Engineering of Low-Loss Metal for Nanoplasmonic and Metamaterials Applications
D. A. Bobb, G. Zhu, M. Mayy, A. V. Gavrilenko, P. Mead, V. I. Gavrilenko, M. A. Noginov
11 Engineering of Low-Loss Metal for Nanoplasmonic and Metamaterials Applications
D. A. Bobb, G. Zhu, M. Mayy, A. V. Gavrilenko, P. Mead, V. I. Gavrilenko, M. A. Noginov
Center for Materials Research, Norfolk State University, Norfolk, VA, 23504
Abstract
We have shown that alloying a noble metal (gold) with another metal (cadmium), which cancontribute two electrons per atom to a free electron gas, can significantly improve the metal’soptical properties in certain wavelength ranges and make them worse in the other parts of thespectrum. In particular, in the gold-cadmium alloy we have demonstrated a significant expansionof the spectral range of metallic reflectance to shorter wavelengths. The experimental results andthe predictions of the first principles theory demonstrate an opportunity for the improvement andoptimization of low-loss metals for nanoplasmonic and metamaterials applications.
Plasmonic materials and devices as well as metamaterials based on metallic nanoinclusions playan increasingly important role in modern photonics and nano-optics [1,2]. Their applicationsinclude but are not limited to surface enhanced Raman scattering (SERS) [3,4], scanningmicroscopy and spectroscopy with nanometer resolution [5,6], negative index of refraction [7,8],super-lens [9] and hyper-lens [10,11] with sub-diffraction resolution, transformation optics[12,13], and optical cloaking [14,15].The common drawback of all metal-based metamaterials is high optical loss in metal atoptical frequencies. It has been shown theoretically [16-18] and experimentally [19-22] that theoptical loss in metallic nanostructures can be compensated and the stimulated emission ofsurface plasmons (SPs) can be obtained if the optical gain is added to an adjacent dielectric.Conquering the optical loss by gain requires intense Q-switched laser pumping, which makessystems and devises prohibitively complex. In addition, some gain media ( e.g. laser dyes) oftenhave low resistance to photobleaching. This calls for alternative loss reduction techniques, whichdo not require laser pumping. It has been demonstrated [23] that the propagation length ofsurface plasmon polaritons (SPPs) can be significantly increased if the laser dye in very highconcentration is added to the dielectric medium adjacent to the silver surface. This effect hasbeen explained in terms of the modification of electronic surface states of silver in the presenceof dye molecules.Optical loss in noble metals in the visible and ultraviolet spectral ranges is determined by thecombination of a free electron loss, defined by the damping constant in the Drude model, and theabsorption loss due to the electron transitions between occupied bound d states and unoccupiedhybridized sp states above the Fermi level [24]. It has been proposed that alloying a noble metal(which contributes one electron per atom to a free electron gas) with a small volume fraction of another metal (which contributes two or three electrons per atom to a free electron gas) can raisethe Fermi level, shift the spectral position of the d ! sp transition band, and, correspondingly,modify metal’s reflection and absorption spectra [24,25], Fig. 1. It has been argued [24] that thiseffect is responsible for the yellowish coloration of brass, which is an alloy of reddish copper andsilvery-white zinc.If the fraction of the impurity metal (amount of n-doping) is sufficiently small, then thealloying will not modify the electron band dispersion of the noble metal significantly and its onlyeffect will be the change of the Fermi level. However, at larger concentrations of the impuritymetal, the change of the band structures of both d and s electrons can influence the electronenergy spectrum much stronger.According to Ref. [31], a blue shift of the spectral band associated with bound electrons canlead to a blue shift of the edge of metallic reflectance, Fig. 1b. An increase of the free electrondensity will increase the plasma frequency " p [24] and, correspondingly, shift the edge ofmetallic reflectance to shorter wavelengths even further. Combined with an increase of thedamping constant (caused by electron scattering on impurity-induced defects), an increase of " p should increase the optical loss associated with free electrons. Thus, the improvement ofplasmonic properties of noble metals via alloying can be achieved only as a result of carefulcomposition optimization.In this Letter, we report on the studies of spectroscopic properties of pure gold and gold-cadmium alloys. The electron configurations of Au ([Xe] 4f ) and Cd ([Kr] 4d )suggest that cadmium can provide one extra electron to a free electron gas of the alloy, similarlyto how zinc provides an extra electron to a free electron gas of brass. The ground state and the electron energy structure of Au-Cd alloys has been studied by theDensity Functional Theory (DFT), employing the CASTEP computational package [33] and thefirst principle pseudopotentials. The super-cell method has been used to model the Au-Cd alloysat cadmium concentration equal to 3.3 at.%. The reliability of this approach has been carefullyproven by the detailed convergence test. We have found that few percent accuracy of the totalenergy convergence can be achieved at 5 x x k -point mesh and energy cut-off of 500 eV. Optical functions of Au-Cd are calculated within the Random Phase Approximation (RPA)using as the inputs the eigenenergies and the eigenfunctions obtained from the ground state run[27]. We have used the equilibrium lattice constants for both bulk Au and Au-Cd alloy ascalculated by the Local Density Approximation (LDA) method. The calculated value of thelattice constant of gold, a =4.013 Å, is somewhat smaller than the experimental value, a=4.08 Å[28]. The resulting compression of the lattice, effectively modifying the widths of the electronicbands, acts as a quasi-particle (QP) correction. No additional QP corrections have been appliedto the electron energy structure in order to avoid substantial complexity of the calculations.Consequently, the positions of the energy bands are calculated with a relatively small systematicerror, which effect can be eliminated if relative changes of the band structure are compared withthe experiment. The calculated optical spectra of pure gold are depicted in Fig. 2a. Four peaks (I–IV),corresponding to the transitions between the d band and the hybridized s-p band, can be clearlyseen in the reflectance spectrum as well as in the spectrum of the imaginary part of the dielectricconstant ” . The spectrum of ” in the Au(96.7 at.%):Cd(3.3 at.%) alloy (along with that of puregold) is shown in Fig. 2b. In the alloy, bands II–IV tend to shift to lower energies while band Ishifts to higher energies and gets partly overlapped with band II. The analysis of the calculated projected density of states indicates that the predictedmodifications of the optical spectra of the alloy are caused by substantial redistributions of theoscillator strengths due to the additional resonances between d- and s- electron states (bothoccupied and unoccupied) of impurity and host atoms. The gold and the gold-cadmium alloy (with nominal concentrations Au(90at.%):Cd(10at.%))have been acquired in a form of ~20 mm beads from Kurt J. Lesker Co. Two types ofexperiments have been conducted. In the first set of experiments, metallic beads were grindedand polished, and the reflectance spectra of shiny flat metallic surfaces were taken using aspectrophotometer equipped with an integrating sphere. Pure gold was more intense-yellow thana noticeably whiter gold-cadmium alloy. Polished alloy samples had darker islands (with sharpboundaries) embedded in a lighter metallic host. We assumed that the darker inclusions hadsmaller concentration of cadmium than the lighter surrounding.In the second type of experiments, beads were placed in water and exposed to short-pulsedlaser radiation ( t pulse !
10 ns, $ =532 nm, ~10 J/cm ). The suspensions of nanoparticles have beenproduced via photo-ablation and their extinction spectra have been studied in a regularspectrophotometer setup. The reflectance spectrum of pure gold and the absorbance spectrum of gold nanoparticles areplotted in Fig. 3 along with the spectra of real ( ! " Au' ) and imaginary ( ! " Au " ) parts of the dielectricfunction of Au [29]. The surface plasmon (SP) band of Au nanoparticles has a maximum at~18900 cm -1 (529 nm), at which ! " Au' is approximately equal to ! " water' (here ! " water' is the real partof the dielectric constant of water). This as well as a nearly symmetric shape of the SP band,indicate that metallic nanoparticles contributing to the SP absorption are sufficiently small(dipole approximation) and the contribution of larger nanoparticles is insignificant. The edge ofthe metallic reflectance range (~20700 cm -1 , 483 nm) corresponds to the energy at which ! " Au' spectrum starts deviating from the Drude behavior.The two maxima, which can be associated with bands I and II in Fig. 2, are seen in both thereflectance spectrum and the spectrum of ! " Au " . The same two bands, although slightly shifted arefound in the absorbance spectrum of Au nanoparticles. The relatively small mismatch betweenthe energy positions of the experimentally measured and theoretically calculated maxima [30] isdue to the LDA-predicted compressed lattice, which effectively acts as a QP correction. As follows from Fig. 4, depicting the reflectance spectra of pure gold, darker Au-Cd alloy( -1 (~66 nm). Thereflectance of alloys in the visible and near-infrared ranges of the spectrum is lower than that ofpure gold. This suggests that the imaginary part of the dielectric function ” (optical loss) isgetting larger when gold is alloyed with cadmium. Both the significant expansion of thereflectance spectrum and the increase of the optical loss in the visible and near-infrared ranges ofthe spectrum are in accord with the predictions of the heuristic model [24]. With the increase ofthe concentration of cadmium, band I shifts to the higher energies and band II shifts to the lowerenergies – in excellent agreement with the results of the first principle calculations, Fig. 2.Absorbance spectra of the suspensions of Au and Au-Cd nanoparticles feature the peakassociated with the SP resonance as well as the wing of a much stronger high-energy band,which is due to the contributions of bound electrons, Fig. 4b. The SP band of the alloy (19120cm -1 , 523 nm) is slightly blue shifted relative to that of pure gold (18900 cm -1 , 529 nm). Thiseffect is in line with the increase of the concentration of free electrons and the correspondingincrease of " p . The SP band of the alloy is nearly symmetrical (after the background is subtracted) and significantly broader than that in pure gold. The symmetric character of the bandsuggests that the SP absorption is predominated by small nanoparticles (dipole approximation)and that the increase of its width is due to the increase of ” (loss) rather than the dispersion ofparticle sizes. This conclusion is in line with that drawn based of the analysis of the reflectancespectra. In the alloy, absorption band II is red shifted relative to that in pure gold, in agreementwith the theoretical prediction (Fig. 2b) and the reflectance experiment (Fig. 4a), and absorptionband I is practically not seen.To summarize, we have demonstrated that alloying gold with cadmium (i) significantlyexpands the spectral range of metallic reflection, moving its high-energy edge from 19600 cm -1 (510 nm) to 22500 cm -1 (444 nm), (ii) causes a blue shift of the SP spectral band in metallicnanoparticles, from 18900 cm -1 (529 nm) to 19120 cm -1 (523 nm), (iii) increases the width of theSP spectral band and slightly lowers the reflectance in the visible and near-infrared ranges of thespectrum, and (iv) causes the shift of the bands in the bound-electron absorption spectrum, in agood agreement with the predictions of the first-principle theory. The first two results are in agood agreement with the predictions of a heuristic model [24], according to which n doping ofgold (alloying Au with Cd) should lead to an increase of the Fermi level and the correspondingblue shift of both the SP resonance and the edge of the metallic reflectance spectrum. It has beenshown both theoretically and experimentally that impurity concentrations " d band in the Au-Cd alloy has moved, closely following the change of the Fermi level, keeping the position of the absorption band intact. Furthermore, thealloying has increased the loss in the green-to-near-infrared range of the spectrum.We conclude that n doping of a noble metal can significantly improve its optical properties incertain spectral ranges and make them worse in the other parts of the spectrum. This opens anopportunity for the improvement and optimization of metals for nanoplasmonic andmetamaterials applications and gives hope to many dream applications [1,2]. The work was supported by the NSF PREM grant grant
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Density of statesEnergy E F1
4s 3d ! E " E E F2 -30-25-20-15-10-50510 0 5 10Energy (eV) ! ' ! ' Drude ! ' bound ! ' total " Reflectance edge shift $% Fig. 1. (a) Schematic density-of-states diagram of a noble metal (copper), showing the bands ofbound 3 d electrons and free 4 s electrons [24,25]. E F1 and E F are the Fermi levels in pure copperand copper alloyed with zinc; % E = E F2 - E F1 . The energy gap & E corresponds to the edge of theabsorption band. (b) Spectrum of the real part of the dielectric function determined by thecontributions of free electrons, ! " Drude' (trace 1); spectra of the bound electron contributions, ! " bound' (traces 2(I) and 2(II)); and net spectra ! " total' calculated as the sums of free electron and boundelectron contributions, (traces 3(I) and 3(II)). Spectra 2(I) and 3(I) correspond to pure copper andspectra 2(II) and 3(II) correspond to the alloy with an increased Fermi level. As a result ofalloying, the edge of the spectral range of metallic reflectance is shifted by &" . a b Figure 2. -1 ) ! " Au-Cd Au1 2I II III IV
Fig. 2. (a) The spectrum of the imaginary part of the dielectric constant ” (trace 1) and thereflectance spectrum (trace 2) calculated for pure gold. (b) The spectrum of ” in pure gold (trace1, same as in figure a) and Au(96.7at.%):Cd(3.3at.%) alloy (trace 2). The four characteristicpeaks are denoted as I–IV. a b Figure 3.
Fig. 3. Reflectance spectrum of gold (1), absorbance spectrum of the water suspension of goldnanoparticles (2), and the spectra of the real ( ! " Au' ) and imaginary ( ! " Au " ) parts of the dielectricconstants of gold [29]. Bands I and II are associated with those in Fig. 2. Horizontal linerepresents ! " water' and vertical lines are guides for eye.5Figure 4. -1 ) R e f l e c t an c e Au Au-Cd(1)Au-Cd(2)%Cd(2)>%Cd(1) -1 ) A b s o r pban c e AuAu-CdI II