Previously I discussed how the existence of plasmons were predicted based on theoretical models of free electrons in a metal. In this post I hope to introduce some more plasmon physics. The derivations discussed previously were quite math heavy, so I hope to make this post a little more qualitative and accessible to the lay reader.
Just to recall, plasmons are quantised quasiparticles arising from the collective oscillation of plasma, akin to how phonons are quantisations of mechanical vibrations. Low energy plasmons will be present due to random thermal and charge density fluctuations in the material, but can also be excited by electrons or photons. Electrons scattering in the metal can transfer energy via in-plane electromagnetic interactions to excite oscillations in the plasma. The electric field of incident photons will cause coherent oscillation of electrons, and by further Coulombic interactions between the electrons and atomic nuclei, a restoring force will cause the plasma to oscillate.
To motivate further discussion of my research, it is important to specifically discuss surface plasmons. As the name suggests, these are simply plasmon oscillations at a metal surface or interface. The movement of charge produces a local electric field internal and external to the metal. The total excitation energy of a surface plasmon takes into account both the movement of electrons, and the associated magnetic field.
Surface plasmons give rise to two interesting phenomena; they enhance local electric fields at the metal surface, and they cause optical absorption to be maximised when the photon frequency is resonant with the oscillation of electrons (known as a surface plasmon resonance). This resonance varies based on the choice of metal and is very sensitive to the nanoscale geometry of the metal [1]. This has led to much research in the field using fabricated nanostructures to produce desirable effects. Gold and silver are the most common materials to use as they support resonances in the near-infrared region with low plasmonic losses [2].
Plasmons will naturally decay via several different mechanisms: Landau damping, radiative emission, and surface damping. The velocities of electrons in a surface plasmon follow a Maxwell-Boltzmann distribution, so there will be more electrons travelling slower than the phase velocity than faster [3]. Due to the associated internal electric field, those travelling slower are accelerated, and those travelling faster are decelerated. This means that more electrons are gaining energy from the surface plasmon than are losing energy to it. This causes the surface plasmon to gradually lose energy, producing energetic electron-hole pairs in the process. These are known as "hot carriers" as they have significantly higher energy than possible due to random thermal fluctuation. This process is known as Landau damping, and it produces a higher non-thermal distribution of hot carriers in the metal. Radiative emission is fairly self-explanatory and simply involves the plasmon relaxing to a lower oscillation state whilst emitting a photon.
Of particular interest in my research is the surface damping term, or more specifically, chemical interface damping. This phenomenon arises due to the presence of adsorbed chemical species on the surface of the metal, allowing electrons to be scattered into unoccupied orbital states in the adsorbate species via the decay of a surface plasmon. This is understood to happen through two distinct mechanisms - direct and indirect charge excitation. In the direct process, the energy from a plasmon decay is resonant with an electronic state in the adsorbate, directly exciting the electron. For the indirect process, the plasmon decays via Landau damping, producing a non-thermal distribution of hot electrons. Some of these will have sufficient energy to scatter into unoccupied orbitals. Since the electron distribution formed has decreasing occupation at higher energies, indirect excitation favors scattering into lower energy orbital states.
These processes lead to some interesting potential applications, specifically by the injection of energetic electrons into chemical species, allowing for hot electron driven catalysis via new reaction pathways. In 2013, the room temperature dissociation of \(H_{2}\) was demonstrated on gold nanoparticles. The injected electron allowed the formation of an unstable \(H_{2}^{-}\) ion due to a Feshbach resonance, stimulating the dissociation of the molecule into two individual hydrogen atoms. This process is possible with other molecules too, some of which may have reactions important to industry.
This physics forms the basis of the theory relevant to my research, which involves trying to understand how chemical interface damping really works, as this is still poorly understood. I will cover some more rigorous theory in the next post or two, where I will discuss Raman scattering and how we can use spectroscopy to probe a plasmonic system, and the two-temperature model.
[1] K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B, vol. 107, no. 3, pp. 668–677, Jan. 2003.
[2] M. Rycenga, C. M. Cobley, J. Zeng, et al., “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev., vol. 111, no. 6, pp. 3669–3712, Jun. 2011.
[3] “ON THE VIBRATIONS OF THE ELECTRONIC PLASMA,” in Collected Papers of L.D. Landau, Elsevier, 1965, pp. 445–460. doi: 10.1016/b978-0-08-010586-4.50066-3.
[4] C. Boerigter, R. Campana, M. Morabito, and S. Linic, “Evidence and implications of direct charge excitation as the dominant mechanism in plasmon-mediated photocatalysis,” Nat. Commun., vol. 7, no. 1, p. 10 545, Jan. 2016.