter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
Fig. 3. SEM images of Si membrane nanopatterned with Al pillars. a) Twelve different areas with phononic crystals patterned on the same membrane. Scale bar corresponds to 100 μm. There is a non-patterned island intentionally left in the middle of each structure. b) Al nanopillars with a diameter of 300 nm and pitch of 500 nm. Insert: Tilted image of the structure. Scale bars correspond to 500 nm.
15 peaks, out of which 12 could be identified using FEM. Modes with frequencies higher than 20 GHz were difficult to identify due to the numerous FEM solutions. Holey PnCs with other hole diameters and pitch were also measured with BLS and the results were in good agreement with FEM simulations. In Fig. 4e) we show an example of a Brillouin spectrum of a PnC made of Al pillars with 270 nm diameter. The presence of the pillars modifies the dispersion relation making possible the appearance of localized modes. We identified seven of the modes using the FEM simulations; however identification of the higher frequency modes was impossible due to the numerous solutions [9]. 5. Conclusions In this paper we have presented a method to fabricate the 2D phononic and photonic crystals starting from free-standing Si membranes, designed to control phonons in the range of GHz. This method allows the fabrication of large-area structures with feature size of a
few hundreds of nanometers. To achieve this we optimized the EBL and RIE parameters, to fabricate square lattices of holes with lattice constant of 300 nm, filling factors ranging from 10 to 50%, specifically adjusting exposure dose in order to avoid proximity effect. Also the applied RIE recipe allows for straight walls of the patterned features. In similar way we demonstrated the possibility of fabrication of metal pillars on top of the membranes by means of ELB and metal evaporation. The influence of surface modification was measured by Brillouin spectroscopy, providing direct information on the phonon frequencies for both patterned and pristine samples. The Brillouin peaks were assigned to corresponding Lamb modes using numerical simulations, providing very good agreement with the elastic theory. Even though only membranes of 250 nm thickness were used to fabricate PnCs in this study, it is possible to use the same method for membranes with different thicknesses, as long as the polymer layer induces enough strain to eliminate buckling. The main limitation for the fabrication process would be the thickness of the membrane. Very
Fig. 4. a) Anti-Stokes part of the Brillouin spectrum for non-patterned 250 nm thick, b) FEM simulated displacement fields of the identified modes propagating in the membrane, c) antiStokes part of the Brillouin spectrum for PnC membrane with air holes with a diameter of 170 nm and 300 nm pitch, d) FEM simulated displacement fields of the modes propagating in the holey PnC membrane, e) anti-Stokes part of the Brillouin spectrum for PnC membrane with aluminium pillars with a diameter of 270 nm, 500 nm pitch and 75 nm height, and f) FEM simulated displacement fields of the modes propagating in the pillar PnC membrane.
M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
thin (for example sub-100 nm) membranes are more fragile and prone to breaking while manipulating. Especially spin coating is a delicate step, because the membrane is subject to strong centrifugal force. Large-scale, free-standing PnCs can be directly used for measurements of thermal conductivity, for example with the novel technique of two-laser Raman thermometry [4]. The use of silicon membranes is compatible with CMOS technology and the reliable fabrication process opens a way for engineering more complex devices with possible applications in fields such as MEMS/NEMS, telecommunication or energy harvesting. Acknowledgments The authors acknowledge the financial support from the FP7 FET Energy Project MERGING (Grant no. 309150); the Spanish MICINN projects nanoTHERM (Grant no. CSD2010-0044); TAPHOR (MAT201231392) and the program Severo Ochoa (Grant SEV-2013-0295). References [1] E. Economou, M. Sigals, Solid State Commun. 86 (1993) 141. [2] M.S. Kushwala, P. Halevi, L. Dobrzynski, B. Djafar-Rouhani, Phys. Rev. Lett. 71 (1993) 2022. [3] P. Ferrando-Villalba, A.F. Lopeandia, Ll Abad, J. Llobet, M. Molina-Ruiz, G. Garcia, M. Gerbolès, F.X. Alvarez, A.R. Goñi, F.J. Muñoz-Pascual, J. Rodríguez-Viejo, Nanotechnology 25 (2014) 185402. [4] J.S. Reparaz, E. Chavez-Angel, M.R. Wagner, B. Graczykowski, J. Gomis-Bresco, F. Alzina, C.M. Sotomayor Torres, Rev. Sci. Instrum. 85 (2014) 034901. [5] E. Chávez-Ángel, J.S. Reparaz, J. Gomis-Bresco, M.R. Wagner, J. Cuffe, B. Graczykowski, A. Shchepetov, H. Jiang, M. Prunnila, J. Ahopelto, F. Alzina, C.M. Sotomayor Torres, APL Mater. 2 (2014) 012113. [6] S. Mohammadi, A. Asghar Eftekhar, A. Khelif, W.D. Hunt, A. Adibi, Appl. Phys. Lett. 92 (2008) 221905.
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[7] Y.M. Soliman, M.F. Su, Z.C. Leseman, C.M. Reinke, I. El-Kady, R.H. Olsson III, Appl. Phys. Lett. 97 (2010) 193502. [8] S. Alaie, M.F. Su, D.F. Goettler, I. El-Kady, Z. Leseman, J. App. Phys. 113 (2013) 103513. [9] B. Graczykowski, M. Sledzinska, F. Alzina, J. Gomis-Bresco, J.S. Reparaz, M.R. Wagner, C.M. Sotomayor Torres, Phys. Rev. B 91 (2015) 075414. [10] B. Graczykowski, J. Gomis-Bresco, F. Alzina, J.S. Reparaz, A. Shchepetov, M. Prunnila, J. Ahopelto, C.M. Sotomayor Torres, New J. Phys. 16 (2014) 073024. [11] P.E. Hopkins, C.M. Reinke, M.F. Su, R.H. Olsson III, E.A. Sahander, Z.C. Leseman, J.R. Serrano, L.M. Phinney, I. El-Kady, Nanolett. 11 (2011) 107. [12] J. Tang, H.-T. Wang, D. Hyun Lee, M. Fardy, Z. Huo, T.P. Russell, P. Yang, Nano Lett. 10 (2010) 4279. [13] Z.-Y. Li, C. Wang, L. Gan, Photonic Crystals Towards Optical Integration, Advances in Photonic Crystals, InTech, 2013. [14] K. Balasubramanian, P.J. Heard, M.J. Cryan, J. Vac. Sci. Technol. B 24 (2006) 2533. [15] G. Si, A.J. Danner, S. Lang Teo, E. Jin Teo, J. Teng, A.A. Bettiol, J. Vac. Sci. Technol. B 29 (2011) 021205. [16] N. Zen, T.A. Puurtinen, T.J. Isotalo, Sa Chaudhuri, I.J. Maasilta, Nat. Commun. 5 (3435) (2014). [17] P.E. Allain, X. Le Roux, F. Parrain, A. Bosseboeuf, Micromech. Microeng. 23 (2013) 015014. [18] J.A. Rogers, M.G. Lagally, R.G. Nuzzo, Nature 477 (2011) 45. [19] A. Shchepetov, M. Prunnila, F. Alzina, L. Schneider, J. Cuffe, H. Jiang, E.I. Kauppinen, C.M. Sotomayor Torres, J. Ahopelto, Appl. Phys. Lett. 102 (2013) 192108. [20] J. Sandercock, in: M. Cardona, G. Gntherod (Eds.), Light Scattering in Solids III, 51, Springer, Berlin Heidelberg, 1982. [21] J.D. Comins, Handbook of Elastic properties of Solids, Liquids and Gases, Academic Press, San Diego, 2001. [22] C.E. Bottani, M.G. Beghi, Phil. Trans. R. Soc. London 362 (2004) 2513. [23] J. Cuffe, E. Chávez, A. Shchepetov, P.-O. Chapuis, E.H. El Boudouti, F. Alzina, T. Kehoe, J. Gomis-Bresco, D. Dudek, Y. Pennec, B. Djafari-Rouhani, M. Prunnila, J. Ahopelto, C.M. Sotomayor Torres, Nano Lett. 12 (2012) 3569. [24] G.W. Farnell, Properties of Elastic Surface Waves, Physical Acoustics 6, Academic, New York, 1970. [25] Y. Pennec, B. Djafari Rouhani, E.H. El Boudouti, C. Li, Y. El Hassouani, J.O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, A. Martinez, Opt. Express 18 (2010) 14301.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Fabrication of phononic crystals on free-standing silicon membranes M. Sledzinska a,⁎, B. Graczykowski a, F. Alzina a, J. Santiso Lopez a, C.M. Sotomayor Torres a,b a b
ICN2 — Catalan Institute of Nanoscience and Nanotechnology, Campus UAB, Bellaterra, 08193 Barcelona, Spain Institucio Catalana de Recerca i Estudis Avancats (ICREA), 08010 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 27 April 2015 Received in revised form 27 July 2015 Accepted 8 September 2015 Available online 12 September 2015 Keywords: E-beam lithography Plasma etching Nanomembrane Phononics
a b s t r a c t Free-standing Si films have been and remain an excellent example to study experimentally the effect of the reduction of the characteristic size on the phonon dispersion relation. A step further in geometrical complexity and, therefore, in increasing the control and manipulation of phonons is achieved by introducing periodicity in the medium to form phononic crystals. Here we report on the development of the fabrication process of large-area, solid–air and solid–solid two-dimensional phononic crystals, directly on free-standing, single crystalline silicon membranes. The patterning of the membranes involved electron-beam lithography and reactive ion etching for holes or metal evaporation and lift-off for pillars. The fabrication was possible due to the external strain induced on the membrane in order to reduce the buckling, which is typically found in large area free-standing structures. As a result, we obtained 250 nm thick structured membranes with patterned areas up to 100 × 100 μm, feature size between 100 and 300 nm and periodicity between 300 and 500 nm. The changes in dispersion relations of hypersonic acoustic phonons due to nanopatterning in free-standing silicon membranes were measured by Brillouin light scattering and the results were compared with numerical calculations by finite elements method. Information on phonon dispersion relation combined with a reliable fabrication process for large-scale structures opens a way for phonon engineering in more complex devices. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Phononic crystals (PnCs) are in general periodic structures made of materials with different elastic properties, with lattice spacing comparable to the acoustic wavelength [1,2]. In analogy to photonic crystals, where propagation of certain electromagnetic waves is prohibited by creating a photonic band gap, a phononic band gap can appear in properly designed PnCs. Engineering of the phonon dispersion relation provides the means to impact on related properties of materials in a controlled manner. In this context, silicon nanomembranes, which are component parts in integrated photonic, plasmonic, mechanical and magnonic devices, appear as an excellent example to study the effect of the reduction of the characteristic size on the phonon dispersion relation and its influence on phonon propagation or material properties such as thermal transport [3–5]. The control and manipulation of phonons can be achieved by introducing periodicity in the elastic properties of the nanomembrane to form phononic crystals [6–8]. Alternatively, placing a periodic arrangement of an array of cylindrical resonators on the membrane can result in the appearance of hybrid slow phonons [9].
⁎ Corresponding author. E-mail address: [email protected] (M. Sledzinska).
http://dx.doi.org/10.1016/j.mee.2015.09.004 0167-9317/© 2015 Elsevier B.V. All rights reserved.
The fabrication of free-standing silicon PnCs-patterned membranes is typically based on processing of the silicon-on-insulator (SOI) wafer with a thin top silicon device layer. The device layer is patterned by means of lithography and reactive ion etching (RIE) and the buried oxide layer (BOX) is removed to obtain a suspended structure [3, 10–12]. However, this method has many disadvantages. First of all, the suspended area has to be relatively small to prevent from bending or collapsing of the structure after suspension. Second of all, etching of the BOX requires harsh chemicals, such as hydrofluoric acid, and critical point drying. Alternatively, focused ion beam (FIB) milling can be used to pattern holes, as it is often done in case of photonic crystals [13]. This approach allows fabrication of large scale PnCs with well controlled diameters, but is usually time consuming. Moreover, the profile of the holes is not perfectly straight: the top diameter is larger than the bottom one [14,15]. In this article we present a method to fabricate phononic crystals with dimensions of 100 × 100 μm, based on free-standing silicon membranes, which avoids the abovementioned problems. With the presented process the suspended areas can be larger than in case of fabrication with SOI wafers and the integration of Al fabricated structures like, for example, electrodes, plasmonic or phononic structures is easier. This fabrication process was already successfully realized using SiN membranes for holey phononic crystals [16].
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M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
First of all, we show that a thin layer of poly(methyl methacrylate) (PMMA) on top of the membrane induces enough strain to reduce the buckling, typical for thin, stress-free membranes. The exact profile of the membrane with and without the PMMA was obtained using optical profilometry. Then we present a fabrication process for obtaining large area PnCs, both holes and metallic pillars. Finally, we compare the Brillouin spectra of the plain and holey membrane and resolve the phonon modes using finite element method calculations (FEM). 2. Fabrication methods We have adapted the electron beam lithography (EBL) and RIE pattern transfer process in order to fabricate square-lattice, holey PnCs over large areas of a free-standing membrane. We have also performed EBL and, metal evaporation in order to achieve square-lattice of aluminium nanopillars on the membrane. In our process we used commercially available, single crystal silicon (100) membranes (Fig. 1 inset), with a window size of 3.2 × 3.2 mm2 and 250 nm thick (Norcada Inc.). These ultra-thin silicon membranes were slightly wrinkled due to the low stress and thickness of the membrane film. The buckling is typical for large free-standing membranes, unless external strain is applied [17,18]. In our approach we used a layer of PMMA, approximately 300 nm thick, on the sample, which induced enough strain in order to flatten the membrane. The membrane profile was measured using optical profilometry on both pristine and PMMA-covered membranes. The pristine membrane shows clear buckling, but after being covered with a thin polymer layer it becomes flat, as shown in Fig. 1. In both of the figures we show a part of the bulk membrane frame as a reference. The PMMA 950k (Allresist) was spun at 4000 rpm for one minute, followed by one hour bake at 100 °C in an oven. We designed PnCs with hole diameters between 100 and 250 nm with a constant period of 300 nm. The EBL (Raith 150-TWO) was performed at 20 kV acceleration voltage, with a different dose for each hole diameter (320–360 μC/cm2) in order to reduce the proximity effect. The writefield area was of 100 × 100 μm and this was the maximum size of the phononic structures. After development in 1:3 methyl isobutyl ketone:isopropanol (MIBK:IPA) the samples were post-baked for one minute at 80 °C on a hot plate. This step additionally hardened the PMMA mask before the RIE. The pattern was transferred to silicon using the Bosch process (Alcatel AMS-110DE). The source power was set to 500 W and the flow of SF6 and C4F8 gases was of 150 sccm and 100 sccm, respectively. The etching time varied between 30 and 60 s, depending on the hole diameter. Finally, after pattern transfer the samples were placed in a plasma system (PVA Tepla), and cleaned in 50 sccm O2 at 400 W for one minute. For the preparation of PnCs made of metal nanopillars the same spin-coating and EBL process as described previously were used, adjusting the exposure dose between 360 and 380 μC/cm2. The EBL was followed by metal evaporation of 5 nm Ti and 70 nm Al (ATC
Orion, Telemark). In this case we fabricated structures with the pitch of 400 and 500 nm and pillar diameter of 300 nm. Lift-off was done in acetone bath at 50 °C.
3. Experimental technique Measurements of the dispersion relations of phonons propagating both in pristine membranes and phononic crystal membranes were performed by means of Brillouin light scattering (BLS). Brillouin light scattering spectroscopy allows the investigation of thermally activated acoustic phonons in the GHz range of frequencies (0.2–250 GHz). BLS is a well-established technique commonly used in non-destructive testing of elastic properties and structural phase transitions in bulk materials [19–21]. BLS has been also found as an excellent tool to characterize phonon propagation in the nm-scale systems, such as ultra-thin free standing membranes [22] and phononic crystals [9]. BLS experiments provide information on the relative change in the frequency (Stokes and anti-Stokes components) of laser light undergoing inelastic coherent scattering by acoustic phonons. For opaque or semi-transparent materials, the main contribution to the scattered light comes from the surface ripple mechanism. Brillouin spectroscopy measurements were performed on a six-pass tandem type Fabry–Perot interferometer (JRS Scientific Instruments) in the p–p (incident and scattered light polarization parallel to the plane of incidence) backscattering geometry. The light source was an argon gas laser generating light at λ = 514.5 nm. For the backscattering geometry the angle of the laser beam incidence onto a given surface studied is equal to the scattering angle and denoted by θ. The magnitude of the scattering wave vector q is given by [19–21]: q ¼ 4π λsinθ : (1) For periodic structures such as phononic crystals, the scattering wave vector q is defined by momentum conservation:q = k + G , (2)where k denotes the wave vector of an acoustic phonon and G is a reciprocal lattice vector. To get a correct dispersion relation for the acoustic waves propagating in 2D phononic crystal membranes we use the FEM approach. The FEM calculations were performed using frequency domain module (COMSOL Metaphysics) and the silicon material properties are gathered in Table 1.
4. Results and discussion Using the above-described procedure we successfully fabricated free-standing holey PnCs with thickness of 250 nm and with a variety of filling factors (relation between hole area and unit cell area), ranging from 10% to 50%, as shown in Fig. 2. The largest filling factor corresponds to the hole diameter of 240 nm, which means that the walls between the holes are 60 nm thick. There is still room for improvement and achieving even larger filling factor, as the limit for standard nanofabrication is around 20 nm.
Fig. 1. Optical profilometry images of a) pristine and b) PMMA-covered membranes. Inset: photo of a Norcada chip indicating the studied area.
M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45 Table 1 Elastic constants Cij and mass density ρ of Si and Al used in FEM calculations [24]. Material
C11(GPa)
C12(GPa)
C44(GPa)
ρ(kg/m3)
Silicon (anisotropic) Aluminium (isotropic)
165.7 111.3
63.9 59.1
79.9 26.1
2331 2700
For all the holey structures we set the periodicity a to 300 nm. PnCs of this size can be used to control the propagation of hypersound and are convenient to perform experiments such as Brillouin light scattering because it allows probing both 1st and 2nd Brillouin zones. Moreover, simultaneous phononic and photonic bandgaps could be obtained with an appropriate design [25]. The SEM images in Fig. 2 show that both the diameter of the holes and periodicity are maintained within each structure. To verify the etching profile of the holes we performed focus ion beam cross-sections on two of the PnCs with holes of 200 and 220 nm (Zeiss 1560XB Cross Beam), and period 300 nm. The SEM image of the latter is shown in Fig. 2e) (FEI Magellan 400). In both of the cases the cut revealed etching profile of 90° and the roughness of the walls is approximately 8 nm (magnification 650,000×). The cuts also confirmed that the etching process is reproducible for different diameters of the holes. For both holey and nano-pillar PnCs it is possible to fabricate various structures on the same sample, as shown in Fig. 3a). For the latter case, we fabricated structures with pillar diameter of 300 nm and pitch of 400 and 500 nm. A pitch size in the range of hundreds of nanometers affects the propagation of the acoustic waves in the GHz range and at the same time can localize phonon modes in the pillars, which can result in sub-
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wavelength features like in metamaterials. It is important that all the pillars have uniform diameter, shape and height. SEM analysis of the structures confirms this uniformity, as shown in Fig. 3b) and the inset. The Brillouin light spectroscopy measurements were done in the [110] axis of the membrane, which corresponds to the Γ-X direction of the first Brillouin zone. For thin homogenous membranes breaking spatial continuity in one dimension results in a propagation of three families of Lamb waves, namely antisymmetric (A), symmetric (S) and shear horizontal (SH) [23]. Fig. 4a) shows the anti-Stokes component of a BLS spectrum obtained at q = 0.0122 nm− 1 for 250 nm thick plain Norcada membrane. After the position of the five peaks in the spectrum was obtained by a fitting procedure to Lorentzian functions, they were identified from the eigenmode FEM solutions (see Fig. 4b)) to belong to the antisymmetric (A) and symmetric (S) families of phonons. There are two fundamental modes A0 and S0 present at 8.15 GHz and 13.24 GHz, respectively and their higher harmonics A1, S1 and S2 at 17.3 GHz, 16.31 GHz and 28.09 GHz, respectively. Since for all SH modes the out-of-plane displacement is zero, therefore they are not present in BLS spectrum. This sample was measured as a reference for the BLS experiments performed on PnCs fabricated on the membranes with the same thickness and elastic properties. There is clear evidence that periodic PnC leads to the change in the phonon frequencies propagating in the membrane. As an example of the influence of a PnC on the propagating phonon modes we measured Si membrane with air inclusions of diameter of d = 170 nm and lattice constant a = 300 nm. It is clearly visible in Fig. 4c) that introducing a periodic modification of the membrane results is the presence of new spectral features for the same wave vector q. In this case we could fit
Fig. 2. SEM images of the nanopatterned Si membranes with 300 nm pitch and filling factors of a) 10%, b) 25%, c) 42%, and d) 50%. The scale bar corresponds to 300 nm. e) SEM image of the cross-section of a patterned membrane with hole diameter of 220 nm and pitch of 300 nm obtained by FIB. The scale bar corresponds to 300 nm. f) Schematic representation of the PnC on the Si membrane, where [110] and ½110 represent crystallographic orientation of the membrane. The unit cell with size a is colored pink and d is the hole diameter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
Fig. 3. SEM images of Si membrane nanopatterned with Al pillars. a) Twelve different areas with phononic crystals patterned on the same membrane. Scale bar corresponds to 100 μm. There is a non-patterned island intentionally left in the middle of each structure. b) Al nanopillars with a diameter of 300 nm and pitch of 500 nm. Insert: Tilted image of the structure. Scale bars correspond to 500 nm.
15 peaks, out of which 12 could be identified using FEM. Modes with frequencies higher than 20 GHz were difficult to identify due to the numerous FEM solutions. Holey PnCs with other hole diameters and pitch were also measured with BLS and the results were in good agreement with FEM simulations. In Fig. 4e) we show an example of a Brillouin spectrum of a PnC made of Al pillars with 270 nm diameter. The presence of the pillars modifies the dispersion relation making possible the appearance of localized modes. We identified seven of the modes using the FEM simulations; however identification of the higher frequency modes was impossible due to the numerous solutions [9]. 5. Conclusions In this paper we have presented a method to fabricate the 2D phononic and photonic crystals starting from free-standing Si membranes, designed to control phonons in the range of GHz. This method allows the fabrication of large-area structures with feature size of a
few hundreds of nanometers. To achieve this we optimized the EBL and RIE parameters, to fabricate square lattices of holes with lattice constant of 300 nm, filling factors ranging from 10 to 50%, specifically adjusting exposure dose in order to avoid proximity effect. Also the applied RIE recipe allows for straight walls of the patterned features. In similar way we demonstrated the possibility of fabrication of metal pillars on top of the membranes by means of ELB and metal evaporation. The influence of surface modification was measured by Brillouin spectroscopy, providing direct information on the phonon frequencies for both patterned and pristine samples. The Brillouin peaks were assigned to corresponding Lamb modes using numerical simulations, providing very good agreement with the elastic theory. Even though only membranes of 250 nm thickness were used to fabricate PnCs in this study, it is possible to use the same method for membranes with different thicknesses, as long as the polymer layer induces enough strain to eliminate buckling. The main limitation for the fabrication process would be the thickness of the membrane. Very
Fig. 4. a) Anti-Stokes part of the Brillouin spectrum for non-patterned 250 nm thick, b) FEM simulated displacement fields of the identified modes propagating in the membrane, c) antiStokes part of the Brillouin spectrum for PnC membrane with air holes with a diameter of 170 nm and 300 nm pitch, d) FEM simulated displacement fields of the modes propagating in the holey PnC membrane, e) anti-Stokes part of the Brillouin spectrum for PnC membrane with aluminium pillars with a diameter of 270 nm, 500 nm pitch and 75 nm height, and f) FEM simulated displacement fields of the modes propagating in the pillar PnC membrane.
M. Sledzinska et al. / Microelectronic Engineering 149 (2016) 41–45
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