Stratified graphene/noble metal systems for low-loss plasmonics applications

We propose a composite layered structure for tunable, low-loss plasmon resonances, which consists of a noble metal thin film coated in graphene and supported on a hexagonal boron nitride (hBN) substrate. We calculate electron energy loss spectra (EELS) for these structures, and numerically demonstrate that bulk plasmon losses in noble metal films can be significantly reduced, and surface coupling enhanced, through the addition of a graphene coating and the wide-band-gap hBN substrate. Silver films with a trilayer graphene coating and hBN substrate demonstrated surface plasmon-dominant spectral profiles for metallic layers as thick as $34$nm. A continued-fraction expression for the effective dielectric function, based on a specular reflection model which includes boundary interactions, is used to systematically demonstrate plasmon peak tunability for a variety of configurations. Variations include substrate, plasmonic metal, and individual layer thickness for each material. Mesoscale calculation of EELS is performed with individual layer dielectric functions as input to the effective dielectric function calculation, from which the loss spectra are directly determined.

Figure 1

Multilayer structure: EELS are calculated for a structure consisting of graphene top layer(s), noble metal middle layer, and semiconductor substrate.

Figure 2

Complex relative dielectric function $\epsilon \left(\omega \right)$ for graphene (a) and hBN (b). Real and imaginary parts [${\epsilon }^{\prime }\left(\omega \right)$ and ${\epsilon }^{\prime \prime }\left(\omega \right)$] are represented by solid and dotted lines, respectively.

Figure 3

EELS: (a)–(c) demonstrate the effect of differing thickness for the Ag, Au, and noble metal layer, respectively, with a SiO${}_2$/Si substrate, and without a graphene coating. Film thicknesses are $34$nm (solid line), $20$nm (long dashes), $10$nm (short dashes), and $4$nm (dotted line).

Figure 4

EELS for varying numbers of layers for the graphene film: (a) $34$nm Ag layer and SiO${}_2$/Si substrate, (b) the surface peak in (a), and (c) $34$nm Ag layer and monolayer hBN substrate. In both cases the graphene layer numbers are 0 (solid line), 1 (long dashes), 3 (intermediate-length dashes), 10 (short dashes), and 20 (dotted line).

Figure 5

EELS: (a) Comparison of the use of a SiO${}_2$/Si substrate (solid line), a mono-, tri-, 10-, and 20-layer hBN substrate (long dashes, intermediate-length dashes, short dashes, and a dotted line, respectively). No graphene coating is used and the Ag film is $34$nm thick. (b) Closeup of EELS peaks for the hBN substrates. The suspended sample (“vacuum substrate”) is represented by the solid line in this case. Mono-, tri-, 10-, and 20-layer hBN substrates are represented by long dashes, intermediate-length dashes, short dashes, and a dotted line, respectively.

Figure 6

(a) EELS: trilayer graphene on Ag layers (of varying thickness) with a monolayer hBN substrate. (b) Free-standing Ag films of various thicknesses. In both (a) and (b) Ag layer thicknesses are $50$nm (solid line), $34$nm (long dashes), $20$nm (intermediate-length dashes), $10$nm (short dashes), and $4$nm (dotted line).

Figure 7

EELS: (a) The effect of various numbers of layers for the graphene film, in the case of a $34$nm Au layer and SiO${}_2$/Si substrate, and (b) The effect of various numbers of layers for the graphene film, in the case of a $34$nm Cu layer and SiO${}_2$/Si substrate. Graphene layer numbers are 0 (solid line), 1 (long dashes), 3 (intermediate-length dashes), 10 (short dashes), and 20 (dotted line).

Figure 8

EELS: $34$nm Au (a) and Cu (b) films, with monolayer graphene coatings and various substrates including SiO${}_2$/Si (solid line), hBN monolayer (dashes), and vacuum (dotted line) substrates.