Correlation between electrical direct current resistivity and plasmonic properties of CMOS compatible titanium nitride thin films

S. Viarbitskaya; J. Arocas; O. Heintz; G. Colas-Des-Francs; D. Rusakov; U. Koch; J. Leuthold; L. Markey; A. Dereux; J.-C. Weeber

doi:10.1364/OE.26.009813

1. Introduction

Titanium nitride (TiN) is a hard, chemically and thermally stable ceramic material, compatible with complementary metal-oxide-semiconductor (CMOS) technology. It is among the materials used for electrical connections in the micro-electronic industry and significant efforts have been made to improve TiN electrical properties [1–3]. At the same time, TiN has generated a steady interest for its optical properties [4–7] prior to attracting recently the attention of the nanophotonics community owing to its potential application for low-cost CMOS compatible plasmonic devices [8–21]. In this context, an optimization of TiN plasmonic performances is highly desirable and can be conducted by taking advantage of the efforts devoted to the improvement of TiN electrical properties. Such an approach requires an unambiguous correlation between electrical and plasmonic properties of TiN established by a combined and direct characterization of the two types of property.

So far, the most pervasive optical characterization method employed to study TiN thin films has been spectroscopic ellipsometry (SE), angular resolved or otherwise [14–16, 18]. In conjunction with Drude-Lorentz model, SE determines complex dielectric function, from which damping of the coupled electric field - free electron excitations propagating at the conductor/dielectric interface [22] - surface plasmon polaritons (SPP), can be calculated indirectly. In this respect, SE provides only an indirect plasmonic characterization of the material. The direct observations of propagating plasmonic modes supported by TiN based structures is limited to date to only a few reports. For example, Long-Range SPP (LR-SPP) mode supported by extremely thin epitaxial TiN waveguides has been demonstrated [12]. Alternatively, SPP damping along fully CMOS-compatible thin TiN layers was examined in the so-called dielectric loaded surface plasmon waveguide (DLSPPW) configuration. In this case, the limited propagation lengths of those intermediate effective index (1.1–1.25) plasmonic modes suggest that TiN can only be operated as a true plasmonic material for low effective index modes such as Long-Range SPPs or interface SPPs and at the price of well-controlled optical properties. Such low effective index modes, although inconvenient for waveguiding applications, are nevertheless of practical interest for CMOS compatible biosensors.

In this work, the propagation distances of SPP modes traveling at TiN/air interfaces (free space wavelength of 1.55μm) are directly measured by operating a fiber-to-fiber configuration and correlated to the direct current (dc) resistivity of the layers sustaining the surface plasmon modes. The combined and direct measurement of the electro-plasmonic properties of the same TiN films is at the core of our approach. By changing the parameters of our fully CMOS deposition process, the empirical dependence of the SPP propagation length on the dc resistivity of the TiN layers is obtained. The relevance of the dc resistivity for characterizating the plasmonic performances of TiN is investigated by considering the SE data collected on TiN samples featuring a low, intermediate and high dc resistivity respectively. We show that dc resistivity is a reliable parameter to predict quantitatively the plasmonic properties of TiN in the near-infrared. In addition, by conducting XPS analysis, we correlate the decrease of the dc resistivity of our TiN samples to decreasing amount of oxygen contamination. For the highly conducting TiN samples, we conclude that the low damping of the SPP mode is not due to a decrease of the absorption TiN but to a lower field confinement of the mode in the metallic layer.

2. Samples fabrication and characterizations

A dc magnetron sputtering machine has been used to prepare series of TiN thin layers on clean glass slides (Agar Scientific, 22mm ×22mm ×170μm) by varying nitrogen to argon ratio, substrate temperature and substrate bias. The latter together with the presence of parasitic oxygen in the vacuum chamber are found to be the key parameters affecting the electrical properties of the deposited layers. Due to inhomogeneity of the plasma density inside of the vacuum chamber, the thickness of the deposited TiN layers is expected to vary within 10% across the glass slide as measured by profilometer, with the mean thickness in the range of 75–160nm. The choice of the final thickness around 120nm is strategic. Indeed, as discussed in more details later, the films are sufficiently thin to allow for TiN/air SPP leakage radiation imaging [23, 24] in transmission, and sufficiency thick to ensure negligible losses of the SPP due to leakage radiation as well as negligible thickness dependence of the electrical resistivity [2,11]. The dc resistivity is determined by 4-point probe (4pp) using van der Pauw method. The prepared set of samples exhibited variation in dc resistivity ρ₄_pp from 28 to 130μΩ.cm. The change in electrical qualities of the TiN samples is correlated with the color of the samples: less resistive samples exhibited a gold-like yellow color, while more resistive samples acquire a slight copper tint. The propagation length L_SPP of TiN/Air SPP is measured using the fiber-to-fiber (f2f) characterization set-up [25] shown in Fig. 1(a). This set-up allows us to perform propagation loss measurements following a procedure mimicking the standard cut-back method. Light from an incoherent broadband light source (ASE-FL7006) is band-pass filtered (full width at half maximum (FWHM)=5nm) around 1550nm. The light is coupled in SPP via input and collected via the output fiber-focuser. The output power in the range of a few μW is measured by a power meter. Quality of the light focusing and alignment are monitored using complementary leakage radiation set-up built on the inverted microscope (Nikon Eclipse TE2000-U equipped with the 60× TIRF oil immersion objective with NA=1.49) and an infrared camera (Xenics XEVA). Input and output coupling gratings comprised of Su-8 resist were fabricated on the surface of TiN by electron beam lithography. Grating’s height is 260nm and their parameters were experimentally optimized, resulting in the grating period of 2.4μm and the filling factor of 0.3 for the 30° angle of incidence we use in this work [Fig. 1(a) and 1(b)]. Light impinging on the input grating is coupled into a collimated SPP jet. The jet collimation is verified by measuring the FWHM of its cross-sectional profile on radiation leakage images (not shown here) along its propagation path, ruling out modification of SPP propagation length due to jet’s focusing or divergence. The collimation of the SPP jet can be adjusted by the relative position of the input grating and the focal plane of the input fiber-focuser. By measuring a relative change in the out-coupled power I as a function of in- and out-coupling grating separation ΔL [Fig. 1(b)], L_SPP values are extracted using the following convention: $I (δ L) = I_{o} e^{- δ L / L_{S P P}}$ , where I₀ is the out-coupled power from the closest grating (ΔL = 15μm see Fig. 1(b)) and where δL = 5μm corresponds to the increase of the propagation distance between two consecutive output-coupler positions. All optical and electrical characterizations are performed at room temperature.

Fig. 1 (a) Schematic view of the experimental set-up. (b) Optical image of the input and output grating couplers implemented on the TiN surface. In red is the profile of incident light spot, propagating and scattered by the out-coupling grating SPP jet. Scale bar is 20μm.

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Figures 2(a) and 2(b) show leakage radiation images of the two SPP jets observed on two TiN layers with dc resistivity of 70 and 29μΩ.cm, respectively. The propagation of TiN/Air interface SPP modes at telecom wavelength is imaged and demonstrated here for what we believe to be the first time. On those images, one sees the incident spot scattered on the in-coupling grating generating a SPP collimated jet propagating to the right of the images, visibly damped by ohmic losses. The jet in Fig. 2(a) exhibits stronger damping than the jet in the Fig. 2(b). The out-coupling grating is absent on these samples. The same sample were studied on the f2f set-up by adding the out-coupling gratings. Figure 2(c) shows the results of the fitting procedure allowing determination of $L_{S P P}^{f 2 f}$ of the jets in Fig. 2(a) and 2(b), as explained above. Note that the leakage radiation microscopy images could be used as well for the measurement of the SPP mode damping distance. However, we found that the values of L_SPP relying on leakage radiation images are highly sensitive to the adjustment of the focus of the microscope objective and are also quite seriously impacted by a non-linear response of the camera.

Fig. 2 (a) and (b) Leakage radiation images of SPP jets propagating on the surface of TiN thin films with the respective dc resistivity as measured by 4pp method of 70 and 29μΩ.cm. Scale bar is 20μm. (c) The corresponding least-square linear fitting results, from which the values of L_SPP were derived.

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3. Results and discussion

Figure 3 shows the experimentally established dependence of the SPP propagation length $L_{S P P}^{f 2 f}$ on the dc electrical resistivity ρ₄_pp of a number of fabricated samples. A nonlinear decrease of $L_{S P P}^{f 2 f}$ is clearly correlated with the increase of the samples dc resistivity ρ₄_pp. The horizontal error bars are due to the uncertainties in the TiN layer thickness determination, the vertical error bars are due to the statistical distribution of the measured $L_{S P P}^{f 2 f}$ values. The dashed curve is a second order polynomial least mean square interpolation of the experimental data given by the equation displayed in Fig. 3. This experimental result suggests a direct evaluation of the damping distance from the simple dc resistivity. However, for an educated interpretation of this result, a closer examination of the relation between ρ and L_SPP is needed. The relation between L_SPP and ρ can be established in the framework of the Drude model which is expected to be fairly accurate in the infrared. According to Drude model, the dispersive relative dielectric function of a material is given by:

ε_{r} (ω) = ε_{\infty} - \frac{ω_{p}^{2}}{ω^{2} + γ_{d}^{2}} + i \frac{ω_{p}^{2} γ_{d}}{ω (ω^{2} + γ_{d}^{2})}

where ε_∞, ω_p and γ_d are the dielectric function at high frequencies, the plasma frequency and the scattering rate of free electrons respectively. The dc resistivity ρ_D is related to Drude’s model parameters by

ρ_{D} = 1 / (ε_{0} ω_{p}^{2} τ)

where ε₀ is the vacuum permittivity and where τ = 1/γ_d is the average collision time. The propagation length is given by

L_{S P P}^{D} = 0.5 / J (k_{S P P})

, where

J (k_{S P P})

denotes the imaginary part of the TiN/Air SPP wavevector with

k_{S P P} = (2 π / λ_{0}) \sqrt{ε_{r} / (1 + ε_{r})}

, where λ₀ is the incident light wavelength in vacuum [22]. In our situation, the dispersion relation of the TiN/air interface mode can be safely used for the computation of

L_{S P P}^{D}

in place of the thin film mode dispersion relation. Indeed, for the thickness of the layers we consider experimentally, the propagation length of the symmetric thin film mode peaked at the TiN/Air interface differs by less than 3% as compared to the TiN/air interface mode. Incidentally, this result indicates that the amount of leaked radiation do not contribute significantly to the damping process of the excited plasmon modes but is enough to observe the SPP jets with the infrared leakage radiation microscope. In attempt to mathematically express the dependence of

L_{S P P}^{D}

on resistivity, it appears that a given value of ρ_D allows for multiple values of

L_{S P P}^{D}

. To gain insight in the behavior of the damping distance as function of the resistivity, typical and realistic values for the Drude model parameters of TiN are needed. Three samples featuring a low, intermediate and high electrical dc resistivity respectively have been characterized by SE (Woollam VASE Ellipsometer). The SE data were fitted by using the Drude model over the telecom free-space wavelength range (1300nm–1800nm) in which the free-electron behavior of the material is dominant. The parameters of Drude model for the three samples of interest are displayed in Table 1.

Fig. 3 Directly measured damping distance $L_{S P P}^{f 2 f}$ as a function of the electrical dc resistivity ρ₄_pp. A subset of samples labeled (#1)-(#3) is additionally studied by SE (red dots) in the following.

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Table 1. Drude model parameters at a free-space wavelength of 1.55μm obtained by the fitting of the SE data taken over the spectral range 1300nm–1800nm.

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The parameters ε_∞, ω_p and γ_d feature a monotonic change as a function of the measured dc electrical resistivity. The dielectric functions of our TiN samples are then expected to be given by Drude parameters lying within the ranges defined by the parameters obtained for sample #1 (low resitivity) and #3 (high resitivity). For example, it is reasonable to speculate that a TiN sample with an intermediate resistivity (30 < ρ₄_PP(μΩ.cm) < 130), features a plasma frequency ω_p verifying 6:1 < ħω_p(eV) < 7:1. By generalizing this approach, we conclude that Drude parameter triplets (ε_∞, ω_p, γ_d) describing our TiN samples belong to a parametric volume with boundaries fixed by the results obtained on sample #1 and #3. For each triplet (ε_∞, ω_p, γ_d) within this parametric volume, the damping distances $L_{S P P}^{D}$ and the resistivity ρ_D can be computed according to relations given above and lead to the shaded area (denoted as Drude area) displayed in Fig. 4. This area is characteristic of the maximum spreading of the damping distance at a given value of ρ_D. For intermediate damping distances around 20μm, the relative width of the Drude area is typically ±10% whereas it drops below ±5% for low resistivity values corresponding longer damping distances around $L_{S P P}^{D} = 30 μ m$ . On the basis of this observation, we conclude that, although dc resistivity cannot be correlated to a unique value of damping distance, it provides a reliable information about the plasmonic performances of TiN at telecom frequencies. This conclusion is further confirmed by the distribution of the experimental data (black crosses) in Fig. 4 compiled from literature [14], which were obtained by independent groups on TiN samples fabricated on a variety of substrates using different methods, resulting in crystalline, polycrystalline, stoichiometric and non-stoichiometric TiN layers. It is very remarkable that, although obtained with different deposition methods, the damping distances $L_{S P P}^{D}$ computed from a Drude-Lorentz model (used to fit experimental SE data) for all TiN samples are almost perfectly distributed along the upper boundary of our Drude area. Those experimental results indicate that, in reality the spreading of $L_{S P P}^{D}$ for a given ρ_D is much narrower than returned by the simple sweeping of the Drude parametric volume. In other words, many of the triplets in this volume are unlikely to be observed in such a way that practically there is an almost univocal relation between ρ_D and $L_{S P P}^{D}$ for TiN at telecom frequencies. Even more importantly, we note that, by comparison to other TiN samples, our samples feature typical plasmonic properties. In this respect, our data correlating directly measured $L_{S P P}^{f 2 f}$ to experimentally measured dc electrical resistivity are expected to be relevant to many TiN samples and not be restricted to our set of samples.

Fig. 4 (a) TiN/Air SPP damping distance computed as a function of the resistivity ρ_D in the framework of the Drude model showing the multi-valued nature of L_SPP as a function of ρ_D. Red dots correspond to the subset of samples investigated by SE. The black crosses are experimental data compiled from the literature and extracted from Ref. [14]

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The relation between the damping distance L_SPP and the resistivity has been discussed in the context of Drude model. It is now instructive to compare the values of the resistivity and damping distances given by this model to the same quantities measured directly for the subset of samples. The values of the computed and directly measured damping distances and resistivities are displayed in Table 2.

Table 2. Comparison of the dc resistivities and damping distances directly measured $(ρ_{4 P P}, L_{S P P}^{f 2 f})$ or computed according to Drude model (ρ_D, L_SPP).

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For the subset of TiN samples studied by SE, a systematic discrepancy of the values of ρ^D relative to ρ₄_pp is found. The resistivity computed from the SE data overestimates the measured 4pp resistivity value by up to 80% for sample (1) featuring the longest SPP propagation distance. Very similar observations have already been reported [2, 26]. The computed $L_{S P P}^{D}$ given in Table. 2, although systematically slightly lower than the directly measured values, deviate by less than 15% for TiN samples featuring significant propagation distances around 20μm. In this respect, we conclude that SE data lead to fairly accurate evaluations of plasmonic properties of TiN in the near infrared but fails in the prediction of dc electrical properties.

Finally, to complement the characterization of our TiN samples, we employed XPS (PHI Versaprobe 5000) on samples (1)-(3) to find out that the increase of the dc resistivity is correlated with the layers’ oxygen content, in qualitative agreement with the previous studies [15, 18]. Figure 5 summarizes the XPS results. All our the samples are nitrogen rich. One can see that the least resistive sample possess 9% of oxygen, and its value is increased up to 14% in the most resistive sample. Increase of the oxygen content is accompanied by the decrease of nitrogen content with titanium content approximately remaining the same and around 37%. The measured oxygen content is not associated with the oxidation layer and is constant throughout the layers’ thickness. Such an increase of the parasitic oxygen is related to the degrading "metallic" character of TiN layers. Indeed, referring to the dielectric functions given in Table 1, we note that whatever the sample, the imaginary part of the dielectric function $ε_{r}^{″}$ is rather unchanged (around 28) whereas the absolute value of real part $| ε_{r}^{'} |$ increases by a factor almost three from the highest to the lowest resistive sample. In the framework of the Drude model, the increase of $| ε_{r}^{'} |$ originates dominantly from the increase of the plasma frequency ω_p and a corresponding increase of the free electron volume density. This last remark is also important to analyze the physical origin of the increase of L_SPP we observe for the less resistive TiN samples. For metals with $ε_{r}^{″}$ much smaller than $| ε_{r}^{'} |$ , it can be shown that [27]:

L_{S P P} ≃ \frac{{(ε_{r}^{'})}^{2}}{k_{0} \times ε_{r}^{″}}

Fig. 5 XPS depth profiles of the three selected samples.

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Although the condition on $ε_{r}^{″}$ and $ε_{r}^{'}$ is not strictly verified in our situation, Eq. (2) is still instructive for a qualitative analysis. The imaginary part $ε_{r}^{″}$ of our TiN samples being rather constant whatever the dc resistivity, we conclude that the increase of L_SPP observed for the less resistive samples is due to the increase of $| ε_{r}^{'} |$ . For increasing values of $| ε_{r}^{'} |$ , the phase constant $ℜ (k_{S P P})$ (where $ℜ$ denotes the real part) of the Air/TiN SPP mode approaches the light line in air. In this case, the SPP mode acquires a quasi-photon behavior with its field delocalized in the superstrate (air in our case). Thus, for the less resistive TiN samples, the SPP mode propagates over a longer distance because its field is repelled out from the metallic layer and not because the TiN layers are less absorbing. In other words, the improved propagation length of the SPP mode for the less resistive TiN is obtained at the cost of a smaller effective index and weaker field confinement at the TiN surface, a situation that can be detrimental to waveguiding or even biosensing applications.

4. Conclusion

In summary, we experimentally investigated the relationship between electrical dc resistivities and plasmonic properties of non-stoichiometric, polycrystalline thin TiN films deposited according to a CMOS compatible physical vapor deposition process. The plasmonic performances of the TiN samples were characterized by direct measurements of TiN/Air SPP damping distances at telecom frequencies. The dc resistivity turns to be a reliable parameter to predict TiN plasmonic performances in the near infra-red as shown by SE characterizations performed on our samples and data compiled from the literature. Based on those results, we conclude that the empirical law we report in this work provides a reliable way for the quantitative evaluation of TiN plasmonic properties on the basis of the dc electrical resistivity. Finally, XPS analysis of our samples reveals that a low resistivity is correlated to a reduced ratio of oxygen within the TiN films. Such a reduced oxygen ratio leads to an increase of the metallic behavior of the TiN layers causing the field of the SPP mode to be pushed out the absorbing layer. However, we note that the increase of the SPP propagation distance for less resistive TiN layers is not caused by a reduced absorption of the material, but by smaller ohmic losses experienced by the SPP modes owing to a weaker confinement of their field in TiN. This property could be of some importance for exploiting the thermo-optical properties of TiN nanoparticles for example.

Funding

H2020-EU.2.1.1 project PlasmoFab (688166).

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sample #	ρ₄_PP (μΩ.cm)	ε_∞	ħω_p (eV)	ħγ_d (eV)	$ε_{r}^{'}$	$ε_{r}^{″}$
(1)	30	6.8	7.0	0.365	−56.6	28.9
(2)	77	5.9	6.3	0.482	−39.6	27.4
(3)	130	5.4	6.1	0.889	−20.6	28.9

sample #	ρ₄_PP (μΩ.cm)	ε_∞	ħω_p (eV)	ħγ_d (eV)	$ε_{r}^{'}$	$ε_{r}^{″}$
(1)	30	6.8	7.0	0.365	−56.6	28.9
(2)	77	5.9	6.3	0.482	−39.6	27.4
(3)	130	5.4	6.1	0.889	−20.6	28.9

Correlation between electrical direct current resistivity and plasmonic properties of CMOS compatible titanium nitride thin films

Abstract

1. Introduction

2. Samples fabrication and characterizations

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (5)

Tables (2)

Equations (2)

Optics Express