Dielectric Band Edge Enhancement of Energy Conversion Efficiency

May 20, 2008 - Using a Maxwell−Bloch two-level atom model to quantify the dye absorption of light and photocurrent generation, we show that the ...
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J. Phys. Chem. C 2008, 112, 8735–8740

8735

Dielectric Band Edge Enhancement of Energy Conversion Efficiency in Photonic Crystal Dye-Sensitized Solar Cell Chan-Hoe Yip,†,⊥ Yet-Ming Chiang,‡,¶ and Chee-Cheong Wong*,†,§ Center for Singapore-MIT Alliance, Nanyang Technological UniVersity, N3.2-01-36, 65 Nanyang DriVe, Singapore 637460, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, and School of Materials Science and Engineering, Nanyang Technological UniVersity, Blk N4.1, Nanyang AVenue, Singapore 639798 ReceiVed: February 16, 2008; ReVised Manuscript ReceiVed: March 25, 2008

We present evidence for the enhancement of light-to-electrical energy conversion efficiency (IPCE) in photonic crystal dye-sensitized solar cells due to an amplified light field at the dielectric band edge. Under angleresolved monochromatic irradiance along the LU direction, the IPCE enhancement peaks match well with the blue shift in the dielectric band edge. The numerical simulation indicates that the photon localization effect at the dielectric band edge causes the intensification of the light field in the dielectric matrix. Using a Maxwell-Bloch two-level atom model to quantify the dye absorption of light and photocurrent generation, we show that the improvement in IPCE is due to an enhanced light-matter interaction between the dye atom and the amplified field. Introduction cell1

(DSC) has attracted wide-spread The dye-sensitized solar research to realize a high-efficiency and low-cost photovoltaic cell. Today, many research efforts are focused on improving the light absorption performance of the dye sensitizer,2 which is the key component for achieving high-efficiency photovoltaic conversion. In terms of research in cell architectures, photonic crystals3 have been introduced into the DSC as a light management technique in order to improve the light confinement property of the DSC. In several past reports of photonic crystal DSCs, the titanium dioxide (TiO2) inverse opaline photonic crystal was embedded into the nanocrystalline TiO2 electrode layer of a DSC.4,5 This enhanced dye absorbance on the longer wavelength side of the photonic band gap (PBG). It was suggested that the enhanced absorption is due to the slow group velocity of light near to the band edge and the localization of light in the dye-sensitized TiO2. In ref 4, a 26% increase of photocurrent was reported over the spectral range of 400-750 nm due to both slow photon propagation and multiple light scattering effects. However, later developments5,6 suggested that the enhancement of light harvesting is largely contributed to by backscattering effects from the photonic crystal and less by the effect of slow photon localization. To date, the effect of slow photons on the DSC’s energy conversion has not been proven convincingly, even though the band edge effect of slow photon localization7–9 has been shown in studies on photonic band edge lasers10 and amplified photochemistry.11 In this article, we elucidate, experimentally and with numerical models, the band edge effect on the enhanced light-to-electrical * To whom correspondence should be addressed. E-mail: wongcc@ ntu.edu.sg. ‡ Massachusetts Institute of Technology. † Center for Singapore-MIT Alliance, Nanyang Technological University. § School of Materials Science and Engineering, Nanyang Technological University. ⊥ E-mail: [email protected]. ¶ E-mail: [email protected].

energy conversion efficiency (IPCE) of an inverse opal DSC. The merit of the band edge effect can be unambiguously highlighted here as the IPCE comparison was done using samples with and without periodic structures using almost similar inverse opal TiO2 material volume and dye loading. In previous studies,4–6 the IPCE comparisons were done using a different TiO2 material volume and thus a different amount of photogenerated current due to a different volume of dye. Our approach of achieving the same material volume for both the periodic and nonperiodic structure included collapsing11 of a section of TiO2 inverse opal. As a result, a true IPCE enhancement due to the band edge effect could be quantified. Experiment Methods The assembly of the DSC was carried out using a similar method as that described in literature,12 beginning with preparation of a TiO2 nanoparticle suspension in water. TiO2 nanoparticles were synthesized by hydrolyzing titanium alkoxide in deionized water. The reagent consisted of 25 mL of titanium isopropoxide (97% Aldrich) modified with the addition of 5 mL of acetic acid (97% Flurka). The titanium isopropoxide solution was added rapidly to a 250 mL of 0.1 M nitric acid (69% Flurka) solution. The reaction flask was capped, and the solution was left stirring for 8 h to complete the hydrolysis process. Finally, the TiO2 nanoparticle suspension was topped up to 500 mL with deionized water, and the final TiO2 solid concentration in water was about 1.5 wt %. The resulting suspension was stable for several weeks of storage at room temperature. Figure 1a shows the powder X-ray diffraction (XRD) of the TiO2 nanoparticle (heat treatment 450 °C, 2 h). Rietveld analysis reported TiO2 phase distributions of 75.7, 19.6, and 4.7% for anatase, rutile, and brookite, respectively. Figure 1b depicts the TEM image of TiO2 nanoparticles; the average size of the nanoparticle was about 15 nm. To deposit a TiO2 nanoparticle film, the TiO2 suspension was concentrated to 14 wt % with a rotary evaporator. A binder solution was prepared by dissolving 4 g of methyl cellulose (MC, molecular

10.1021/jp801385k CCC: $40.75  2008 American Chemical Society Published on Web 05/20/2008

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Yip et al. photonic crystal (C-PC) bilayer electrode at almost the same amount of TiO2 in one cell. The polystyrene template and MC binder were removed by calcination at 450 °C for 2 h. At the same time, the heat treatment sintered the TiO2 matrix, and phase transformation was carried out. Finally, a commercial dye, Solaronix SA Ruthenium 535-bisTBA dye, was sensitized12 throughout the entire structure (film-PC and film-C-PC), and the cell was filled with Solaronix TG50 Iodolyte electrolyte. The film-PC bilayer and film-C-PC bilayer are about 6.4 and 4.7 µm thick, respectively (alpha-step profilemeter, Tencor Instrument). Figure 2a,b depicts the cross-sectional scanning electron micrographs of the film-PC bilayer, and Figure 2c shows the C-PC layer. The SEM cross-sectional samples were prepared as follows. A small crack was made at the edge of the nonsensitized sample using a diamond scribing pen. Then, the crack was carefully propagated through the sample. Scanning electron microscopy was performed on the cross section of the fracture surface. Results

Figure 1. (a) Powder XRD reported a predominantly anatase TiO2 phase by Rietveld analysis; (b) TEM image of the synthesized TiO2 nanoparticle. The mean size is about 15 nm.

weight 14000, Aldrich) in 20 mL of deionized water. Finally, a sol-gel of a final mixture of 20 mL of concentrated TiO2 suspension and 20 mL of MC binder solution was stirred overnight. A TiO2 nanoparticle film was then doctor-bladed onto the fluorinedoped tin oxide conducting glass (TEC 7, Pilkington) aided with adhesive tapes. The composite film was annealed at 350 °C for 2 h to achieve a mechanically robust platform for the subsequent colloidal self-assembly process. Monodispersed polystyrene (PS) colloids of diameter 285 nm were synthesized by emulsion polymerization.13 A PS colloidal crystal (opal) layer was grown on top of the TiO2 film by the convective self-assembly technique.14 The PS colloidal crystal was annealed at 90 °C for 2 h to achieve a stronger structure for subsequent TiO2 infiltration. The interstitial of the PS opal was infiltrated with TiO2 nanoparticles (1.5 wt % suspension) by repeated dip coating. After each dip coating, the PS opal was left to dry vertically in air and then heated to 90 °C for 15 min. The dip coating cycle was completed when an 8% shift15 in the Bragg reflection peak was observed in a spectrometer (USB2000, Ocean Optics). This signifies a near-full filling of TiO2 nanoparticle in the PS opal interstices. To ensure a similar volume of TiO2 nanoparticles for comparison across samples, a section of a PS opal/TiO2 infiltrated structure was collapsed11 using toluene and 10 min ultrasonic treatment. The sample was placed horizontally in an empty Petri dish with the polystyrene opal/TiO2 infiltrated structure facing up. A few drops of toluene were carefully spread across a selected section of the polystyrene opal/TiO2 infiltrated structure. Then, the Petri dish was placed in an ultrasonic bath in order to collapse the TiO2 matrix. Toluene dissolved the polystyrene opal and evaporated within 10 min. The TiO2 matrix collapsed and dispersed upon sonication. The dispersed TiO2 nanoparticles were confined to the same area where toluene was applied. The toluene drop did not spread out even under sonication. The sample was carefully handled in the horizontal orientation and placed in a furnace for sintering. Thus, the energy conversion efficiency can be compared between a PC bilayer electrode and a collapsed

The final bilayer electrode structure is shown in Figure 3a together with the angular optical setup to measure the transmission spectrum, Figure 3b. The 400-800 nm diffused light was directed onto the DSC, on the TiO2 electrode side, without the platinum-coated counterelectrode so that the transmission intensity could be measured directly by a spectrometer. The electrolyte solution attenuates the strength of the transmitting light and separates the counterelectrode from the TiO2 bilayer electrode in the DSC. Therefore, it can be assumed that the absence of a counterelectrode has a small effect on the transmission spectrum. For the same reason, we irradiated the DSC from the side of the TiO2 bilayer side so that more Ru dye would be exposed to the light before attenuation. The incidence angle θ was varied along the ΓLU direction,16 defined from the normal of the (111) inverse face-centered cubic structure. Optical transmission spectra measurements were carried out to simulate the passage of light through the DSC and to probe the PC’s effect on the energy conversion efficiency spectrum. Figure 3c suggests the expected electron injection concentration with respect to the distance traveled as light propagates through the PC. Transmittance spectroscopy was used to measure the Bragg peak or the PBG of the PC bilayer electrode. The 400-800 nm diffused light was impinged on the TiO2 nanoparticle film side. The spectrometer was placed at the opposite side to detect transmitted light. Angular transmission spectra are shown in Figure 4a for incidence angles of 0 (transmission dip at wavelength 641 nm), 15 (630 nm), and 30° (612 nm). As the incidence angle increases, there is a blue shift in the transmission dips, which corresponds to the central wavelength of the PBG17,18 of the inverse opal. The transmittance plots presented in Figure 4a do not have sharp dips. This is because some amount of light was absorbed by the nanoparticle film layer before reaching the inverse opal layer. Nevertheless, the variation in PBG with incidence angle can be observed from the transmittance plot, and this is confirmed by matching the dips with numerical simulation result in the following section. Under angle-resolved noncollimated monochromatic irradiance for the same incidence angles, the incident photon-to-current conversion efficiency (IPCE) measurement was carried out using a 300 W Xeon lamp, Oriel monochromator, Newport Merlin photometer, and a Keithley sourcemeter. The IPCE and enhancement factor (FIPCE) for incidence angles 0, 15, and 30° are shown

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Figure 2. Cross-sectional SEM images of (a) TiO2 inverse opal (layer 1) on a mesoporous TiO2 film (layer 2), (b) TiO2 inverse opal (PC), and (c) collapsed TiO2 inverse opal (C-PC).

Figure 3. (a) Schematic of a PC and C-PC bilayer electrode on the same FTO substrate. (b) Angular transmission setup for the film-PC bilayer electrode; dPC is the thickness of the PC layer. (c) The expected distribution of the electron injection concentration as the light intensity reduces in the PC.

in Figure 4b-d. The enhancement factor FIPCE is defined as (IPCEPC - IPCEC-PC)/IPCEC-PC. The FIPCE graphs have distinct peaks on the red-edge of the PBG (dielectric band). Unlike previous reports,4,5 the FIPCE peaks appearing at the spectral location of the dielectric band are unambiguous because we are comparing a DSC based on the same volume of TiO2 material with and without a photonic crystal. In the past, the general increase in FIPCE as observed in Figure 4b-d over the spectral range of 500-760 nm has been attributed to the scattering effect5,6 of the photonic crystal

as a back reflector. In Figure 4b-d depicting an FIPCE plateau, the scattering effect accounts for a nearly 60% increment over C-PC samples. To separate the PBG effect from random scattering, angular monochromatic irradiance measurements were necessary, and they provided valuable insight. For the PC back reflection effect at spectra locations designated by dashed lines in Figure 4b-d, FIPCE improves slightly to 60-65%. For dielectric band edge effects, which correspond to the highest peak of the FIPCE plots in Figure 4b-d, the edge effects provide an approximate 10% increment on top of the 60% increment due to the scattering effect. Computational Methods We represent the same angular effect in the photonic band diagram of a TiO2 inverse opal in Figure 5 when spanning the parallel wavevector k||(2π/a) ) jk sin θ from ΓL toward ΓU. The lattice constant, a, of a FCC structure is 2D, where D is the diameter of the polystyrene colloidal spheres. This band diagram was calculated using the plane-wave expansion method,19 using the following values:6 nTiO2 ) 2.25, nTG-50 ) 1.43, and a filling factor18 of 45% for TiO2 in air interstices. The transmission dips from Figure 4a, denoted as black dots, match the photonic band diagram in Figure 5 (left panel). To estimate the effect of electric field localization, the eigenfunction

Figure 4. (a) Angled-resolved transmission measurement of the bilayer electrode DSC for incidence angles 0, 15, and 30°. (b-d). The IPCE graph for DSC devices: PC bilayer electrode (solid circles) and C-PC bilayer electrode (solid triangles). FIPCE is (IPCEPC - IPCEC-PC)/IPCEC-PC (%). The arrows indicate the gap centers for the three different incidence angles.

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Yip et al.

Figure 5. Left panel: Photonic band diagram of a TiO2 PC in the LU direction. The y axis is the angular frequency, ω, normalized with the lattice constant, a, and the speed of light in vacuum, c, and a factor of 2π. The x axis is the magnitude of the parallel wave vector in the LU direction. L1-L6 denotes the modes at the respective locations in the photonic band diagram. The black dots indicate the transmission dips (0, 15, and 30°) in the angle-resolved transmission measurement (from Figure 2). Right panel: The intensity plot |E|2 of modes L1 and L2 (0°), L3 and L4 (15°),and L5 and L6 (30°). White indicates high intensity.

|E|2 in the inverse opal was computed by exciting eigenmodes L1, L2, L3, L4, L5, and L6, as shown in Figure 5 (right panel). The interior of a sphere represents the region of the TG-50 electrolyte, while the exterior is the TiO2 region. Figure 5 (right panel) shows plots of the electric intensity |E|2 of modes L1 and L2 (0° incidence), L3 and L4 (15°), and L5 and L6 (30°). The white color represents high intensity. Localizations of |E|2 in the TiO2 region are found in modes L1, L3, and L5, where they are in the dielectric band collectively. Therefore, dielectric band localization helps in the Ru dye absorption and electron injection in the TiO2 region. Conversely, localization of |E|2 in the TG-50 electrolyte region is found in the air band: L2, L4, and L6 modes. Because there is no Ru dye and electron injection in the TG-50 electrolyte region, there is no effect from air band localization. Therefore, we deduce that the FIPCE peak at the dielectric band (640-740 nm for 0° incidence) results from enhanced photocurrent generation due to light localization at the TiO2 PC, while the general improvement (∼60%) of FIPCE over the 460-760 nm spectral range is the result of increased photocurrent generation of the TiO2 film from the scattering effect of the PC layer. Photons propagate slowly near the PBG edge due to the flatter photonic band and could enhance the interaction between light and matter. In this section, we perform a quantitative analysis on the field enhancement phenomenon due to the band edge effect.7–9,20 The intensification of the electric field strength inside of PC layer (|EePC|2) against the C-PC layer (|EeC-PC|2) is simulated using a finite-difference time-domain (FDTD) simulator21 for incidence angles 0, 15, and 30° in Figure 6. We represent the frequency-dependent material dispersion of TiO2 as the sum of harmonic resonances,22 and the parameters are ωn ) 3.1 rad, γn ) 0.008, and ∆εn ) 0.1. For the TG-50 electrolyte, the measured absorbance spectrum is relatively flat in the spectral range of interest (500-800 nm) and is assumed to be nondispersive. The geometry of the structures is based on the film thicknesses stated earlier. The rest of the simulation parameters are similar to those used in the plane-wave expansion method earlier. First, the film-PC bilayer’s transmission spectrum was simulated to describe the light propagation behavior through the bilayer. In Figure 6, the computed transmission gap center locations match well with experimental

Figure 6. Angled-resolved FDTD simulation of the transmission spectra and time-averaged |EePC|2 - |EeC-PC|2 electric field strength plots; (a) 0° incidence angle, (b) 15°, and (c) 30°. The PC enhances the electric field strength near the PBG red edge, which shifts in accordance with the PBG.

transmission results shown in Figure 4a. The experimental gap width is larger than the numerical solution due to the inhomogeneous broadening effect23 and computation nonideality. No gap was computed for a film-C-PC bilayer. In addition, the time-averaged difference in the electric field strength |EePC|2 |EeC-PC|2 are shown in Figure 6 at dielectric bands at different incidence angles. The electric field strength enhancement is greatest at the edge of the dielectric band, that is, approximately 680, 670, and 650 nm for incidence angles 0, 15, and 30° respectively. Theoretical Calculations The intensification of the electric field strength inside of the PC influences the interaction between light and the Ru dye. The Maxwell-Bloch equation24 is commonly used to study the

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dynamics of electron excitation in a simplified two-level atom model. Here, we consider the Ru dye to be a two-level atom with an electron excitation frequency ωEG corresponding to its peak absorption frequency. Absorption of a photon of energy pω takes place when an electron is excited from the ground to the excited energy level. The Maxwell-Bloch equation is described by the dynamic relationships for a singly polarized, unidirectional traveling wave

∂Pe/ ∂ t + [γEG + i(ωEG - ω )]Pe ) ip Ee N/p 2

∂N ⁄ ∂t - i2(E /e Pe - EeP /e )/p ) -γEEN

[

4γEG p2N 2 γEEp2[γEG + (ωEG - ω)2]

]

|Ee|2

(5)

(2)

It is assumed that ∇Fn is independent of the position and constant across the entire film.27 At the boundary x ) 0, the surface exposure of the dye atom and TiO2 nanoparticles to the electrolyte is higher. A larger amount of electron loss is expected at the surface due to the tunneling effect.26 Simplifying the boundary condition to be ∆n(0,ω) f 0 and at steady state condition, the distribution of ∆n is

(3)

From eq 3, G(ω) is proportional to |Ee|2, resulting in a higher excitation density or dye absorption for the amplified light field. We denote G(ω) ) [•]|Ee|2 henceforth for all analysis that follows. For simplicity, we assume that the G(ω) is the effective excitation density at all dye-TiO2 locations, independent of spatial position. The overall electron action in the dye-TiO2 can be examined and modeled using a continuity equation, which equates the overall change in electron concentration with time by considering the net flow in and out of that region. We consider only the injected electrons ∆n(x,ω) from the Ru dye while assuming that the bulk concentration n0 of n-type1 TiO2 remains unchanged. Unless specified otherwise, ∆n(x,ω) is denoted simply as ∆n. The continuity equation takes the following form

∂∆n/ ∂ t ) ∂∆n/ ∂ t|GEN - ∂∆n/ ∂ t|REC - ∇ · Jn/q

∂∆n/ ∂ t ) NdyeγEEG(ω) - ∆nkrec - (µn ∇ Fn/q) ∂ ∆n/ ∂ x

(1)

where N, γEG, and γEE denote the two-level inversion density, polarization, and population damping constant, respectively. Under the influence of the electric field, the distorted electron cloud leads to the induction of dipoles in the dye atom. The matrix p indicates the strength of the dipole transition induced by an incident wave. The envelope amplitude of the electric field and dipole polarization are denoted as Ee and Pe, respectively. Population inversion is lost through electron-hole recombination and electron injection to the TiO2 conduction band. To model the replenishment in the loss of inversion, an excitation rate of γEEG(ω) is added to the right-hand side of eq 2. The excitation density G(ω) is dependent on the excitation frequency and has units of reciprocal volume. The population damping constant has units of reciprocal time. Under the steadystate condition, the time derivatives of Pe and N go to zero, and the excitation density is simplified to

G(ω) )

the strongest. This results in a concentration gradient of ∆n, where ∆n(d,ω) > ∆n(0,ω). The concentration gradient creates an antiflow of electrons away from the electrode. In practice, the DSC supplies electrons out from the electrode and holes out from the counterelectrode. Thus, a negative term -(1/q)∇ · Jn accounts for the loss of electrons due to the concentration gradient. Rewriting the continuity equation

(4)

The time derivative of the ∆n due to electron generation is the product of the dye concentration per unit volume Ndye and the excitation density rate γEEG(ω). The difference in Ndye between the C-PC and PC is expectedly small since the volume of TiO2 remains unchanged. For ease of analysis, Ndye is assumed to be constant throughout the PC and C-PC. The time derivative of the ∆n due to electron recombination is the product of ∆n and the charge recombination rate krec, described as electron trapping/detrapping processes25 and electron-hole recombination in the electrolyte by tunneling through the dye.26 The electron current density, Jn, can be represented in a compact form27 Jn ) µn∆n∇Fn, where µn and ∇Fn are the electron mobility and spatial derivative of the quasi Fermi level, respectively. Irradiance is directed on the bilayer electrode side of the DSC, as depicted in Figure 3b. Hence, more electrons are excited nearer to the electrode side where the irradiance is

∆n ) (NdyeγEEG(ω)/krec )[1 - exp(-Ax)]

(6)

where A represents the term qkrec/µn∇Fn. The exponential relationship in eq 6 matches well with the suggested electron distribution described earlier and schematically in Figure 3c and in ref 28. The excitation rate γEEG(ω) is directly in competition with the recombination rate krec. In the case of PC, ∆n is higher for a larger excitation density rate γEEG(ω), which corresponds to higher |Ee|2. To study the FIPCE peaks in Figure 4b-d and the effect of large |Ee|2, we restrict the analysis to a comparison between electron action in the PC region and that of the C-PC regions. The increase of photocurrent density26 in the PC structure to C-PC can be calculated as

[∫

∆J(ω) ) (q ∇ Fnµn)

dPC

0

dx ∆ nPC/dPC -

∫0d

C-PC

]

dx ∆ nC-PC/dC-PC

and simplified to

∇J(ω) ) q ∇ Fnµn NdyeγEE[•]{|EePC|2 - |EeC-PC|2}/krec (7) by approximating |exp(-AdPC) - 1/AdPC| , 1 and |exp(-AdC- 1/AdC-PC| , 1. From eq 7, the enhancement of the photocurrent density is proportional to the difference between |EePC|2 and |EeC-PC|2. In Figure 7, we illustrate this relationship by comparing the experimental FIPCE peaks with the numerically computed ∆J(ω) term, thus linking the photonic crystal’s amplified light field and photocurrent density. The peak positions of FIPCE and ∆J(ω) match well, and both blue shift synchronously with the incidence angle. This dielectric band edge enhancement is most effective at the edge and decreases in prominence at wavelengths far from the edge. This can be seen in Figure 7 where the wavelengths to the left side and right side of the ∆J(ω) peak show reduced ∆J(ω) even though FIPCE is still generally maintained constant at about 60%. This constant FIPCE region can be ascribed to the back-scattering effect of PC, as described earlier. Thus, we show that the intensification of |EePC|2 in the dielectric band causes the enhancement in photocurrent density and hence a higher IPCE for a film-PC bilayer electrode. PC)

Conclusion In conclusion, we have experimentally and theoretically shown the enhancement in the incident photon-to-current conversion efficiency of a bilayer photonic crystal dye-sensitized solar cell due to the photonic crystal’s dielectric band edge

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Yip et al. Supporting Information Available: Finite-difference timedomain simulation parameters. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 7. Comparison of the FIPCE peak plot (from Figure 2) with the numerically computed ∆J(ω) in a proportional relationship with |EePC|2 - |EeC-PC|2 plot (from Figure 3). ∆J(ω) is plotted in the vicinity of the dielectric band edge range; κ denotes the q∇FnµnNdyeγEE[•]/krec term in eq 7; (a) 0° incidence angle; (b) 15°; (b) 30°.

effect. Under angle-resolved monochromatic irradiance along the LU direction, the IPCE enhancement peaks match well with the blue shift in the dielectric band edge. Numerical simulation is used to show the intensification of the electric field strength at the photonic band edge. Using a Maxwell-Bloch model of the Ru dye atom as a simplified two-level atom, the excitation density or the absorption of the Ru dye is found to increase with the electric field strength in the photonic crystal. The increased excitation density rate causes greater electron injection into the conduction band of TiO2, which consequently increases the photocurrent and improves IPCE. This work resolves previous ambiguities regarding this mechanism and suggests that higher-performance DSCs may be developed based on the photonic crystal enhancement concept. Acknowledgment. We thank Mr. Koh Yaw Koon, Dr. Madhavi Srinivasan, and Dr. Martin Schreyer of Nanyang Technological University for fruitful discussion and helpful comments. We also thank and acknowledge Mr. Pierrick Aguesse for his participation in the work during his internship.

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