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Physics Letters A ••• (••••) •••–•••
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Optical response of noble metal alloy nanostructures Amit Bansal ∗ , S.S. Verma Department of Physics, Sant Longowal Institute of Engineering & Technology (SLIET), Longowal – 148106, District Sangrur, Punjab, India
a r t i c l e
i n f o
Article history: Received 16 September 2014 Received in revised form 6 November 2014 Accepted 12 November 2014 Available online xxxx Communicated by R. Wu Keywords: Alloys Scattering yield Absorption Bandwidth Ag–Cu Discrete dipole approximation
a b s t r a c t The optical response, stability, and cost-effectiveness of individual noble metals can be improved by combining them to form alloy nanostructures. The present work reveals the influence of shape, size, and metal type on the optical response of alloy nanoparticles using discrete dipole approximation (DDA) simulations. It is found that sharp corner nanostructures show enhanced plasmonic properties in comparison to rounded counterpart. For all the three shapes, viz., nanocubes, rectangular, and nanobar particles, the increase in length resulted in redshifts of the longitudinal plasmon resonance alongwith enhancement in the scattering yield as well as relative efficiency parameters except for nanocubes of edge length 120 nm. The effect of size on full width at half maxima (FWHM) has also been studied and found to be maximal for nanocubes in comparison to other nanostructures. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Among metal nanoparticles (NPs) which can support surface plasmons, the noble metals of size smaller than the incident wavelength exhibit fascinating optical properties due to excitation of a surface plasmon resonance in the visible to near infrared (NIR) region of the electromagnetic (EM) spectrum [1–3]. The optical properties such as absorption, scattering, and therefore, extinction are strongly enhanced at surface plasmon resonance in comparison to their geometrical cross-sections. This is due to the large electromagnetic field enhancement in the surrounding of metal NPs. The calculations of several parameters such as scattering, absorption, localized surface plasmon resonance (LSPR) in wavelength region, and its full width at half maxima (FWHM) are necessary for a particular plasmonic application. The surface plasmon resonance can be tuned from UV–visible to IR (infrared) region of the EM spectrum and said parameters can be controlled by various factors such as size, shape, surrounding medium and metal type, etc. [4–6]. The particle shape plays an important role in deciding the optical properties i.e. the materials having sharp corners and edges provide larger LSPR excitation and redshift in comparison to their spherical counterparts because of strong electric field enhancement as a result of more accumulation of charges at corners during plasmon oscillations [7–9]. Isotropic NPs (say, nanosphere) show only
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http://dx.doi.org/10.1016/j.physleta.2014.11.018 0375-9601/© 2014 Elsevier B.V. All rights reserved.
plasmonic peak whereas anisotropic nanostructures show several plasmon resonances associated with the polarization state of the incident light along different particles axes [8–10]. This is due to the different free electron oscillations along different axes of the anisotropic nanostructures e.g., nanorods exhibit two orthogonal plasmonic peaks, one along short-axis at shorter wavelength (transverse plasmon resonance) and another along long-axis at longer wavelength (longitudinal plasmon resonance) [11]. Depending upon LSPR wavelength, FWHM, and scattering efficiency parameters, the noble metal NPs can be used for many plasmonic applications. To enhance the efficiency of plasmonic solar cells, we require the metal NPs having high scattering efficiency in the broad region of the EM spectrum where the underlying semiconductor is weakly absorbing and/or solar spectrum is highly intense [12,13]. For better plasmon sensing, a strong shift in plasmon resonance alongwith narrower FWHM with small change in medium refractive index is desired [6]. Strong scattering and absorption efficiencies are required for the use of metal NPs in optical imaging and photo-thermal therapy treatments, respectively [14,15]. The most commonly used noble metal NPs on the active layer of thin-film solar cells to enhance its absorption efficiency and for biomedical treatments are of silver (Ag) and gold (Au). However, Ag is optimized and preferred as the better choice over Au because of its highest scattering efficiency in the broad region of the spectrum, low-cost and comparable stability in the ambient conditions. The material’s cost and its availability are the most important factors while considering the metal NPs for plasmonic solar cells and biomedical purposes. The NPs of copper (Cu) and aluminum (Al)
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have also been reported in literature [16–19] towards cost-effective plasmonic applications. Cu NPs show comparable plasmonic properties with Au in the longer wavelength region and therefore, has attracted the researchers owing to its lowest cost and high abundance relative to other noble metals. Moreover, the advances in shape and size controlled synthesis of Ag and Cu NPs motivates the researchers to study their optical properties theoretically. There have been several theoretical and experimental studies [12,17–19] available in literature on calculating the shape and size dependent optical properties of noble metal NPs. Sosa et al. [4] calculated the geometry and size dependent scattering, absorption, and extinction efficiencies of silver and gold NPs using DDA method. Salzemann et al. [20] reported the optical properties of different shape copper NPs with change in plasmon resonance for spherical NPs at 560 nm to that of nanodisks at 650 nm. The optical properties of noble metals can be drastically improved by combining the individual metals to form alloys [21–23] and core–shell nanostructures [24,25]. The potential of using these nanostructures may contribute to more cost-effective applications. However, low cost, better stability, and easy synthesis of alloy nanostructures alongwith metal composition dependent improved optical response in UV–visible to IR region of the spectrum and linear relationship of plasmon resonance with the metal composition makes them most studied plasmonic materials [22,23,26]. The optical properties of alloy NPs can be tuned in between the pure metals over the wide bandwidth with change in metal composition. Many studies have been performed in literature which indicates that alloys have potential applications in plasmonic solar cells [27–30], catalytic [31], plasmon sensing [6], biomedical [21] and antibacterial applications [22, 26]. The alloying of Ag and Cu may use the advantages of both metals and will be useful for enhanced cost-effective plasmonic applications with controllable stability. Moreover, our earlier studies [32] reported that Ag–Cu alloy nanospheres have better optical properties for plasmonic solar cells in comparison to Ag–Au and Au–Cu alloys if one can control the oxidation effect. Further, as similar to the Cu oxidation [33], no significant effect of oxidation over the optical properties of Ag–Cu alloy NPs has been found [34]. Several researchers have synthesized the Ag–Cu NPs with controllable size and shapes using various experimental techniques such as microwave assisted chemical reduction method [26], onepot method [29], chemical reduction route [35], co-complexation method [36], electrochemical codeposition method [37], galvanic replacement reaction [31], polyol method [38] and so on but no theoretical studies are performed to calculate their optical properties. Therefore, Ag–Cu nanostructures may be preferred over other alloys in cost-effective plasmonic solar cells and hence, their optical properties as a function of shape and size also need to be investigated. Similar to the other bimetallic Ag–Au and Au–Cu alloy nanostructures [22,23,39], the optical properties of Ag–Cu can also be varied over the wider region than the individual metals with size, shape, and metal composition. Therefore, in the present work, we studied the optical properties of alloy NPs of various shape and size by using DDA simulations. The main aim is to calculate the shape and size dependent scattering over absorption in the extinction, LSPR wavelength, and FWHM of the plasmon resonance with improved plasmonic applications. 2. Methodology Analytically, it is not possible to solve Maxwell’s equations for arbitrary shape NPs in order to study their optical properties. Therefore, several numerical methods like discrete dipole approximation (DDA), finite element method (FEM), and finite difference time domain (FDTD) have been developed. DDA is one of the most powerful, freely available and useful technique to calculate the optical properties of arbitrary shape NPs. In the present work we
have used the DDA method to calculate the scattering and extinction spectra, FWHM, and LSPR wavelength of different shaped Ag–Cu alloy NPs of various sizes. DDA source code DDSCAT7.2 used is given by Draine and Flatau [40]. In all the simulations, the number of dipoles used are nearly ∼ 74 × 103 in order to accurately represent the target shape and for better convergence of the optical properties. All the calculations have been performed in surrounding medium having refractive index numerically equal to 1.33 (dielectric constant 1.77). Further, the direction of polarization of incident plane wave is considered to be along the long-axis of the nanoparticle because of strong electric-filed enhancement in this direction. The complete detail of the mathematical description of the DDA can be found in [41,42]. 3. Results and discussion DDA simulations have been performed to calculate the optical response of alloy NPs. The dimensions of the nanostructures are considered greater than the mean free path of the conduction electrons so as the surface scattering effects are not important and hence, no size corrections due to surface scattering are included in the bulk dielectric constants. Therefore, the same wavelength dependent dielectric constants for NPs as that of bulk metals are used as input in DDA calculations and have been obtained from Palik [43] for individual metals. Whereas for alloys it has been calculated by average weighted method, given as εalloy (ω) = (1 − x)εAg (ω) + (x)εCu (ω ) [23,34,44], x represents the metal composition in Ag–Cu NPs. The behavior of surface plasmons of noble metal nanostructures can be described on the basis of complex dielectric constants as real part of the metal dielectric function determines the LSPR peak position in response to the surrounding medium while imaginary part determines the relative contribution of absorption and scattering in the extinction alongwith the plasmon resonance linewidth (FWHM). Therefore, when individual metals are combined to form alloys, variations in dielectric constant values are responsible for the changes in optical properties of alloy NPs from that of individual metals. The organization of the paper follows as: we first address the effect of shape on the scattering spectrum and then discuss the size dependent changes in the optical properties of different shape alloy nanostructures. For instance, the results of Ag1−x –Cux alloy with metal composition x = 0.50 have been shown and later the effect of metal type on the scattering spectrum is briefly addressed. 3.1. Effect of particle shape To calculate the effect of particle shape on the optical response of alloy NPs, different shapes such as spherical (a = b = c), prolate (a = b < c ), nanocube (l = b = h), rectangular (l < b = h), and nanobar (l = b < h) have been considered. The simulations have been performed by approximating the volume of each shape equal to the volume of 50 nm sphere radius (in other words the effective radius of all the nanostructures is assumed to be 50 nm). The prolate NPs are formed by enlarging the nanospheres along its one axis (say c). Similarly, the nanobar and rectangular particles are formed by enlarging the nanocubes along one (say h) and two (say b and h) axes, respectively. An important feature of prolate, rectangular, and nanobar particles is that their optical properties are dominated by two plasmon resonances, one in the shorter wavelength called transverse plasmon resonance and other in the longer wavelength called longitudinal plasmon resonance due to the polarization of incident light along the short and long axis, respectively. As the long-axis length of the nanostructure increases, the large change in optical properties of longitudinal plasmon resonance has been observed in comparison to the transverse plasmon
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(a) Fig. 1. Calculated scattering spectra of Ag–Cu alloy nanostructures of effective radius 50 nm.
resonance [45,46]. Therefore, to compare the scattering spectra of different shape Ag–Cu alloys, the longitudinal plasmon resonances for each nanostructure are calculated and have been presented in Fig. 1. A good variation has been found in LSPR wavelength, intensity, and FWHM with change in shape of NPs. LSPR for all the nanostructures lies in the different wavelength regions due to different free electron oscillations as the charge separation between electron cloud and positive core changes with shape. A redshift in LSPR wavelength has been found as the shape changes from nanosphere to the nanobars and therefore, as we proceed from unsymmetrical to symmetrical nanostructure, the LSPR position shifts towards shorter wavelength region and follows the order as nanobar > prolate > rectangle > nanocube > sphere. The LSPR wavelength can be tuned from 570 nm (nanosphere) to 945 nm (nanobar) of the EM spectrum for different considered shapes of the alloy NPs. A similar trend in shifting the LSPR wavelength has been found as for individual metals [4] but with larger variation in FWHM and scattering efficiency alongwith enhanced stability and cost effectiveness. It is clear from the obtained scattering spectra that cube and rectangular alloy NPs show better plasmonic properties in comparison its spherical counterpart in the visible region of the EM spectrum and nanobar in comparison to prolate NPs of similar dimensions. This is due to the large accumulation of free electrons at the sharp corners and edges of nanocube, rectangular, and nanobar particles and therefore, induces strong electric-field enhancement which in turn enhances the scattering efficiency. Further, due to the accumulation of free electrons at the sharp corners, the increased separation contributes for the reduction in restoring force which in turn causes the LSPR wavelength towards the longer wavelength region as compared to their rounded corner counter parts [7–9]. This trend is obviously obtained because as sharp corners are rounded, a small decrease in particle size, blue shifts the LSPR wavelength alongwith decrease in scattering efficiency approaching to its spherical counterpart. By comparing the optical response of different shaped NPs, it is concluded that the shape having sharp corners has better plasmonic properties and could be preferred in future plasmonic applications. Therefore, in the next part of the manuscript, the detailed studies of size dependent plasmonic properties of cube, rectangular, and nanobar particles have been discussed.
(b) Fig. 2. Calculated scattering spectra for Ag–Cu alloy nanocubes with change in edge length from (a) 20 to 50 nm, (b) 60 to 120 nm.
3.2. Effect of particle size It is well known that the optical properties are significantly controlled with changing the size of the metal NPs [2,9,24]. To study the influence of size, the edge length of nanocube, long-axes length of rectangular and nanobar particles are varied from 20 to 120 nm with smaller axes length of the NPs kept fixed at 20 nm. The calculated scattering spectra of Ag0.50 –Cu0.50 nanocubes as a function of edge length (L) are shown in Fig. 2. Scattering spectra have been plotted in two different panels: one with edge lengths 20–50 nm and other with 60–120 nm, to see the results clearly. It has been found that the scattering efficiency representing 20 nm nanocube has a negligible peak and lies in the near interband transition region of the Cu which results in damping of the plasmon resonance in this region and therefore, contributes towards absorption only (similar to that of bare Cu NPs [7]). The inset in Fig. 2(a) shows that the two peaks with almost similar scattering can be seen for 20 nm nanocubes designated as peak 1 and peak 2. This is due to the splitting of the dipole resonance as a result of sharp corners of a nanocube. As the edge length of the nanocube increases from 20 to 50 nm (Fig. 2a), the peak 2 intensity becomes
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much larger than the peak 1 and only single dipole peak is observed with further increase in edge length (Fig. 2(b)) alongwith redshift in the LSPR wavelength. The similar trend has been found for Ag–Cu alloy nanocubes as obtained by Zhou et al. [10] for Ag nanocubes but with larger redshift in the LSPR wavelength due to the contribution of the Cu NPs. The scattering spectra of other two shapes (nanobar and rectangular) have also been calculated as a function of long-axis length. However, the spectra are not shown here to avoid the complexity of the article but the results obtained from those spectra are presented and compared with the nanocubes. Further, to clarify the results found in the spectra, the long-axis length (edge length for nanocubes) dependent LSPR wavelength, its FWHM, scattering yield ( Q sca / Q ext ), and relative efficiency of scattering over absorption ( Q sca / Q abs ) has been calculated and summarized in following figures. Size dependent LSPR wavelength and scattering efficiency of different shapes have been calculated and shown in Fig. 3. For all the nanostructures, as the long-axis length increases, the increased separation between the charges reduces the restoring force which results in shift of the plasmon resonance towards the longer wavelength region (Fig. 3(a)) as for nanospheres and nanorods [11,32]. However, this shift is larger in case of nanobar in comparison to other shapes. This is due to the larger separation between the charges in nanobar as there is only one longer axis. The shift in LSPR is exponential in nature for nanocube and rectangular particles and their exponential fit equation is given by
(a)
λ = y 0 + A exp
L
(1)
t
The linear fit equation for nanobar is given as
λ = A ∗ L + y0
(2)
where λ and L represent the LSPR wavelength and long-axis length of the nanostructures, respectively. The observed fitting to the data points shown collectively in Fig. 3(a). The obtained values of constants y 0 , A, and t are given in Table 1. The fitting equations to the calculated data points give the general expression to calculate the LSPR wavelength at any arbitrary chosen long-axis length for a given aspect ratio in case of rectangular and nanobar particles of the nanostructures in surrounding medium refractive index of 1.33. The vertical line shows that for a fixed length of the NPs, the LSPR position shifts towards the longer wavelength region with shape of the NPs from nanocube (square) to nanobar (up triangle). Therefore, the LSPR wavelength of the alloy NPs can be tuned from the visible to NIR region of the EM spectrum with change in size and shape. For rectangular and nanobar particles, the maxima of scattering efficiency increases continuously with increasing long-axis length but for nanocubes, it is maximum for 80 nm edge length (square, Fig. 3(b)) and decreases with further increase in edge length. This decrease after a particular edge length is due to the origin of a quadrupolar resonance at a shoulder in the smaller wavelength in addition to the dipolar resonance, because of inclusion of retardation effects such as radiation damping and dynamic depolarization at such larger size [2]. However, the similar effect is not marked for rectangular and nanobar particles of same length because the effective volume for these nanostructures is smaller than the nanocubes. Thus, the
(b) Fig. 3. Length dependent (a) LSPR wavelength and (b) scattering efficiency of Ag–Cu alloy nanostructures.
scattering efficiency is found to be larger for rectangular and nanobar in comparison to the nanocubes and follows the increasing order as nanocubes < nanobar < rectangular, for all the lengths except smaller than 50 nm. This is because for smaller length, the LSPR lies below the wavelength region of 630 nm (Fig. 3(a)) where the imaginary part of the Ag–Cu alloys decreases regularly [34] which results in enhancement of scattering efficiency and follow the similar order of increasing scattering efficiency as for LSPR wavelength with change in shape from nanocube to nanobar. The maximum scattering and absorption are found for Ag–Cu alloy nanocubes of dimensions 80 nm and 60 nm, respectively. However, the optimized dimensions are nearly similar to the dimensions of Cu nanocubes i.e., 100 nm for scattering and 60 nm for absorp-
Table 1 The obtained values of constants defined in Eqs. (1) and (2). Nanostructure
Fit type
y0
A
T
Regression coefficient
Nanotube Rectangular Nanobar
Exponential Exponential Linear
556.24 ± 5.96 372.09 ± 49.92 388.35 ± 8.29
10.33 ± 2.67 158 ± 42.46 5.71 ± 0.10
43.47 ± 3.60 112.54 ± 17.19 –
0.99947 0.99968 0.99934
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(a)
Fig. 4. Length dependent FWHM of Ag–Cu alloy nanostructures.
tion [7] but the main advantage of using Ag–Cu over Cu are about the stability, and further tunability of the optical properties with change in metal composition. Since FWHM plays a significant role in deciding the use of metal NPs for a particular application, e.g., larger FWHM with enhanced scattering efficiency is required to increase the absorption efficiency of plasmonic solar cells and lower FWHM is required for considering the material in plasmon sensing applications. The absorption efficiency of thin-film plasmonic solar cells can be enhanced either by covering larger region of the EM spectrum i.e. concentrating only towards larger FWHM due to the inclusion of higher order peaks but at the cost of reduced scattering efficiency or by enhancing scattering efficiency at a particular region of the EM spectrum where only the dipolar peak contributes. The FWHM mainly determined by the imaginary component of the dielectric function alongwith particle size as well as shapes, hence its effect on the optical properties is necessary to study. Therefore, the edge length dependent calculated FWHM have been shown in Fig. 4 and found that the nanocubes show the larger value of FWHM in comparison to other two nanostructures for each length. For nanocubes of smaller edge length (≤50 nm), the appearance of two dipolar peaks as explained earlier (Fig. 2(a)) results in the enhancement of FWHM. Another reason for increase in FWHM is due to the larger value of imaginary part of the dielectric constants in the wavelength regime where the LSPR falls for these smaller nanocubes in near the interband transition region of the Cu NPs. However, both the dipolar peaks are combined to form single dipole peak as the edge length increases, therefore, reduces the FWHM with change in edge length of the nanocube from 20 to 60 nm and found minimum for 60 nm size. A further increase in edge length resulting in a continuous increase with much enhancement has been seen above 80 nm due to the commencement of a contribution from the quadrupolar resonance to the dipolar resonance and hence covers the larger wavelength region. Therefore, in the case of Ag–Cu alloy nanocubes, larger spectral region is covered having edge length larger than 100 nm with good scattering efficiency (Fig. 3(b)), hence, optimized as the better choice of Ag–Cu alloy nanostructure to enhance the efficiency of plasmonic solar cells over the wider region of the wavelength, whereas, 60 nm nanocubes with minimum FWHM may be useful for better plasmon sensing applications. On the other hand, a regular increase in FWHM with long axis length has been found in case of rectangular and nanobar particles but rectangular NPs show larger values of FWHM in comparison to the nanobar. Therefore, the nanostructures repre-
(b) Fig. 5. Length dependent calculated (a) Scattering yield and (b) Relative efficiency of Ag–Cu alloy nanostructures.
sent the increasing order of FWHM as nanobar < rectangular < nanocube over the entire range of considered lengths. Thus, scattering efficiency and FWHM of all the nanostructures have to be compromise with each other for plasmonic solar cells. Further, for efficient plasmonic solar cells, metal NPs of larger scattering efficiency and at the same time, the smaller absorption efficiency should be required. Therefore, to calculate the scattering contribution in the extinction and scattering over absorption, a scattering yield and relative efficiency parameters have been calculated which may be defined as the ratio of scattering to the sca extinction i.e. η1 = Q |LSPR and scattering to absorption i.e. η2 = Q Q sca | Q abs LSPR
ext
at each LSPR, respectively. Fig. 5 shows the size dependent calculated scattering yield and relative efficiency for different shapes of Ag–Cu alloy NPs. In comparison to the other nanostructures, nanocube shows the large scattering yield (Fig. 5(a)) and relative efficiency (Fig. 5(b)) for all edge lengths except 120 nm and both these parameters follow the behavioral order as nanobar < rectangular < nanocube. This behavior can be understood on the basis of larger effective volume of the nanocubes and imaginary part of the dielectric constants in different LSPR region of the
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Fig. 6. Comparison of scattering spectra of alloy nanocubes, rectangular, and nanobar particles.
nanostructures. Since, the LSPR for the nanobar particles lies in the longer wavelength region (Fig. 3(a)), where the larger imaginary part of the dielectric constant is responsible for decrease in both the parameters. At the same time, a small increase has been found with increase in size and therefore, mainly useful for absorption based plasmonics applications just like nanorods [47]. The LSPR for rectangular NPs lies in the smaller region of wavelength than nanobars, therefore, reduces the imaginary part of the dielectric constant and hence, increasing both the parameters. A linear increase in relative efficiency has been seen with long-axis length but scattering yield starts decreasing slowly at the longer length due to the inclusion of damping effects at such sizes. However, the contribution of damping effects becomes larger as the NPs change from rectangular to the nanocubes due to their larger effective volume as explained earlier. Therefore, in case of nanocubes, the scattering yield follows the similar behavior with rectangular but with good enhancement for same length alongwith a decrease in relative efficiency at an edge length of 100 nm. Since, the scattering yield increases with edge length even at larger size which shows that there is still a larger contribution of scattering over absorption in the extinction but its relative efficiency decreases. Therefore, it is noted that absorption is dominant for smaller length while larger length offer better scattering properties for nanocubes and rectangular particles. This behavior of different nanostructures of Ag–Cu particles is due to the different effective volumes used in numerical simulations equivalent to the similar lengths. The scattering efficiency can further be enhanced by considering the incident polarization state along the average of all the polarization states which results in the generation of many surface plasmon resonances and therefore covers the larger region of the EM spectrum [17]. The combination of different alloy nanostructures placed on the top surface of the active layer of thin film solar cells will cover the broad region of the spectrum and therefore, may enhances efficiency [48]. 3.3. Effect of metal type Depending upon the dielectric constant, the noble metal NPs show different plasmonic properties in the UV–visible region of the EM spectrum. Au is more costly among noble metals but its NPs and combination with other noble metals to form alloys and core– shell nanostructures can be easily synthesized with long term stability in embedding medium and better biocompatibility, therefore, attracted much attention mainly in biological and sensing applications [21,47]. In this section, simulated scattering spectra of other
alloys containing Au i.e. Au–Cu and Ag–Au have also been obtained and compared with the Ag–Cu nanostructures. Presently, the previously [32] optimized alloy compositions such as Ag0.75 Au0.25 and Au0.25 Cu0.75 have been considered and dimensions i.e., long-axis length for all the nanostructures is kept fixed at 100 nm. The effect of metal type on the scattering properties of Ag–Cu nanostructures has been calculated in embedding medium of refractive index 1.33 and presented in Fig. 6. The calculated scattering spectra for Ag0.50 Cu0.50 , Ag0.75 Au0.25 , and Au0.25 Cu0.75 are represented by solid line, dash dot, and dashed line, respectively. In all the nanostructures, the Ag–Au alloy shows an enhanced scattering efficiency with larger bandwidth in comparison to other two alloys but relatively better enhancement in scattering efficiency has been seen in case of nanobars. The larger scattering efficiency and FWHM has been obtained in case of rectangular and nanocubes, respectively, for all the alloy nanostructures. The reason for increased scattering efficiency in case of nanobar and FWHM in case of nanocubes has been explained earlier in Figs. 3b and 4, respectively. However, the tunability in LSPR peak position with change in alloy for all the nanostructures is very small. This is due to the similar values of dielectric constants of noble metals in the NIR region of the spectrum where the LSPR peaks falls for these nanostructures. Therefore, due to the smaller difference in optical properties of alloy NPs in the longer wavelength region, the experimentally synthesized cheapest and most abundant Ag–Cu alloy nanostructures may be utilized in future plasmonic applications in place of other alloys and bare noble metals. The present work calculates the plasmonic response of alloy NPs by varying size, shape, and metal type without paying a particular attention to the change in metal composition and short-axis length. As studies reported [21,26] that the tunability in optical properties may further be well controlled with change in metal composition of alloy NPs and the contribution of scattering over absorption is significantly enhanced with changes in the width (short-axis length) of the nanobar and rectangular particles similar to the nanorods [49,50]. Therefore, further studies are required to know the effect of metal composition and short-axis length on the optical properties of alloy nanostructures. 4. Conclusion It is concluded that by changing shapes and size, the optical properties of alloy NPs can be controlled over the wider region of the spectrum than the individual nanostructures alongwith enhanced stability and cost-effectiveness. The scattering efficiency has been found larger for rectangular and nanobar particles in comparison to the nanocubes but better enhancement in other parameters such as FWHM, scattering yield, and relative efficiency has been found for nanocubes alongwith its LSPR in the visible region. The LSPR shifts towards the longer wavelength region with change in nanostructure from nanocube to nanobar for all longaxis lengths (edge length for nanocubes). Therefore, depending upon the scattering efficiency, scattering yield, relative efficiency, and LSPR wavelength, the alloy nanostructures may be useful in desired range of the EM spectrum for a particular application. Larger absorption efficiency of nanobars alongwith their LSPR in the longer wavelength region may be preferred for absorptionbased applications. Alloy nanocubes having edge length greater than 100 nm shows good scattering efficiency over the wider region of the wavelength and, therefore, may be useful for plasmonics solar cells whereas, 60 nm nanocubes with minimum FWHM may be useful for sensing applications. Rectangular and nanobar particles may be preferred over nanocubes in sensing due to their smallest FWHM. The scattering yield and relative efficiency parameters follow the increasing order as nanobar < rectangular < nanocube, except at edge length of 120 nm. A limited control in
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optical properties has been observed with change in metal type in the Ag–Cu alloys due to the similar values of dielectric constants in the longer wavelength region and therefore, the cheapest and possible synthesized Ag–Cu alloy nanostructures may be preferred over others for future plasmonic applications. Therefore, for cost effective practical applications, the LSPR based optical properties can be enhanced and tuned in large region of the EM spectrum by combining the individual metals. It is expected that the present simulation results will motivate the experimentalists to synthesize alloy NPs of various shapes, size, and metal compositions for low cost specific applications with more tunability. Acknowledgements The author, Amit Bansal, would like to thank SLIET authorities for the financial support in the form of institute fellowship towards his Ph.D. (PPH1201). References [1] S. Bakhti, N. Destouches, A.V. Tishchenko, Analysis of plasmon resonances on a metal particle, J. Quant. Spectrosc. Radiat. Transf. 146 (2014) 113–122. [2] K.L. Kelly, E. Coronado, L.L. Zhao, G.C. Schatz, The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment, J. Phys. Chem. B 107 (2003) 668–677. [3] J.S. Sekhon, S.S. Verma, Controlling the LSPR properties of Au triangular nanoprisms and nanoboxes by geometrical parameter: a numerical investigation, J. Mod. Optics (2014), http://dx.doi.org/10.1080/09500340.2014.954650. [4] I.O. Sosa, C. Noguez, R.G. Barrera, Optical properties of metal nanoparticles with arbitrary shapes, J. Phys. Chem. B 107 (2003) 6269–6275. [5] C. Noguez, Surface plasmons on metal nanoparticles: the influence of shape and physical environment, J. Phys. Chem. C 111 (2007) 3806–3819. [6] K.S. Lee, M.A. El-Sayed, Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition, J. Phys. Chem. B 110 (2006) 19220–19225. [7] T.V. Alves, W. Hermoso, F.R. Ornellas, P.H.C. Camargo, On the optical properties of copper nanocubes as a function of the edge length as modelled by the discrete dipole approximation, Chem. Phys. Lett. 544 (2012) 64–69. [8] A.Q. Zhang, D.J. Qian, M. Chen, Simulated optical properties of noble metallic nanopolyhedra with different shapes and structures, Eur. Phys. J. D 67 (2013) 231, http://dx.doi.org/10.1140/epjd/e2013-40240-1. [9] W. Hermoso, T.V. Alves, C.C.S. de Oliveira, E.G. Moriya, F.R. Ornellas, P.H.C. Camargo, Triangular metal nanoprisms of Ag, Au, and Cu: modeling the influence of size, composition, and excitation wavelength on the optical properties, Chem. Phys. 423 (2013) 142–150. [10] F. Zhou, Z.Y. Li, Y. Liu, Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles, J. Phys. Chem. C 112 (2008) 20233–20240. [11] K.S. Lee, M.A. El-Sayed, Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index, J. Phys. Chem. B 109 (2005) 20331–20338. [12] Y.A. Akimov, K. Ostrikov, E.P. Li, Surface plasmon enhancement of optical absorption in thin-film silicon solar cells, Plasmonics 4 (2009) 107–113. [13] K.R. Catchpole, A. Polman, Plasmonic solar cells, Opt. Express 16 (2008) 21793–21800. [14] X. Huang, P.K. Jain, I.H. El-Sayed, M.A. El-Sayed, Gold nanoparticles: interesting optical properties and recent applications in cancer diagnostics and therapy, Nanomedicine 2 (2007) 681–693. [15] N.G. Khlebtsov, L.A. Dykman, Optical properties and biomedical applications of plasmonic nanoparticles, J. Quant. Spectrosc. Radiat. Transf. 111 (2010) 1–35. [16] J. Katyal, R.K. Soni, Size- and shape-dependent plasmonic properties of aluminum nanoparticles for nanosensing applications, J. Mod. Phys. 60 (2013) 1717–1728. [17] T.L. Temple, D.M. Bagnall, Optical properties of gold and aluminium nanoparticles for silicon solar cell applications, J. Appl. Phys. 109 (2011), 084343-1. [18] T.M.D. Dang, T.T.T. Le, E.F. Blanc, M.C. Dang, Synthesis and optical properties of copper nanoparticles prepared by a chemical reduction method, Adv. Nat. Sci: Nanosci. Nanotechnol. 2 (2011) 015009, http://dx.doi.org/10.1088/ 2043-6262/2/1/015009. [19] G.H. Chen, J. Zhao, E.M. Hicks, G.C. Schatz, R.P.V. Duyne, Plasmonic properties of copper nanoparticles fabricated by nanosphere lithography, Nano Lett. 7 (2007) 1947–1952. [20] C. Salzemann, A. Brioude, M.P. Pileni, Tuning of copper nanocrystals optical properties with their shapes, J. Phys. Chem. B 110 (2006) 7208–7212.
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