Infrared Plasmonics with Conductive Ternary Nitrides - ACS Applied

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Infrared plasmonics with conductive ternary nitrides Chryssoula Metaxa, Spyros Kassavetis, Jean Francois Pierson, D. Gall, and Panos Patsalas ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b16343 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 14, 2017

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ACS Applied Materials & Interfaces

Infrared plasmonics with conductive ternary nitrides C. Metaxa$, S. Kassavetis$, J.F. Pierson#, D. Gall&, P. Patsalas$,* $

#

Aristotle University of Thessaloniki, Department of Physics, GR-54124 Thessaloniki, Greece

Institut Jean Lamour (UMR CNRS 7198), Université de Lorraine, Parc de Saurupt, 54011 Nancy cedex, France &

Rensselaer Polytechnic Institute, Department of Materials Science and Engineering, Troy, NY 12180, USA *Corresponding author: tel: +30-2310-998298, e-mail: [email protected]

ABSTRACT: Conductive transition metal nitrides are emerging as promising alternative plasmonic materials that are refractory and CMOS-compatible. In this work, we show that ternary transition metal nitrides of the B1 structure and consisting of a combination of group-IVb transition metal, such as Ti or Zr, and group III (Sc, Y, Al) or group II (Mg, Ca) elements can have tunable plasmonic activity in the infrared range in contrast to Ta-based ternary nitrides, which exhibit plasmonic performance in the visible and UV ranges. We consider the intrinsic quality factors of surface plasmon polariton for the ternary nitrides, and we calculate the dispersion of surface plasmon polariton and the field enhancement at the vicinity of nitride/silica interfaces. Based on these calculations, it is shown that among these nitrides the most promising are TixSc1-xN and TixMg1-xN. In particular, TixSc1-xN can have plasmonic activity in the usual telecom bands at 850, 1300 and 1550 nm. Still, these nitrides exhibit substantial electronic losses mostly due to fine crystalline grains that deteriorate the plasmonic field enhancement. This unequivocally calls for improved growth processes that would enable the fabrication of such ternary nitrides of high crystallinity. KEYWORDS:

1.

Surface

Plasmon

Polariton;

2.

Infrared;

Conductor/Dielectric Interfaces. ACS Paragon Plus Environment

3.

Conductive

Nitrides;

4.


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I. INTRODUCTION The emergence of plasmonics has promised radical breakthroughs in various technological sectors, such as microelectronics [1-4], solar energy harvesting [5-9], photo-detection [10-12], optical storage of information [13-16], metamaterials [17-19], and telecommunications [20-24]. The most widely used plasmonic materials are gold and silver, which are not compatible with CMOS processing and their plasmonic response is mostly in the visible spectral range [25,26]. The implementation of plasmonic technology into mainstream telecom applications calls for new plasmonic materials that would be compatible with the established Si and fiber optic technology, i.e. materials that would have plasmonic response at the 850, 1300 and 1550 nm wavelengths [27] and be grown and processed by CMOS-compatible techniques. Conductive transition metal nitrides (TMN), such as TixTa1-xN [28,29], TixZr1-xN (0≤x≤1) [30,31] and TixAl1-xN (0.55300 nm) polycrystalline TixSc1-xN, TixY1-xN, TixMg1-xN, and TixCa1-xN films were deposited at room temperature on polished stainless steel substrate using a hybrid reactive arc evaporation – magnetron sputtering process. The Ti vapors were created using a cathodic arc source (63-mm diameter and 35-mm thick), while the Sc, Y, Mg or Ca were sputtered from a magnetron cathode (50-mm diameter and 3-mm thick). The deposition of the films was realized in a reactive mixture of argon and nitrogen (40 and 70 sccm, respectively; purity 99.999%). A substrate bias voltage of -100 V was applied during the film growth and the arc current applied to the titanium target was maintained at 90 A, while the composition x was varying by adjusting the pulsed DC current applied to the sputtering target (Advanced Energy Pinnacle+ generator with a 50 kHz frequency and an off time of 3 ACS Paragon Plus Environment


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4 µs); more details on these experiments are described in Ref. 41. Opaque (1500 nm thick) ZrxY1-xN films were grown on floating Si substrates by pulse-DC (Advanced Energy Pinnacle+ generator with a 50 kHz frequency and an off time of 4 µs) reactive magnetron sputtering at room temperature using three individual targets (pure Zr, Zr doped with Y 8% or 16%; purity 99.9%) in a mixed Ar/N2 ambient (30/4 sccm, respectively; purity 99.999%) of a working pressure of 0.44 Pa. Opaque (200 nm thick) epitaxial TixSc1-xN films were grown on 10×10×0.5 mm3 MgO(001) substrates at 750 °C by ultra-high vacuum reactive magnetron sputter deposition in 99.999% pure N2 discharges at 0.66 Pa. The Sc to Ti ratio was controlled by the relative power applied to two symmetrically positioned magnetrons with 5cm-diameter Sc (99.9% purity) and Ti (99.999%) targets, respectively, as described in more detail in Ref. 44, 45. The composition x of the films, the [N]/[Metal+RE] or [N]/[Metal+AE] ratios, as well as their crystal structure were studied by energy dispersive x-rays (EDX), x-ray photoelectron spectroscopy (XPS), and x-ray diffraction (XRD), respectively. EDX were acquired in a JEOL 840A scanning electron microscope equipped with an Oxford Instruments X-Ray, analyzer; XPS expereiments were carried out in a Kratos Axis Ultra DLD instrument equipped with a monochromated Al-Kα beam and a hemispherical sector electron analyzer, a pass energy of 20 eV was used that provided a broadening of less than 500 meV for the Ag 3d line; XRD experiments were carried out in θ-2θ mode using a Bruker (Siemens) D500 apparatus with Co radiation (λ=0.179 nm) for Ti-based polycrystalline films, and a Bruker (Siemens) D5000 apparatus with Cu radiation (λ=0.154 nm) for ZrxY1-xN. The complex dielectric function spectra (ε=ε1+iε2) of the opaque polycrystalline films were determined by spectroscopic ellipsometry in the spectral range 0.6-6.5 eV (2067-191 nm) with a step of 50 meV at 70o angle of incidence. Optical transmission and reflection spectra of epitaxial TixSc1-xN were obtained using a Perkin–Elmer Lambda 9 spectrophotometer, equipped with integrating sphere for light collection, in the spectral range 0.496-6.2 eV (2500-200 nm). Spectral intensity distributions were calibrated using reflection spectra from an undoped single-crystal Si(001) wafer; then the dielectric 4 ACS Paragon Plus Environment

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function spectra were determined from the optical reflectivity following the procedures described in the on-line supporting information. Additionally, spectroscopic data for TixAl1-xN in the infrared range (beyond the range reported in Ref. 32) are also included in this study for comparison purposes.

III.

RESULTS AND DISCUSSION Ti/Zr and Sc/Y belong to the groups IVb and IIIb of the periodic table of elements, respectively.

As such, they have four or three valence electrons, respectively, in d and s orbitals. Consequently, their nitrides are conductors and semiconductors, respectively. In particular, the electrical conductivity of all TMNs is due to the excess of d electrons of the metal [28-32]. Ti/Zr and Sc/Y form bonds with nitrogen atoms (valence electron configuration 2s22p3) in a stable cubic rocksalt (B1) phase [30,31,41-43]. As a result, the ternary TixSc1-xN system is stable over the entire compositional range in the B1 structure [41, 44,45] in contrast to the TixAl1-xN system, which can be stabilized in the B1 phase only in a limited compositional range [32]. Therefore, it is expected that the plasmonic properties of TixSc1-xN films might be extended into the infrared range, while the plasmonic properties of TixAl1-xN lie in the deep red range [32]. TixY1-xN has similar electron configuration with TixSc1-xN, but the large lattice mismatch between TiN and YN results in TixY1-xN films of low crystalline quality, which have high electron losses due to scattering at the grain boundaries [41]. For this reason, in this study we investigate also the ZrxY1-xN system, which has similar electron configuration with TixSc1-xN and TixY1-xN, but smaller mismatch between ZrN and YN [30,41,42]. On the other hand, TixAE1-xN (AE=Mg, Ca) are stable in the B1 structure in a limited compositional range [41], similar to the TixAl1-xN. However, even relatively small concentrations of Mg or Ca may reduce substantially the carrier density of TiN due to their two valence electrons [41]. So for small concentrations of Mg, or Ca the TixAE1-xN can have conduction electron density below the range that can be achieved by the TixAl1-xN system. Therefore, TixAE1-xN films also have rational perspectives for infrared plasmonic behavior. The abundance of Mg

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and Ca, in contrast to the shortage of Sc and Y, is also a significant reason for investigating their plasmonic performance. The spectra of the real (ε1) and imaginary (ε2) parts of the dielectric function of various TMN films in the visible (400-700 nm), near-infrared (700-1400 nm), and in the most of the shortwavelength-infrared (1400-2067 nm) spectral ranges are presented in Figures 1 and 2. In particular, Fig. 1 shows the dielectric function spectra of ternary compounds of a Group IIIb (Sc, Y) and a Group IVb (Ti, Zr) element. In order to evaluate the effect of the morphology and crystallographic features to the optical properties in the infrared range of the ternary nitrides we also considered the optical reflectivity spectra (Fig. 2a) of sputtered, epitaxial TixSc1-xN on MgO(001) substrates. The dielectric function spectra were extracted from the optical reflectivity as described in the supporting information; the relevant ε1 spectra are presented in Fig. 2b and they are characteristic of good conductors with varying absolute values of ε1 depending on the composition x. Fig. 3 shows the dielectric function spectra of ternary compounds of a Group IIa (Mg, Ca) element and Ti. Similar dielectric function spectra for the TixAl1-xN system, but in a narrower spectral range, can be found in Ref. 39. All the studied films act optically as semi-infinite materials due to their conductive character and large thickness (>200 nm) with the major exceptions of the Sc-rich (x=0.19 and 0.045) epitaxial TixSc1-xN, which exhibit interference fringes indicating their relative transparency. Therefore, these samples will not be considered in the rest of this study. The ε1 spectra of TMNs have attracted particular attention because they provide a clear qualitative view of their conductive character that renders negative ε1 values [28-30, 36-39]. In all cases it is evident that the enrichment of TiN or ZrN with a group IIIb (Sc, Y) or a group IIa (Mg, Ca) element results in less negative ε1 values in the entire infrared range. In the cases of TixMg1-xN and TixCa1-xN (Fig. 3a,c) the ε1 values exhibit a broad plateau beyond 1600 nm due to excessive electron losses that were quantified in Ref. 41. For short wavelengths, ε1 gets positive values due to interband transitions and the accompanying dielectric losses, which are more evident in the ε2 spectra (Fig. 1b,d,f, and 3b,d);


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the dielectric losses, though, are not a source of concern in our study due to their spectral separation from the infrared range. Of particular practical importance is the screened plasma energy Eps=ħωps=hc/λps (c being the speed of light in free space), which is the spectral energy at which the ε1 becomes zero (ε1=0), a phenomenological parameter that may be affected by both the intraband and interband absorption; despite of the lack of any solid physical meaning of Eps, it is associated with the spectral energy at which LSPR occurs [38,39]. It is clear from Fig. 4 that λps (=hc/Eps) varies from 450 to almost 770 nm, stretching the potential limits of the plasmonic behavior of ternary conductive nitrides into the infrared spectral range. In particular, Eps is substantially reduced with decreasing the group-IV element’s atomic concentration (x) for all the studied cases of conductive ternary nitrides. In the cases of good lattice match group-III/group-IV ternary nitrides (TixSc1-xN, ZrxY1-xN, TixAl1-xN) there is a linear dependence between Eps and x and the slope of the reduction is quite similar for all cases, although the Eps for sputtered Ti-based nitrides (TixAl1-xN and epitaxial TixSc1-xN) is shifted to lower absolute values, which is a common observation for sputtered nitrides [46]. On the contrary, the structurally unstable TixY1-xN (due to the lattice mismatch between the constituent TiN and YN phases [41]) does not exhibit a linear dependence of Eps with x. Similar linear dependencies of Eps with x are also observed for TixMg1-xN and TixCa1-xN, albeit with twice the slope. This clearly implies that the Eps is mostly affected by the conduction electron density, whereas the contribution of dielectric losses to it is of secondary importance; given the three valence electrons of Sc, Y, and Al and the two valence electrons of Mg, and Ca the reduction of conduction electrons is faster when we substitute Ti or Zr by atoms of the later than the former elements. In order to quantify that, we consider the effective number Neff of valence electrons of the constituent metals of the ternary nitrides:

= ∙ + (1 − ) ∙ ,

(1)



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where V1=4 (for Ti and Zr) and V2=2 and 3 for Mg, Ca, and Sc, Y, Al, respectively. Indeed, Eps is directly scaled with Neff, as shown in the inset of Fig. 4, unequivocally proving the association of Eps with the conduction electron density for all ternary nitrides. The potential of any conductor to sustain a SPP close to the wavelength λps (=hc/Eps) can be evaluated by the maximum intrinsic quality factor, which is determined by quantities associated with the volume plasmon, and it is defined as [47]:

=

,

(2)

where ωpu and γD are the unscreened plasma frequency, i.e. the frequency of light where a bulk plasmon with energy Epu=ħωpu occurs in the conductor, and the Drude broadening factor of the conductor, respectively. ωpu and γD are associated with the conduction electron density Ne [30,32,38,41]:

ωpu =

Ne e2 , εom*

(3)

where e is the electron charge, εο is the permittivity of free space and m* is the electron effective mass, in SI units, and with the conduction electron relaxation time τD [30,32,38,41]:

= ,

(4)

respectively, and they can be determined by fitting the dielectric function spectra by a Drude-2 Lorentz model, which determines the complex dielectric function ε~(ω) of the material with the frequency ω of the incoming light [30,32,38,41]: 8 ACS Paragon Plus Environment

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ε~(ω ) = ε

inf

2 f j ⋅ ωoj2 ω 2pu . − 2 +∑ ω − iγ Dω j=1 ωoj2 − ω 2 + iγ jω

(5)

In Eq. (5) εinf is a background constant, larger than unity, which is due to high-energy contributions (beyond the experimental spectral range) referring to transitions that are not taken into account by the Lorentz term(s). Each of the Lorentz oscillators is describing an interband transition [41] and it is located at an energy position E0j=ħω0j, with strength fj and damping (broadening) factor γj. Figure 2c summarizes the variations of Epu and γD for polycrystalline and epitaxial TixSc1-xN for various x values, while the values for all the samples are listed in the on-line supporting information. In an effort to evaluate the intrinsic plasmonic potential of the considered nitride conductors and associate it with the spectral range where SPP can occur, we correlate and display the QiSPP values with Eps and the corresponding value of the wavelength λps in Fig. 5. The QiSPP values of all the considered ternary nitrides are orders of magnitude inferior to the values reported for Ag and Au [47]; however, the reported QiSPP values for Ag and Au [47] refer to highly crystalline metals with grain size larger than 300 nm [48,49], while the studied nitride samples consist of ultrafine grains less than 20 nm long [32,41]. Therefore, a fair comparison would be to the Ag and Au of the same grain size; in that case, the ternary nitrides are still inferior but their plasmonic performance is comparable in the same order of magnitude to Au and Ag [38,39], as it is also shown in the on-line supporting information. In Fig. 5 there is a general trend that the redshift of Eps, and consequently of the spectral position of SPP, comes in expense of the quality factor QiSPP. Among the considered ternary nitrides TixSc1-xN shows the highest quality factor in the entire spectral range, and only TixMg1-xN can be comparable, though only in a narrow spectral window. The general trend of reducing QiSPP at longer wavelengths is quite well understood considering Eq. (2). Indeed, the reducing Eps for all cases is associated with the reduction of the conduction electron density due to the smaller number of valence electrons of the group 9 ACS Paragon Plus Environment


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II or group III elements compared to Ti and Zr, thus reducing ωpu as well [32,41]. Subsequently and in most cases, γD is increasing as Ti and Zr are gradually replaced by atoms of the group II or group III elements [32,41] either due to the crystal grain refinement (e.g. as in the case of TixY1-xN [41]), or due to structural defects (e.g. as in the cases of TixAl1-xN [39] and TixSc1-xN [41]). The former quantity (ωpu) cannot contribute to further enhancement of the quality factor QiSPP, because it is intentionally reduced in order to shift SPP towards the infrared spectral range. Thus, further work should be dedicated for the reduction of γD in order to improve QiSPP. This can be achieved by elimination of the structural defects by growth at higher temperature and on lattice-matched substrates; indeed, this is clearly indicated by the substantially higher QiSPP values for the epitaxial TixSc1-xN films grown at high temperature (750 oC) on lattice-match MgO(001) substrates as shown in Fig. 5, however, the improvement is less pronounced in the infrared range. Especially the vacuum arc deposition, which was used in this work to deposit TiN, was found to be inferior and superior to the conventional dc-magnetron sputtering [50] and high-power impulse magnetron sputtering [51], respectively, in terms of the grain size and of the structural defects of conductive nitride films. The importance of the growth optimization is also illustrated by the inferior properties of ZrN compared to TiN in this study in contrast to ZrN and TiN grown by multi-cathode sputtering and reported in Ref. 39, where ZrN was found to be less lossy than TiN. Also, the ZrxY1-xN films were not found to have superior performance compared to TixY1-xN, as originally anticipated, due to the existence of a substantial amount of structural defects; indeed, the XRD analysis (for details see on-line supporting information) revealed that the studied ZrxY1-xN exhibit micro-strain (which is associated with structural defects [41,45]) and macro-strain (which is associated with hydrostatic stresses in the films [45, 52,53]) in the ranges 4.1-5.8×10-3 and 3.7-6×10-3, respectively. The microstrain values of the ZrN nitride of this work (5.8×10-3) are substantially higher than that of TiN (3.2×10-3 [41]), and the microstrain values of ZrxY1-xN are intermediate between those of TixY1-xN and TixSc1-xN [41]. Indeed, sputtered ZrN films deposited at the same growth conditions (pressure, substrate bias and target power) with TiN, exhibited substantially higher compressive intrinsic stress [54] due to the 10 ACS Paragon Plus Environment

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backscattered Ar+ ions from the Zr target, the reduced thermalization of Zr atoms in the gas phase and the reduced mobility of Zr adatoms on the active growing surface [54, 55], all of them due to the higher atomic mass of Zr compared to Ti; for all these reasons the growth of pure epitaxial ZrN films was achieved quite recently [56], despite of the growth of ZrN films, which include some epitaxial domains since the late eighties [57]. Consequently, ZrN, which is the basis for ZrxY1-xN, is the source of the structural defects in sputtered ZrxY1-xN mostly for kinetic reasons, despite of the lattice match between ZrN and YN. The QiSPP as expressed in Eq. (2) and as displayed in Fig. 5 vs. Eps provides an indication of the intrinsic plasmonic properties of the conductor as it based on quantities associated with bulk plasmons into the corresponding conductors, and cannot describe accurately the SPP that occurs at conductor dielectric interfaces when illuminated via the dielectric. Therefore, a more realistic view of the potential of ternary conductive nitrides for infrared plasmonics can be extracted from the dispersion relation that correlates the frequency ω with the wave vector kx in the direction of propagation of SPP, in such a configuration, i.e. along a conductor/dielectric interface. The general equation that defines the aforementioned relation is the following [58]:

=

!

∙!

! "#$ ! , "#

(6)

where %̃'( and %̃ are the complex dielectric functions of each ternary nitride and dielectric (silica or silicon in our case), respectively. Given that the dielectric functions are inherently complex, Eq. (6) should be modified to:

=

!

∙!

)* + ! "#$ ! ,, "#

(7)



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when optical attenuation in the conductor exists; this is very important for the conductive nitrides, due to their strong electron losses. A more convenient way of writing the dispersion relation in order to be more easily compared to the experiments is:

!

∙!

ℏ . = ℏ/ ∙ )* + ! "#$ ! ,. "#

(8)

Figure 6 presents the calculated (via Eq. 8) SPP dispersion relations at the interfaces between air, silica or silicon and (a) TixSc1-xN, (b) TixY1-xN, (c) TixMg1-xN, (d) ZrxY1-xN, (e) TixAl1-xN, (f) TixCa1xN,

respectively, using the dielectric function spectra presented in Figures 1, 2 and 3 for the conductive

nitrides, reported in Ref. 59 for a commercial pure n-type Si(001) wafer after removal of the native oxide and reconstruction of its surface, and reported in Ref. 60 for silica glass. Note that the calculation for silicon was performed only for the transparent region, i.e. for photon energies in free space below the band gap of 1.112 eV (wavelength longer than 1115 nm), which lies exclusively in the infrared spectral range. The first significant observation is that in all cases the dispersion relations are characteristic of lossy metals and, therefore, involve finite extreme values of kx [58] due to conduction electron (due to finite γD values of all ternary nitrides) and dielectric (due to the existence of interband transitions) losses. The consequence of this observation is the existence of quasi-bound modes at which the slope of the dispersion curve is inversed and the existence of a cross-over energy at which the SPP dispersion curve crosses the photon line (black lines in all panels of Fig. 6). Secondly, the maximum ħkxcmax, which defines the SPP point, is scaled to the screened plasma energy Eps for all the ternary nitrides in the infrared spectral range; this is clearly illustrated in Fig. 7 where the free space wavelength of light at SPP (i.e. at ħkxcmax) is plotted vs. Eps for the silica dielectric. However, these two quantities do not coincide and the wavelength of photons in free space that


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corresponds to ħkxcmax is longer than the wavelength λps that corresponds to Eps and fulfills the requirement for operation at 850 nm for silica fiber optics when Ti0.32Sc0.68N is used, while Ti0.73Mg0.27N and Ti0.75Ca0.25N are also pretty close to fulfill this requirement possibly with a small further enrichment with Mg or Ca. This is also illustrated in Fig. 8a, where the SPP wavelength is depicted vs. the free space wavelength of light at the SPP point (i.e. at ħkxcmax); the SPP wavelength is shorter than the wavelength of light, as expected, although their difference is not very large (as in the case of Ag) due to the substantial electron losses. Thirdly, air can hardly sustain a SPP mode for all cases, while clear SPP is observed for silica albeit at shorter wavelengths than the 850 nm telecom band in most cases. The inability to meet the requirement of 850 nm wavelength is not a deficit of the experimental range of the current work, but it is also due to physical limitations for various ternary conductive nitrides; for example further enrichment with Al or Y in order to extend the range of operation of TixAl1-xN and TixY1-xN would cause a phase transition from the B1 phase to pseudo-wurtzite [32] or further grain refinement due to the lattice mismatch between TiN and YN [41], respectively, while TixCa1-xN is characterized by inherent excessive electron loss [41]. The only family of conductive nitrides that can sustain a SPP for the silicon telecom bands (1300 nm and 1550 nm) is the Sc-rich TixSc1-xN, while for the silica fiber band (850 nm) both TixSc1-xN and TixMg1-xN might be considered. The later is inferior in terms of the quality factor QiSPP but given the abundance of Mg, in contrast to the shortage of Sc, it is worth dedicating efforts for the improvement of its growth and plasmonic performance in order to implement it industrially. Fourthly, the differences between the wavenumbers kx of the SPP and of the photon in the same dielectric (black lines in all panels of Fig. 6) can be used as a measure of the electronic loss; the bigger the difference the smaller the loss and the better the plasmonic performance of the corresponding conductor. This is quantified in Fig. 8b, where the difference λSPP-λphoton is plotted vs. the free space wavelength of light; λSPP and λphoton are the wavelengths of SPP (at ħkxcmax) and of the photons in the silica dielectric, respectively. This difference is reduced at longer wavelengths for all the considered 13 ACS Paragon Plus Environment


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ternary nitrides proving that the redshift of the plasmonic performance comes in expense of the electron loss, making the manifestation of SPP quite ambiguous [note however that the manifestation of LSPR is more pronounced due to its finite line shape; indeed, LSPR is clearly observed for the studied nitrides more details are presented in the on-line supporting information - thus proving the plasmonic potential of these materials]. The same behavior is also observed for QiSPP vs. the free space wavelength of light (Fig. 8c), meaning that the intrinsic characteristics (QiSPP) define to a great extend the extrinsic plasmonic performance (λSPP-λphoton). Therefore, the considerations expressed in the previous paragraphs regarding the improvement of QiSPP via improving the growth process of TixSc1-xN and TixMg1-xN would establish a guide towards the improvement of infrared plasmonic devices incorporating such nitrides, as well. For most applications the enhancement of the electric field at the vicinity of the conductor’s surface due to SPP is crucial and, therefore, should be considered for the evaluation of the studied ternary nitrides. According to Ref. 40 and 61 the field enhancement factor (FEF) can be calculated using the dielectric function spectra of the conductor (in our case the ternary nitrides) and of the dielectric (e.g. silica) via the equation:

FEF =

ε 1,TN + ε 1, d ε 12,TN , × ε 1,TN ⋅ ε 1, d ε 2,TN

(9)

where ε1,TN and ε2,TN are the real and imaginary parts of the dielectric function of each ternary nitride, and the ε1,d is the real part of the dielectric function of the adjacent dielectric (in our case ε1,d=ε1,Silica=1.9). Figure 9 displays the calculated FEF for the most promising cases of ternary nitrides with plasmonic activity in the infrared range, namely TixSc1-xN and TixMg1-xN with solid symbols/continuous lines, and open symbols/dashed lines, respectively. The parentheses show the equivalent Neff for each x value. Note that there is no field enhancement (FEF300 nm thick) measured in the Visible-infrared ranges by ellipsometry for (a),(b) TixSc1-xN, (c),(d) TixY1-xN, and (e),(f) ZrxY1-xN. Fig. 2: (a) Optical reflectivity spectra of 200 nm thick epitaxial TixSc1-xN films grown on MgO(001) substrates, (b) ε1 spectra of the same films, (c) the variation of the Drude parameters Epu and γD with x for polycrystalline and epitaxial TixSc1-xN. Fig. 3: Spectra of the real (ε1) and imaginary (ε2) parts of the dielectric function of opaque films (>300 nm thick) measured in the Visible-infrared ranges by ellipsometry for (a),(b) TixMg1-xN, (c),(d) TixCa1xN.

Fig. 4: The correlation of the screened plasma energy Eps, and of the associated wavelength (λps=hc/Eps) with the composition x for various conductive ternary nitrides in the B1 structure; the inset demonstrates the scaling of Eps with effective number Neff of the valence electrons of the constituent metals. Fig. 5: The correlation of the maximum intrinsic quality factor for SPP (QiSPP) vs. the Eps and the equivalent wavelength λps for the various nitrides studied in this work. The solid black line is a guide to the eye for the optimal case of TixSc1-xN. Fig. 6: SPP dispersion relations at the nitride/dielectric interfaces for air and the two most widely used dielectrics in telecom technologies, i.e. silica and silicon. The black lines are the dispersion relations of the light into the dielectrics. Horizontal grey lines indicate the three bands used for telecommunications with today’s technology. Fig. 7: The correlation of the free space wavelength of light at SPP, which corresponds to the maximum ħkxcmax, with the screened plasma energy Eps for the bare conductive nitrides, as well as of the equivalent wavelength λps, respectively.



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Fig. 8: The variations of the (a) SPP wavelength, (b) the difference between the wavelengths of SPP and photon at the interface and in the silica dielectric, respectively, and (c) of the intrinsic QiSPP for the various nitrides studied in this work. Fig. 9: The field enhancement factor for SPP at the TixSc1-xN/silica (solid symbols/continuous lines) and TixMg1-xN/silica (open symbols/dashed lines) interfaces for various x; in parentheses are the equivalent Neff for each case. Note that there is no field enhancement (FEF300 nm thick) measured in the Visible-infrared ranges by ellipsometry for (a),(b) TixSc1-xN, (c),(d) TixY1-xN, and (e),(f) ZrxY1-xN. 669x452mm (96 x 96 DPI)

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Fig. 2: (a) Optical reflectivity spectra of 200 nm thick epitaxial TixSc1-xN films grown on MgO(001) substrates, (b) ε1 spectra of the same films, (c) the variation of the Drude parameters Epu and γD with x for polycrystalline and epitaxial TixSc1-xN. 669x499mm (96 x 96 DPI)



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Fig. 3: Spectra of the real (ε1) and imaginary (ε2) parts of the dielectric function of opaque films (>300 nm thick) measured in the Visible-infrared ranges by ellipsometry for (a),(b) TixMg1-xN, (c),(d) TixCa1-xN. The correlation of the screene 669x660mm (96 x 96 DPI)


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Fig. 4: The correlation of the screened plasma energy Eps, and of the associated wavelength (λps=hc/Eps) with the composition x for various conductive ternary nitrides in the B1 structure; the inset demonstrates the scaling of Eps with effective number Neff of the valence electrons of the constituent metals. 669x548mm (96 x 96 DPI)



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Fig. 5: The correlation of the maximum intrinsic quality factor for SPP (QiSPP) vs. the Eps and the equivalent wavelength λps for the various nitrides studied in this work. The solid blue line is a guide to the eye for the optimal case of TixSc1-xN. 669x551mm (96 x 96 DPI)


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Fig. 6: SPP dispersion relations at the nitride/dielectric interfaces for air and the two most widely used dielectrics in telecom technologies, i.e. silica and silicon. The black lines are the dispersion relations of the light into the dielectrics. Horizontal grey lines indicate the three bands used for telecommunications with today’s technology. 1338x967mm (96 x 96 DPI)



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Fig. 7: The correlation of the free space wavelength of light at SPP, which corresponds to the maximum ħkxcmax, with the screened plasma energy Eps for the bare conductive nitrides, as well as of the equivalent wavelength λps, respectively. 669x642mm (96 x 96 DPI)


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Fig. 8: The variations of the (a) SPP wavelength, (b) the difference between the wavelengths of SPP and photon at the interface and in the silica dielectric, respectively, and (c) of the intrinsic QiSPP for the various nitrides studied in this work. 669x892mm (96 x 96 DPI)



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Fig. 9: The field enhancement factor for SPP at the TixSc1-xN/silica (solid symbols/continuous lines) and TixMg1-x/silica (open symbols/dashed lines) interfaces for various x; in parentheses are the equivalent Neff for each case. Note that there is no field enhancement (FEF

Infrared Plasmonics with Conductive Ternary Nitrides - ACS Applied

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