Fröhlich resonance splitting in hybrid GaN nanowire-Ag nanoparticle structures

Plasmonic nanoparticles (NPs) have attracted significant attention due to their unique optical properties and broad optoelectronic and photonic applications. We investigate modifications of emission in hybrid structures formed by 60 nm silver NPs and GaN planar nanowires (NWs). Bare GaN NWs exhibit photoluminescence (PL) spectra dominated by broad bands peaking at ∼3.44 eV and ∼3.33 eV, attributed to basal plane stacking faults. In hybrids, two new narrow PL lines appear at 3.36 and 3.31 eV, resulting in PL enhancement at these energies. While the 3.36 eV line in hybrid structures can be explained using the Fröhlich resonance approximation based on the electric dipole concept, the appearance of two features at 3.36 and 3.31 eV indicates the splitting of resonance lines. This phenomenon is explained in framework of theoretical model based on the interaction of the dipole with its charge image, taking into account the quadrupole moment of the silver sphere and the quadrupole field of the charge image. A good agreement is obtained between the calculated Fröhlich resonance frequencies and the experimental PL lines in hybrid structures.


Introduction
Nowadays, plasmonic nanoparticles (NPs) gain significant importance in various fields of science and technology due to their unique optical properties and potential applications [1].The properties of plasmonic NPs provide a platform for exploring innovative optoelectronic and photonic devices with enhanced capabilities.Their ability to confine and manipulate light at the nanoscale enables the development of plasmonic waveguides [2], nanoantennas [3], and nanoscale optical circuits [4].Plasmonic NPs can be integrated into devices such as solar cells [5], light-emitting diodes [6], and photodetectors [7] to enhance their performance or enable new functionalities.
Surface plasmons, the collective oscillations of free electrons, occur at the interface between metal and dielectric [8].The incident electromagnetic wave induces the movement of electrons which oscillate at a surface plasmon resonance (SPR) frequency.This specific frequency depends on metal properties and the dielectric constant of the adjacent material.The optical properties demonstrated by metal NPs are due to a phenomenon called localized SPR, when the light interacts with particles that are significantly smaller than the incident wavelength and when the oscillation of free electrons is limited by the volume of NPs.For a metal NP in a dielectric medium, collective oscillations of free electrons in the metal NPs result in the appearance of surface modes with spectral positions determined by the Fröhlich condition for the permittivity of the metal and the matrix.
Noble metal NPs, particularly Ag and Au, support plasmonic resonances that can be tuned throughout the UV-vis-NIR region [9][10][11].A requirement for the localized SPR is a large negative real part and small imaginary part of dielectric function, hence a number of other metals (Li, Na, Al, In, Ga, Pt and Cu) should theoretically support plasmon resonances [12,13].However, most of these metals are either unstable or difficult to work with, or they are prone to surface oxidation as Cu, which can significantly affect optical properties.Among different metals, silver exhibit high refractive index sensitivity and higher figure of merit [9] and is considered as one of the most important materials for plasmonics that can support a strong surface plasmon at a desired resonance wavelength in a broad spectrum from 300 to 1200 nm [14].Given the significance of modifying and enhancing spontaneous emissions, ongoing efforts are directed towards exploring diverse semiconductor nanostructures with unique optical properties, ranging from Tamm plasmon photonic crystals and periodic Bragg structures to meso-resonators and hybrid structures [15][16][17][18][19][20].
Previously, we have studied optical properties of hybrid structures formed by Ag NPs and GaN planar nanowires (NWs) [21], when GaN planar NWs were grown along the [10 10] in-plane crystallographic directions.In this case, the GaN NWs have demonstrated almost ideal geometric shape and high crystalline quality [22].The effect of small Ag NPs on the emission properties reveals in the appearance of an additional narrow line at ∼3.36 eV in photoluminescence (PL) spectra in the vicinity of the Ag NPs, which was explained using a theoretical model based on the Fröhlich resonance approximation and the effective medium approach.The experimental results were well fitted by considering an effective medium composed of air and 10% GaN.
In this work, we study a hybrid structure formed using Ag NPs and GaN planar NWs grown along the [11 20] in-plane crystallographic direction and develop a model to explain the experimental results.In this configuration, the GaN NWs possess structural defects such as stacking faults with associated broad emission bands at ∼3.44 eV and ∼3.33 eV.In these hybrid nanostructures, we observe the appearance of two strong and narrow emission lines at ∼3.36 eV and 3.31 eV.To explain the results and the observation of two additional resonance peaks in the experimental luminescence spectra, we have developed a theoretical model.The calculations are based on the method of images of charges and take into account the influence of the substrate on polarizability tensor considering the quadrupole moment of the sphere and the quadrupole field of the image.

Results and discussion
The morphology of samples has been studied using scanning electron microscopy (SEM) and cathodoluminescence (CL).The GaN planar NWs grown by selective area metal-organic vapor phase epitaxy (MOVPE) in the [11 20] direction are shown in figure 1.While the growth process was conducted with identical parameters and on the same template as in the case of the GaN planar NWs formed along the [10 10] axis, the morphology of the NWs grown along the [11 20] crystallographic axis exhibits shape imperfection as depicted by SEM image in figure 1(a).
The difference in quality between planar NWs oriented in different directions can be attributed to the dependence of the lateral and vertical growth rates on orientation.The shape of NWs is determined by slow-growing semi-polar {11 01} facets [23].In addition, the emission, as revealed by the anchromatic CL map (figure 1(b)), is non-uniform across the facets, where the darker intensity contrast corresponds to areas with the presence of stacking faults.
The size and shape of the Ag NPs were characterized by a scanning transmission electron microscope (STEM) detector in situ SEM at 30 kV electron beam voltage (figure 2(a)).The particles exhibit a shape close to spherical, with a diameter of ∼60 nm.Optical absorption spectra were measured in the temperature range of 5-295 K.We did not observe a notable dependence of absorption on temperature, as illustrated in figure 2(b), which is consistent with previous findings [24].The broad absorption band of the Ag NPs, centered at ∼460 nm, is likely to overlap at the high-energy tail with the GaN emission.In addition, reflection spectra of the Ag NPs on GaN templates have been measured (see figure S1 in the supplementary information).
The hybrid structure Ag NPs/GaN NWs is shown in figure 3(a).To provide a closer look at the distribution of the Ag NPs, the region marked by a red square is magnified and shown in figure 3(b).While the size of the NPs varies, it is important to note that all of them possess dimensions significantly smaller than the wavelength of light ∼400 nm.
The properties of the near-bandgap (NBG) emission of the hybrid Ag NPs/GaN NWs were examined using µ-PL and time-resolved PL (TRPL) techniques.Figure 4(a) displays the typical time-integrated PL spectrum at 5 K for the bare GaN NW (depicted by the red line), while figure 4(b) shows the spectrum measured for the hybrid Ag NPs/GaN NW structures.The NBG spectrum of the bare GaN planar NWs possessing structural defects such as stacking faults, reveals the presence of three distinct features.In addition to the excitonic line X at ∼3.47 eV, there are two characteristic bands labeled as SF1 at ∼3.44 eV and SF2 at ∼3. 32-3.33 eV.These bands are associated with basal-plane stacking faults of intrinsic type I1 and I2, respectively [25].Several PL spectra measured at randomly chosen places are shown in figure S2 (supplementary data) After the deposition of Ag NPs, notable changes occur in the PL spectrum.Two distinct and narrow lines appears at ∼3.36 eV and 3.31 eV, labeled as FR1 and FR2, respectively.The relative intensity of these lines can vary, as illustrated in figure 4(b), where spectra were captured from different points across the structure.In some cases, the dominance of FR1 at 3.36 eV is evident (curve 3), while in other cases, FR2 at ∼3.31 eV exhibits a stronger intensity (curves 1 and 2).More spectra taken in hybrid structure are presented in figure S3 (supplementary data).
It is clear from TRPL image in figure 5(a) that no additional lines are present in the case of the bare GaN NWs.On the contrary, TRPL image in figure 5(b) measured for the hybrid Ag NPs/GaN NWs at place 1 (see curve 1 in figure 4(b)) exhibits that PL emissions peaking at ∼3.36 eV and 3.31 eV have different temporal behaviors compared to the SF-related emissions.The narrower FR1 line partly overlaps with the broader SF2 emission, however, the PL decay characteristics of these features are distinct as visible from the TRPL images in figure 5.The decay of the PL intensity is illustrated in figure 6(a), where TRPL spectra are plotted with a delay time of ∼43 ps and are shifted vertically for clarity.The spectrum at the bottom was taken at the time of the incoming laser pulse when luminescence related to X, SF1 and FR1 and FR2 appears.Clearly, the PL lifetime is longer for the FR1and FR2 lines compared to the excitonic and SF1 emissions, which decay very rapidly.The PL decay curves are plotted in figure 6(b) for energy positions corresponding to the X (blue), FR1 (green) and FR2 (cyan) lines, respectively.The increase in temperature leads to a rapid thermalization of the emission processes.In figures 7(a) and (b) we compare TRPL measurements taken at 5 K and 75 K for place 3 (see PL spectrum 3 in figure 4(b)).The intensity of the FR-related lines is rapidly reduced and almost disappears above 80 K, indicating a rather weak localization potential.To demonstrate in detail that the intensity of the FR1 line is indeed decreases more rapidly compared to the SF1 and SF2 bands, we show PL spectra measured at different temperatures in figure 7(c).Simultaneously, the decrease in PL lifetime for the FR1 line is not as rapid as for the SF2 line with increasing temperature, as it is depicted in figure 7(d).The SF emission can be associated with recombination of electrons and weakly localized holes in the type II quantum well [26].Even with a slight increase in temperature, the hole becomes less localized, and the recombination time is affected by the increasing contribution of nonradiative recombination channels.However, the SF-related emission itself still appears in PL spectra at elevated temperatures.In contrast, for the FR1 line, the recombination time is less sensitive to increasing temperature, but the line vanishes above ∼75 K.This further illustrates that the origin of the FR lines is not related the GaN exciton or stacking faults.

Modeling
Here, we do not account for the potential oxidation of the Ag NPs, which typically does not occur under normal environmental conditions.Previously, we addressed this issue by calculating the effects of the oxidation layer, revealed only a minor shift in the energy position of the resonance, without causing the splitting of the lines.
As a result of light interaction with a metal NP on the surface of a semiconductor substrate, the field's amplitude near the NP significantly increases in the substrate, which correlates with the intensity of spontaneous emission [27,28].
To explain the experimental results and the appearance of two resonance lines in the vicinity of the metal NPs, i.e. the splitting of the Frölich resonance, we suggest the following theoretical model.Let us consider a sphere with permittivity ε i , lying in a half-space with permittivity ε 1 , above a boundary with a half-space having permittivity ε 2 .A schematic representation of the system is shown in figure 8.When an electric field is applied to the sphere, it polarizes the spherical object in a certain way.To describe this process, we can employ the method of images of charges.The core idea behind the image method is to select an effective system of point charges that provides the required boundary conditions.These charges are called 'image charges' .The principles of constructing image charges are similar to the construction of point sources in a mirror image.When a vector quantity is reflected from an interface plane, the vector component parallel to the plane is preserved, while the perpendicular component changes direction.This leads to the fact that the problem becomes anisotropic, and instead of a scalar polarizability that characterizes the response of the system to the action of the field, a polarizability tensor appears [29,30]: where p is a polarization vector, α is a polarizability tensor, E 0 is the electric field and z is the direction perpendicular to the interface plane.We transit from the static approximation to the case when an electromagnetic wave is incident on the dielectric interface.This is a so-called quasi-static approximation, which is valid when the size of the polarized object is much smaller than the wavelength.Then, the s-polarized wave (with respect to the dielectric interface, that is, the plane of the substrate) will have an electric field along the interface.Consequently, it will induce polarization (and scattering) corresponding to the polarizability coefficients α xx = α yy = α || .At the same time, the p-polarized wave has an electric field both along and across the interface plane, thereby exciting the polarization of the system in accordance with both polarizability coefficients α || and α ⊥ .The simplest approximation considers the influence of the substrate on polarizability through the image dipole.This approach assumes that the electric field of the image dipole in the part of the space, where the sphere is located, can be considered as uniform.This approximation is valid when the distance from the sphere's center to the substrate is significantly larger than the radius of the sphere.However, if the NP is placed on a substrate, then this approximation is, in general, not justified.
To obtain a more accurate approximation, it is necessary to consider the deviation of the induced field of the substrate from uniformity in the region where the spherical NP is located.This can be achieved if we take into account the quadrupole moment of the sphere and the quadrupole field of the image.The method described earlier [31] allows to consider the effect of the substrate on polarizability in arbitrary multipole order.However, it was shown by a comparative calculation using the quadrupole approximation and  considering higher multipoles, that accounting for orders higher than the quadrupole does not lead to a significant improvement in accuracy.
To describe our results, we consider the quadrupole moment of the metal sphere on the substrate and obtain the following equations for the components of the polarizability tensor [31]: Figure 8. Silver sphere on the surface of a nanowire.Schemes the operation of the imaging method for different relative positions of pairs of negative and positive charges with respect to the interface plane.(For the case when the substrate is optically denser than the medium in which the nanosphere is located.).
where χ is an auxiliary parameter that defines the dielectric contrast between the substrate and the external space, and it is equal to zero in the case of a spherical NP embedded in a homogeneous medium.R is the nanosphere radius, h is the distance from the center of the sphere to the interface.The Fröhlich resonance of a metal sphere occurs when the polarizability of the sphere reaches its peak value.The polarizability peak is reached near the frequencies at which the denominator of the expression approaches zero.In this situation, we have different expressions for polarization depending on the direction of the field, with different denominators that will approach zero at different points.This leads to the splitting of the resonance into two peaks.
The scattering cross-section is given: where k is the wave vector in the medium.The dielectric constant for silver was calculated according to the Drude model (hω p = 8.98 eV, ε ∞ = 4.96, ℏγ = 18 meV), and the dispersion of GaN was taken according to [32].The spectrum of the scattering cross-section is significant as it determines the intensity of the electric field confined in the vicinity of a metal NP situated on a semiconductor NW.This intensity is directly proportional to the scattering cross-section of the NP.As a result, a direct correlation exists between specific features within the scattering cross-section spectrum and the PL spectrum of NWs [20,32,33].
In the figure 9, we show the calculated scattering cross-section for a silver NP placed on a GaN substrate.The blue color represents the scattering cross-section for the normal component of the field, and the orange color shows the tangential component.The obtained resonance peaks have frequencies of 3.31 eV and 3.36 eV, which are in very good agreement with the experimental features in the PL spectrum.The positions of the experimental peaks FR1 and FR2 are marked with dotted lines.

Conclusions
We have investigated the optical properties of hybrid structures formed by the plasmonic Ag NPs with a size of 60 nm and planar GaN NWs grown by selective area MOVPE in the [11 20] crystallographic direction.The bare GaN NWs demonstrated low-temperature PL bands with maxima at ∼3.44 eV and ∼3.33 eV, denoted as SF1 and SF2, associated with emissions related to the basal plane stacking faults of intrinsic type I1 and I2, respectively.However, in the presence of the Ag NPs, we observed the appearance of two distinct and narrow emission lines at ∼3.36 eV and 3.31 eV, denoted as FR1 and FR2, respectively.TRPL measurements have shown that these lines exhibited different PL lifetimes compared to both the exciton and stacking faults emissions.Increasing the temperature to ∼75 K resulted in rapid thermalization of the FR1 and FR2 lines.We proposed a theoretical model to explain these experimental results and the splitting of the Frölich resonance into two peaks in the presence of Ag NPs on GaN.This model considered the influence of the GaN substrate on polarizability tensor through the image dipole and the quadrupole moment of the sphere and the quadrupole field of the image.The calculated scattering cross-section of Ag NPs on a GaN substrate showed resonance peaks at 3.31 eV and 3.36 eV, in good agreement with the experimental PL spectrum.

Methods
We utilized selective-area MOVPE to create planar GaN structures.This approach involved an initial growth of a 3 µm thick GaN layer on a (0001) sapphire substrate.Subsequently, a 5 nm thin Si 3 N 4 mask layer was deposited.The growth process occurred at a temperature of 1000 • C. The mask's pattern was etched using a focused ion beam (FIB) instrument in situ SEM.Planar NWs in this study were grown within a pattern consisting of rectangular trenches with a 500 nm width, aligned in the [11 20] direction.After a subsequent MOVPE overgrowth, this resulted in broader planar NWs with an approximate width of 4 µm.Details on the FIB processing and used current were published previously [22].
As plasmonic NPs, we employed commercially available spherical Ag NPs from Sigma-Aldrich with a size of ∼60 nm as determined by transmission electron microscopy by supplier.We applied a ZEISS GeminiSEM 560 instrument equipped with STEM detector for control of NPs size and shape at electron beam voltage of 30 kV.The selection of the Ag NPs with 60 nm in diameter was based on an overlap between the emission of GaN and the absorption spectra of the Ag NPs.To create hybrid structures, Ag particles were deposited onto the GaN NWs using a drop-deposition method.
CL measurements were performed using a cold stage that enabled a low temperature of 5 K in a MonoCL4 system integrated with a Zeiss Sigma 300 SEM.The spatial resolution was ∼200 nm, using an electron beam acceleration voltage of 5 kV.PL was measured using a µ-PL setup allowing a spatial resolution of ∼1 µm.PL and TRPL measurements were carried out employing the third harmonic of a 76 MHz Ti:sapphire femtosecond pulsed laser with an excitation wavelength of λ e = 266 nm.Detection was facilitated by a Hamamatsu syncroscan streak camera with a temporal resolution of ∼20 ps.During PL measurements, sample temperature was regulated using an Oxford Microstat, enabling a temperature range between 5 K and 295 K.

Figure 1 .
Figure 1.(a) SEM and (b) panchromatic CL images of four GaN planar NWs formed in the [11 20] in-plane crystallographic direction.

Figure 2 .
Figure 2. (a) STEM image of the Ag NPs.(b) Absorption spectra of Ag NPs measured at different temperatures.

Figure 3 .
Figure 3. (a) SEM image of the hybrid structure.(b) SEM image of Ag NPs on the surface of GaN NWs taken from the region indicated by the square in (a).

Figure 4 .
Figure 4. PL spectra for (a) the bare GaN NW and (b) the hybrid structure.Spectra 1, 2 and 3 were acquired from different places on the Ag NPs/GaN NWs.

Figure 5 .
Figure 5. TRPL images for (a) the bare GaN NW and (b) the hybrid structure.

Figure 6 .
Figure 6.(a) Time-resolved PL spectra for place 1 (curve 1 in figure 4(b)) are shown with a time step of ∼43 ps.(b).PL decay curves measured at energies corresponding to different PL emissions.Red lines show fitting by a single exponential decay law.

Figure 7 .
Figure 7. (a) and (b) TRPL images measured at 5 and 75 K, respectively.(c) PL spectra measured at place 3 (see spectrum 3 in figure 4) at different temperatures.(d) Estimated PL decay time as a function of temperature for different emissions measured at place 3.

Figure 9 .
Figure 9.The splitting of the Fröhlich resonance for a silver particle on a GaN surface.The blue color indicates the scattering cross-section for the normal component of the field, and the red color represents the tangential component.The positions of the experimental peaks are marked with dotted lines.