Thickness dependence of the resistivity of Platinum group metal thin films
Shibesh Dutta, Kiroubanand Sankaran, Kristof Moors, Geoffrey Pourtois, Sven Van Elshocht, Jurgen Bommels, Wilfried Vandervorst, Zsolt Tokei, Christoph Adelmann
TThickness dependence of the resistivity of platinum-group metalthin films
Shibesh Dutta,
1, 2
Kiroubanand Sankaran, Kristof Moors,
1, 2
Geoffrey Pourtois,
1, 3
Sven Van Elshocht, J¨urgen B¨ommels, Wilfried Vandervorst,
1, 2
Zsolt T˝okei, and Christoph Adelmann ∗ Imec, B-3001 Leuven, Belgium KU Leuven, Department of Physics and Astronomy, B-3001 Leuven, Belgium Department of Chemistry, Plasmant Research Group,University of Antwerp, B-2610 Wilrijk-Antwerpen, Belgium
Abstract
We report on the thin film resistivity of several platinum-group metals (Ru, Pd, Ir, Pt). Platinum-group thin films show comparable or lower resistivities than Cu for film thicknesses below about5 nm due to a weaker thickness dependence of the resistivity. Based on experimentally determinedmean linear distances between grain boundaries as well as ab initio calculations of the electronmean free path, the data for Ru, Ir, and Cu were modeled within the semiclassical Mayadas–Shatzkes model [Phys. Rev. B , 1382 (1970)] to assess the combined contributions of surface andgrain boundary scattering to the resistivity. For Ru, the modeling results indicated that surfacescattering was strongly dependent on the surrounding material with nearly specular scattering atinterfaces with SiO or air but with diffuse scattering at interfaces with TaN. The dependence ofthe thin film resistivity on the mean free path is also discussed within the Mayadas–Shatzkes modelin consideration of the experimental findings. ∗ Author to whom correspondence should be addressed. Electronic mail: [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] A ug . INTRODUCTION Finite size effects in the resistivity of metallic thin films or nanowires have been a topicof research for several decades both from a fundamental as well as an applied point ofview. While the resistivity of bulk metals is dominated by phonon (and possibly impurity)scattering at room temperature, surface scattering can become dominant when the sizeof the thin films or nanowires is reduced [1–3]. In addition, grain sizes ( i.e. mean lineardistances between grain boundaries) in polycrystalline films or wires have typically beenfound to decrease for decreasing film thickness or wire diameter, which leads to an increasingcontribution of grain boundary scattering in thin films or nanowires [4, 5]. Ultimately, whenthe structure size becomes of the order of a few nanometer, electron confinement effectswill also alter the resistivity of metallic nanostructures [3, 6–13]. While this behavior isuniversally found in all metals, there is still controversy over the relative importance of thedifferent additional scattering contributions even for the most studied material, Cu [14–23],and only few comparative studies for different metals have been reported [24–26].From an applied point of view, the understanding of the resistivity of metals in smalldimensions is crucial since metallic nanowires form the interconnect structures that are usedin integrated microelectronic circuits. At present, the widths of scaled interconnect wires areof the order of 25 to 30 nm and are expected to reach dimensions of about 10 nm in the nextdecade. At such dimensions, surface and grain boundary scattering in Cu, the standard con-ductor material presently used in interconnects, dominate over phonon scattering, resultingin resistivities much larger than in the bulk [14–16, 27, 28] and leading to a deteriorationof the interconnect properties [29–32]. In addition, Cu-based interconnects require diffusionbarriers and adhesion liners to ensure their reliability. Since their resistivity is typically muchhigher than that of Cu, their contribution to the wire conductance is often negligible. Barriersand liners are difficult to scale and may occupy a significant volume when the interconnectwidth approaches 10 nm, reducing the volume available for Cu. Therefore, alternative metalshave recently elicited much interest as they could serve as a barrierless replacement for Cu.Among them, platinum-group metals (PGMs) have emerged as promising candidates dueto the combination of low bulk resistivity, resistance to oxidation, and high melting point,which can be considered as a proxy for resistance to electromigration [33–36].The main quest for alternatives to Cu is motivated by the observation that the resistivity2ncrease for thin films due to surface or grain boundary scattering depends on λ/(cid:96) . Here, λ isthe intrinsic mean free path (MFP) of the charge carriers in the metal and the characteristiclength scale (cid:96) is the film thickness for surface scattering or the average linear distance betweengrain boundaries for grain boundary scattering [1–5]. Hence, metals with short MFPs shouldbe inherently less sensitive to surface or grain boundary scattering for a given (cid:96) . As a result,such metals may show lower resistivities than Cu for sufficiently small dimensions despitetheir larger bulk resistivity [27, 37, 38]. In addition, quantum effects for very small (cid:96) mayalso lead to such a behavior [13, 39, 40]. However, such a crossover behavior has been elusiveso far despite its strong interest for interconnect metallization.In this paper, we discuss the thickness dependence of the resistivity of PGM (Ru, Pd,Ir, Pt) ultrathin films with thicknesses between 3 and 30 nm. We demonstrate that theirresistivity exhibits a much weaker thickness dependence than that of Cu films in the samethickness range. As a result, for films thinner than about 5 nm, the resistivities of Ru and Irfilms fall below that of Cu. The thickness dependence of the resistivity of Ru and Ir is thenmodeled using the analytical semiclassical Mayadas–Shatzkes approach. We demonstratethat, within the Mayadas–Shatzkes model, the shorter MFP of PGMs is indeed predomi-nantly responsible for the resistivity crossover with respect to Cu. The data suggest thatRu, and Ir are promising metals for future interconnects in advanced technology nodes withinterconnect widths below 10 nm [41]. II. EXPERIMENTAL AND THEORETICAL METHODS
All films were deposited by physical vapor deposition (PVD) at room temperature on Si(100). Prior to metal deposition, a 90 nm thick thermal oxide was grown on the Si wafersto ensure electrical isolation. Cu, Ru, and Ir films were deposited on 300 mm wafers in aCanon Anelva EC7800 system. In addition to films directly deposited on SiO , Cu and Rufilms were also grown in situ on 1.5 nm thick PVD TaN and capped by 1.5 nm thick PVDTaN. This was done to prevent the oxidation of the Cu surface, to avoid Cu diffusion intothe underlying SiO during annealing, and to study the effect of the “cladding” materialon the Ru thin film resistivity. Pt films were sputter deposited on small samples in a homebuild system using thin ( ≈ α radiation in a Bede MetrixLdiffractometer from Jordan Valley or a Panalytical X’Pert diffractometer. Film thicknesses byXRR were cross-calibrated by Rutherford backscattering spectrometry (RBS) measurementsusing a 1.52 MeV He + ion beam in a rotating random mode at a backscatter angle of 170 ◦ .In all cases, the contribution of the adhesion layers to the sheet resistance was obtainedby independent measurements and taken into account in the determination of the PGMthin film resistivity. The diffractometers mentioned above were also used to assess the filmcrystallinity using x-ray diffraction (XRD). Surface roughnesses were measured by atomicforce microscopy (AFM) using a Bruker IconPT microscope. Lateral correlation lengths ofthe surface roughness were obtained from the autocorrelation function. The microstructureof the films was determined from plan-view transmission electron microscopy (TEM) imagesusing Tecnai F30 and Titan3 G2 microscopes. Based on these images, the mean linear grainboundary intercept distance (the average linear distance between grain boundaries) wasdetermined [42, 43]. Due to the almost columnar nature of the microstructure and theirexpected relatively weak contribution to the resistivity, grain boundaries parallel to thesurface were neglected.Electronic structures of the PGMs, Ru, Rh, Pd, Os, Ir, and Pt, as well as of Cuwere obtained by first-principles calculations based on density functional theory as imple-mented in the Quantum Espresso package [44]. Projector augmented wave [45] potentialswith the Perdew–Burke–Ernzerhof generalized gradient [46] approximation of the exchange-correlation functional have been used together with a 40 × ×
40 Monkhorst–Pack k -pointsampling grid and an energy cutoff of 80 Ry to ensure the convergence of the total energydifferences (10 – 12 eV). The Fermi surface S F,n ( k ) was determined from the calculated elec-tron energy as a function of the wave vector k for each band with index n . In addition,using the obtained Fermi surfaces and electronic densities of states, scattering times due toelectron–phonon interactions have been calculated using standard first-order perturbationtheory [47]. Details of these calculations can be found in Ref. [34].4 II. MATERIAL PROPERTIES AND RESISTIVITY OF PLATINUM-GROUPMETAL THIN FILMS
All films were polycrystalline as deposited. The Θ-2Θ XRD patterns were consistent withthe expected crystal structures of the stable phases (hcp for Ru, fcc for all other metals) with(partial) texture [(001) for Ru, (111) for other metals]. Post deposition annealing at 420 ◦ C informing gas for 20 min improved both the crystallinity and led to strong texturing [Fig. 1(a)].The out-of-plane Scherrer crystallite size of annealed films [Fig 1(b)] was typically of theorder of the film thickness for films up to about 15 nm and deviated slightly towards smallervalues for thicker films. This indicates that the microstructure of the films was (nearly)columnar.Figure 2 shows the root-mean-square (RMS) roughness of Cu (TaN/Cu/TaN), Ru (bothRu/SiO and TaN/Ru/TaN), Ir, Pd, and Pt films as a function of the film thickness afterpost deposition annealing at 420 ◦ C. The roughness of the annealed films increased withincreasing film thickness but remained below 0.4 nm even for 30 nm thick PGM films. Cufilms were slightly rougher with RMS values of 0.5 to 0.6 nm for the thickest films. XRRmeasurements (not shown) indicated that the roughness of the top surface was very similarto that of buried interfaces (typically also 0.3 to 0.5 nm). The lateral correlation length ξ ofthe surface roughness (obtained with Gaussian correlation statistics) was between 10 and15 nm for all films with insignificant differences between materials/stacks and only littlecoarsening in the studied thickness range up to 30 nm.Figure 3 shows the resistivity of Cu (TaN/Cu/TaN), Ru (Ru/SiO and TaN/Ru/TaN),Pd, Ir, and Pt as a function of the film thickness. All films were annealed at 420 ◦ C for 20 minin forming gas. Cu showed a strong increase with decreasing film thickness, as observedpreviously and ascribed to the combination of surface and grain boundary scattering. Notethat the Cu resistivity values were close to the ones reported in the literature for scaled Cuinterconnect lines of the same critical dimension [48, 49].By contrast, all PGM thin films showed a much weaker thickness dependence of theresistivity than Cu. For films with thicknesses of 10 nm and above, the resistivities weremuch higher than for Cu owing to the higher bulk resistivities of PGMs. However, for filmthicknesses of about 5 nm and below, the resistivities of Ru and Ir became comparable andeven lower than the resistivity of Cu. From a technological point of view, this resistivity5rossover renders PGMs, in particular Ru and Ir highly interesting for scaled interconnectswith critical dimensions of 10 nm and below, where the current combination of Cu, diffusionbarriers, and adhesion liner layers may be outperformed by barrierless Ru or Ir metallization.Indeed, scaled Ru filled interconnect structures have already shown first promising results[41] demonstrating the prospects of these materials for future interconnect technology nodes.From a more fundamental point of view, these data raise the question of the materialdependence of the thin film scattering contributions, such as surface and grain boundaryscattering. It has been asserted that a shorter electron MFP leads to a weaker thicknessdependence of both surface and grain boundary scattering [27, 37, 38]. However, to confirmthis argument, effects of potentially different microstructures ( e.g. the thickness dependenceof the mean linear distance between grain boundaries) have to be understood.
IV. FERMI SURFACES AND ELECTRON MEAN FREE PATHS OF PLATINUM-GROUP METALS
In a first step, we have computed the bulk electron MFPs of the PGMs as well as of Cu.The MFP in transport direction t of an electron with wave vector k is given by λ n, t ( k ) = τ n ( k ) × | v n, t ( k ) | , where τ n ( k ) is the relaxation time of an electron with wave vector k and v n, t ( k ) is the projection of the Fermi velocity v n ( k ) = (1 / (cid:126) ) ∇ k E F,n on the transportdirection. Here, E F,n is the Fermi energy of the band with index n .In a semiclassical approximation, the conductivity along the transport direction t can beexpressed as [50, 51] σ t = − e (2 π ) (cid:88) n (cid:90) d k | v n, t ( k ) | τ n ( k ) ∂f n ( k ) ∂(cid:15) , (1)where f n ( k ) is the (Fermi) distribution function, and (cid:15) has the dimension of an energy.The summation is carried out over the band index n . At low temperature, ∂f n ( k ) /∂(cid:15) = − δ ( (cid:15) n ( k ) − E F ). Assuming that the relaxation time is isotropic and does not depend on theband index, i.e. τ n ( k ) ≡ τ , one obtains [36] σ t τ = 1 τ ρ t = e π (cid:126) (cid:88) n (cid:90) S F,n d S | v n, t ( k ) | | v n ( k ) | . (2)6ere, the integration is carried out over the Fermi surface. Hence, the product of the relax-ation time and the bulk resistivity depends only on the morphology of the Fermi surface.When the bulk resistivity is known, τ can be deduced and thus the MFP in the transportdirection, λ n, t ( k ) = τ × | v n, t ( k ) | . For polycrystalline materials, suitable averages can beobtained from the isotropic τ in combination with an average of v n, t ( k ) over the relevanttransport directions.Using ab initio calculated Fermi surfaces (Fig. 4), τ × ρ was calculated for all PGMs aswell as for Cu as a reference. Based on these values and experimental bulk resistivities ρ [52], relaxation times τ were then deduced. In addition, relaxation times τ c due to electron–phonon scattering were directly calculated [34, 47]. Since all films were polycrystalline andtextured, an effective Fermi velocity v ave was obtained by averaging v n, t ( k ) over transportdirections perpendicular to [001] for the hcp metals (Ru, Os) and [111] for the fcc metals(Rh, Pd, Ir, Pt, and Cu). MFP values λ and λ c were then calculated using τ and τ c ,respectively. The results are summarized in Tab. I. Note that the resistivity of bulk hcp Ruand Os is anisotropic with the higher resistivity perpendicular to [001] [53], i.e. along thetransport direction of our textured films. The values are generally in good agreement witha previous report [36].As discussed above, metals with short MFPs may be less sensitive to surface or grainboundary scattering and thus may show a weaker thickness dependence of the resistivitythan Cu [27, 37, 38]. As indicated in Tab. I, all PGMs show significantly shorter MFPs thanCu. Since the thin film resistivity for a given thickness or linear grain boundary distancealso depends on the bulk resistivity, ( λρ ) − has been used as a figure of merit of a metal forthe expected resistivity scaling at small dimensions [34–36]. As shown in Tab. I, all PGMsshow higher figures of merit than Cu with Pt showing the highest value. However, due to acomparatively high bulk resistivity, Pt (as well as Pd and Os) may show benefits only forvery small thicknesses or short linear grain boundary distances. V. SEMICLASSICAL THIN FILM RESISTIVITY MODELING
To gain further insight into the contributions of surface and grain boundary scattering, theresistivity of Ru, Ir and Cu was modeled using the semiclassical model developed by Mayadasand Shatzkes [5]. Despite recent advances in ab initio modeling [10, 11, 13, 54, 55], the7pproach by Mayadas and Shatzkes remains the only tractable quantitative model for thinfilm resistivities in the studied thickness range up to 30 nm that contains both surface andgrain boundary scattering. Here, transport is calculated within a Boltzmann framework usingan isotropic Fermi surface. Band structure effects are however included in our calculationsvia an anisotropic mean free path, as discussed above.The model also neglects confinement effects that are expected to further increase theresistivity. For nanowires, ab initio calculations have shown an orientation dependent in-crease of the resistivity although the magnitude of the increase varied between studies[10, 11, 13, 54, 55]. As a consequence, the thickness dependence of confinement effects innanowires (and the transition to bulk-like behavior) cannot be considered as fully understoodfor (Cu) nanowires and even less so for (Cu or PGM) thin films, where confinement effectsare expected to be weaker than for nanowires. Estimations of confinement effects within ananisotropic effective mass approximation (using anisotropic effective masses calculated fromthe above Fermi surfaces) lead to characteristic energies of the order of a few ( <
15) meV for5 nm thick Cu, Ru, and Ir films and the experimentally observed textures. These confinementenergies are much smaller than the Fermi energy (and hence a large number of subbands areoccupied) and even k B T at room temperature. Recent ab initio results by Zhou et al. [54]and Lanzillo [13] for Cu suggest that expected confinement effects are still small comparedto the experimentally observed increase of the thin film resistivity with respect to the bulk;therefore, grain boundary and surface scattering are expected to dominate over confinementeffects in our thin films. We also note that we have observed no different trends for thethinnest films of 5 nm thickness and below, in the sense that fitting data subsets includingthicker films only did not lead to significantly different fitting parameters. However, futurework will be required to unambiguously identify the effect of band structure and confinementon the thin film resistivity, especially for film thicknesses far below 10 nm.In the Mayadas–Shatzkes model, the resistivity of a thin film with thickness h and averagelinear distance between grain boundaries (average linear intercept length [56]) l is given by ρ tf = ρ GB − πκρ (1 − p ) π/ (cid:90) dφ ∞ (cid:90) dt cos φH × (cid:18) t − t (cid:19) − e − κtH − pe − κtH (cid:21) − ≡ (cid:20) ρ GB − ρ SS , GB (cid:21) − , (3)8ith ρ GB = ρ [1 − α/ α − α ln (1 + 1 /α )] − , H = 1+ α/ cos φ (cid:112) (1 − /t ), κ = h/λ ,and α = ( λ/l ) × R (1 − R ) − [57]. p and R are parameters that describe the surface andgrain boundary scattering processes, respectively. The phenomenological surface specularityparameter p varies between 0 for diffuse and 1 for specular scattering of charge carriers at thesurface or interface; R is the reflection coefficient (0 < R <
1) of a charge carrier at a grainboundary. In general, p can take different values at the top and bottom interface, e.g. whenthe surface and interface roughnesses are strongly different, as described by the model ofSoffer [58]. However, given the observation that surface and buried interface roughnesses inthe stacks considered here are low and very similar, we will assume that a single parameter p can describe both interfaces of the metal films. A. Film thickness dependence of the linear grain boundary distance
While surface scattering depends directly on the film thickness, grain boundary scatteringdepends on the average linear distance between grain boundaries, l , along the transportdirection. Therefore, a quantitative model of the thin film resistivity as a function of filmthickness requires the knowledge of the thickness dependence of l in polycrystalline films.Historically, it has often been assumed that l is identical or proportional to the film thicknessand this assumption has often been used to model the thickness dependence of the resistivity.However, it has been pointed out that such simple relations are generally not valid [59].We have therefore experimentally determined the average linear grain boundary distanceusing the intercept method [42, 43] from plan-view transmission electron micrographs for 5,10, and 30 nm thick Ru/SiO (as deposited and after annealing at 420 ◦ C), TaN/Ru/TaN(annealed), Ir/SiO (annealed), and TaN/Cu/TaN (annealed) thin films. Figure 5 showsboth sample TEM images as well as the deduced film thickness dependence of the meanlinear grain boundary intercept length. While for TaN/Cu/TaN and annealed Ru/SiO themean linear intercept length was close to the film thickness, other stacks clearly showed asaturating effect for ∼
30 nm thick films. Linear intercept lengths for in-between thicknesseswere obtained by piecewise linear interpolation. Other more nonlinear interpolation schemesdid not have any significant effects on the modeling results discussed below.9 . Semiclassical modeling results and discussion
Figure 6 shows the experimental thickness dependence of the resistivities of Ru/SiO ,TaN/Ru/TaN, Ir/SiO , and TaN/Cu/TaN, together with the best fits using the Mayadas–Shatzkes model in Eq. (3). All films were annealed at 420 ◦ C for 20 min except for an addi-tional data set of as deposited Ru/SiO . To obtain best fits, the experimentally determinedthickness dependences of the linear distance between grain boundaries for the different ma-terials and stacks, as discussed in the previous section, were used. In addition, bulk electronMFPs obtained by ab initio calculations, λ (see Tab. I), were employed in combinationwith experimental bulk resistivities. As discussed above, quantum confinement effects aredifficult to quantify and have been neglected as they can still be expected to be small forthe studied film thicknesses at room temperature except maybe for the very thinnest films(see also the discussion in Ref. [60]). For Ru, the bulk resistivity has been reported to beanisotropic [53]. Since all films studied here showed strong (001) texture, the bulk in-planeresistivity (perpendicular to the hexagonal axis) has been used. Only p and R were used asadjustable parameters. In general, the model described well the thickness dependence of thethin film resistivity for all materials and stacks over the entire thickness range. The resultingparameters are listed in Tab. II.Using the Mayadas–Shatzkes model, the best fit to the data for Cu films (within aTaN/Cu/TaN stack) indicated that both surface ( p = 0 .
05) and grain boundary scatter-ing ( R = 0 .
22) contribute to the thin film resistivity. The values of p and R fall well withinthe range of published values [14–23]. Moreover, they are in good agreement with a recentreview [18] that concluded that the scattering at TaN/Cu interfaces is highly diffuse, inagreement with our results.By contrast, fitted grain boundary reflection coefficients for Ru and Ir were larger than forCu with R = 0 .
43 to 0.58 for the different Ru stacks and R = 0 .
47 for Ir/SiO . Although grainboundary configurations, in particular the average misorientation angle of contiguous grains,can have an influence on the grain boundary resistance, as discussed below, a simple model ofthe material dependence of R for polycrystalline films has been proposed by relating R to thesurface energy (and to the melting point) of the material [61]. This is fully consistent with ourobservations that R was larger for the more refractory Ru and Ir than for Cu. Moreover, ourfitted values of R ∼ . R = 0 .
47 for Ir are in reasonable quantitative agreement10ith the predictions of this model of R = 0 .
55 for Ru and R = 0 .
57 for Ir [61]. Note that thepredicted value for Cu is R = 0 .
35, also in reasonable agreement with our results. Recently,Lanzillo calculated R for twin boundaries in PGMs (Pt, Rh, Ir and Pd) by ab initio methods[13] and found them to be higher than for Cu, in qualitative agreement with our results. Itshould however be noted that all such fitted R values describe ”effective“ grain boundaryreflection coefficients since the grain structures of the films certainly contain many differentgrain boundary structures. Moreover, the grain boundary transmission might also be affectedby confinement effects for the thinnest films. For this reason, the quantitative understandingof grain boundary reflection coefficients both in Cu and PGMs will still require further work.The fitted grain boundary coefficients of Ru/SiO showed a significant reduction uponannealing ( R = 0 . vs. R = 0 . R upon annealing. The intermediate fitted value for the TaN/Ru/TaN stackis also in qualitative agreement with this argument since the observed small grain size evenafter annealing may be correlated with larger grain boundary resistances than for annealedlarge grain Ru on SiO .Interestingly, the best fits indicated that both Ru and Ir on SiO showed nearly specularsurface scattering with p > .
9. Hence, in those films, the Mayadas–Shatzkes model suggeststhat, despite their small thicknesses, surface scattering did not appear to contribute stronglyto the resistivity. It has been calculated that the surface scattering coefficient for a giveninterface should be a strong function of both the magnitude (RMS) as well as its lateral cor-relation length of the surface roughness [9, 68–70]. Although the Ru/SiO and Ir/SiO filmswere somewhat smoother than the TaN/Cu/TaN films (Fig. 2), the difference is small andthe lateral correlations lengths are similar. Therefore, it appears unlikely that the differencebetween Ru/SiO as well as Ir/SiO and TaN/Cu/TaN was only due to differences in thephysical surface properties. Thus, the electronic structure and the scattering potentials atthe interface may contribute significantly [71].Moreover, the fits indicated strongly diffuse scattering at Ru/TaN interfaces (as in11aN/Ru/TaN stacks) with p = 0 .
01. This implies that surface scattering depends less on theconducting metal (Ru vs.
Cu) than on the cladding material of the thin film (SiO /air vs. TaN). Note that surface roughnesses for TaN/Ru/TaN and Ru/SiO were almost identical.Similar observations have been made for Cu [14, 72, 73]. In particular, Rossnagel and Kuan[14] have observed that the surface scattering contribution to the thin film resistivity waslower in contact with oxides (SiO , Ta O ) than with TaN, very similar to our observations.Several models for the surface specularity parameter p have been reported in the liter-ature [58, 68–71, 74] that quantitatively link p to the surface roughness and the intrinsicproperties of the Fermi surface of the conducting material. However, only very few studieshave considered the effect of the cladding material [71, 74], which appears essential in view ofthe experimental results. Zahid et al. [71] have studied the resistivity of Cu films surroundedby different metals using ab initio calculations and found that metals can both lower as wellas increase p with respect to a free Cu surface, depending on the difference of the density ofstates at the Fermi level of conducting metal (Cu) and the cladding atom at the interface.Although the density of states at the Ru/TaN interface has not yet been calculated, the bulkdensities of states of Ru and TaN at the respective Fermi levels are rather similar. Additionalwork is thus needed to clarify the contributions of the properties of the conductor and thecladding material and its interface on the surface scattering parameter. C. Relative contributions of surface and grain boundary scattering in theMayadas–Shatzkes model and deviations from Matthiessen’s rule
Equation (3) does not fulfill Matthiessen’s rule and the contributions of grain boundaryand surface scattering can therefore not be separated. While the first term in Eq. (3),1 /ρ GB ≡ σ GB , describes grain boundary scattering independently of surface scattering, thesecond term, 1 /ρ SS,GB ≡ σ SS,GB describes combined effects of surface and grain boundaryscattering. Nonetheless, the ratio of the two terms can be evaluated and allows to shedsome light on the relative importance of grain boundary and surface scattering within theMayadas–Shatzkes model. Figure 7 shows the ratio of σ SS,GB and σ GB as a function ofthe surface scattering parameter p for TaN/Cu/TaN, Ru/SiO , TaN/Ru/TaN, as well asIr/SiO and film thicknesses of 5 nm [Fig. 7(a)] and 20 nm [Fig. 7(b)]. Experimental meanlinear intercept lengths and surface scattering parameters R corresponding to best fits were12sed. It should be noted that in Eq. (3), a ratio of σ SS , GB /σ GB = 0 . σ GB (cid:29) σ SS,GB for all values of p , the second term canbe neglected and the thin film resistivity in the Mayadas–Shatzkes model is dominated bygrain boundary scattering. However, due to the violation of Matthiessen’s rule, the oppositeconclusion, namely the dominance of surface scattering for σ GB ≈ σ SS,GB , is not necessarilyvalid.The data indicate a general prevalence of grain boundary scattering over surface scat-tering within the Mayadas–Shatzkes model for all stacks even for the most diffusive case of p = 0 since generally σ SS , GB /σ GB (cid:28) .
5. Only for TaN/Cu/TaN (in particular for 5 nm filmthickness), σ SS , GB contributed strongly to the overall conductivity. By contrast, the contri-butions were weak for PGM containing stacks—even for fully diffusive surface scattering, asobserved for TaN/Ru/TaN.The different magnitudes of 1 /ρ GB ≡ σ GB and 1 /ρ SS , GB ≡ σ SS , GB have strong repercus-sions on the accuracy of the extracted p and R values. Figures 7(c)–(e) show the sum ofsquared errors (SSE) of the different fits as a function of the fitting parameters p and R for TaN/Cu/TaN, Ru/SiO , and TaN/Ru/TaN. In general, due to the small contribution of σ SS , GB , SSE minima were rather elongated along the p -axis but well defined along the R -axis.Generally, a rather weak gradient was visible along the elongated SSE minima towards thevalues reported in Tab. II. Correlations between p and R were also visible that increase theotherwise very small errors in R . Nonetheless, this resulted in much larger error bars (byabout 3 × ) of p as compared to R .This shows that the surface scattering specularity parameter of PGMs can therefore onlyapproximately be determined by modeling of the thickness dependence of the resistivitywithin the Mayadas–Shatzkes model, at least for the film thicknesses and grain sizes consid-ered here. However, the discussion above suggests that grain boundary scattering dominatesthe Ru and Ir thin film resistivities, even more so than for Cu, due to the much smallerMFP and that this holds independently of the exact value of p . This also indicates that theabsolute value of p should not necessarily be taken as a measure whether surface scatteringcontributes significantly or not.By contrast, the contribution of σ SS , GB was much larger for TaN/Cu/TaN [Figs. 7(a) and(b)]. This can be linked to the long MFP of 40.6 nm and indicates that surface scatteringcannot be simply neglected for thin Cu. Although both σ GB and σ SS , GB are reduced with13ncreasing MFP [via the dimensionless parameters α and κ in Eq. (3)], σ SS , GB appears moresensitive than σ GB , leading to an increasing prevalence of σ GB for large α . In addition, thegrain boundary reflection coefficient of Cu, R = 0 .
22 was found to be much smaller thanfor PGMs ( R ∼ . σ GB for Cu withrespect to PGMs.Among the PGMs, σ SS , GB /σ GB of Ru/SiO showed a much stronger dependence on p [Figs. 7(a) and (b)] than TaN/Ru/TaN or Ir/SiO . This can be linked to deviations fromMatthiessen’s rule, as shown in Fig. 8. As pointed out by Mayadas and Shatzkes [5], the(effective) MFP that determines surface scattering in a polycrystal ( i.e. in presence of grainboundary scattering) is reduced over the bulk value by λ GB = ( ρ /ρ GB ) λ . This leads to adependence of surface scattering on α . The effect is illustrated in Fig. 8(a) for h = 10 nm,which shows σ SS , GB as a function α . To make the curves more comparable, p = 0 was assumedin all cases. For comparison, the dependence of σ GB on α is also shown in Fig. 8(b). The datashow that an increase of α ( i.e. stronger grain boundary scattering) leads to an decrease in σ SS , GB that is generally faster than for σ GB . At h = 10 nm, due to the combination of largegrains and short MFP, α = 0 . , much smaller than for TaN/Ru/TaN ( α = 1 . ( α = 1 . σ SS , GB of Ru/SiO for a given valueof p . In practice however, the scattering at Ru/SiO and Ru/air interfaces was found to benearly specular and the contribution of σ SS , GB to the thin film resistivity was also negligiblefor Ru/SiO . D. Influence of the mean free path on the thickness dependence of the resistivity
Finally, we evaluate within the Mayadas–Shatzkes model the relative impact of the dif-ferent material parameters ( λ , p , R , l ) on the slope of the thickness dependence of the thinfilm resistivity. It has been previously proposed that metals with a shorter MFP may showa much weaker thickness dependence of their thin film resistivity. However, this effect maypotentially be complemented or domineered by other factors such as the material (stack)dependence of surface and grain boundary scattering coefficients as well as the thickness de-pendence of the mean linear grain boundary intercept length, which will in generally dependboth on the material and the applied thermal budget.To gain further insight in the importance of the electron MFP, we have calculated the14xpected thickness dependence of the resistivity of Cu or Ru as a function of the MFP,keeping λ × ρ constant as it is only a function of the Fermi surface morphology. Theresult, using the experimentally deduced parameters ( p , R , and mean linear grain boundaryintercept length) for Cu, is shown in Fig. 9(a). The data indicate that the overall slope ofthe resistivity vs. thickness curves shows a strong dependence on the MFP. Reducing theMFP to that of Ru (6.6 nm, see Tab. I) while keeping λ × ρ constant (6 . × − Ωm )leads to both a slope and absolute resistivities that are close to what was experimentallyobserved for annealed Ru/SiO [Fig. 9(a)].Conversely, as shown in Fig. 9(b), using the parameters obtained for annealed Ru/SiO ( p , R , and average linear intercept between grain boundaries) and increasing the MFP tothat of Cu (40.6 nm, see Tab. I) while again keeping λ × ρ constant (5 . × − Ωm ) leadsto a slope almost identical to that experimentally observed for TaN/Cu/TaN. The residualdifferences stem from the material dependence of λ × ρ (see Tab. I), R , and p (see Tab. II), aswell as from the different thickness dependence of the mean linear grain boundary interceptlength, and are rather small. The larger deviations for the 3 nm thick films in both graphscan be ascribed within the Mayadas–Shatzkes model to the much stronger contributionof surface scattering to the Cu resistivity, which becomes significant only for such smallthicknesses. As a whole, however, this confirms that the shorter MFP is the main root causefor the different thickness dependence of the resistivity of Cu and the PGMs. VI. CONCLUSION
In conclusion, we have studied the thickness dependence of the resistivity of ultrathinPGM films in the range between 3 and 30 nm. All studied PGMs (Ru, Pd, Ir, Pt) show amuch weaker thickness dependence than Cu, the reference material. As a consequence, PGMthin film show comparable or even lower resistivities than Cu for film thicknesses of about5 nm and below.The thickness dependence of the resistivity of TaN/Cu/TaN, Ru/SiO , TaN/Ru/TaN,and Ir/SiO was modeled using the Mayadas–Shatzkes model [5] and experimentally deter-mined mean linear grain boundary intercept lengths as well as ab initio calculations of theMFP for bulk metals. Fitted grain boundary scattering coefficients for Ru and Ir ( R ∼ . R = 0 . p > .
9) wasobserved for both Ru and Ir on SiO but the interface scattering was much more diffuse( p ≈
0) for TaN/Ru/TaN indicating that specular surface scattering is not an intrinsic ma-terial property of Ru. This behavior is currently not yet well understood owing to the lackof a general predictive theory for the material dependence of interface scattering. However,it should be noted that in all cases—irrespective of p —surface scattering contributed onlyweakly to the overall resistivity, which was dominated by grain boundary scattering, exceptfor the thinnest TaN/Cu/TaN films.Simulations within the Mayadas–Shatzkes model showed that the much shorter MFP ofRu and Ir was indeed responsible for the much weaker thickness dependence of the thin filmresistivity. This confirms earlier predictions [27, 37, 38] and justifies the usage of ( λρ ) − as a figure of merit of alternative metals for beyond-Cu interconnects [34, 36], in particularwith respect to the the expected scaling behavior. Indeed, PGMs—and in particular Ru—have recently shown excellent prospects to replace Cu in future nanoscale interconnects withscaled widths of 10 nm and below [41, 75–78]. Supplementary Material
See the supplementary material for the derivation of the correct definition of α in Eq. (3). Acknowledgments
The authors would like to thank Sofie Mertens, Thomas Witters, and Karl Opsomer(imec) for the support of the PVD depositions, as well as Christian Witt (GlobalFoundries)for many stimulating discussions. Olivier Richard and Niels Bosman are acknowledged forthe TEM imaging as well as Danielle Vanhaeren, Lien Landeloos, and Inge Vaesen (imec) forthe AFM measurements. Johan Meersschaut is acknowledged for the RBS measurements.S.D. would like to thank Anamul Hoque, Kristof Peeters, Michiel Vandemaele, ChristopherGray, and Margo Billen (KU Leuven) for their assistance in the TEM image analysis. This16ork has been supported by imec’s industrial affiliate program on nano-interconnects. [1] K. Fuchs, Math. Proc. Camb. Philos. Soc. , 100 (1938).[2] E. H. Sondheimer, Adv. Phys. , 1 (1952).[3] X.-G. Zhang and W. H. Butler, Phys. Rev. B , 10085 (1995).[4] A. F. Mayadas, M. Shatzkes, and J. F. Janak, Appl. Phys. Lett. , 345 (1969).[5] A. F. Mayadas and M. Shatzkes, Phys. Rev. B , 1382 (1970).[6] Z. Teˇsanovi´c, M. V. Jari´c, and S. Maekawa, Phys. Rev. Lett. , 2760 (1986).[7] N. Trivedi and N. W. Ashcroft, Phys. Rev. B , 12298 (1988).[8] A. E. Meyerovich and I. V. Ponomarev, Phys. Rev. , 155413 (2002).[9] K. Moors, B. Sor´ee, and W. Magnus, J. Appl. Phys. , 124307 (2015).[10] G. Hegde, M. Povolotskyi, T. Kubis, J. Charles, and G. Klimeck, J. Appl. Phys. , 123704(2014).[11] S. L. T. Jones, A. Sanchez-Soares, J. J. Plombon, A. P. Kaushik, R. E. Nagle, J. S. Clarke,and J. C. Greer, Phys. Rev. B , (2015).[12] R. C. Munoz and C. Arenas, Appl. Phys. Rev. , 011102 (2017).[13] N. A. Lanzillo, J. Appl. Phys. , 175104 (2017).[14] S. M. Rossnagel and T. S. Kuan, J. Vac. Sci. Technol. B , 240 (2004).[15] J. J. Plombon, E. Andideh, V. M. Dubin, and J. Maiz, Appl. Phys. Lett. , 113124 (2006).[16] S. Maˆıtrejean, R. Gers, T. Mourier, A. Toffoli, and G. Passemard, Microelectron. Engin. ,2396 (2006).[17] H. Marom, J. Mullin, and M. Eizenberg, Phys. Rev. B , 045411 (2006).[18] D. Josell, S. H. Brongersma, and Z. T˝okei, Annu. Rev. Mater. Res. , 231 (2009).[19] T. Sun, B. Yao, A. P. Warren, K. Barmak, M. F. Toney, R. E. Peale, and K. R. Coffey, Phys.Rev. B , 041402(R) (2009).[20] R. L. Graham, G. B. Alers, T. Mountsier, N. Shamma, S. Dhuey, S. Cabrini, R. H. Geiss, D.T. Read, and S. Peddeti, Appl. Phys. Lett. , 042116 (2010).[21] T. Sun, B. Yao, A. P. Warren, K. Barmak, M. F. Toney, R. E. Peale, and K. R. Coffey, Phys.Rev. B , 155454 (2010).[22] J. S. Chawla, F. Gstrein, K. P. O’Brien, J. S. Clarke, and D. Gall, Phys. Rev. B , 235423 , 252101 (2009).[24] J. W. C. De Vries, Thin Solid Films , 25 (1988).[25] M. Tay, K. Li, and Y. Wu, J. Vac. Sci. Technol. B , 1412 (2005).[26] J. M. Camacho and A. I. Oliva, Microelectron. J. , 555 (2005).[27] P. Kapur, J. P. McVittie, and K. C. Saraswat, IEEE Trans. Electron Devices , 590 (2002).[28] W. Steinh¨ogl, G. Schindler, G. Steinlesberger, and M. Engelhardt, Phys. Rev. B , 075414(2002).[29] F. Chen and D. Gardner, IEEE Electron Device Lett. , 508 (1998).[30] P. Kapur, G. Chandra, J. P. McVittie, and K. C. Saraswat, IEEE Trans. Electron Devices ,598 (2002).[31] K. J. Kuhn, IEEE Trans. Electron Devices , 1813 (2012).[32] A. Ceyhan and A. Naeemi, IEEE Trans. Electron Devices , 4041 (2013).[33] C. Adelmann, L. G. Wen, A. P. Peter, Y. K. Siew, K. Croes, J. Swerts, M. Popovici, K.Sankaran, G. Pourtois, S. Van Elshocht, J. B¨ommels, and Z. T˝okei, Proc. IEEE Int. Intercon-nect Technol. Conf., pp. 173 (2014).[34] K. Sankaran, S. Clima, M. Mees, C. Adelmann, Z. T˝okei, and G. Pourtois, Proc. IEEE Int.Interconnect Technol. Conf. pp. 193 (2014).[35] K. Sankaran, S. Clima, M. Mees, and G. Pourtois, ECS J. Solid State Sci. Technol. , N3127(2015).[36] D. Gall, J. Appl. Phys. , 85101 (2016).[37] C. Pan and A. Naeemi, IEEE Electron Device Lett. , 250 (2013).[38] W. Zhang, S. H. Brongersma, O. Richard, B. Brijs, R. Palmans, L. Froyen, and K. Maex,Microelectron. Engin. , 146 (2004).[39] A. J. Simbeck, N. Lanzillo, N. Kharche, M. J. Verstraete, and S. K. Nayak, ACS Nano ,10449 (2012).[40] N. Gao, J. C. Li, and Q. Jiang, Appl. Phys. Lett. , 263108 (2013).[41] L. G. Wen, P. Roussel, O. Varela Pedreira, B. Briggs, B. Groven, S. Dutta, M. I. Popovici, N.Heylen, I. Ciofi, K. Vanstreels, F. W. Østerberg, O. Hansen, D. H. Petersen, K. Opsomer, C.Detavernier, C. J. Wilson, S. Van Elshocht, K. Croes, J. B¨ommels, Z. T˝okei, and C. Adelmann,ACS Appl. Mater. Interfaces , 26119 (2016).
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08 0 . ± .
02 6.6 7.6 0.99Ru/SiO (annealed) 0 . ± .
09 0 . ± .
04 6.6 7.6 0.92TaN/Ru/TaN (annealed) 0 . ± .
06 0 . ± .
02 6.6 7.6 0.99Ir/SiO (annealed) 0 . ± .
09 0 . ± .
03 8.1 5.2 0.95TaN/Cu/TaN (annealed) 0 . ± .
04 0 . ± .
02 40.6 1.71 0.99 u (111)Ru (002)Ir (111)Pt (111)Pd (111) (b) TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO Pd/TiN
Film thickness (nm) S c h e rr e r g r a i n s i z e ( n m ) (a)
30 35 40 45 502Θ (⁰) I n t e n s i t y ( a r b . un i t s ) FIG. 1: (a) Θ-2Θ XRD pattern of 20 nm thick films of platinum-group metals and Cu, as indicated(Ru was deposited on SiO ). All layers have been annealed at 420 ◦ C for 20 min. The patternsindicate strong (111) texture for fcc materials (Pd, Pt, Ir, Cu) and (001) texture for hcp Ru. (b)Out-of-plane Scherrer grain (crystallite) size determined from the XRD pattern. The dashed lineindicates the expected behavior for ideal columnar growth, i.e. for crystallite sizes equal to the filmthickness. Film thickness (nm) R m s r o u g hn e ss ( n m ) TaN/Cu/TaN
Ru/SiO TaN/Ru/TaNIr/SiO Pd/TiNPt/TiN
FIG. 2: RMS surface roughness of platinum-group metal and Cu thin films as a function of theirthickness.
Film thickness (nm) R e s i s t i v i t y ( µ Ω c m ) TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO Pd/TiNPt/TiN
FIG. 3: Thickness dependence of the thin film resistivity of platinum-group metals and Cu, asindicated. All films have been annealed at 420 ◦ C for 20 min. u IrRu Rh PdOs Pt Fermi velocity (m/s)1.6×10 FIG. 4: Fermi surfaces of platinum-group metals. The Fermi surface of Cu is also shown as areference. The color scheme indicates the Fermi velocity.
50 nm 50 nm50 nm (a) (b) (c)
50 nm (d) (e)
Film thickness (nm) L i n e a r i n t e r c e p t l e n g t h ( n m ) TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO Ru/SiO (as dep.) FIG. 5: Plan-view TEM images of 30 nm thick films of (a) TaN/Cu/TaN, (b) TaN/Ru/TaN,(c) Ru/SiO , and (d) Ir/SiO . All films have been annealed at 420 ◦ C for 20 min. (e) Grain sizedistributions of Ru/SiO for both annealed and as deposited films with thicknesses of 5, 10, and30 nm, as indicated. (e) Mean linear intercept length between grain boundaries deduced from theTEM images vs. film thickness. The dashed line represents the case where the linear interceptlength is equal to the film thickness. R e s i s t i v i t y ( µ Ω c m ) TaN/Cu/TaNRu/SiO (as dep.)TaN/Ru/TaNIr/SiO Ru/SiO FIG. 6: Best fits (dashed lines) using the Mayadas–Shatzkes model [see Eq. (3)] to the experi-mental thickness dependence (symbols) of the resistivity of platinum-group metal and Cu films,as indicated. The resulting fit parameters are listed in Tab. II. All stacks have been annealed at420 ◦ C except as deposited Ru/SiO . (c) Ru/SiO (d) TaN/Cu/TaN TaN/Ru/TaN (e) p R p p TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO σ SS , G B / σ G B (a) σ SS , G B / σ G B TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO p (b) p FIG. 7: σ SS , GB /σ GB as a function of the surface scattering parameter p for (annealed) stacks asindicated for film thicknesses of 5 nm (a) and 20 nm (b), respectively. Experimental mean linearintercept lengths and surface scattering parameters R corresponding to best fits were used. (c) –(e) Sum of squared errors (SSE) of fits to the experimental data ( cf. Fig. 6) vs. p and R fittingparameters for (c) TaN/Cu/TaN, (d) Ru/SiO , and (e) TaN/Ru/TaN, all after post-depositionannealing at 420 ◦ C. The color scale corresponds to the range between 1 × and 4 × the minimumSSE for all graphs. The white crosses represent the positions of minimum SSE. σ SS , G B ( S ) -1 -2 -3 (a) TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO σ G B ( S ) -1 -2 -3 (b) TaN/Cu/TaNRu/SiO TaN/Ru/TaNIr/SiO α FIG. 8: Deviations from Matthiessen’s rule: (a) σ SS , GB and (b) σ GB as a function of the dimen-sionless grain boundary scattering parameter α = ( λ/l ) × R (1 − R ) − . Here, the thickness wasset to 10 nm and fully diffuse surface scattering with p = 0 was assumed to make the curves morecomparable. (b) (a) Ru/SiO (exp.) λ = 3 nmλ = 6.6 nmλ = 10 nmλ = 20 nmλ = 40.6 nm R e s i s t i v i t y ( µ Ω c m ) λ = 3 nmλ = 6.6 nmλ = 10 nmλ = 20 nmλ = 40.6 nm R e s i s t i v i t y ( µ Ω c m ) TaN/Cu/TaN(exp.)
FIG. 9: Calculated thickness dependence of the resistivity as a function of the mean free path(MFP) λ with λ × ρ constant using (a) Cu parameters ( i.e. λ × ρ , p , and R ) and linear distancesbetween grain boundaries as well as (b) Ru parameters and linear distances between grain bound-aries. For λ equal to the value for Ru (6.6 nm), the simulated curve using Cu parameters in (a) isclose to the Ru/SiO experimental resistivities (green squares); analogously, the λ of Cu (40.6 nm)in combination with Ru parameters in (b) leads to a thickness dependence of the resistivity close tothat of Cu (blue circles). This indicates that the weaker film thickness dependence of the resistivityof platinum-group metals as compared to Cu can be attributed mainly to their shorter MFPs.of Cu (40.6 nm)in combination with Ru parameters in (b) leads to a thickness dependence of the resistivity close tothat of Cu (blue circles). This indicates that the weaker film thickness dependence of the resistivityof platinum-group metals as compared to Cu can be attributed mainly to their shorter MFPs.