Resonant nanostructures for highly confined and ultra-sensitive surface phonon-polaritons

Plasmonics on metal-dielectric interfaces was widely seen as the main route for miniaturization of components and interconnect of photonic circuits. However recently, ultra-confined surface phonon-polaritonics in high-index chalcogenide films of nanometric thickness has emerged as an important alternative to plasmonics. Here, using mid-IR near-field imaging we demonstrate tunable surface phonon-polaritons in CMOS-compatible interfaces of few-nm thick germanium on silicon carbide. We show that Ge-SiC resonators with nanoscale footprint can support sheet and edge surface modes excited at the free space wavelength hundred times larger than their physical dimensions. Owing to the surface nature of the modes, the sensitivity of real-space polaritonic patterns provides pathway for local detection of the interface composition change at sub-nanometer level. Such deeply subwavelength resonators are of interest for high-density optoelectronic applications, filters, dispersion control and optical delay devices.

Topography of 1000x500 nm germanium resonator on silicon carbide. a Atomic-force microscopic image recorded in s-SNOM together with optical data shown in Fig. 2a in the main text of the article. Sporadic dot-like features are resulted solely from contaminations in EBL step and can be routinely eliminated in technology by optimizing the lithography process. b Profiles of the resonator taken along the same cross-section (marked with dashed vertical line in panel (a)) at 1 and 16 days respectively.

Supplementary Note 1. Derivation and analysis of the SPhP wavelength scaling relation.
An approximate dispersion relation for a TM-polarized surface-polariton wave in the fourlayer system (Eq. (1) in the main text) is derived from Maxwell's equations assuming highlyconfined nature of the mode. For solving Maxwell's equations, we expand the approach introduced for two-and three-layer systems 1 to the case of four-layer interface ( Supplementary Fig. 2), and additionally applying simplifications to the mode fields before obtaining the final dispersion formula. and : a, , , s denote corresponding layers ( Supplementary Fig. 2) of the interface; , *, . , 1 . , 1 are complex coefficients; 7 8 is the polariton complex wavevector and 7 is the wavevector in free space. Continuity of and at interfaces , 0 and results in the following system of six linear equations:

Supplementary Note 2. Additional analysis of germanium film oxidation.
The oxidation of germanium film has been additionally analysed using X-ray photoelectron spectroscopy ( Supplementary Fig. 3a), which directly indicates the chemical presence of both elemental semiconductor and its oxide, as well as the oxide time-dependent development during the sample exposure to the ambient atmosphere. Fitting of the XPS data (see Supplementary Fig. 3b and Methods section in the main text) shows that the oxide is primarily composed by GeO 2 (i.e. Ge 4+ ) component with smaller presence of suboxides (Ge 3+ , Ge 2+ , Ge 1+ ). A control measurement of the oxide layer thickness, performed by scanning transmission electron microscopy for the final state of oxidation (i.e. 16 days), gives a value of 3.6 nm (see inset in Supplementary Fig. 3b and Methods section). Fig. 3 Additional analysis of germanium film oxidation. a Normalized XPS spectra recorded after different time of the sample exposure to the ambient atmosphere. The data marked as "fresh" on the panel (a) corresponds to less than 5 min exposure time of the sample transferring from the evaporator to the XPS chamber. The data were recorded at 70° emission angle in the XPS system to maximize the photoelectron collection from the sample surface. b Fitting of the 16-days data from the panel (a). The inset in panel (b) shows darkfield STEM image of germanium film vertical cross-section, which consists of (from left to right) SiC substrate, Ge and oxide layers, and protective Pt cap.

Supplementary
The extraction of the oxide thickness from measured phonon polariton wavelength is based on literature data for permittivity of thick crystalline GeO 2 films 3 , which we have considered: (1) exactly at the position of the laser line, and (2) by taking an approximate lossless value in the broad transparency window (refractive index of ~1.5), which nearly overlaps with the laser line and covers blue part of the spectrum. While both approaches provide qualitatively comparable results, the approximate lossless permittivity model gives better agreement with control STEM measurement (oxide thickness extracted from 1-day, 10-days and 16-days near-field data are: 2.71, 3.17 and 3.31 nm (based on as-taken from Supplementary ref. 3 permittivity), and 2.99, 3.45 and 3.66 nm (lossless model)). We note that position and strength of germanium oxide infrared absorption peaks may depend on the crystal structure, chemical composition and morphology of the film. We do not exclude possibility that the

Supplementary Note 3. Potential performance of few-nm thick Ge-SiC resonators for refractive index spectroscopic sensing.
Using numerical simulations, we show an example of refractive index sensing on the introduced Ge-SiC platform. The results, summarized in Supplementary Table 1 and Supplementary Fig. 5 below, show that the figure of merit (FOM) for spectroscopic index sensing (FOM = HI JK /(HM Nres_width), the higher the better) on the introduced platform is as good as, if not better than, the state-of-the-art mid-IR devices reported in literature.