The resistivity increase of a metal wire with decreasing cross-section 1,2 is referred to as the resistivity size effect 3,4 and represents a major challenge for the continued downscaling of integrated circuits 5 because of the resulting increased signal delay and power consumption in interconnect lines. The resistivity size effect is primarily due to electron scattering at surfaces [6][7][8][9][10] and grain boundaries [11][12][13][14][15][16] which are affected by the surface chemistry and structure 8,14,[17][18][19][20][21] and the relative grain orientations. 2,11,16,[22][23][24][25] The semiclassical Fuchs and Sondheimer 26,27 and Mayadas and Shatzkes 28 models use the phenomenological surface scattering specularity parameter p and the grain boundary reflection coefficient R to describe electron scattering at surfaces and grain boundaries and predict an overall resistivity increase that is proportional to ρoλ/d, where ρoλ is the product of the bulk resistivity times the bulk electron-phonon scattering mean free path, and d is the distance between scattering interfaces, that is the width of the conductor or the average grain size. 29 We note that these classical-models deviate from the quantum mechanical descriptions [30][31][32][33] and diverge from experimental measurements for narrow (< 10 nm) conductors. [34][35][36][37] Nevertheless, they are useful in the search for metals for narrow interconnects as they provide a single performance metric, the ρo×λ product, which promises a low resistivity in the limit of narrow wires. 38,39 Iridium has a predicted ρoλ = 3.69×10 -16 Ωm 2 which is 45%, 50%, 55%, and 28% smaller than the corresponding predictions for Cu, Co, W and Ru, respectively, 39 suggesting its potential to outperform competing metal solutions in highly scaled interconnect lines. In addition, the high melting point and the reported stability of Ir films on SiO2 lead to a superior electromigration resistance with the potential for barrierless metallization 40 which provides a considerable conductance benefit. 9,41 The predicted low ρoλ product is, however, no guarantee for a small resistivity scaling, since the calculated ρoλ agrees well with experiments only for some metals including Ru(0001), 42,43 Cu(001), 8 and Ag(001) 13 but disagrees with the measured resistivity vs thickness for epitaxial Rh(001), 44 Co(0001), 9,37 W(001), 45 W(011), 45 Nb(001) and Nb(011), 46 and Ni(001) 47 where ρoλ values are 39%, 67%, 72%, 68%, 293-743%, and 349% larger than predicted from first principles. Thus, experiments that directly quantify the resistivity size effect in Ir are required to confirm or correct the theoretical prediction. A previous investigation using polycrystalline Ir/SiO2 layers found a relatively small resistivity size effect with a 71% increase in ρ with decreasing d = 31 to 3 nm. 15 Their data fitting, using λ = 8.1 nm, yields a grain boundary reflection coefficient R = 0.47 and nearly specular surface scattering (p > 0.9). However, λ is not uniquely defined by the measured data which can also be described by other combinations of λ, R and p values. This challenge motivates our study on the measurement of the resistivity scaling in epitaxial Ir layers where confounding effects from grain boundary scattering are absent.
In this paper, we experimentally determine λ and the ρoλ product for Ir from measurements of the thickness dependent resistivity of epitaxial Ir(001) and Ir(111) layers which are sputter deposited on single-crystal MgO(001) and Al2O3(0001) substrates. The growth of single-crystal Ir(001)/MgO(001) layers which have a high crystalline quality, low surface roughness, and are thin but continuous is quite challenging: (i) growth at Ts = 1000 C results in a high crystalline quality but a large roughness or even a discontinuous microstructure if the thickness is reduced to d = 11.5 and 7.7 nm, (ii) a lower Ts = 700 C leads to continuous layers, however, with a lower crystalline quality, and (iii) growth at Ts = 700 C followed by stepwise in situ annealing to 1000 C results in a multi-domain polycrystalline microstructure which is attributed to renucleation into 111-oriented grains with an excellent crystalline quality, smooth surfaces, and a width-to-height aspect ratio > 10 3 such that electron scattering at domain boundaries is negligible. The measured in situ and ex situ resistivity at 295 K and 77 K as a function of thickness is well-described by the classical Fuchs-Sondheimer (FS) model 26,27 and indicates a lower-bound room-temperature effective mean free path λeff = 7.4 ± 1.2 nm for Ir layers grown on MgO(001) at 1000 C. The corresponding ρoλeff = (3.8 ± 0.6) ×10 -16 Ω-m 2 agrees very well with predictions from first principles. However, it is two times larger for Ts = 700 C, and 26% smaller for annealed layers deposited at Ts = 700 C, suggesting that ρoλeff is strongly affected by atomic-level surface irregularities and/or misfit dislocations even for epitaxial layers. Ir growth on Al2O3(0001) leads to a two-domain epitaxial microstructure and an increased resistivity which indicates a 52% probability for electron scattering at grain boundaries described by a 60 rotation about the <111> axis. Overall, the low measured ρoλeff product for Ir is smaller than previously reported ρoλ values of other elemental metals, 8,37,42,[44][45][46][47] confirming that Ir is a promising alternate interconnect metal for narrow-high conductivity interconnect lines.
Iridium layers were grown in a three-chamber ultrahigh vacuum DC magnetron sputter deposition system with a base pressure of 10 -9 Torr. 48 Polished MgO(001) and Al2O3(0001) substrates were cleaned by successive ultrasonic baths in trichloroethylene, acetone, isopropanol, and deionized water. They are then blown dry with nitrogen and mounted onto a Mo holder using colloidal silver paint, introduced into the sputter deposition system via a load lock, and degassed at 1000 °C for 1 hour. Deposition was performed in 10 mTorr 99.999% pure Ar at a constant power of 75 W applied to a 5-cm-diameter 99.9% pure Ir target facing the substrate at a 9 cm distance and with a 45 tilt, yielding a deposition rate of 0.19 ± 0.01 nm/s. The deposition time was adjusted to obtain a series of Ir layers with thickness d = 5-140 nm. A set of four sample series were prepared: Ir deposited (i) on MgO(001) at Ts = 700 °C, (ii) on MgO(001) at Ts = 1000 °C, (iii) on MgO(001) at Ts = 700 °C, immediately followed by in situ vacuum annealing at 800, 900, and 1000 °C for 30 min each, and (iv) on Al2O3(0001) at Ts = 700 °C followed by the same annealing as for (iii). After deposition, the samples were allowed to cool to room temperature in vacuum for 12 hours, followed by transfer to the analysis chamber for in situ resistivity measurements using a 1-100 mA current applied to the outer probes of a linear four-point probe with spring loaded tips and a 1.0 mm inter-probe spacing. Samples were removed from the deposition chamber via a load lock vented to atmospheric pressure using dry N2 and were immersed in liquid N2 within 2 s to limit air exposure and possible Ir surface oxidation prior to low-temperature transport measurements. Resistivity measurements at 77 K were taken with a similar linear four-point probe with both sample and probe tips completely immersed in liquid N2. Subsequent ex situ measurements were performed in air with the same setup after the samples were warmed to room temperature by blowing dry N2 onto the sample to minimize condensed ice/water accumulation on the Ir surface.
X-ray diffraction (XRD) analyses were performed using a PANalytical X'pert PRO MPD system with a Cu source with a parabolic mirror yielding a parallel beam with a <0.055° divergence and a PIXcel solid-state line detector operating in receiving mode with a 0.165 mm active length corresponding to a 2 opening < 0.04. Rocking curves were acquired by scanning in while keeping the 2 value fixed to detect the desired 002 or 111 reflections. scans were acquired using a fixed 2 value corresponding to Ir 113 reflections and using an offset in of 25.24° and 29.50° for 001 and 111 oriented grains, respectively. X-ray reflectivity (XRR) measurements were performed in the same system with the same incident and diffracted beam optics as described above. The measured XRR data were fitted using the PANalytical X'Pert Reflectivity software which employs the Parratt formalism. For this purpose, the densities for Ir, MgO, and Al2O3 were kept fixed at 22.4, 3.58, and 3.98 g/cm 3 , while the free fitting parameters were the Ir layer thickness, the root-mean-squared (rms) surface roughness, and the rms layer-substrate interface roughness.
Crystallographic orientation maps and pole figures were obtained using electron backscatter diffraction (EBSD) in a VERSA scanning electron microscope (SEM) column with a NordlysNano detector from Oxford Instruments at a pressure of 10 -6 torr. Secondary electron micrographs and backscatter patterns were obtained with a 10 keV and 1 nA electron beam at a 13 mm working distance. The collected patterns were acquired and analyzed using the Flamenco acquisition software and the HKL Channel 5 software packages from Oxford Instruments, respectively.
Figure 1 shows typical x-ray diffraction results from three representative samples. The scans in Fig. 1(a) are from a 100.6 nm-thick Ir layer deposited on MgO(001) substrates at Ts = 1000 C. The -2 pattern shows a double peak feature due to CuKα1 and CuKα2 reflections from Preprint, published as: Atharv Jog and Daniel Gall, "Resistivity size effect in epitaxial iridium layers," J. Appl. Phys. 130, 115103 (2021); https://doi.org/10.1063/5.0060845 the substrate MgO 002 planes and a peak at 2 = 47.22° which is attributed to Ir 002. This is the only detectable peak from the Ir layer over the entire measured 2 = 10-90, indicating a 001 out of plane orientation. The discontinuity of the pattern at 2 = 41.32° is an experimental artifact due to electronic noise in the line detector caused by the strong reflection from the substrate. The inset shows an -rocking curve of the Ir 002 peak from the same sample, indicating a full-width at halfmaximum (FWHM) of Γ ω 002 = 0.37 which confirms the strong out-of-plane alignment. Figure 2 shows representative x-ray reflectivity curves for Ir layers with d = 25.4 and 23.3 nm deposited on MgO(001) and Al2O3(0001) substrates, respectively. The measured intensity is plotted as solid red and green lines in a logarithmic scale as a function of the scattering angle 2θ = 0.2-4.0°. The dotted curves are the result from curve fitting using the Parratt formalism for reflectivity and are shifted by a factor of four for clarity purposes. The data fitting describes well the measured characteristic Kiessig fringes and provides values for the film thickness, density, and rms surface and interface roughness. The determined thicknesses d = 25.4 and 23.3 nm are in good agreement (<4% deviation) with 26.6 and 22.9 nm from deposition rate calibrations. The measured surface roughness = 0.33 and 0.32 nm indicates smooth Ir surfaces on both MgO(001) and Al2O3(0001) substrates. Similarly, the roughness values of the layer-substrate interfaces are 0.63 and 0.27 nm, suggesting negligible chemical reaction at the interface. We note that adjusting the fitting procedure by adding a 0.2-nm-thick Ir-oxide surface layer to the model decreases the fit quality (increases 2 ), suggesting that our Ir layers have a negligible (< 0.2 nm) surface oxide. The thickness and roughness data from XRR analyses of all Ir layers in this study are summarized in Tables 1 and2, and briefly discussed below. We note that the layer thickness for the thickest sample with d = 133.1 nm is determined from the deposition rate and time, since the spacing between XRR fringes is too small to be resolved for this sample.
XRD and XRR analyses are performed for all 22 samples from the four series in this study, yielding the following overall results:
(1) Ir deposited on MgO(001) at Ts = 1000 °C yields epitaxial single-crystal Ir(001) layers with an increasing crystalline quality with increasing thickness, as evidenced by the Ir 002 rocking curve width which decreases from Γ ω 002 = 1.3 to 0.37 for d = 7.7 -100.6 nm. The RMS roughness measured from XRR is small ( ≤ 0.53 nm) for thick (d ≥ 19.5 nm) layers but becomes larger ( = 0.87-1.1 nm) at small thickness d = 7.7-11.5 nm (as also summarized in Table 1). This increase is attributed to a discontinuous microstructure for d ≤ 11.5 nm. More specifically, the layer with d = 7.7 nm consists of separated islands with negligible coalescence as determined from SEM micrographs as the one shown as Supplementary Figure S1. Increasing d to 11.5 nm results in considerable but incomplete coalescence as indicated by the micrograph shown as Supplementary Figure S2, showing partial surface coverage with elongated islands. This discontinuous microstructure for d < 19.5 nm is attributed to the thermodynamic driving force for dewetting, caused by the surface energy which is expected to be larger for the metallic Ir layer than the ceramic MgO substrate. The discontinuous microstructure causes a large sheet resistance and motivates growth at lower temperatures as done in the following sample series.
(2) Ir deposited on MgO(001) at Ts = 700 °C also yields epitaxial single-crystal Ir(001) layers. A representative set of XRD scans is provided as supplementary Figure S3. The Ir 002 rocking curve width ranges from Γ ω 002 = 1.9 to 0.67° for d = 6.8 -133.1 nm, indicating a lower crystalline quality than for Ts = 1000 °C. The surface roughness ≤ 0.46 nm is smaller for Ts = 700 °C than for Ts = 1000 °C for all d. Thus, reducing Ts from 1000 °C to 700 °C is effective in limiting the adatom mobility to suppress dewetting and the formation of a discontinuous microstructure at small d. However, the limited atomic diffusion also results in a lower crystalline quality.
(3) Ir deposition on MgO(001) at Ts = 700 °C with subsequent step-wise vacuum annealing to 1000 °C results in a microstructure which is strongly affected by the layer thickness. Thick layers with d = 46.4 -103.9 nm are epitaxial Ir(001) single crystals with a good crystalline quality (Γ ω 002 = 0.6-0.8) and small rms surface roughness ( ≤ 0.39 nm). In situ annealing causes a small/negligible 3-9% reduction in Γ ω 002 and a negligible improvement in the surface smoothness in comparison to the as-deposited layers with Ts = 700 °C, suggesting no effect from annealing for layers with d ≥ 46.4 nm. However, as discussed below, annealing causes an overall reduction in the resistivity which we attribute to some improvement in crystalline quality or surface smoothness that is not detected by our XRD and XRR analyses. In contrast to these thick layers, annealed layers with d = 5.2, 9.9 and 19.5 nm exhibit a multi-domain microstructure with primarily 111oriented and some residual 001-oriented domains, with a measured XRD 111-vs-002 peak intensity ratio I111/I002 = 15, 117, and 4, respectively. That is, while the as-deposited layers exhibit a pure 001 orientation as discussed above, subsequent annealing causes a transition to microstructures with 111-oriented grains. We attribute this to renucleation of 111-oriented grains during the annealing procedure. The driving force for this transition is not known but may be related to strain relaxation or a reduction in the surface energy which is lower for Ir(111) than Ir(001). 50 The transition is most prominent for thin (d ≤ 9.9 nm) layers, is less dominant for d = 19.5 nm as indicated by the smaller I111/I002, and is completely suppressed for d ≥ 46.4 nm. The measured rocking curve widths of the 111-oriented grains, Γ ω 111 = 0.054, 0.049, and 0.031 for d = 5.2, 9.9 and 19.5 nm, respectively, are approximately an order of magnitude smaller than the asdeposited Γ ω 002 , indicating an excellent crystalline quality of the renucleated grains. Γ ω 111 decreases with decreasing d, suggesting wider renucleated domains for the thinner layers, consistent with the EBSD data presented below. In addition, the measured = 0.23, 0.16, and 0.39 nm indicate that the surface roughness during annealing (including renucleation) decreases by 36-65%.
(4) All layers deposited on Al2O3(0001) at Ts = 700 C and followed by in situ stepwise annealing to 1000 C are 111-oriented two-domain epitaxial layers with Γ ω 111 decreasing from 1.9 -0.36 for d = 6.4 -89.3 nm. The surface roughness is small, ≤ 0.46 nm, for all layers. Their microstructure consists of two epitaxial domains which are related to each other by a 60 or 180 rotation about the [111] axis along the growth direction. We attempt to estimate the average separation between domain boundaries from the in-plane coherence length determined from the -rocking curve width. 51 This analysis is convoluted because the rocking curves consist of a broad and narrow peak from strained and relaxed sections of the layer. The broad peak widths yield an in-plane coherence length that increases from Dbroad = 6.5 to 15.5, 19.3, 27.0, and 35.3 nm for d = 6.4, 12.6, 23.3, 46.7, and 89.3 nm, while the coherence lengths from narrow peaks indicate an approximately thickness-independent Dnarrow = 300 -400 nm. The large variation in the domain sizes based on the XRD analyses, from 6.5 -400 nm for these Ir(111)/Al2O3(0001) layers, may be an artifact caused by a non-uniform development of misfit dislocations and related strain relaxation. Correspondingly, alternate measurements to determine the domain size are used, as described in the following. Figure 3 shows secondary electron SEM micrographs, EBSD inverse pole figure (IPF-X) orientation maps and {100} pole figures from four representative Ir layers. The micrograph in Fig. 3(a) is from a 100.6-nm-thick epitaxial Ir(001)/MgO(001) layer grown at Ts = 1000 C. The micrograph exhibits negligible contrast variations, indicating a continuous layer with a relatively smooth surface and no pits. This is consistent with the small surface roughness = 0.53 nm measured by XRR. We note that pits due to dewetting would result in evident contrast, similar to what is detected for thin layers that are annealed [supplementary Fig. S4]. The IPF-X orientation map in Fig. 3(a) is from the same sample area as the secondary electron micrograph. It is completely red, indicating a single [100] in-plane orientation. That is, Ir[100] is aligned with the horizontal x-axis which also corresponds to the MgO[100] direction, confirming the single-crystal Ir(001)/MgO(001) cube-on-cube epitaxial relationship detected by the XRD results presented in Fig. 1(a). This is also consistent with the Ir{100} pole figure in Fig. 3 with respect to each other. The two domains appear in nearly identical shades of green in the IPF-X map, indicating that both exhibit an Ir<1 ̅ 01> type in-plane orientation along the horizontal direction of the micrograph which corresponds to the in-plane Al2O3[11 ̅ 00] substrate direction. Thus, this analysis confirms the layer-substrate epitaxial relationship determined from XRD, with the two Ir domains having their in-plane Ir [1 ̅ 01] or Ir[011 ̅ ] direction || Al2O3 [11 ̅ 00]. A quantitative analysis of the IPF-X orientation map yields an average lateral domain size Davg = 88 nm, which is within the range estimated from the XRD rocking curves discussed above.
Fig. 3(c) shows orientation data from a 9.9-nm-thick Ir layer deposited on MgO(001) at 700 C and stepwise annealed to 1000 C. The secondary electron micrograph shows contrast variations which suggest a polycrystalline microstructure with 20-70 m wide grains. The corresponding IPF-X map from the same sample area confirms that these apparent grains are, in fact, domains with distinct in-plane orientations. The corresponding {100} pole figure exhibits 12 peaks, indicating four 111-oriented domains which are 90 rotated with respect to each other about the 111 growth direction. Thus, the orientation map shows four Ir domains colored in purple, violet, green, and green, which have their [1
and [1 ̅ 01], directions parallel to MgO[100], respectively, suggesting local epitaxy of each domain. We note that the domains are very large, their width of 20-70 m is over three orders of magnitude larger than their height, which corresponds to the layer thickness of 9.9 nm. Thus, we hypothesize that the domains form in a nucleation-limited growth during annealing of the as-deposited epitaxial Ir(001) layer. Nucleation may occur at defect sites at the layer-substrate interface, followed by subsequent lateral near diffusion-less growth. The driving force for this renucleation is likely a combination of the surface energy which is lower for the close-packed Ir(111) vs the Ir(001) surface as well as the out-annealing of dislocations and associated strain fields caused by the misfit of epitaxial asdeposited Ir(001) on MgO(001). The pole figure plotted in Fig. 3(c) has no detectable central peak, indicating that the density of residual 001-oriented domains is negligible and that renucleation during annealing results in a nearly complete transition from 001 to 111-oriented domains, consistent with the 117 times stronger 111 vs 002 peak in the -2 pattern from the same sample in Fig. 1(b). In contrast, the polefigure in Fig. 3(d) from an annealed layer with d = 19.5 nm exhibits both, 12 peaks at a 54 angle as well as a central peak and four peaks at 90, indicating a mixture of the domains discussed in Figs. 3(a) and(c). More specifically, a fraction of this layer consists of four 111-oriented domains that appear in purple, violet, green and green in the IPF-X map, but also residual 001-oriented Ir which appears in red and has not transformed during annealing. The micrograph in Fig. 3(d) is purposely recorded from an area of the sample with approximately equal fractions of renucleated and residual domains to illustrate the mixed domain microstructure. However, a larger area analysis shown in Supplementary Fig. S5 suggests that this layer is predominantly 001 oriented with a small fraction of renucleated 111 domains. We note that the XRD -2 pattern from this sample (not shown) has a 111 vs 002 peak intensity ratio of 4, which is primarily attributed to the much stronger crystalline alignment or the renucleated 111 domains. The factor of 4 is much smaller than 117 mentioned above for the 9.9-nm-thick layer, confirming the observed trend of a considerably smaller fraction of grain renucleation for the thicker layer.
We note that reducing the thickness further to below ~10 nm results in a discontinuous microstructure with a partial coverage of the substate by the deposited Ir, as determined by electron microscopy analyses. An example micrograph from a d = 5.2 nm layer deposited at Ts = 700 C followed by in situ annealing is provided as Supplementary Figure S4. It shows 40-200 nm wide holes in the layer which extend to the substrate and are terminated by six facets along Ir <110>, indicating dewetting for this d = 5.2 nm layer during deposition at 700 C and/or annealing at 1000 C, similar to what has been reported for single-crystal Ni(001) layers grown on MgO(001) at room temperature and annealed to 900 C. 52 We attribute the dewetting to the larger surface energy of the metallic Ir layer than the ceramic MgO substrate. An out-of-plane orientation map from the same d = 5.2 nm sample indicates strong 111 preferred orientation with no evidence of residual 001-domains, in agreement with XRD -2 scans. The corresponding {100} pole figure exhibits 6 poles indicating two epitaxial domains in contrast to 4 domains observed for d = 19.5 and 9.9 nm layers, suggesting possibly an even faster lateral grain growth for the thinner layer, consistent with the narrowest rocking curve width for this d = 5.2 nm layer.
In summary, the EBSD analyses confirm the XRD results, showing that layers deposited on MgO(001) at 1000 C are epitaxial single-crystal Ir(001) while layers grown on Al2O3(0001) form 111-oriented two-domain microstructures with an average domain width D = 88 nm. Most interesting are the layers deposited on MgO(001) at 700 C and annealed to 1000 C: The asdeposited layers are epitaxial Ir(001). Annealing causes renucleation of 111-oriented grains for d ≤ 19.5 nm. The 111-oriented grains are very wide, with aspect ratios exceeding three orders of magnitude, and form four domains with a local epitaxy with the substrate. Annealing causes complete transformation to a 111-oriented layer for d = 5.2 and 9.9 nm, but only partial renucleation for the d = 19.5 nm layer which exhibits a large fraction of residual Ir(001) domains, and no renuclation for d ≥ 46.4 nm, suggesting a clear thickness effect. To explore this further, an additional layer was deposited with a measured d = 10.0 nm, which is identical (within experimental uncertainty) to the d = 9.9 nm layer. Its EBSD analysis (see Supplementary Figure S6) indicates a significantly higher fraction of residual 001-oriented domains as well as a higher fraction of random grain boundaries than the 9.9 nm thick Ir layer discussed previously. In fact, this new d = 10.0 nm exhibits a microstructure comparable to the d = 19.5 nm layer presented in Fig. 3(d). This result suggests a considerable stochasticity in the renucleation process. From the overall data, we derive an approximate critical thickness 5 nm < dc ≤ 10 nm for complete transformation while partial transformation occurs between d = 10 and 40 nm. The large domain sizes particularly for completely transformed layers minimizes electron scattering at grain (domain) boundaries, as discussed in Section IV.
Figure 4 shows the resistivity ρ measured in situ at 295 K and at liquid nitrogen at 77 K vs thickness d from the four series of Ir layers presented above. The data is also summarized in Tables 1 and2. The plotted ρ increases with decreasing d for all four series and at both temperatures. This is attributed to electron scattering at the Ir top and bottom surfaces. The plotted blue triangles are data from the samples deposited at Ts = 1000 °C. The thickest layer (d = 100.6 nm) in this series has a room-temperature resistivity ρ = 5.37 ± 0.26 µΩcm. This is identical (within experimental uncertainty) to the reported Ir bulk resistivity ρo = 5.2 µΩcm, 53 indicating a negligible resistivity size effect for d = 100.6 nm at 295 K. The resistivity increases to ρ = 5.44 ± 0.02 and 6.04 ± 0.04 µΩcm with decreasing thickness d = 46.0 and 19.5 nm. Decreasing the thickness further to d = 11.5 nm leads to a dramatic 248% resistivity increase to ρ = 18.7 ± 0.2 µΩcm which is outside the plotted range, while the resistivity of the layer with d = 7.7 nm could not even be measured with our experimental setup, indicating ρ > 10 6 µΩcm and suggesting that the 7.7-nm-thick sample is discontinuous. This is consistent with the dewetting arguments presented above and the relatively large measured surface roughness σ = 1.1 and 0.87 nm for the nominally 7.7 and 11.5 nm thick layers, respectively, suggesting that the thin film nuclei have not coalesced for d = 7.7 nm and that coalescence occurs approximately at d = 11.5 nm, resulting in a partially discontinuous layer and a correspondingly high ρ for the 11.5 nm thick layer. We note that the latter layer has a measured σ = 0.87 nm which is twice the roughness of the d = 19.5 and 46.0 nm layers, such that the large ρ can partially be attributed to a roughness effect. 17,54 The purple diamonds in Fig. 4 indicate the measured resistivity of six layers deposited at a lower Ts = 700 °C. The resistivity could be measured for all thicknesses d = 6.8-133.1 nm and the surface roughness is relatively low (σ < 0.46 nm) for all samples in this series, indicating that the lower Ts results in continuous layers which is attributed to the reduced adatom mobility at lower temperatures. The room-temperature resistivity of the thickest layer with d = 133.1 nm is 14% larger than the reported Ir bulk resistivity, 53 indicating considerable electron scattering at crystalline defects. In fact, all layers deposited at Ts = 700 °C are significantly (13-27%) more resistive than continuous layers with a comparable d but deposited at Ts = 1000 °C. Thus, the reduction from 1000 to 700 °C results in a degradation of the crystalline quality, which is in perfect agreement with the measured 64-81% increase in the measured rocking curve width.
The red circles in Fig. 4 show the resistivity from Ir layers deposited at Ts = 700 °C followed by in situ step-wise annealing to 800, 900, and 1000 °C for 30 min each. This deposition and annealing procedure is chosen in an attempt to simultaneously obtain the high crystalline quality characteristic for Ts = 1000 °C with the continuous layer microstructure at small d observed for Ts = 700 °C. However, as discussed above, annealing causes a transformation into a multidomain polycrystalline microstructure containing renucleated 111-domains for d ≤ 19.5 nm. The resistivity ρ = 6.41 ± 0.31 µΩcm of the d = 9.9 nm layer is particularly low. It is 34% below the as-deposited layer (purple diamond) and just 23% above the Ir bulk resistivity. In comparison, the resistivity for 10-nm-thick epitaxial Cu(001), 8 Co(0001), 37 W(110), 45 Mo(110), 38 Rh(001), 44 and Ru(0001) 42 layers is 168%, 89%, 86%, 64%, 54%, and 30% larger than their bulk resistivity, respectively. That is, the resistivity size effect for this Ir layer is considerably smaller than for other known metals. We attribute the resistivity reduction during annealing to a considerable increase in the crystalline quality and surface smoothness during the renucleation process. The XRD, XRR and EBSD analyses discussed above indicate a reduction in the rocking curve width by 1-2 orders of magnitude, a 3-fold reduction in the surface roughness to = 0.16 nm, and a domain size of 10-200 m. The latter value is 10 3 times larger than the predicted electron mean free path such that electron scattering at grain (domain) boundaries has a negligible effect on the resistivity. The annealed layer with a two times larger thickness d = 19.5 nm has a ρ = 6.55 ± 0.12 µΩcm that is slightly larger (equal within experimental uncertainty) than for d = 9.9 nm. This is opposite to the trend of an increasing ρ with decreasing d and is attributed to the incomplete transformation (presented above) which results in residual 001 oriented domains that have a lower crystalline quality and a 2.4 times higher surface roughness than the renucleated 111-oriented domains. We note that ρ for this layer is 8% larger than for the epitaxial Ir(001) layer with a similar d but deposited at Ts = 1000 °C (blue triangle). This difference is attributed to a 25% larger Γ ω 002 = 1.12°
for the annealed layer in comparison to Γ ω 002 = 0.90° for the layer deposited at Ts = 1000 °C, suggesting a higher density of crystalline defects for this annealed layer and consequently a higher resistivity due to additional electron scattering at these defects. The thinnest annealed layer with d = 5.2 nm has a considerably larger ρ = 11.3 ± 0.5 µΩcm which we attribute to the non-uniform surface coverage caused by dewetting during annealing as discussed above and shown in Fig. S4.
The resistivity of the fourth series of Ir layers deposited on Al2O3(0001) substrates is plotted in Fig. 4 as green square symbols. The measured values are also tabulated in Table 2. Like for the other Series, ρ increases with decreasing d which is attributed to electron scattering at surfaces. However, the resistivity is larger than for the Ir deposited on MgO(001) at 1000 °C or at 700 °C and annealed to 1000 °C. This is attributed to additional electron scattering at the 60° inplane rotated domain boundaries for the Ir(111)/ Al2O3(0001) layers, as discussed quantitatively in Section IV.
Tables 1 and2 include ex situ room-temperature resistivity values. They are measured after sample removal from the deposition system and low temperature measurements, as described in Section II. The values are slightly larger than the in situ ρ measured before air exposure. However, the increase is smaller than the experimental uncertainty for most samples and < 6% for all Ir layers in this study. This suggests that Ir surface oxidation causes a slight or negligible decrease in surface scattering specularity as discussed in Section IV. 1 and2. The values are lower than for 295 K, due to the reduced electron-phonon scattering at 77 K, but the increase in ρ with decreasing d is nearly independent of temperature. Thus, the resistivity difference ρ between the two temperatures is nearly thickness independent. More specifically, ρ = 4. 40
DISCUSSION We now discuss the measured resistivity size effect in epitaxial Ir layers using the semiclassical transport models by Fuchs and Sondheimer (FS) for surface scattering 26,27 and Mayadas and Shatzkes (MS) for grain boundary scattering. 28 The FS model describes resistivity scaling due to electron scattering at the surfaces by two parameters: (1) the electron phonon scattering mean free path λ and (2) the surface scattering specularity p which can be further divided into p1 and p2 for the top Ir surface and bottom Ir/substrate interface. 12 Measured ρ vs d data typically cannot uniquely determine both p and λ. 8 To circumvent this problem, we set p1 = p2 = 0 (assuming electron surface scattering is completely diffuse) and obtain a lower bound to the effective mean free path eff by fitting a FS curve to the measured resistivity using the exact version of the FS model. 12,42 Thus, in the following, the presented λ values should be interpreted either as (a) a lower limit of possible λ values, or (b) the λ under the assumption of completely diffuse surface scattering. We note that our data analysis is complicated by the fact that epitaxial Ir layers in our study exhibit (a) film discontinuity for d < 19.5 (Ts = 1000 °C), (b) poor crystalline quality (Ts = 700 °C), or (c) a multi-domain microstructure (Ts = 700 °C followed by in situ stepwise annealing) on MgO(001) and Al2O3(0001) substrates.
We begin our analysis by fitting the FS model to resistivity data from Ir(001) oriented layers grown at Ts = 700 °C, because these are epitaxial single crystal layers with no grain boundaries and negligible dewetting. The solid and dashed purple lines in Figure 4 are the result from such curve fitting to the resistivity measured at 295 and 77 K, respectively, using as fitting Preprint, published as: Atharv Jog and Daniel Gall, "Resistivity size effect in epitaxial iridium layers," J. Appl. Phys. 130, 115103 (2021); https://doi.org/10.1063/5.0060845 parameters the bulk resistivity ρo and the effective electron mean free path λeff. This yields ρo = 5.75 ± 0.09 µΩcm and λeff = 14.3 ± 0.8 nm at 295 K, and ρo = 1.07 ± 0.12 µΩcm and λeff = 83 ± 16 nm at 77 K, as also listed in Table 3. These values indicate that reducing the temperature from 295 to 77 K lowers ρo five-fold but increases λ six-fold, resulting in an approximately temperatureindependent product ρoλeff = (8.2 ± 0.4) × 10 -16 and (8.9 ± 1.8) × 10 -16 Ωm 2 at 295 K and 77 K, respectively. The decrease in ρo and increase in λeff are a direct consequence of the reduced electron-phonon scattering and the temperature-independence of ρoλeff is expected from classical electron transport models with a negligible temperature-dependence in the electronic structure. 39 We note that the ρo values are 11% and 62% above the reported bulk resistivity at 295 and 77 K, respectively. This is attributed to electron scattering at crystalline defects which causes an increase in ρo. The defects may include threading dislocations, stacking faults, vacancies, strain-fields near the layer-substrate interface and edge dislocations which account for crystalline misalignment. The defects are due to the limited adatom mobility at Ts = 700 °C which, as previously discussed, leads to a limited crystalline quality with a relatively large XRD rocking-curve width Γ ω 002 = 0.67 -1.9°.
The measured Γ ω 002 decreases with increasing thickness such that the defect density is likely also a function of d and, in turn, the "bulk resistivity" is no longer independent of d for this sample series, as is assumed during the fitting procedure. Consequently, the ρoλeff value deduced for this series may not represent an intrinsic property of Ir because it could be strongly affected by the thicknessdependence in the defect concentration. We note that we do not consider grain boundary scattering in this analysis because a small-angle boundary with a ~1° tilt (corresponding to the rocking curve width) corresponds to an array of edge dislocations which are vertically separated by 16 nm, assuming the Burgers vector equals the interatomic spacing of 0.27 nm. Thus, "grain boundaries" for d = 10-50 nm would consist of zero to three dislocations which are more appropriately described as discrete crystalline line defects rather than as a 2D grain boundary.
We apply a similar fitting procedure for Ir layers grown at 1000 °C, yielding the solid and dashed blue lines in Figure 4. The layers with d = 11.5 and 7.7 nm are not considered for this data analysis due to their discontinuous microstructure and resulting large resistivity. Data fitting yields a room temperature ρo = 5.17 ± 0.08 cm which matches the reported Ir bulk resistivity of 5.2 cm, suggesting negligible defect scattering which renders the deduced data more reliable than for Ts = 700 °C. In contrast, a minor effect from defect scattering can be detected from analysis of the low-temperature data yielding ρo = 0.80 ± 0.04 cm which is 21% above the reported 0.66 cm for bulk Ir at 77 K. 53 The fitting indicates a room-temperature λeff = 7.4 ± 1.2 nm and a corresponding temperature-independent ρoλeff = (3.8 ± 0.6) ×10 -16 and (3.5 ± 0.4) ×10 -16 Ωm 2 for 295 and 77 K, respectively. These values are quite small, indicating a small resistivity scaling for Ir. More specifically, ρoλeff = 3.8 ×10 -16 Ωm 2 is 1.7, 2.6, 3.2, 1.3 and 1.2 times smaller than the reported values for competing interconnect materials like Cu with 6.7×10 -16 Ωm 2 , 8 W with 10.1×10 -16 Ωm 2 , 45 Co with 12.2×10 -16 Ωm 2 , 37 Ru with 5.06×10 -16 Ωm 2 , 42 and Rh with 4.5×10 -16 Ωm 2 , 44 respectively. That is, ρoλeff for Ir is smaller than that of all previously measured elemental metals, indicating great promise for Ir as an alternative metal for narrow high-conductivity interconnects. The impact of this small ρoλeff on the resistance of polycrystalline interconnect lines has been estimated in Refs. 38 and 41, suggesting that Ir will outperform all other elemental metals for narrow lines. The measured ρoλeff = 3.8 ×10 -16 Ωm 2 for Ir is also in excellent agreement with ρoλ = 3.69 ×10 -16 Ωm 2 calculated from first principles. 39 The red solid and dashed lines in Fig. 4 are from fitting ρ vs d data from the Ir layers deposited at 700 °C and annealed to 1000 °C. The analysis excludes the layer with d = 5.2 nm due to its non-uniform surface coverage. The resulting mean free paths λeff = 5.1 ± 1.8 and 11.8 ± 4.8 nm at 295 and 77 K, respectively, and the corresponding ρoλeff = (2.8 ± 1.0) ×10 -16 and (1.5 ± 0.6) ×10 -16 Ωm 2 . We note that the uncertainty in the deduced ρoλeff is quite large, as the data is not very well described by the FS curve. We attribute this to a changing microstructure with varying d. More specifically, as discussed above, d ≥ 46.4 nm results in an 001-oriented epitaxial microstructure, the layer with d = 19.5 nm exhibits a mixture of residual 001 and renucleated 111oriented domains, while the two nominally identical layers with d = 9.9 and 10.0 nm show a different degree of transformation: The d = 9.9 nm layer has almost completely transformed into a multi-domain 111-oriented microstructure and has a 10% lower resistivity than the d = 10.0 nm layer with a mixed-domain microstructure similar to that for d = 19.5 nm. This suggests that the renucleation process leads to a reduction in the resistivity which we attribute to the excellent crystalline quality and low surface roughness of renucleated 111-oriented Ir domains, resulting in the lower resistivity for the d = 9.9 nm layer which exhibits a nearly complete transformation. To summarize: the measured ρ is lower for the annealed layers than for the as deposited Ts = 700 °C samples, indicating that annealing improves the crystalline quality and lowers ρ. However, for samples where annealing causes only a limited or no renucleation of the 001-oriented crystal, the measured ρ is larger than for Ts = 1000 °C. This is because growth at 700 °C followed by annealing at 1000 °C leads to lower crystalline perfection than growth at 1000 °C, which is due to the lower activation barrier for surface than bulk diffusion which facilitates more effective mass transport during deposition than post-deposition annealing. In contrast, samples with nearly complete renucleation during annealing exhibit the largest crystalline quality and a corresponding low resistivity, exemplified by the d = 9.9 nm layer. Due to this thickness-dependent crystalline quality, the ρoλ product deduced from the third series likely underestimates the actual intrinsic value of Ir.
We discuss now the resistivity of Ir(111) layers grown on Al2O3(0001) substrates. Ir(111) layers have an increased resistivity which we attribute to additional electron scattering at the domain walls between 60° in-plane rotated domains. The approximate form of the MS model predicts that electron scattering at grain boundaries causes an additive resistivity term ρgb = 3ρoλR/[2D(1-R)]. 12 Thus, ρgb is a function of ρoλ, the grain size D and the reflection coefficient R. For our Ir(111)/Al2O3(0001) layers, D corresponds to the average lateral domain size Davg = 88 nm, as determined by EBSD. Both XRD and EBSD analyses indicate that the grain boundary type (60° rotation about the <111> axis) is independent of d. We therefore assume R and D and, in turn, also ρgb to be independent of the Ir(111) layer thickness. Correspondingly, data fitting for the Ir(111) resistivity is done by adding a constant ρgb to the FS model predictions, where ρgb is a thickness-independent fitting parameter. We use a fixed ρo = 5.17 µΩcm at 295 K and ρo = 0.80 µΩcm at 77 K from the layers with Ts = 1000 °C to perform data fitting, yielding the solid and dashed green lines in Fig. 4 and values for ρoλeff of (4.5 ± 0.5)×10 -16 and (4.7 ± 0.4)×10 -16 Ωm 2 at 295 K and 77 K, respectively, and a ρgb = 0.86 ± 0.19 and 0.84 ± 0.12 µΩcm at 295 K and 77 K, respectively. These two ρgb values are identical within experimental uncertainty, indicating that grain boundary scattering is temperature-independent, as expected from the approximate MS model. We determine the grain boundary reflection coefficient R from the above expression for ρgb, using Davg = 88 nm and ρoλ and ρgb from the data fitting, yielding R = 0.52 ± 0.02 and 0.51 ± 0.03 at 295 K and 77 K, respectively. These values are larger than the previously measured R = 0.26, 2 0.43, 55 or 0.30 12 for Cu but are within the large range of reported first-principles predictions for the reflection coefficient R = 0.02 -0.56 of high-symmetry grain boundaries ( 3, 5, 9, and 11) in metals including Ir, Rh, Cu, Pt, Pd, and Co. 16,25,44,56,57 We note that our measured R = 0.52 ± 0.02 is for a specific grain boundary which is characterized by a 60° rotation about the <111> axis. Similarly, the high-symmetry coherent 3 boundary for which the predicted R = 0.16 56 or 0.25 41 can also be defined by a 60° rotation about the <111> axis. However, for the former the grain boundary is parallel and for the latter perpendicular to the <111> rotation axis, such that the large difference in R may be attributed to the boundary orientation even for identical relative grain orientations.
Our results indicate a slight increase in the room-temperature resistivity upon air exposure for all four Ir sample series. This increase can be attributed to experimental uncertainty but may also indicate a decrease in the surface scattering specularity caused by surface oxidation, similar to what has previously been reported for Ni, 47 Nb, 46 Co, 37 and Cu. 8 To quantify this effect, we follow the procedures in Refs. 44,46,47 and attribute the resistivity increase to a decrease in the room-temperature scattering specularity p1 at the top surface of the Ir layers. Data fitting of the measured ex situ room temperature resistivity yields p1 = -0.09 0.03, -0.14 0.11, -0.46 0.36, and -0.12 0.10 for the four Ir layer series grown on MgO(001) at Ts = 700 °C, 1000 °C, Ts = 700 °C and annealed, and on Al2O3(0001), respectively. The overall average p1 = -0.20 0.15 is relatively modest and similar in magnitude to the error bar, confirming that the observed effect can potentially be to experimental uncertainty. Its magnitude is smaller than the reported p1 = -0.6 or -0.7 reported for Cu, 8,20 -0.4 for Ag, 13 and -0.9 or -0.8 for Nb, 46 and similar to the negligible air-exposure effect reported for Ru, 42 W, 45 and Rh. 44 The small to negligible effect of oxygen exposure on the electron scattering at Ir surfaces is promising for potential liner-free Ir interconnects which would be in direct contact with an oxidizing dielectric.
V. CONCLUSIONS Ir growth on MgO(001) at Ts = 1000 C leads to smooth epitaxial Ir(001) layers for d 19.5 nm, but to a high roughness and a discontinuous layer if the thickness is reduced to d = 11.5 and 7.7 nm, respectively. The continuity problems are resolved with a reduced Ts = 700 C which, however, causes a lower crystalline quality with a 45% smaller in-plane x-ray coherence length. Growth at Ts = 700 C followed by step-wise in situ annealing to 1000 C results in smooth layers with a high crystalline quality but grain re-nucleation and a multi-domain epitaxial microstructure. That is, the Ir microstructure and surface morphology is strongly affected by both deposition conditions and layer thickness, making direct experimental quantification of the resistivity size effect challenging. Fitting the measured ρ vs d at 295 and 77 K to the Fuchs-Sondheimer model indicates a lower-bound room-temperature effective mean free path λeff = 7.4 ± 1.2 nm and a corresponding temperature-independent ρoλeff = (3.8 ± 0.6) ×10 -16 Ωm 2 . This ρoλeff is in good agreement with the ρoλ = 3.69×10 -16 Ωm 2 determined from first principles. However, it is 116% larger for as-deposited layers at Ts = 700 C and 26% smaller for annealed layers deposited at Ts = 700 C. We note that the small ρoλeff = (2.8 ± 1.0) ×10 -16 Ωm 2 evaluated from the annealed layers has a relatively large uncertainty due to a non-uniform microstructure for the layers in this series: Layers with d 19.5 nm exhibit a mixture of residual 001 and renucleated 111 domains, with an increasing renucleated volume fraction as the layer thickness decreases. The renucleated domains exhibit a low surface roughness = 0.2 nm, a low x-ray diffraction rocking-curve width of 0.04, and are 20-70 m wide, corresponding to a >10 3 width-to-height aspect ratio. The resulting large distance between domain boundaries makes electron scattering at boundaries negligible. Ir(001)/MgO(001) layers with d ≥ 46.4 nm and Ts = 700 C do not undergo renucleation during annealing, yielding a lower crystalline quality and higher resistivity in comparison to layers grown directly at 1000 C. Ir growth on Al2O3(0001) substrates yields a two-domain epitaxial microstructure with an average domain size D = 88 nm, evaluated from electron backscatter diffraction orientation maps. The domain boundaries are described by a 60 rotation about the <111> axis and cause a thickness independent resistivity contribution ρgb = 0.86 ± 0.19 and 0.84 ± 0.12 µΩcm at 295 and 77 K, indicating an electron reflection coefficient R = 0.52 ± 0.02. The overall results suggest that resistivity scaling in Ir is strongly influenced by microstructural features including strain fields from misfit-dislocations and/or surface/interfacial roughness. The Ir(001)/MgO(001) layer series deposited at Ts = 1000 C is likely the most representative to quantify the intrinsic Ir resistivity scaling, due to its high crystalline quality and small surface roughness which are nearly thickness-independent for d ≥ 19.5 nm. The measured ρoλeff = (3.8 ± 0.6)×10 -16 Ωm 2 from this series is quite small. It is 1.7, 2.6, 3.2,1.3, and 1.2 times smaller than the reported values for competing interconnect materials including Cu, W, Co, Ru, and Rh, respectively, indicating great promise for Ir as an alternate metal in narrow high conductivity interconnects.
Preprint, published as: Atharv Jog and Daniel Gall, "Resistivity size effect in epitaxial iridium layers," J. Appl. Phys. 130, 115103 (2021); https://doi.org/10.1063/5.0060845