The absorption properties of metal-semiconductor. hybrid nanoparticles

Transcription

1 Supporting information for The absorption properties of metal-semiconductor hybrid nanoparticles Ehud Shaviv a*, Olaf Schubert b,c*, Marcelo Alves-Santos d, Guido Goldoni d,e, Rosa Di Felice d,fabrice Vallée f, Natalia Del Fatti f, Uri Banin a and Carsten Sönnichsen b, **. * contributed equally a Institute of Chemistry and center for Nanoscience & Nanotechnology, The Hebrew University of Jerusalem, Jerusalem 91904, Israel b Institute of Physical Chemistry, University of Mainz, Jakob-Welder-Weg 11, Mainz, Germany c Current address: Department of Physics, University of Regensburg, Universitätsstraße 31, Regensburg, Germany d CNR Institute of Nanoscience, S3 Center, Via campi 213/A, Modena, Italy e Dipartimento di Fisica, Università di Modena e Reggio Emilia, Via campi 213/A, 41125, Modena, Italy f FemtoNanoOptics Group, LASIM, CNRS and Université Lyon 1, 43 Bd. du 11 Novembre, F Villeurbanne, France

2 ** 1. Convergence tests for DDA Figure S1. (a) Calculated spectra of an Au sphere (diameter: 7 nm) in a medium with refractive index of n med =1.5. The black line indicates the Mie result 1. The different colors correspond to different dipole-dipole spacing as indicated in the legend. (b) A typical spectrum of a rod shaped CdSe semiconductor nanoparticle in a medium with refractive index of n=1.5 for different dipole densities. In all self-consistency tests we found a grid size of 30 dipoles along the direction of the short axis to be sufficient for calculating spectra of hybrid structures. 2. Calculations of dielectric functions of CdS and CdSe nanorods We determine the dielectric function of a semiconductor nanorod with given length and diameter by means of an iterative procedure 2, starting from the experimental absorption spectrum of a sample with the desired sizes. In our computational scheme the nanorod with diameter D and length L is approximated with an ellipsoid that has main axis a and b, being 2

3 a/b=d/l and the ellipsoid volume equal to the target nanorod volume. The Separation of Variables Method (SVM) 3 is used to calculate the extinction spectrum of the ellipsoid. Typical experimental absorption spectra are available in a limited energy range close to the absorption edge. This limitation can be overcome by matching exactly the imaginary part ε 2 (E) of the dielectric function of the nanorod with the imaginary part ε bulk 2 (E) of the bulk dielectric function at high energies beyond the experimental range, with an intermediate matching range. Thus, using the Kramers-Krönig (KK) relations that link the real and imaginary parts, it is possible to extract the complete dielectric function of the nanorod as a function of the energy. To describe in more detail the extension of the dielectric function beyond the experimentally available range, let us specify the relevant energy values: E=[E 0,E 1 ] is the energy range where the experimental absorption spectrum of a given nanorod is known, E 2 is the energy value where ε bulk 2 has the first sharp maximum and E 3 is the maximum energy value for which the bulk dielectric function is known. ε 2 (E) is assigned as follows in the different energy intervals identified by such values: 1. In the interval [0,E 0 ], ε 2 (E) = 0 2. In the interval [E 0,E 1 ], ε 2 (E) is determined from the experimental extinction cross section 3. In the interval [E 1,E 2 ], ε 2 (E) = ε 2 bulk (E)+(ε 2 (E1)- ε 2 bulk (E1)) E E 2 E 1 E 2 4. In the interval [E 1,E 3 ], ε 2 (E) = ε 2 bulk (E) 5. For E>E 3, we use a Drude-like function for ε 2 (E). The real part ε 1 (E) is determined uniquely via KK integration up to E 4 =6.50 ev. 3

4 Figures S2 and S3 summarize the results of this computational scheme for a CdS nanorod with w = 5.7 nm and L = 16.5 nm and a CdSe nanorod with w = 4.7 nm and L = 23.0 nm respectively. The dielectric functions illustrated in Figures S2 and S3 were obtained from measured absorption spectra. These dielectric functions were employed later on in the DDA simulations of the hybrid nanoparticles. Figure S2. Real (dashed) and imaginary (solid) part of the dielectric function computed for a CdS nanorod with diameter w = 5.7 nm and length L = 16.5 nm. The black lines are the final results of the iterative procedure, performed with E 0 = 1.24 ev, E 1 = 3.54 ev, E 2 = 5.42 ev and E 3 = 15.0 ev. The solid colored black lines represent the outcome at intermediate iterations and the solid gray line is the imaginary part of the bulk dielectric function. The inset is a zoom that magnifies the convergence in the experimental energy range [E 0,E 1 ]. The superscripts in the legend indicate the iteration steps. 4

5 Figure S3. Real (dashed) and imaginary (solid) part of the dielectric function computed for a CdSe nanorod with diameter w = 4.7 nm and length L = 23.0 nm. The black lines are the final results of the iterative procedure, performed with E 0 = 1.95 ev, E 1 = 3.64 ev, E 2 = 4.75 ev and E 3 = 10.0 ev. The solid colored black lines represent the outcome at intermediate iterations and the solid gray line is the imaginary part of the bulk dielectric function. The inset is a zoom that magnifies the convergence in the experimental energy range [E 0,E 1 ]. The superscripts in the legend indicate the iteration steps. 3. Preparation of metal-semiconductor samples Synthesis of CdS-Au matchstick shaped sample CdS-Au matchstick shaped particles (single gold tip) were prepared according to the photo-induced procedure reported by Banin and co-workers 4. In a typical synthesis the CdS nanorods were cleaned from excess ligands by methanol addition, followed by centrifugation. The supernatant was discarded and the precipitate was dissolved in 2 ml of toluene. The concentration of nanorods was tuned to give an optical density of ~1.2 at the exciton absorbance peak. Next, a gold growth solution was prepared by dissolving 5 mg 5

6 gold(iii) chloride (AuCl 3 99%, kept in dry conditions), 12 mg of DDAB (didodecyldimethylammounium bromide, 98%) and 25 mg of DDA(dodecylamine, 98%) in 6 ml toluene. Both the nanorods and gold solutions were sonicated in sealed vials and purged with argon for 5 minutes to remove oxygen from the reaction. Finally, the nanorods solution was placed inside a Peltier cooled sample holder (Temp. ~3 o C). At this stage, 1 ml of the gold growth solution was added to the nanorods and the sample was irradiated with a CW diode-laser at 473 nm (40 mw) for approximately 60 minutes. The reaction was monitored by taking aliquots and measuring their absorbance. The formation of gold tips was evident by the development of a strong plasmon absorption peak. The procedure given above results typically in the formation of approximately 6 nm gold tips on the apex of the nanorods, based on statistics of TEM images. Synthesis of CdSe-Au dumbbell shaped sample The CdSe-Au dumbbell shaped sample (gold tips on both apexes) was prepared according to the procedure developed by Banin and co-workers 5. In a typical synthesis CdSe nanorods were dissolved in toluene and cleaned from excess ligands by adding methanol (anti-solvent) and centrifugation. The supernatant was discarded, the precipitate was dissolved in 10 ml toluene and the absorption spectrum was measured. The amount of nanorods in the solution was calculated based on Beer s law and the molar absorption coefficients of the nanocrystals. In a separate vial the gold growth solution was prepared by dissolving gold(iii) chloride (AuCl 3 99%, kept in dry conditions) in 4 ml toluene, keeping the nanocrystals:gold mole ratio at ~1:7000. In addition, DDA (dodecylamice,98%) 12 time the weight of gold salt powder and DDAB (didodecyldimethylammounium bromide, 98%) 7.5 times the weight of gold salt powder, were added to the gold solution to render the gold soluble in toluene. The solution was sonicated for 5 minutes until it reached a pale yellow color. For the gold growth, the gold growth solution was added to the nanorods solution 6

7 drop-wise under vigorous stirring. Typically, the growth took place within seconds followed by a change of color from red to brown. The gold growth could be verified by observing the washing out of the exciton absorption peak of the semiconductor. The particles were precipitated by adding a small amount of acetone followed by centrifugation. The typical average gold tip size was 4 nm, based on statistics on TEM images. The size statistics for the CdS-Au and CdSe-Au for which the absorbance was studied using DDA simulations are given in figure S4. Figure S4: Histograms showing the sizing statistics of the gold tip (D, upper panels), the semiconductor rod length (L, middle panels) and semiconductor rod width (w, lower panel) within the CdS-Au and CdSe-Au samples for which the absorption was studied using DDA simulations. The average size and its distribution were obtained based on a Gaussian fit (blue curve). 7

8 4. Experimental determination of absorption cross sections of CdS nanorods For semiconductor nanocrystals, beyond the band gap absorption threshold, the absorption efficiency rises steeply at higher energies due to significant increase in the density of electronic states. As a result, at energies far above the band gap, the density of states is approximately continuous and the nanocrystal exhibits bulk-like behavior while quantum confinement effects are negligible 6, 7. Under these conditions, the absorption cross section of the nanocrystal at 350 nm (3.54 ev) can be calculated from the optical constants of the medium and the bulk semiconductor 7-10 : ω Cext = cεmedium 2 f ( ω) Im( εsemiconductor ) Vnanocrystal (1) In equation 1 C ext is the absorption cross section (in cm 2 ), ω is the frequency of the optical transition, c is the velocity of light, ε medium is the dielectric constant of the embedding medium (i.e the solvent) and Im(ε semiconductor ) is the imaginary part of the dielectric function of the bulk. Equation 1 indicates that the absorption cross section is proportional to the volume of the nanocrystal (V nanocrystal ) and the cross section per unit volume can be obtained directly from the optical constants and the field factor [f(ω)]. The field factor depicts the ratio between the field inside the particle and the external incident electromagnetic field which is given by 7, 11 : f ( ) E = E inside medium ω (2) incident = ε 3ε semiconductor + 2ε medium Where ε medium and ε semiconductor are the complex dielectric functions of the solvent and the bulk semiconductor respectively. Once the absorption cross section at 350 nm is calculated, 8

9 the cross section at any given wavelength (C ext,λ ) can be obtained from the measured absorption spectra: OD C λ ext λ = Cext, 350nm OD350nm, (3) Here OD λ and OD 350nm are the measured absorption values at the desired wavelength and at 350 nm respectively. 5. Determining molar absorption coefficients for gold nanoparticles The absorption of 2 ml aqueous solutions of gold nanoparticles was measured with a UV-VIS spectrometer. The optical density of the samples at the plasmon absorption peak was in the range of Next, an Aqua regia solution was prepared by mixing 2 ml of nitric acid (>67%) with 6 ml of HCl (37%) (yellow colored solution) ml of this solution was added to each gold nanoparticles solution. An immediate change of color from purple-red to pale yellow indicated the digestion of the nanoparticles. The solutions were diluted to a total volume of 10 ml with triple distilled water (TDW) prior to the inductive coupled plasma atomic emission measurement (ICP-AES). The gold content of each sample was analyzed on a ICP-AES instrument (Perkin Elmer Optima 3000) using commercially available gold standard solution for calibration. For a typical calibration curve we used four solutions of gold: blank (containing 2 drops of aqua regia ), 5PPM, 10PPM, and 50PPM. The total volume of the standard solutions was 20 ml (all the dilutions were carried out with TDW). Preliminary test measurements indicated that the gold emission line at 242.8nm is the most accurate for use. The total amount of gold in each solution obtained from ICP-AES enabled the determination of the nanoparticles concentration based on the estimated gold content of a single nanoparticle. This was calculated in the following manner: 9

10 N gold 4 3 / nanoparticle = ( πr ) ρ (4) 3 Where r denotes the average radius of the gold nanoparticles (in nm units) and ρ denotes the density of bulk gold (fcc lattice 59 atoms/nm 3 ). As a final step, the absorption of each gold sample was plotted as a function of the calculated concentration. The molar absorption coefficient (ε) was obtained from the slope of this plot according to Beer s law. References 1. Van de Hulst, H. C., Light Scattering by Small Particles. Dover: New York, Alves-Santos, M.; Di Felice, R.; Goldoni, G., Dielectric Functions of Semiconductor Nanoparticles from the Optical Absorption Spectrum: The Case of CdSe and CdS. Journal of Physical Chemistry C 2010, 114 (9), Voshchinnikov, N. V.; Farafonov, V. G., Optical-Properties of Spheroidal Particles. Astrophysics and Space Science 1993, 204 (1), Menagen, G.; Macdonald, J. E.; Shemesh, Y.; Popov, I.; Banin, U., Au Growth on Semiconductor Nanorods: Photoinduced versus Thermal Growth Mechanisms. Journal of the American Chemical Society 2009, 131 (47), Mokari, T.; Rothenberg, E.; Popov, I.; Costi, R.; Banin, U., Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods. Science 2004, 304 (5678), Shaviv, E.; Salant, A.; Banin, U., Size Dependence of Molar Absorption Coefficients of CdSe Semiconductor Quantum Rods. Chemphyschem 2009, 10 (7), Leatherdale, C. A.; Woo, W. K.; Mikulec, F. V.; Bawendi, M. G., On the absorption cross section of CdSe nanocrystal quantum dots. Journal of Physical Chemistry B 2002, 106 (31), Moreels, I.; Lambert, K.; De Muynck, D.; Vanhaecke, F.; Poelman, D.; Martins, J. C.; Allan, G.; Hens, Z., Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots. Chemistry of Materials 2007, 19 (25), Moreels, I.; Lambert, K.; Smeets, D.; De Muynck, D.; Nollet, T.; Martins, J. C.; Vanhaecke, F.; Vantomme, A.; Delerue, C.; Allan, G.; Hens, Z., Size-Dependent Optical Properties of Colloidal PbS Quantum Dots. Acs Nano 2009, 3 (10), Yu, P. R.; Beard, M. C.; Ellingson, R. J.; Ferrere, S.; Curtis, C.; Drexler, J.; Luiszer, F.; Nozik, A. J., Absorption cross-section and related optical properties of colloidal InAs quantum dots. Journal of Physical Chemistry B 2005, 109 (15), Ricard, D.; Ghanassi, M.; Schanneklein, M. C., Dielectric Confinement and the Linear and Nonlinear-Optical Properties of Semiconductor-Doped Glasses. Opt. Commun. 1994, 108 (4-6),