Polaritons, the hybrid quasiparticles of photons and electric dipoles1–3 (collective free electron oscillations, optical lattice vibrations or excitons) have attracted significant interest for numerous infrared nano-photonic applications4 including nano-laser5,6, non-linear optics7–9, heat-harvesting10–12 etc. Due to their sub-diffraction mode confinement and field enhancement, plasmon- and phonon-polaritons are also researched extensively for overcoming the fundamental resistance-capacitance (RC) delay in electronics and the diffraction limit in photonic devices13,14. However, applications of polaritons in practical devices so far are limited primarily due to the significant optical losses arising from the scattering of the free electrons and optical phonon modes. Therefore, materials exhibiting low-loss and high-quality plasmon-polariton in the near-to-mid IR and phonon-polaritons in the LWIR are in great demand15. Practical applications also require that such materials should exhibit structural and high-temperature stability, CMOS compatibility, ease-of-fabrication, ease-of-integration with existing optoelectronic devices, and abundance.
Achieving plasmon resonance in the IR region of the electromagnetic spectrum requires materials to exhibit carrier concentration in the 1019-1021 cm−3 range with high carrier mobilities. Further, to accomplish low-losses, such materials should not exhibit interband/intraband transitions in the wavelength range of interest and should comprise a low defect density. As a result, heavily doped semiconductors such as n-type InAs16, n-type and p-type Si17, CMOs18 such as indium tin oxide (ITO), aluminum-doped zinc oxide (AZO), gallium-doped zinc (GZO) oxide, cadmium oxide (CdO)19,20, patterned graphene structures21,22, and semiconductor meta-surfaces23 are used as plasmonic materials in the near (0.8-1.4 µm) and mid (3-15 µm)-IR spectral ranges. However, achieving low-loss high-quality plasmon resonance in the SWIR (1.4-3 µm) spectral region with high-mobility materials has been challenging. SWIR is an important spectral window for long-distance telecommunication (1.260-1.675 µm), hyperspectral imaging, solar cell, electronic board and produce inspection, anti-counterfeiting, surveillance, and a host of other applications14,24.
Achieving phonon-polaritons, on the other hand, requires polar dielectric materials, where macroscopic electric field stiffens the force constant of the longitudinal-optical (LO) phonons and splits the LO and transverse-optical (TO) phonon modes at the zone center25. Within the frequency range bounded by the LO and TO, termed as the Reststrahlen band, the real component of the dielectric permittivity (\({{\epsilon }}_{1}\)) becomes negative, and electromagnetic modes couple to the TO phonon giving rise to its evanescent character and confinement at the surface. Such confined surface-phonon-polariton (SPh.P) has emerged as a promising light-matter coupling mechanism in the LWIR range and several other applications such as passive radiative cooling, bio-molecular fingerprinting, diagnosis tools for cancer and dentistry detection are proposed24,26. So far, excitation and engineering of SPh.P are performed with well-established dielectric materials such as 4H-SiC27, h-BN28, or AlN29 with large bandgap and low carrier densities.
Due to the conflicting physical property requirements, demonstration of plasmon- and phonon-polaritons in one host material has been challenging. Conceptually, achieving plasmon and phonon-polariton in one host material is possible if the electronic and phonon resonances are spectrally separated from each other (see Eq. 1 for the total dielectric permittivity), and the carrier concentration can be tuned from as low as 1018 to 1021 cm−3 while retaining a moderately high mobility at the same time. To achieve this, dopants should not introduce defect states inside the bandgap of semiconductors that otherwise could pin the Fermi level. Additionally, dopant states should not alter the valence and/or conduction band edges, which could drastically change carrier effective mass and mobility. Satisfying all of the conditions has proven quite challenging for most well-established semiconductors.
\({\text{ɛ}}_{total}\left(\omega \right)\) = \({\text{ɛ}}_{} \left(1-\frac{{\omega }_{p}^{2}}{{\omega }^{2}- i \gamma \omega }+\frac{{{\omega }_{LO}}^{2}-{{\omega }_{TO}}^{2}}{{{\omega }_{TO}}^{2}-{\omega }^{2}-i\omega {\Gamma }}\right)\) (1)
$${\omega }_{p}=\sqrt{\frac{n{e}^{2}}{{m}^{*}{ϵ}_{0}}}$$
2
$${\text{ɛ}}_{plasmon}\left(\omega \right)=-\frac{{\omega }_{p}^{2}}{{\omega }^{2}- i \gamma \omega }$$
3
Where, \({\text{ɛ}}_{total}\left(\omega \right)\) is the total dielectric permittivity24 with contributions from the plasmon or Drude component (second term) and phonon (third term) resonances. \({\text{ɛ}}_{}\), \({\omega }_{p}\), \({\omega }_{LO}, {\omega }_{TO}, \gamma\),\({\Gamma }\), \(n\) and\({m}^{*}\) are the high-frequency dielectric constant, plasma frequency, longitudinal optical and transverse optical phonon frequencies, plasmon and phonon damping constants, carrier concentration and effective mass respectively.
In this work, we demonstrate that n-type (oxygen) and p-type (magnesium)-doping in epitaxial ScN thin films lead to its tunable carrier concentration from 5 ×1018 to 1.6 × 1021 cm−3 range, while retaining a moderately high mobility that gives rise to tunable high-quality low-loss SWIR plasmon- and LWIR high-quality phonon-polariton resonance that was considered to be mutually exclusive previously.
ScN is a rocksalt group-III (B) semiconducting transition-metal-nitride (TMN) and exhibits corrosion-resistant high hardness, high melting temperature (~ 2600\(℃\) ) and is stable at ambient temperature and pressure30–34. Due to the degenerate semiconducting nature with a direct bandgap of 2.2 eV and indirect gap of 0.9 eV35,36, ScN has attracted significant interest in recent years for thermoelectric energy conversion37. Lattice-matched (111) ScN seed-layers are also utilized to reduce the dislocation densities in (0002) GaN epilayers for light-emitting diodes38,39. As-deposited ScN thin films exhibit an n-type carrier concentration of (2-4) × 1020 cm−3 primarily due to the presence of oxygen impurities and exhibit a mobility in the 60-90 cm2/Vs range. Due to such high carrier concentrations, Fermi level in ScN resides inside the conduction band, about 0.2-0.3 eV inside the conduction band minima35. Recently, Mg-hole doping is used to reduce the high carrier concentration and p-type ScN is achieved with high mobility (~ 25 cm2/Vs)40. Photoemission measurement and first-principles calculation have demonstrated that both the oxygen and magnesium-doping in ScN do not introduce defect states within its bandgap, and they do not alter the valence and conduction band edges41. Due to such a rigid electronic band, the Fermi level moves freely from the conduction band to the valence band, giving rise to very high electron and hole-concentrations and large thermoelectric power factors37. Moreover, since optical phonons in ScN exhibit a maximum energy of ~ 84 meV42, plasmon-resonances in the SWIR region are well-separated from the phonon-polariton resonance. Therefore, high-mobility and tunable carrier concentration in ScN provide a perfect testbed to achieve high-quality plasmon- and phonon-polariton in one host medium.
ScN thin films with carrier concentration ranging from 1.6 × 1021 cm−3 to 5 × 1018 cm−3 (see Table 1) are deposited inside an ultra-high vacuum (UHV) chamber at a base pressure of (2-4) × 10−9 Torr (see Methods). Without any intentional doping, n-type ScN films exhibit a carrier concentration of 3.6 × 1020 cm−3 with a mobility of 43 cm2/Vs. Intentional oxygen-doping increase its carrier concentration up to 1.6 × 1021 cm−3, while Mg-hole doping reduces carrier concentration to as low as 5 × 1018 cm−3. Though the intentional doping reduces the mobility slightly, it remains sufficiently high (see Table 1) for achieving low-loss resonances.
Plasmon-polariton resonance
The \({{\epsilon }}_{1}\) of ScN (measured with a spectroscopic ellipsometer, see Fig. 1a, Methods and Supplementary) with the highest carrier concentration of 1.6 ×1021 cm−3 exhibits a positive-to-negative cross-over at 1.83 µm that is representative of the onset of its plasmonic character (see Fig. 1b). At longer wavelengths, \(\left|{{\epsilon }}_{1}\right|\) increases monotonically due to the increasing metallic response. The optical loss, characterized by the imaginary component of the dielectric permittivity (\({{\epsilon }}_{2}\)) at \({\lambda }_{p}\) is 1.2, which is smaller than the \({{\epsilon }}_{2}\)of visible wavelength plasmonic materials such as Au43, TiN44 etc. at their respective \({\lambda }_{p}\). \({{\epsilon }}_{2}\) of ScN is also comparable with the NIR plasmonic materials such as ITO, AZO; as well as with the MIR plasmonic materials such as CdO (see Supplementary Fig. S1 and S2). Below 1.83 µm, ScN acts as a dielectric medium with positive\({{\epsilon }}_{1}\) and a peak in \({{\epsilon }}_{2}\) near ~ 430 nm (see Supplementary Fig. S3) corresponds to the direct bandgap interband transition. Polarization-dependent reflectivity measurements (see Fig. 1b) show a clear dip near \({\lambda }_{p}\) representative of the plasmonic nature. Angle-dependent reflectivity measurements (see Fig. 1c) clearly show the Brewster’s angle in the p-polarized/s-polarized reflection curve. The calculated reflectance spectrum (see Fig. 1d) utilizing the permittivity of ScN in the Fresnel’s equation (see Supplementary section 5) matches well with the measured reflectivity which highlights consistency between the experiment and ellipsometry data fitting.
Excitation of the surface plasmon-polaritons (SPP) is demonstrated (see Fig. 1e) with polarization-dependent reflectivity measurement in the attenuated-total-reflection (ATR) configuration inside an FTIR-spectrometer in the Kretschmann configuration at 45\(^\circ\) angle-of-incidence. Diamond is used as a high refractive index medium and to provide the additional momentum for the light coupling to the SPP modes. A clear dip in the p-/s-polarized reflection spectrum at ~ 1.95 µm (see Fig. 1f) with a full-width-at-the-half-maxima (FWHM) of ~ 0.27 µm demonstrate the coupling of energy from the incident radiation to the SPP mode. The SPP dispersion45 is calculated (see Fig. 1f) taking into account the measured dielectric permittivity of ScN that show close matching of the \({\lambda }_{SPP}\) (wavelength corresponding to the SPP mode frequency) with the experimentally measured dip in reflectivity curve.
While the above analysis unambiguously demonstrates SWIR plasmon excitation in ScN, spectral position of the plasmon-resonance and the SPP mode frequencies are varied by altering the carrier concentration (see Eq. 2) through doping control. With a decrease in the carrier concentration from 1.6 × 1021 cm−3 (a) to 1.4 × 1021 cm−3 (b), 7.7 × 1020 cm−3 (c) and 3.3 × 1020 cm−3 (d), ellipsometry measurements show that the \({\lambda }_{p}\) shifts from 1.83 µm to 2.08 µm, 2.25 µm and 2.35 µm, respectively (see Fig. 2a). Such monotonic red-shift in the \({\lambda }_{p}\) is consistent with the predictions from the Drude model (see Eq. 3) of dielectric permittivity, and cover a wide SWIR range. \({{\epsilon }}_{2}\) of ScN with 3.3 × 1020 cm−3 carrier densities show the lowest value, primarily due to its higher mobility of 43 cm2/Vs. Since the highest mobility and the lowest optical loss is obtained in the as-deposited ScN without any intentional doping, \({\lambda }_{p}\) of 2.35 µm with the lowest optical loss of 1.0 could be regarded as the baseline plasmon response in ScN. Dielectric permittivity at the longer wavelength regions (1.5- 5 µm) is measured further with an IR-ellipsometer (see Supplementary Fig. S1) which demonstrates ScN’s metallic response in the SWIR-to-mid-IR spectral region. Similar to the tunable bulk plasmon frequency, tunability of the SPP mode frequencies are further demonstrated by the polarization-dependent ATR measurements, which show a dip at 2.70 µm with a FWHM of 0.56 µm for ScN with 3.3 × 1020 cm−3 (d) carrier concentrations.
The plasmonic response is further characterized by temperature-dependent Hall measurements (see Fig. 2d). The resistivity of all ScN films increases slightly with an increase in temperature (see Fig. 2e) which is representative of their degenerate semiconducting or semi-metallic nature due to high carrier concentrations. On the other hand, mobility decreases with an increase in temperature as found in Fig. 2f. A combination of ionized impurity and dislocation scattering model is found to fit the temperature-dependence of mobility very well with a high dislocation density in the 109-1011 cm−2 range (see Supplementary Fig. S4), which can be seen as well in transmission electron microscopy (TEM) images. The carrier concentration of the ScN films remain nearly unchanged within the measured temperature range (see Fig. 2g).
Temperature-dependent dielectric permittivity is measured further to highlight the refractory plasmonic behavior of ScN. Results show that with an increase in temperature from 100 K-to-500 K, \({\lambda }_{p}\) exhibits a redshift from 1.76 µm to 1.83 µm (see Fig. 3a), and \({{\epsilon }}_{2}\) increases from 0.95 to 1.32 at the corresponding \({\lambda }_{p}\) for the ScN film with 1.6 × 1021 cm−3 carrier concentrations. Such an increase in \({\lambda }_{p}\) and optical losses, especially at longer wavelengths (see Fig. 3b) can be directly attributed to the decrease in mobility as shown in Fig. 3c. However, near the \({\lambda }_{p}\) wavelength region, the increase in \({{\epsilon }}_{2}\) is rather small that highlight the suitability of ScN for high-temperature applications. It is important to note here that though the permittivity is measured till 500 K due to instrumental limitations, ScN exhibits a high melting temperature of ~ 2600\(℃\), and hence could be useful for many plasmonic applications at high-temperatures.
With the above refractory plasmonic properties in the SWIR spectral range, ScN’s suitability for various nano-photonic applications18,46 such as in SPP waveguides, localized surface-plasmon-resonance (LSPR), epsilon-near-zero (ENZ), hyperbolic metamaterials (HMM), and transformation optics are determined. Each of these applications requires its own optimum operating conditions that are determined by the structure and geometry of devices, as well as material properties. Our analysis show (see Supplementary Fig. S5) that the plasmon-resonance and SPP in ScN should be useful for the non-resonant SWIR applications such as waveguides, ENZ, HMM18. As an example, ScN exhibits a high SPP propagation length (L) and low electric-field confinement length (D) that is comparable to other doped-semiconductors and CMOs for high-performance waveguides. A ratio between the L and D, referred as the figure-of-merit (\({M}_{1}^{2D})\)47 is high in ScN and compares well to its alternatives in the near and mid-IR spectral range. Similarly, a low \({{\epsilon }}_{2}\) of 1.00 at \({\lambda }_{p}\) should be suitable for ENZ device applications48 such as photon funnels, or spatial filtering for beaming. Even for the localized SPP resonance, the figure-of-merit (FOM) of ScN is comparable to its counterparts. Nevertheless, it should be highlighted that with more advanced deposition methods such as molecular-beam-epitaxy (MBE) and hybrid vapor phase epitaxy, mobility of ScN could be increased further which should improve its performance metrics.
Phonon-polariton resonance
While the carrier concentration control leads to the SWIR plasmonic response in ScN, demonstration of SPh.P. excitation requires that the electronic resonance do not contribute to the total dielectric permittivity in the LWIR spectral range. To achieve this condition, Mg (hole)-doped ScN films with low carrier concentrations are deposited (see Table 1). To separate the contributions of MgO (substrate) phonon modes, a 100 nm IR reflective TiN buffer layer is deposited on (001) MgO substrates before ScN depositions (see Supplementary Fig. S6). Infrared reflectivity measurement (see Fig. 4a) of ScN with 5 × 1018 cm−3 carrier concentration shows well-defined Reststrahlen band (see Fig. 4b), a highly reflective region between the TO (359 cm−1) and LO (686 cm−1) phonon modes where light couples with the polar optical lattice vibrations. Calculated \({{\epsilon }}_{1}\) is found to exhibit negative values within the Reststrahlen band, with an epsilon-near-pole (ENP) resonance at 359 cm−1 since light couples directly to the TO phonon mode (see Fig. 4c). Concomitantly, \({{\epsilon }}_{2}\)exhibits a sharp peak at the TO phonon frequency. Both LO and TO phonon frequencies are consistent with recent inelastic X-ray scattering phonon dispersion of ScN42.
Further, polarization-dependent ATR measurements are performed which show a dip at 626 cm−1 in the p-polarized light, representing coupling of light with the SPh.P mode. Calculated SPh.P dispersion is consistent with the experimental observations, and also highlight the bulk phonon-polaritons at frequencies above and below the Reststrahlen band. Performance FOM of SPh.P modes26 is calculated and compared with other well-established polar dielectric materials such as SiC27, h-BN28, c-BN49, AlN29, and GaN50. SPh.P FOM of ScN is found to be around two times higher than its peers due to its high \({\epsilon }_{\infty }\) of 12.8 (see Supplementary Fig. S7).
Microstructure characterization
While the compelling optical properties of ScN makes it an attractive IR polaritonic material, SPP waveguides, HMM, ENZ and other device implementations require low surface roughness, a lattice-matched interfaces with the substrate and compatibility with industrially relevant materials.
Scanning transmission electron microscopy (STEM), energy-dispersive x-ray spectroscopy (EDS) mapping and electron diffraction were applied to characterize the microstructure of the film. Both oxygen and magnesium-doped ScN films deposited in this work on (001) MgO substrates at high-temperatures grow epitaxially with [001](001) ScN || [001](001) MgO(see Fig. 5a and 5b). The ScN/MgO interface is sharp despite the presence of a few misfit-dislocations, resulting from the 7% lattice-mismatch between ScN and MgO. Importantly, both oxygen and magnesium dopants make homogeneous solid-solutions with ScN without any precipitations or secondary phase formations (see EDS maps in Fig. 5 c-f) resulting in a small rms. surface roughness of ~ 2 nm (see Supplementary Fig. S9). Electron energy loss spectroscopy (EELS) O K-edge and Mg L-edges are consistent with the bonding of O with Sc and Mg with N respectively and splitting of the peaks highlight hybridization between different orbitals (see Supplementary Fig. S10). While the present work utilizes (001) MgO as a substrate with the same crystal structure, it must be mentioned that ScN films are regularly deposited on industrially important Al2O3 and Si substrates that should provide seamless chip integration. In addition, due to its perfect lattice-matching, ScN films have been deposited on (0001) GaN with very little defects39 that would also lead to its integration with GaN-based light-emission and power electronic applications.
Concluding remarks
In conclusion, we present epitaxial refractory group-III scandium nitride (ScN) as a dual plasmon- and phonon-polariton material, where tunable plasmon resonance in the short-wave-infrared (SWIR) spectral range and the phonon-polariton in the long-wave-infrared (LWIR) region are obtained by carrier concentration control. Oxygen-doped ScN films with carrier concentrations between 1020-1021 cm−3 exhibit high-quality and low-loss plasmon resonance in the 1.8-2.3 µm SWIR spectral region, where most plasmonic materials do not work satisfactorily. High figure-of-merit (FOM) surface phonon-polariton resonance is also achieved in the long-wavelength-infrared (LWIR) by reducing the carrier concentration with Mg-hole doping in ScN. Demonstration of plasmon- and phonon-polariton in one host material, ScN with doping-control makes it an attractive material for applications in waveguides, hyperbolic and epsilon-near-zero metamaterials, optical communication, solar-energy harvesting and infrared photonic applications.