Plasmonic hybridization modes in VO₂@Au nanoshell: A comprehensive review and theoretical analysis

Phase transition materials (PTMs) have become popular due to their unique and unstable physical properties, especially in the field of optical tuning. One such material, vanadium oxide (VO₂), is noteworthy for its ability to undergo different changes in physical properties when exposed to specific external factors.¹ In the context of creating adjustable plasmonic nanoparticles (PNPs), VO₂ is an excellent material for optical phase transitions. When VO₂ reaches its critical temperature of 68 °C, it undergoes a phase transition from being an insulator to becoming a conductor. This transition causes a sudden change in the dielectric coefficient and its corresponding optical behavior.² So, combining plasmonic materials with VO₂ offers several advantages, particularly in enhancing the optical properties of VO₂-based materials. Plasmonic materials can manipulate light at the nanoscale, allowing for control over light absorption, scattering, and transmission properties of VO₂. This greater control over light can have applications in various fields, including optoelectronics, sensors, and energy devices.^3,4

To better understand the behavior of complex metal nanostructures such as metal nanoshells and polymer nanostructures, the plasmon hybridization model has been suggested. This model considers the theory of plasmon hybridization, which suggests that the plasmon response observed in these metal-based nanostructures is a combination of different plasmons originating from simpler sphere and cavity shapes. The interaction between these various plasmons gives rise to a complex system.⁵ 

A common method used to demonstrate hybridization in metallic nanoshells is by utilizing plasmon resonances and carefully adjusting the frequency dependence between the inner and outer radii of the metal shell.⁵ This process is similar to the way atomic orbitals interact to form molecular orbitals in electron structure theory.⁶ Experimental studies using different techniques have shown that the plasmon resonance frequency of these structures is significantly influenced by both the geometry of the nanostructure and the surrounding environment.⁵In prior investigations, dielectric/metal cores with low refractive indices were studied without a particular focus on optical resonance at various core–shell radii.^5–10 Theoretical and experimental investigations have been conducted on the optical resonances of core–shell nanospheres featuring a high refractive index core (approximately n = 4). These nanospheres are specifically designed to target the lowest Mie resonance within the visible range.¹¹ Semiconductors such as silicon (Si)¹² and gallium phosphide (GaP)¹³ are materials commonly used in the composition of these nanospheres, which enable them to serve as high-index dielectric cores. Drawing on the correlation between plasmonic modes and the refractive index of the core,¹¹ the use of PTMs provides the potential to modify hybridization modes solely by adjusting the temperature, without the need to change the size of the nanoshell environment.⁵ This capability makes PTMs suitable for various applications, including temperature sensing within the environment.

This study marks the first exploration of plasmonic modes in a VO₂@Au smart nanoshell without altering its size but by changing the refractive index during the transition. Initially, the theory of plasmon hybridization is reviewed for the conducted work. Subsequently, plasmonic modes for the proposed core–shell, encompassing sphere and cavity plasmonic modes in both semiconductor and metallic phases of the VO₂ core, are calculated. Notably, the results reveal that beyond 778 nm wavelengths, the cavity frequency of the metallic phase dominates. Last, for a more in-depth examination, the charge density is calculated using a finite-element approach (COMSOL Multiphysics). The conclusive findings indicate that the proposed nanoshell can exhibit both modes at the same wavelength without the necessity for scaling or altering the size of the container, employing a temperature-dependent approach.

The plasmonic response to the nanoshell is the interaction of the plasmonic response of the nanosphere and the nanocavity with constant frequency. The cavity plasmonic mode denotes a distinct mode of localized surface plasmons that can be stimulated within the cavity structure. The cavity plasmonic state is characterized by the collective oscillations of electrons on the surface of a metal or nanoscale cavity. These cavities can take various forms, such as rectangular, circular, or irregular shapes, and the specific modes that can be triggered depend on their geometry. When light interacts with a metal cavity, it can couple with the free electrons on the metal surface, resulting in the generation of localized surface plasmons. These plasmons, in turn, produce standing waves within the cavity, leading to resonance modes with specific frequencies and field distributions. The resonance frequency is dependent on factors such as the cavity size, shape, and surrounding dielectric environment.⁷ 

Similarly, the spherical plasmonic mode refers to a specific mode of localized surface plasmons that can be excited in a spherical geometry. When a metallic nanoparticle or nanosphere is irradiated, it supports plasmonic resonances, which are collective oscillations of the metal's conduction electrons. This resonance increases the electromagnetic fields around the nanoparticle, leading to local field enhancement and light scattering at specific wavelengths. In both cases, the excitation and behavior of plasmonic states in cavities and spheres are controlled by the interaction between the incident light, the metal surface, and the dielectric medium.⁷ 

Here, x is the ratio of the inner radius to the outer radius of the nanoshell, $| ω +⟩$ and $| ω −⟩$ are the state corresponding to the antisymmetric and the symmetric coupling between the sphere and cavity states, respectively, and l is the angular momentum.⁶  $ω B= 4 π e 2 n 0 / m e$ is the bulk plasma frequency of the metal obtained using the Drude model, where m_e is the effective mass of the electron, and n₀ refers to the free carrier concentration in the metal.¹⁵ 

As shown in Fig. 1, the resonance frequency, which is a function of n_c, w_s is less than w_c when n_c is less than 2, whereas this relationship is reversed for n_c greater than 2.¹¹ 

On the other hand, when the environment changes, the dielectric constant of the environment must also be considered. The inclusion of dielectric in the nanoparticle core or the surrounding medium causes the formation of screening charges on the metal/dielectric surfaces, which are polarization charges due to the interaction of the electric field and the dielectric medium.¹⁸ 

By adjusting the refractive index within the core, it is possible to regulate the prevalence of cavity and sphere plasmonic modes.¹¹ This regulation can be accomplished through the use of PTMs, eliminating the need for alterations to the core material. Upon reaching a critical temperature, the dielectric coefficient of VO₂ undergoes a significant change as a result of a phase transition. Consequently, variations in temperature can cause a shift in modes without necessitating any modifications to the structure itself.¹⁹ 

$ε n ~( i ∞)=3.95, ω p , n ~=3.33eV, γ n ~=0.66 eV, ε n( i ∞)=4.26,$ $ω ∞=15 eV$⁠; the other parameters in Eqs. (26) and (27) are given in Table I.

In line with the change in the dielectric coefficient in the two semiconducting and metallic phases, the frequency of the sphere and the cavity according to the wavelength is plotted [Eqs. (12) and (13)].

To observe the change in the plasmonic frequency during phase change, the plasmonic frequency was plotted according to wavelength, temperature, and filling factor.

Figures 2(a) and 2(b) show the changes in the cavity frequency in terms of wavelength, phase change factor, and temperature, respectively, which increases with increasing temperature and phase change. This increase in wavelengths greater than the specific wavelength of 778 nm is intensified with increasing temperature and phase change, which is in line with the result of Fig. 3.

In Figure 4, to further investigate the effect of core phase change, plasmonic modes have been calculated and drawn for two plasmonic modes bonding (w_n) and antibonding (w_p) [Eq. (14)].

Figures 4 and 5 show the cavity frequency changes based on the phase change filling factor, wavelength, and temperature. With increasing temperature and phase change at a constant wavelength, we see an increase in the bonding and antibonding frequency. On the other hand, an increase in the antibonding frequency is observed at wavelengths larger than a specific wavelength, at constant temperature and after phase change.

In Figs. 4(b) and 5(b), homogeneous behavior was expected as in Figs. 4(a) and 5(a). However, in the range marked by an oval (dash line), the inhomogeneous behavior in terms of wavelength change for the antibonding frequency in the wavelength range of 600–700 nm is observed.

The connection between the cavity resonance frequency and hybrid modeling techniques is effectively demonstrated by Eqs. (12)–(14). Through the utilization of these mathematical expressions, one can acquire a comprehensive comprehension of the intricate interplay among these elements. This, in turn, facilitates a more profound understanding of the fundamental relationship they possess.

The correlation between the frequency and refractive index indicates the potential existence of two dominant modes: the antisymmetric and symmetric modes. This phenomenon has been previously observed. By manipulating the refractive index, the frequency modes undergo a shift, leading to the identification of two distinct modes at a specific wavelength. This remarkable finding is achieved through the application of phase change materials, which enable control over the refractive index and subsequent mode behavior.

As is evident from the drawn charge density, with increasing wavelength in the range of 620–672 nm, the bonding mode is dominant in the semiconductor phase. In contrast, the antibonding mode dominates the metallic phase. At high wavelengths, the semiconductor mode transitions from bonding to antibonding, while the antibonding mode remains constant for the metallic phase. This effect is due to the change in the refractive index of the core, which is only due to the change in the temperature.

In Fig. 3 and the point of intersection of the sphere (gold) frequency and the cavity in the VO₂ metal phase, it is the metal phase that characterizes the plasmonic mode at wavelengths greater than 778 nm. At shorter wavelengths, bonding and antibonding modes can be seen due to the smaller difference between the cavity mode in the semiconductor and metallic phases. As is evident from the charge density, there are two bonding and anti-bonding modes at the smaller wavelengths, while at the larger wavelengths, the plasmonic mode of the metallic phase is dominant and the semiconductor phase changes to anti-bonding.

In the realm of metallic nanostructures, the plasma resonances or modes can be categorized based on the induced surface charge distribution, encompassing dipole, quadrupole, or higher modes, which are contingent upon the incident field. These resonances can be meticulously adjusted by manipulating the dimensions, morphology, and composition of the metal nanostructure, affording precise command over the resonant frequency and spatial distribution of the electromagnetic fields.

The plasmonic coupling in select systems manifests two distinct modes: symmetric and asymmetric plasmonic hybridization. In the symmetric mode, the electron oscillations within the metal nanostructure or nanoparticle synchronize, resulting in a symmetrical charge distribution. This mode is associated with low-energy resonances, typically of the dipole plasmonic nature. On the other hand, the asymmetric mode entails electron oscillations that are out of phase, giving rise to an asymmetrical charge distribution. This mode often corresponds to higher-energy resonances, including quadrupole or higher-order plasmonic resonances. In certain plasmonic systems, both symmetric and asymmetric hybridization modes can coexist, arising from the interaction and pairing of multiple resonances within the system. This interplay leads to the simultaneous manifestation of symmetry and asymmetry in the resulting plasmonic response.

In our study, we focused on investigating the smart nanoshell and observed the concurrent presence of symmetric and asymmetric plasmonic modes at a specific wavelength. Notably, these modes were exclusively reliant on temperature variations, without any manipulation of other parameters. Our investigation unveiled that the charge distribution of the nanoshell, when the VO₂ core resided in the semiconductor phase, transitioned from a symmetric to an antisymmetric configuration as the wavelength increased. Conversely, in the metallic phase, the charge distribution of the nanoshell exhibited a transition from an antisymmetric to a symmetric configuration at longer wavelengths. Furthermore, we made the intriguing discovery that within the wavelength range of 640–667 nm, both modes coexisted regardless of whether the VO₂ nucleus was in the semiconducting or metallic phase.

The authors acknowledge CMC Microsystems for the support and providing access to COMSOL Multiphysics software through computer-aided design (CAD).

The authors have no conflicts to disclose.

Neda Amjadi: Conceptualization (equal); Data curation (lead); Methodology (lead); Validation (equal); Visualization (equal); Writing – original draft (lead). Ali Hatef: Conceptualization (equal); Project administration (equal); Supervision (lead); Validation (equal); Visualization (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.