Tunable optical properties of graphene wrapped ZnO@Ag spherical core-shell nanoparticles

In this paper, we studied theoretically and numerically the material’s response to incident electromagnetic wave of graphene wrapped zinc-oxide/silver (g − ZnO@Ag) core–shell spherical nanoparticles embedded in a dielectric host matrix. As the nanoparticles size is ∼30 nm, a size much smaller than the wavelength of light, the quasi-static approximation is utilized to obtain analytical expressions for the electric polarizability and the corresponding extinction cross-section. It is found that the spectra of the extinction cross-section of g − ZnO@Ag nanoparticles exhibit two sets of localized surface resonance peaks in the visible and near infra-red (NIR) spectral regions. The first set of peaks observed below ∼900 nm are due to the coupling of the energy gap of the ZnO core with the local surface plasmon resonances of Ag shell, and the second set of graphene-assisted narrow peaks located in the NIR region (above ∼900 nm) are attributed to the plasmons excited at the Ag/graphene interface. It is found that the intensity of the extinction cross-section as well as the positions of the resonance wavelengths are interesting that the graphene-assisted narrow peaks are strongly dependent on the number of layers (N g ) and the chemical potential (μ) of graphene. It means that the response of ZnO@Ag core–shell nanoparticles to electromagnetic fields are greatly enhanced when it is wrapped with graphene and can also be tuned in the therapeutic NIR spectral region by varying N g and μ. The results may be used for possible application in the medical fields, especially for cancer detection and drug delivery.


Introduction
The bulk zinc-oxide (ZnO) semiconductor is a direct band gap material.The wurtzite phase of ZnO is characterized by high dielectric constant, high binding energy of the order of 60 meV at ambient temperature, and a relatively wide energy gap of 3.37 eV [1,2].On the other hand, ZnO nanoparticles (NPs) exhibit unique material properties that can be tuned by varying their size and shape, which makes these NPs suitable for various applications such as diode lasers [3], light emitting diodes [4] and local surface plasmon resonance (LSPR)-based optical sensors [5,6] in the visible spectral region.The size-tunable properties of quantum dots are due to the quantum mechanical confinement effect.Smaller particles are increasingly confined and give rise to higher energy electronic transitions and, consequently, a blue-shifted fluorescent emission [7].Furthermore, the optical, physical, electrical, and chemical properties of ZnO NPs can be enhanced by coating them with noble metal such as gold and silver [8].In particular, a ZnO/noble-metal core-shell composite nanoparticles exhibit strong coupling between the energy gap of the semiconducting material and the plasmon resonance of the noble metals, which gives rise to unique device properties that can be controlled by varying the size of the core, the thickness of the shell, as well as the shape of the core-shell NP itself.
Pristine graphene is a two-dimensional honeycomb carbon lattice with zero band gap semiconducting material [9].Being the thinnest material, graphene's plasmons exhibit exceptionally high light localization.The band gap as well as the localized surface plasmon resonance of graphene can be tuned by adjusting its chemical potential via doping, electrostatic grating, and optical excitations [10].Moreover, graphene possesses a unique material properties such as high conductivity and carrier mobility [11,12], broad-band absorption in the nearinfra-red (NIR) spectral region [13], and higher internal quantum efficiency [14], which makes it a viable candidate for enhancing the optical properties of core-shell dielectric-metal nanostructures for various optoelectronic applications [15][16][17][18][19][20].In addition, graphene NP has low toxicity and large surface-to-volume ratio which enables it to make strong interaction with biological tissues and easily penetrate in cancer tumors [21].
Furthermore, recently the design and fabrication of various types of core-shell nanostructures that consists of graphene or graphene-oxide nanoshells have been numerically and experimentally investigated and reported by various researchers.Graphene coated ZnO@Ag core-shell NP exhibit enhanced photocatalytic activity that is attributed to the effective electron-hole separation and reduced recombination of photogenerated carriers [22][23][24][25].Enhanced photocatalytic efficiency is reported in TiO 2 NPs wrapped with graphene nanosheets [26].The photoluminescence spectra of ZnO@graphene NP shows enhanced electron transport from ZnO core to graphene layer as well as enhanced room temperature magnetization due to increased defect concentration [27].ZnO hollow nanospheres wrapped with a graphene layer are demonstrated to have enhanced electromagnetic wave absorption properties in the x-band spectral region compared with the bare ZnO NP [28].The plasmonic resonance of spherical and ellipsoidal Ag@SiO 2 @Graphene core-shell nanostructures possess two peaks in the wavelength range of 0.3 − 2 μm and is numerically shown to be tuned by varying the Fermi energy of the graphene layer [29].
At the nanoscale, both ZnO and Ag NPs have unique optical and catalytic properties suitable in the medical applications.In fact, the bare ZnO and Ag nanoparticle proved to have unique antibacterial properties which lead to their extensive use in fields such as biomedicine and cosmetic industry [30].Compared to other metallic nanoparticles, Ag NPs exhibit lowered toxicity, excellent biocompatibility, and antimicrobial properties [31][32][33].Furthermore, combining these unique material properties of ZnO and Ag NPs in ZnO@Ag core-shell structures gives rise to excellent photothermal, photodynamic, biocompatibility, and bactericidal properties as demonstrated by [34].Also, the antibacterial and anticancer activities of ZnO@Ag NPs has been studied and reported by [35,36].Optical transmission through the biological tissues are optimal in the NIR spectral region [37].For instance, nanoparticle-assisted photothermal therapy uses core-shell NPs to convert NIR radiation to vibrational energy, thus generating heat sufficient for killing cancer cells [21,38].Hence, to use dielectric/metal core-shell NPs for different applications in the medical diagnostics, immunoassay as well as targeted drug delivery, detection, and imaging, it is necessary to shift the LSPR wavelengths of the NPs to the NIR therapeutic window.This can be achieved, partly, using the conventional nanoshell by varying the dimensions of the core and shell layers, until the practical limit of attainable red-shift of about 1, 200 nm [39].However, this practical limitation can be overcome by further manipulating the geometry of the NPs like using multilayered nanoshells or wrapping the conventional core-shell NP with a grpahene second shell.It has been reported that the plasmon resonance of graphene wrapped core/bi-shell of SiO 2 @Au and Cu 2 O@Au can be tuned in the wavelength regions between 500 − 1600 nm [14,40].
In this paper, we studied a composite nanoparticle (NP) that is composed of a ZnO semiconducting core and a double shell-a first inner metallic (silver) shell and a second outer shell of graphene with the whole composite NP embedded in a dielectric host matrix.In particular, we investigated the effect of wrapping the ZnO/Ag coreshell NP with a monolayer graphene outer shell on the material properties of the composite NP.For the theoretical and computational analysis, we employed the electrostatic approximation to obtain the polarizability of the system and the corresponding extinction cross-section.It is shown that the graphene wrapped ZnO/Ag NPs exhibit two sets of resonance peaks in the selected frequency region of interest-the first set of peaks in the visible spectral region are due to the metallic shell, while the second narrow set of peaks are in the NIR spectral region, which is attributed to the graphene outer shell.Moreover, the second graphene-induced narrow peak may find potential application in the medical fields, since the resonance peak can be tuned to lie in therapeutic window, i.e., in the wavelength regions of 700 − 900 nm and 1000 − 1700 nm, by varying the chemical potential and/or the thickness of the graphene layer [14].

Theoretical method and model
The quasi-static approximation (QSA) and Mie theory are among the well-known approaches to simulate the scattering of light in core-shell NPs.However, the QSA considerably simplifies the mathematical analysis of the scattering problem of complex geometries such as core-bishell systems of dimensions below 100 nm [41].The QSA refers to the assumption that when a particle's size is much smaller than the wavelength of the incident electromagnetic field, its electric field may be regarded as spatially uniform over the extent of the particle [39].Unlike the Mie approach, in QSA all multipole orders higher than the dipole are neglected, so that the electrostatic solution can be obtained by solving Laplace's equation (∇ 2 Φ = 0) of the electric potential, Φ, from which we will be able to calculate the electric field E = − ∇Φ [39,41].Here, we first calculate the potential in the different regions of the NPs, and then the polarizability and the corresponding extinction cross-section using the QSA.
The system considered in this study is a graphene wrapped spherical core-shell nanocomposite, as shown in figure 1.It consists of a spherical dielectric core, a metallic shell, and a second graphene shell embedded in a dielectric host matrix.The radii and dielectric functions of the core, first and second shells, respectively, are r 1 , r 2 , r 3 , and ò 1 , ò 2 , ò 3 , while the permittivity of the host matrix is ò 4 .When the composite core/shell/shell NP is illuminated with incident electromagnetic field, electric field is induced in the composite due to polarization.The size of the NP (r 3 ∼ 30 nm) considered in this study is assumed to be much smaller than the wavelength of the incident light, and hence the quasi-static approximation is valid to analyze the distribution of the fields in the different layers of the NP.Accordingly, the distribution of the electric potential Φ associated with the induced field are obtained by employing the Laplace equation.Hence, assuming that the static electrostatic field is polarized along the z-axis, the general solution for the potential in each region is given by [39,42]: where Φ 1 , Φ 2 , Φ 3 , and Φ 4 are the potentials in the dielectric core, metallic shell, graphene shell, and host matrix, respectively.In addition, r is the distance from the center of the NP, θ is the zenith angle, A i and B i are the constants multiplying the monopole and the dipole terms, respectively; and the subscripts i = 1, 2, 3 , 4 denotes the core, first shell, second shell, and host matrix, respectively.The application of the appropriate boundary conditions (see the appendix) to equations (1)-( 4) results in a set of six equations and six unknowns that can be solved to obtain the constants A i and B i , allowing the determination of the potential in the core, shell, and embedding medium.
In particular, the optical properties of the system may readily be described by the induced field outside the concentric spheres that consists of the core, first, and second shells.Hence, it is suffice to determine the value of the coefficient B 4 .Accordingly, we find the following relation for B 4 to be (see the appendix):  3 .Also, the following notations are used in equation (5):

⎡
The induced electric potential in the host matrix outside the three-layered concentric spheres is given by In the electrostatic approximation, the induced potential outside the concentric spheres may also be given by [43] ( ) where p is the magnitude of the induced electric dipole moment.Moreover, equating equations ( 6) and (7), we find that where the electric polarizability α is given by where B 4 is given by equation (5).
The response of nanoparticles to incident electromagnetic field may be described by the extinction crosssection, which characterizes the complete loss of incident radiation in the NPs.It is the sum of the scattering and absorption cross-sections given by [44] where ò 0 is the permittivity of the vacuum, α is the polarizability of the system, and is the wave vector inside the nanoparticles with λ being the wavelength of the incident radiation.In equation (10), the first term represents the absorption cross-section, while the second term corresponds to the scattering cross-section.
In this work, the size-dependent dielectric function of the metallic shell is calculated using the modified Drude-Lorentz model given by [42] where ω p is the bulk plasma frequency and Γ 0 is the bulk collisional frequency.Also, Γ = Γ 0 + v F /R is the bulk collisional frequency which takes into account the size dependence of the electron scattering in the NPs, where v F is the Fermi velocity and 2 1 3 is the effective mean free path of electrons; and ( )  w exp is the experimental bulk dielectric function defined by [45] where the first two terms are associated with intraband contributions to the dielectric function with w W = f p p 0 being the plasma frequency, Γ 0 is the damping parameter and f 0 is the oscillator strength.The third term represents the interband contribution to the dielectric function, where p is the number of oscillators with frequency ω j , oscillator strength f j , and damping constant Γ j .For numerical evaluations, all the parameter values shown in equations (11) and (12) are taken from [45].
Furthermore, the dielectric function of the graphene shell is given by [14, 46] where σ tot is the total optical conductivity that takes into account both the intraband and interband transitions and t g (in nm) = N g × 0.34 is the thickness of the graphene shell, with N g being the number of graphene layers.The optical conductivity, σ tot , of graphene is calculated using the Kubo formula given by [14, 46] where where , μ is the chemical potential, k B is Boltzmann's constant, T is the temperature, and t is the hopping parameter.In equation ( 16), the value of t is taken to be 2.7 eV at a temperature of 300 K, while μ may take on values in the range 0 − 1.5 eV.

Results and discussion
In this work, we investigated the extinction cross-section of graphene wrapped zinc-oxide/silver core-shell spherical nanoparticles (g − ZnO@Ag) embedded in a host matrix.Unless otherwise specified, the values of the materials parameters used for numerical analysis are the following: The size of the core-shell NP and the thickness of the graphene shell are kept constant at r 2 = 30 nm and t g = 0.34 nm (i.e., mono-layer graphene), respectively.The core dielectric material is assumed to be zinc-oxide NP of dielectric constant ε 1 = 8.5 and the host is water with permittivity ε 4 = 1.77; unless stated otherwise.For the graphene monolayer, the Fermi energy (i.e., chemical potential) is fixed to be 1.2 eV and the hopping parameter is taken as 2.7 eV at a temperature of 300 K.In addition, for the parameters of the permittivity of the silver shell shown in equations (11) and (12), the following values are used [45]: ω p = 9.6 eV, Γ 0 = 0.048 eV, f 0 = 0.845, f 1−5 = (0.065, 0.124, 0.011, 0.840, 5.646), ω 1−5 = (0.816, 4.481, 8.185, 9.083, 20.290)eV, Γ 1−5 = (3.886,0.452, 0.065, 0.916, 2.419)eV.Also, the Fermi velocity is v F = 1.4 × 10 6 m s −1 and the effective mean free path of electrons 2 1 3 are used.It is worth noting that the particles size as well as the graphene parameters (μ and N g ) are selected in such a way that the extinction spectra lies in the wavelength region between 600 − 1700 nm.
Figure 2 is the graph of the extinction cross-section (σ ext ) as a function of wavelength for five different coreshell radii, i.e., r 1 /r 2 = 0.80, 0.75, 0.70, 0.65, 0.60; keeping at the same time r 2 constant at 30 nm.It is observed that between λ = 450 − 950 nm, two sets of resonance peaks occur-the first sets below λ = 850 nm corresponds to the coupling between the energy gap of ZnO with that of the silver shell; while the second set of peaks above λ = 850 nm are the graphene-assisted narrow peaks due to resonances at the silver/graphene interface.The origin of the two resonance peaks may be explained in terms of the plasmon hybridization model in the quasi-static limit [41,47].In this model, the sphere and cavity plasmons of a nanoshell are formed on the outer and inner surfaces of the shell, respectively.The sphere and cavity plasmons hybridize to excite two new resonance modes-the symmetric plasmon mode at lower energy and the antisymmetric plasmon mode at higher energy [48].The strength of the plasmon modes is controlled by the thickness of the metallic shell.In our case, the first and second sets of resonance peaks correspond to the symmetric and antisymmetric plasmon modes, respectively.From figure 2, it is observed that the first sets of peaks are enhanced in value and blueshifted with an increase in the thickness of the metallic shell (i.e., a decrease in r 1 /r 2 ).The enhancement of the resonance peaks with an increase in shell thickness is attributed to an increase in the available free electrons that are participating in the surface plasmon oscillations at the Ag/ZnO interface [38].On the other hand, the graphene-assisted narrow peaks occur at almost the same peak position of wavelength (λ ∼ 876 nm) with the peak values slightly increasing with an increase in Ag thickness.These results are in agreement with that reported by [40] for graphene wrapped Cu 2 O@Au NPs embedded in water.
To see the effect of increasing the size of the nanoparticles (i.e., the sizes of ZnO core and Ag shell; keeping t g constant) on the extinction cross-section, we increased r 2 from 30 nm to 40 nm, while all other parameters are the same as that of figure 2. This plot is shown in figure 3 and the pattern of the curves are the same as that shown in figure 2. Comparison of figures 2 and 3 shows that both sets of peaks are enhanced in value for r 2 = 40 nm than for r 2 = 30 nm, while the corresponding peaks positions remains the same in both cases.For instance, the peaks position for the graphene assisted second set of peaks occur at λ ∼ 877 nm.In brief, the size of the NPs does not affect the resonance peak positions, instead it is the change in the ratio r 1 /r 2 that is responsible for tuning the peaks position to the desired wavelength; provided that all other parameters remain constant.However, increasing the size r 2 has significantly increased the extinction cross-section.
The LSPR peaks of g − ZnO@Ag NPs are strongly dependent on the combined material parameter values of the silver and graphene shells.Figure 4 is the spectra of the extinction cross-section of g − ZnO@Ag nanoparticles, for five different number of graphene layers, i.e., N g = 1, 2, 3, 4, and 5; with r 2 = 30 nm, r 1 /r 2 = 0.70, and μ = 1.2 eV.It is observed that when the thickness of the graphene layer N g increases, there is a slight red-shift of the coupled LSPR peaks of the ZnO core with the Ag shell.The figure shows that when the number of graphene layers increase, the graphene assisted narrow LSPR peak shifts significantly towards lower energy (i.e., longer wavelengths) in the near-infra-red (NIR) spectral regions (refer to table 1).The first narrow peak occurs at a wavelength of λ = 876.6 nm for N g = 1, while it becomes separated from the first set of LSPR peaks for N g > 1.For N g = 5, the resonance peak position is located at λ = 1599.0nm.Also, as the number of the graphene layer increases from N g = 1 to N g = 5, the intensity of the extinction cross-section is found to increase from σ ext = 2.502 × 10 −14 m 2 to σ ext = 1.208 × 10 −13 m 2 , respectively, which is an increase of Δσ ext = 9.580 × 10 −14 m 2 .The increase in the intensity of the extinction spectra is attributed to an increased  number of surface plasmon charges with an increase in the number of graphene layers, N g [49].In brief, by varying the number of graphene layers, the graphene assisted narrow peaks of ZnO@Ag NPs can be tuned to the NIR therapeutic window, i.e., 700 − 900 nm and 1000 − 1700 nm) [14].These results are in agreement with the findings of [14,40] for SiO 2 @Au and Cu 2 @Au NPs wrapped with a graphene shell.The intensity of the extinction cross-section and the corresponding graphene-assisted second narrow peak values are extracted from figure 4 and displayed in table 1.
Another factor that affects the position and intensity of the LSPR resonance peaks of g − ZnO@Ag nanoparticles is the chemical potential of the graphene shell.Figure 5 shows the extinction spectra of the NPs for different chemical potential (i.e., μ = 0.9, 1.0, 1.1, 1.2, 1.3 eV) drawn with N g =1, r 2 = 30 nm, r 1 /r 2 = 0.70, and ò = 1.77.It is shown that as μ increases the graphene assisted narrow peaks are found to shift to lower wavelengths accompanied with an increase in the peak values.For μ > 1.3 eV (not shown in the graphs), the second peak overlaps with the first peak; while for μ < 1.3 eV the LSPR peaks dramatically splits with split positions between consecutive peaks decreasing from Δλ = 80 nm to Δλ = 43 nm as μ increases form 0.9 eV to 1.3 eV (refer to table 2).It is observed that for μ = 0.9 eV, the resonance peak position is located at the wavelength of λ = 1078.0nm, while the peak value of the extinction cross-section is σ ext = 8.86 × 10 −15 m 2 .Also, for μ = 1.3 eV, the peak position and the intensity of the extinction spectra are λ = 832.6 nm and σ ext = 1.656 × 10 −14 m 2 .Moreover, increasing μ will result to an increase in the intensity of the extinction spectra.For instance, as μ increases from 0.9 eV to 1.3 eV, the intensity increases by Δσ ext = 7.32 × 10 −15 m 2 .The increase in intensity of the LSPR peaks with an increase in μ values is attributed to an increase in the conductivity of the graphene shell as well as enhancement of the surface plasmon oscillations at the Ag/graphene interface [49].The second resonance peak positions and the corresponding intensity of the extinction crosssection are summarized in table 2.
The spectra of the extinction cross-section as a function wavelength for different host matrices, i.e., ò 4 = 1.0, 1.5, 2.0, 2.5, 3.0, is shown in figure 6.The parameters used for the plot are r 2 = 30 nm, r 1 /r 2 = 0.7, N g = 1, and μ = 1.0 eV; while the rest parameters are the same as that of figure 2. The figure shows that as ò 4 increases, the intensity of the LSPR of both sets of peaks increases, which is due to the fact that an increase in ò helps the NPs in generating an increased number of LSPR resonance at the respective interfaces.In addition, both sets of resonance peaks shows a red shift with an increase in ò 4 with second sets of peaks (see the inset) shifted slightly compared with the first set of peaks.This result is in agreement with that reported in [49] for graphene wrapped dielectric NPs.

Conclusion
We investigated the spectra of the extinction cross-section of a system that consists of graphene wrapped ZnO@Ag core-shell spherical nanoparticles embedded in a host matrix by employing the quasi-static approximation.It is found that in the wavelength region between 400 − 1200 nm, the spectra of the extinction cross-section of the nanoparticles exhibit two set of peaks, corresponding to the surface plasmon resonance effects at the ZnO dielectric/silver interface, and that induced at the silver/graphene shell, respectively.Moreover, the graphene-assisted narrow peaks that occurs above the wavelength of ∼850 nm are significantly dependent on the graphene material parameters, namely its layer thickness (N g ) and chemical potential (μ).It is observed that as N g increases, there is a slight red-shift of the coupled LSPR peaks of the ZnO core with the Ag shell.On the other hand, as μ is increased the graphene-assisted narrow peaks are found to shift to lower wavelengths accompanied with an increase in the peak values.Another factor that affects the extinction spectra of the investigated nanoparticles is the size of the inner ZnO@Ag core-shell.As the size is increased from 30 nm to 40 nm, the corresponding sets of resonance peaks are highly enhanced (by more than 4-folds-see figures 2 and 3); whereas the peaks position remains the same in both cases provided that the corresponding values of the ratio r 1 /r 2 is fixed constant.Finally, the wavelength position of the graphene-assisted narrow peaks can be tuned to coincide with the therapeutic window by varying N g and/or μ.This enables graphene wrapped nanocomposites to be used for possible medical applications such as cancer detection and drug delivery.enhancement of the local field inside the NP.In the quasi-static approach, the electric field the different regions of the NP is obtained by solving the Laplace's equation, ∇ 2 Φ = 0, and the corresponding electric field is obtained from the equation, E = − ∇Φ.In the spherical coordinate system, the solution of the Laplace's equation in each region of the structure is given by [39,42] ⎛ ⎝ ⎞ ⎠ ( ) ( ) where r is the distance from the center of the NP, θ is the zenith angle, A i and B i are the constants multiplying the monopole and the dipole terms, respectively; and the subscripts i = 1, 2, 3 , 4 denotes the core, first shell, second shell, and host matrix, respectively.Since the potential must be finite in the core for r → 0, B 1 = 0; and the potential q F = -E r cos 4 0 must be recovered in the host medium, far from the shell, yielding A 4 = − E 0 , where E 0 is the magnitude of the applied electric field.Moreover, the following boundary conditions must be satisfied at the boundaries [39,42]: The application of the boundary conditions to equation (17), together with the known values of A 4 and B 1 , results in a set of six equations and six unknowns.Manipulating, these set of equations, we obtained the following values for the coefficients:

Figure 1 .
Figure1.Schematic of a graphene wrapped core/shell spherical nanocomposite embedded in a matrix.The dielectric functions and radii are ò 1 , r 1 , for the core; ò 2 , r 2 for the shell; and ò 3 , r 3 for the graphene shell.The permittivity of the host matrix is ò 4 .

Figure 5 .
Figure 5. Extinction cross-section as a function of wavelength for different chemical potential.N g = 1, ò 4 = 1.77 and r 2 = 30 nm fixed constant.

Table 1 .
The intensity of the extinction spectra and the corresponding resonance peak positions for different values of N g (refer to figure4).

Table 2 .
The intensity of the extinction spectra and the corresponding resonance peak positions for different values of μ (refer to figure5).