**2. Surface plasmon resonance effect on PMNMs and its fast relaxations**

The phenomenon of collective excitation of free electrons present in the noble metals when subjected to an external field generates plasmon resonance. For bulk metals, the density of the free electrons decides the characteristic frequency (ωp) of plasmon resonance, that is, ωp = (4πn/me) 1/2e; here n = density of conducting electrons, me = effective mass, and e = charge unit of electrons [13]. The plasmon resonance frequencies of metals such as gold, silver, and copper in bulk were found to be 9.0, 9.0, and 7.9 eV, respectively. Noticeably, the energy of interband transition is lower compared to the transition energies. This leads to the retardation of intraband transition, which in turn results in a fairly large damping constant. The fairly accurate relaxation time has been calculated as about 10 fs [14].

Compared to gold, silver, and copper bulk metals, the frequency of SPR gradually shifts to the longer wavelength as the size of metals gets decreased under the surface effect. The lower excitation energy of silver nanostructures hinders the interband pathway, but considerably unusual optical characteristics are displayed by the intraband transition [15]. **Figure 1A** shows the SPR of a spherical PMNMs excited by visible light and the absorption and scattering of light on the noble PMNMs are primarily decided by the effect of SPR. The SPR effect is vital for the formation of sub-wavelength area (hot spot), which results from the conversion of far-field light irradiation into near-field photonic energy [16]. The probing molecules can display the effect of SERS/actuate the reactions of surface photochemistry, as they are adsorbed on the sub-wavelength area. The existence of SPR effect can be observed on transition metals unlike noble metals (copper, gold, and silver). The shorter lifetime of SPR is however due to the following reasons: (i) the radiative relaxation based on the photon emission or (ii) non-radiative relaxation via producing hot carriers. The property of metals, size of nanostructures, energy and the polarization of lasers can also determine the process of relaxation [17].

The size, shape, and dielectric constant of the medium of environment in which the single metal nanoparticles are present determine the frequency of SPR. The SPR lifetime is around 10 fs as the 2.2-eV incident photonic energy falls on gold nanospheres (**Figure 1B**). This results in higher energy photogeneration (around 2.0 eV) of hot electrons compared to the Fermi level, but the energy of the hot hole (lower than the Fermi level) was estimated to be around 1.0 eV [19]. The extinction spectrum of a spherical silver nanoparticle (diameter = 15 nm) shows 380 nm as its SPR frequency. A considerable decrease in the lifetime of hot carriers was observed as the size of silver nanoparticles increased [20]. For instance, in the excitation light, the major distribution of hot carriers was seen surrounding the Fermi level for

#### **Figure 1.**

*(A) SPR of a spherical PMNM excited by visible light. (B) Normalized distribution of hot electrons and hot holes on Au slab with thicknesses: (i) 10 nm, (ii) 20 nm, and (iii) 40 nm with incident photonic energy of 2.22 eV (reproduced with permission from Govorov et al., published by Elsevier, 2014 [18]).*

### *Nanoplasmonics*

the spherical silver nanoparticle possessing a diameter of 25 nm. When the size of metal nanoparticles increases, a considerable increase in the probability of radiation procedure was witnessed unlike nanoparticles with smaller size. In the case of PMNMs, as the lifetime of SPR gets longer, a larger probability in the distribution of hot carriers (high energy) was observed. The lifetime of SPR is longer for spherical silver nanoparticles relative to gold nanoparticles based on the respective interband transition energy values (3.2 and 2.3 eV) [19, 20].
