resistivity scaling and electron surface scattering in...

Manuscript, published as: Erik Milosevic, Sit Kerdsongpanya, Mary E. McGahay, Amirali Zangiabadi, Katayun Barmak, Daniel Gall, “Resistivity scaling and electron surface scattering in epitaxial Co(0001) layers,” J. Appl. Phys. 125, 245105 (2019) https://doi.org/10.1063/1.5086458

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Resistivity Scaling and Electron Surface Scattering in Epitaxial Co(0001) Layers

Erik Milosevic1, Sit Kerdsongpanya1, Mary E. McGahay1, Amirali Zangiabadi2, Katayun

Barmak2, Daniel Gall1

1Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY 12180, USA 2Department of Applied Physics and Applied Mathematics, Columbia University, 116th St & Broadway, New York, NY 10027,

USA

In situ and ex situ transport measurements on epitaxial Co(0001)/Al2O3(0001) layers with

thickness d = 7 - 300 nm are used to quantify the resistivity ρ scaling due to electron-surface

scattering. Sputter deposition at 300 °C followed by in situ annealing at 500 °C leads to single-

crystal layers with smooth surfaces (< 1 nm roughness) and an epitaxial relationship:

Co[0001]║Al2O3[0001] and Co[ 0110 ]║Al2O3[ 0211 ]. The measured ρ vs d data is well described

by the classical expression by Fuchs and Sondheimer at both 295 and 77 K, yielding a temperature-

independent product of the bulk resistivity times the mean free path ρo×λ and an effective room-

temperature λ = 19.5 ± 1.0 nm. The resistivity increases by 9 - 24 % upon air exposure for layers

with d ≤ 21 nm, indicating a transition from partially specular (p = 0.55 ± 0.05) to completely

diffuse (p = 0) surface scattering during native oxide formation. The overall results suggest that

Co exhibits a resistivity scaling that is comparable to W and approximately 2× smaller than that

of Cu, and that the resistance of narrow Co lines can be reduced considerably by engineering the

Co-liner interface to facilitate specular electron scattering.

I. INTRODUCTION

The decreasing width of interconnect lines in integrated circuits below the electron mean

free path leads to an increase in the resistivity1–3 which is caused by electron scattering at surfaces4–

8 and grain boundaries,9–14 and by an increasing effect from surface roughness.15–18 This resistivity

size effect represents a major challenge for the continued device downscaling and is most

problematic for the smallest interconnect features closest to the logic devices, that is the middle of

line (MOL) structures and the first levels of metallization for which the common metals of choice

are W and Cu, respectively. Tungsten is a common metal for MOL applications due to its resistance

to electromigration and device contamination, and its compatibility with wet cleans and other

downstream processes.19 Challenges for W metallization include CVD precursors that cause

defects in TiN liner layers,20 high resistivity ALD nucleation layers,21 and a negligible grain

growth which results in a large resistivity contribution from grain boundary scattering. The

resistivity size effect in W interconnects is exacerbated by these challenges and the requirement

for liner and nucleation layers which considerably reduce the available trench area for metal fill.19

Extensive studies of electron transport in W11,14,17,22–26 suggest an orientation-dependent size effect

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with measured electron mean free paths λ = 19 and 33 nm for conduction in (110)23,26 and (100)26

oriented films, respectively, with corresponding ρo×λ products of 10.1×10-16 and 17.5×10-16 Ωm2

for a bulk resistivity of 5.3 µΩcm.24,26 This ρo×λ product acts as a useful metric for quantifying the

resistivity size effect because it is a common scaling factor in the additive resistivities predicted

by the Fuchs and Sondheimer (FS)27,28 and Mayadas and Shatzkes (MS)29 models which describe

surface and grain boundary scattering, respectively. As a result, a metal with a low λ exhibits a

small resistivity size effect and the material with the smallest ρo×λ product is expected to have the

highest conductivity in the limit of thin films and narrow lines. Consequently, Cu with a relatively

large λ = 39 nm30 yields less conductive lines than some competing metals, despite its smaller bulk

resistivity, as has been shown with the resistivity cross-over between, for example, Ru and Cu for

a 7.4-nm-wide square wire.3 We note that these mean free path arguments have considerable merit

and are a useful starting point to explore possible interconnect metal replacement options.

However, they are based on semi-classical transport models which have been shown to diverge

from both experiments and pure quantum mechanical treatments for narrow (< 10 nm)

conductors.11,17,31,32 In addition, different metals are also expected to exhibit different surface

scattering specularities and grain boundary reflection probabilities which are also affected by their

surface5,6,16,33–35 and grain boundary9,12–14,36,37 structures and chemistries. Therefore, it is essential

that the predicted resistivity size effect for promising metals is experimentally verified using

idealized sample structures that limit ambiguities in data fitting and parameter space. This last

point is the motivation for the present study.

Co is a promising metal to replace W and/or Cu for narrow interconnect lines.38–41 It has

some processing advantages over W including benign CVD precursors, deposition without high-

resistivity nucleation layers, and grain growth through annealing.19 The theoretically predicted

ρo×λ products for Co in the basal plane and along the z-axis of its hexagonal structure are

7.31×10-16 and 4.82×10-16 Ωm2, yielding corresponding mean free paths λ = 11.8 and 7.77 nm for

a room temperature ρo = 6.2 µΩcm.42,43 These values are promising and suggest that Co has an

estimated 40% lower resistivity than W for 20-nm-wide interconnects. Experimental values for λ

of Co vary widely and tend to be larger than the theoretical prediction. The majority of studies

deposit polycrystalline Co films by evaporation and use the FS model to fit the measured resistivity

vs thickness data, yielding λ = 13 nm,44 or a range λ = 16.0 – 34.8 nm45 which converges to λ =

24.5 nm when accounting for grain boundary scattering,46 or also λ = 43-49 nm47 or λ = 36.5 nm.48

In contrast, a more recent study employing MOCVD deposited Co films reports a significantly

smaller λ = 5.97 nm.49 We attribute the large variation in these measured λ values to (i) the use of

polycrystalline films which contain grains with variable spacing (i.e. grain size), orientation, and

unknown electron reflection coefficients that are expected to be dependent on the boundary

orientation and structure.14 This increases the uncertainty in the classically fitted results4 because

both surface and grain boundary scattering cause similar resistivity contributions such that the two

effects typically cannot be uniquely separated.4,23 In addition, (ii) surface roughness is not well

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characterized in these studies but is known to significantly affect the resistivity size effect of thin

metallic films.15,17,18,50–54

In this paper, we use epitaxial Co(0001) films to determine the electron mean free path

from the measured resistivity vs thickness data. The key advantage of epitaxial layers is the

absence of grain boundaries, which removes the confounding effects from grain boundary

scattering, allowing a direct quantification of the resistivity due to surface scattering. Co layers

with thickness ranging from 7 to 300 nm were sputter deposited onto Al2O3(0001) and in situ

annealed to reduce surface roughness to a level which does not affect electron transport. Their

resistivity was measured in situ and ex situ and analyzed using the FS model,27,28 yielding a lower

bound for the room temperature mean free path of 19.5 ± 1.0 nm and suggesting a shift from

partially specular (p = 0.55) to diffuse (p = 0) surface scattering upon air exposure.

II. PROCEDURE

Co layers were deposited on Al2O3(0001) by DC magnetron sputtering in a three-chamber

ultrahigh vacuum system with a base pressure of 10-9 Torr.55–58 Single-side polished 10×10×0.5

mm3 c-plane sapphire substrates were cleaned in consecutive ultrasonic baths of trichloroethylene,

acetone, isopropyl alcohol, and deionized water, blown dry with dry N2, mounted on a Mo holder

with colloidal sliver paint, and inserted into the deposition system via a load lock. Before

deposition, substrates were degassed at the deposition temperature of 300 °C for 1 hour, and a 5-

cm-diameter Co (99.95% pure) target was sputter cleaned for 10 min. Deposition was done in 3

mTorr 99.999% pure Ar with a fixed power of 50 W to the Co target facing the substrate at 30 cm,

yielding a deposition rate of 0.5 ± 0.1 nm/s. The deposition time was adjusted to yield layer

thicknesses ranging from 7 to 300 nm. Subsequently, the samples were annealed in vacuum at 500

°C for 1 h, allowed to cool in situ to room temperature for 12 h, and transferred to an attached

analysis chamber for in situ transport measurements. All these steps were performed without air

exposure. The resistivity was measured with a linear 4-point probe with 1-mm inter-probe spacings

using a variable current of 1 - 100 mA. The samples were removed from the system after venting

with N2 and immediately (within 2 s) submerged in liquid nitrogen to minimize air exposure. The

resistivity at 77 K was then measured with both sample and measurement tips immersed in liquid

nitrogen. Ex situ room-temperature resistivity measurements were taken after warming the samples

up to 295 K using a continuous flux of N2 gas. Resistivity measurements were also taken after 24-

48 h, to confirm that extending the air-exposure beyond the initial approximately 2 minutes has a

negligible effect on electron scattering.

X-ray diffraction was done using a Panalytical X’pert PRO MPD system with a CuKα

source. Reciprocal space maps were acquired using a hybrid mirror Ge(220) two bounce

monochromator which yields a λKα1 = 1.5406 Å beam with a 0.0068° divergence, and a PW3018/00

PIXcel line detector operated in scanning mode. -scans were recorded with a point-focus optics

using a poly-capillary lens that yields quasi-parallel Cu Kα x-rays with a <0.3° divergence, and a

0.27° parallel-plate collimator in front of a scintillation point detector. X-ray reflectivity (XRR)

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measurements were done in the same system, using a parabolic mirror which yields a source

divergence of <0.055°, and a scintillation point detector. XRR patterns were analyzed using a

fitting procedure based on the recursive theory of Parratt, assuming a Gaussian distribution to

model the surface and interface roughness. The XRR oscillations for layers with d > 100 nm could

not be resolved. Thus, the thicknesses of these samples were determined using the deposition rate,

as calibrated from the thinner samples.

The nominally 10 and 40 nm-thick Co films were examined in cross section by

transmission electron microscopy (TEM) in an FEI Talos F200X instrument operating at 200 kV.

The electron transparent section was prepared by focused ion beam (FIB) milling in an FEI Helios

NanoLab 660 dual beam instrument. A final milling step at 1 kV was used to remove the ion beam

damaged layer. The direction chosen to be normal to the prepared section was parallel to [1120]

in sapphire and thus parallel to [1010] in Co.

III. RESULTS AND DISCUSSION

Figure 1 shows representative X-ray diffraction and reflection results from a nominally 40-

nm-thick Co(0001)/Al2O3(0001) layer. Fig. 1(a) is a reciprocal space map for 41° < 2θ < 46° and

20.5° < ω < 23.2°, displaying isointensity contours on a logarithmic scale. The two detected peaks

within the plotted region are attributed to the substrate Al2O3 0006 and the layer Co 0002

reflections. The substrate peak at 2θ = 41.685° and ω = 20.843° is narrow in comparison to the

large plotted region, with a full-width at half-maximum (FWHM) peak width of 0.03° along 2θ

and 0.01° along ω. The layer peak at 2θ = 44.54° and ω = 22.27° is 10 times less intense and 8

times broader in 2θ than the substrate peak. Its 2θ value corresponds to an out-of-plane lattice

parameter of 0.4065 nm. This is 0.1% smaller than the reported Co z-axis lattice parameter of

0.4069 nm, indicating a small in-plane biaxial tensile stress of -0.3 GPa, as determined using the

elastic constants in Ref. 59. This stress may be attributed to the 9.4% lattice mismatch between the

c-plane sapphire surface and the Co basal plane60 and/or the difference in thermal expansion

coefficients, which are 8.1×10-6 °C-1 for the basal plane in Al2O361 and 10.97 × 10-6 °C-1 for the Co

basal plane.59 The width of the Co 0002 peak along ω corresponds to the rocking curve width and

is 0.14° (FWHM). This corresponds to approximately the yellow colored region in the map.

However, in addition to this high-intensity narrow part of this peak, there are also two lobes of

relatively low intensity indicated by green, cyan, and blue in Fig. 1(a). They extend in the positive

and negative ω directions about the Co 0002 peak and are attributed to diffuse scattering from

misfit dislocations62 that exist at the Co-Al2O3 interface. The map also shows a periodic array of

peaks along the line which intercepts the centers of the substrate and layer peaks. The intensity

along this line for which θ = ω is reproduced in Fig. 1(b). It corresponds to a symmetric ω-2θ scan

and clearly shows the periodic fringes which are attributed to Laue oscillations due to the finite Co

layer thickness.63–66 The fringes in Fig. 1(b) have an average 2θ spacing of 0.29 ± 0.02° and suggest

a film thickness of 32.1 ± 1.3 nm. This is slightly smaller than d = 36.1 ± 0.2 nm determined by

XRR (presented below) which can be attributed to strain fields near the Co-substrate interface that

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are due to misfit dislocations and effectively reduce the coherent thickness measured by XRD. We

note that the Scherrer width of the peak in 2θ is 34 nm, also in reasonable agreement with the

above thickness values.

Fig. 1(c) shows an XRD ϕ-scan acquired using a constant 2θ = 47.44° and ω = 23.73°, and

a χ = 61° tilt to detect the Co 10 11 reflections. The pattern exhibits six peaks at ϕ = 30, 90, 150,

210, 270, and 330°, indicating a 6-fold rotational symmetry with a 60° spacing between each of

the Co 10 11 peaks. A corresponding ϕ-scan of the Al2O3 [1129] reflections (not shown), indicates

in-plane alignment of the Co < 0110 > with the Al2O3 < 0211 > directions. Thus, the epitaxial layer-

substrate relationship is Co[0001]║Al2O3[0001] and Co[ 0110 ]║Al2O3[ 0211 ], in agreement with

a previous report on the epitaxial growth of Co on c-plane sapphire,60 and similar to the reported

epitaxy of Ru on Al2O3(0001).3,67,68 The average measured peak width in ϕ is 0.6°. This width is

due to convoluted instrumental/geometric broadening (~0.3°) and in-plane and out-of-plane grain

misalignment such that in-plane misalignment between the Co film and the substrate is <0.6°. That

is, there is a strong in-plane alignment of the Co crystal, despite the large basal plane lattice misfit

of 9.4%. In summary, Figs. 1(a-c) show that the Co layers are epitaxial crystals with a negligible

(not-detected) density of misoriented grains. This is important for the interpretation of the electron

transport measurements presented below. More specifically, the absence of any significant density

of misoriented grains renders electron scattering at grain boundaries negligible such that the

measured resistivity allows direct quantification of the effect from electron surface scattering.

Fig. 1(d) shows a representative XRR curve (blue) from a nominally 40-nm-thick Co(0001)

layer. The measured intensity is plotted in a logarithmic scale vs the scattering angle 2θ, showing

the characteristic interference fringes that are used to determine the layer thickness. The red curve

represents the result from curve fitting and is offset by a factor of 100 for clarity purposes. The

XRR fitting procedure yields values for the Co film thickness as well as the thickness of the native

cobalt oxide, assuming literature bulk densities of 8.9 and 6.0 g/cm3, respectively. In addition, the

XRR analysis yields values for the RMS roughness of the cobalt oxide surface, the cobalt oxide-

Co interface, and the Co-substrate interface. The fitting shown in Fig. 1(d) results in a Co layer

with a thickness d = 36.1 ± 0.2 nm, in reasonable agreement with the expected 40 nm from

deposition rate calibrations. Fitting also returns a surface oxide thickness of 1.7 ± 0.3 nm with an

RMS surface roughness σ = 0.7 ± 0.3 nm, and roughnesses of the cobalt oxide-Co interface of 0.3

± 0.2 nm and Co-substrate interface of 0.4 ± 0.2 nm. Similar XRR measurements and fitting were

also done for the three thinner samples in this study, yielding thicknesses of d = 6.9 ± 0.1, 8.8 ±

0.1, 21.1 ± 0.1 nm. We note that the partial consumption of the Co layer by the native oxide results

in a smaller ex situ measured Co thickness than the in situ as-deposited thickness. The latter is

determined by calculating an equivalent Co metal thickness from the Co content of the measured

surface oxide, assuming that the oxide adopts the room temperature thermodynamically stable

Co3O4 phase. Thus, we determine for layers with ex situ d = 6.9, 8.8, 21.1, and 36.1 nm the

corresponding in situ Co thicknesses d = 7.9, 9.7, 22.3, and 36.9 nm, respectively, which is used

in the following for analyzing the in situ transport data. All layers lose 1.0±0.2 nm Co due to

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surface oxidation. This is a negligible fraction (< 1%) for layers with thickness d > 100 nm.

Therefore, no thickness correction is done for d > 100 nm.

Figure 2 is a high resolution transmission electron micrograph from the nominally 40 nm-

thick Co(0001)/Al2O3(0001) layer. It shows the substrate-layer interface at approximately half-

height in the micrograph. Lattice fringes are visible for both the substrate and the Co layer, as

indicated by the pair of lines that highlight the Al2O3 (1102) planes that are expected at an angle

of 57.6° relative to the Co/sapphire interface for the c-axis oriented Al2O3 substrate. The horizontal

fringes in the Co layer correspond to (0002) planes and are parallel to the film-substrate interface.

The inset in Fig. 2 is a selected area electron diffraction pattern acquired with the aperture centered

around the Co-Al2O3 interface of a nominally 10-nm-thick layer. Using the two superimposed

patterns, the interplanar spacing for the (0002) planes of Co and the (0006) planes of sapphire were

computed as 0.204 and 0.218 nm, respectively. These values are in good agreement with values of

0.203 and 0.217, respectively, obtained from the reported lattice parameters for Co and sapphire.

The corresponding interplanar spacing of the (1102) planes of sapphire of 0.348 nm is also

marked on the high-resolution image. We note that the sample orientation for Fig. 2 is chosen

such that the selected area diffraction patterns simultaneously correspond to the Co [10 10 ] and

sapphire [1120 ] zone axes, which is done by choosing the sample thinning direction based on

XRD -scan analyses of both layer and substrate. Thus, the overlay of the Co and Al2O3 patterns

in the inset confirm the epitaxial substrate-layer orientation relationship determined by XRD as

discussed above. Larger area TEM micrographs (not shown) for the two analyzed films with d =

10 and 40 nm indicate no evidence of misoriented grains or grain boundaries. In summary, the

TEM studies confirm the epitaxial growth of Co(0001) on Al2O3(0001) and indicate the absence

of any grain boundaries.

Figure 3 is a plot of the Co(0001) resistivity ρ vs film thickness d, measured both in vacuum

(in situ) and air (ex situ) at 295 K, and immersed in liquid N2 at 77 K. The resistivity increases

with decreasing d for all three data sets. This is attributed to electron scattering at the Co surfaces,

which becomes increasingly dominant with decreasing d. The thickest three layers with d = 293,

194 and 118 nm have an in situ measured ρ = 6.37 ± 0.21, 6.46 ± 0.22, and 6.51 ± 0.22 µΩcm.

That is, these values increase slightly with decreasing d but this increase is within the experimental

uncertainty, suggesting that surface scattering is negligible for d > 100 nm at room temperature.

This is consistent with the quantitative analysis below, which indicates that surface scattering is

expected to cause only a 1%, 2%, and 5% resistivity correction for these three samples, and

suggesting a bulk resistivity for our Co(0001) layers of ρo = 6.37 ± 0.21 µΩcm. This value is

slightly (3 – 10%) above the reported isotropic bulk resistivity range of 5.8-6.2 µΩcm,69,70 and

13% and 15% above the resistivities (5.645 and 5.544 µΩcm) reported for conduction along the

Co [10 10 ] and [1120 ] basal plane directions.71 We attribute the deviation of our ρo from the

literature values primarily to residual impurities from the 99.95% pure Co target and possibly also

to crystalline defects that could not be detected by our TEM analyses, and note that we assume for

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the following analysis that this deviation is the same for all samples. This assumption leads to a

5% uncertainty in our reported values for λ and p, which is included in our reported uncertainties.

The in situ measured resistivity plotted in Fig. 3 increases with decreasing d = 36.9, 22.3, 9.7, and

7.9 nm to ρ = 7.24 ± 0.40, 7.87 ± 0.12, 10.77 ± 0.58, 12.27 ± 0.64 µΩcm. The plot also shows the

ex situ resistivity measured after air exposure of the same Co samples. The ex situ and in situ values

are identical, within experimental uncertainty, for d > 30 nm. However, the thinner Co(0001)

layers show a significantly higher resistivity after air exposure, with ρ = 8.58 ± 0.44, 12.55 ± 0.76,

and 15.17 ± 0.46 µΩcm for d = 21.1, 8.8, and 6.9 nm. This corresponds to a 24% resistivity increase

during air exposure for the 6.9 nm layer, which has a ρ that is 137% above the measured bulk in-

plane resistivity. The fact that the thick layers show no change in ρ upon air exposure indicates

that the resistivity increase is a surface effect. Correspondingly, we attribute the increase to a

decrease in the Co(0001) surface specularity upon oxidation, and/or significant roughening of the

Co surface during oxidation, as discussed in detail below. The third dataset in Fig. 3 is from low-

temperature measurements taken in liquid N2 at 77 K. As expected, the values are considerably

lower than for 295 K, but show a similar resistivity increase from ρ = 0.76 ± 0.30 to 0.77 ± 0.29,

0.96 ± 0.33, 1.72 ± 0.28, 2.18 ± 0.10, 4.95 ± 0.59, and 6.71 ± 0.50 µΩcm for a decreasing

thicknesses d = 293, 194, 118, 36.1, 21.1, 8.8, and 6.9 nm. We note that, in contrast to the room

temperature data, ρ77K for all layers is considerably affected by electron surface scattering. This is

because bulk electron-phonon scattering is smaller at lower temperatures, such that surface

scattering is responsible for a larger fraction of the overall resistivity of a thin layer. More

specifically, for the thickest layer with d = 293 nm, 26% of the resistivity is attributed to electron

surface scattering. The corresponding in-plane bulk resistivity is 0.55 ± 0.05 µΩcm. This is 0.06

± 0.05 µΩcm above the reported isotropic bulk value of 0.49 µΩcm.69 Thus, at both temperatures,

the measured extrapolated bulk resistivity is slightly (0.06 ± 0.05 and 0.2 ± 0.2 µΩcm) above the

reported bulk values, consistent with this deviation being attributed to temperature-independent

scattering at impurities and/or crystalline defects.

In the following, we discuss the results in Fig. 3 within the semiclassical framework by

Fuchs and Sondheimer.27,28 A well-known challenge3,4,23 when applying this FS model to describe

resistivity vs thickness data is that it does not allow for independent determination of the two

parameters that quantify electron scattering, which are the surface scattering specularity p and the

bulk mean free path λ. More specifically, for any arbitrary choice of p, a value for λ can be found

such that the model predicts a ρ vs d curve that matches the measured data. The specularity is

limited within the FS model to 0 ≤ p ≤ 1, leading to a corresponding mean free path range of λmin

≤ λ ≤ ∞, where λmin is a lower bound for the mean free path consistent with a specific ρ vs d data

set. Correspondingly, as a first step, data fitting is done assuming completely diffuse electron

scattering at both the upper and lower film surfaces (p1 = p2 = 0), yielding λ values which can be

interpreted as a lower bound for the mean free path. This is done for each of the three data sets in

Fig. 3, using ρo as a second independent fitting parameter to account for deviations from the

reported bulk resistivity as discussed above. This yields λ = 14.0 ± 0.5 nm and ρo = 6.3 ± 0.1 µΩcm

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for the in situ measurements and λ = 19.5 ± 1.0 nm and ρo = 6.3 ± 0.1 µΩcm for the ex situ data

points at 295 K, while the corresponding values at 77 K are λ = 217 ± 20 nm and ρo = 0.55 ± 0.05

µΩcm.

We first note that, as expected, the room temperature bulk resistivity for in situ and ex situ

data is identical within experimental error. In contrast, ρo at 77 K is considerably lower, which is

due to the reduced electron-phonon scattering that also leads to a larger λ at 77 K. This is

quantitatively illustrated by the product ρo×λ, which is 8.8×10-16, 12.2×10-16, and 12.0×10-16 Ωm2

for 295 K in situ, 295 K ex situ, and 77 K measurements, respectively. Here the latter two values

are in excellent agreement while the in situ ρo×λ product is considerably lower. This suggests that

the initial assumption of completely diffuse surface scattering for all data sets is incorrect and that

the surface specularity decreases upon air exposure, similarly to what has previously been reported

for Cu.5–7,33 To quantitatively evaluate this explanation, we perform curve fitting of the in situ data

using a fixed λ = 19.5 nm but allowing the scattering specularity of the top surface p1 to vary, while

assuming that electron scattering at the bottom (Co-Al2O3) interface is unaffected by air-exposure

and is completely diffuse (p2 = 0), similar to the reported diffuse scattering at Cu/MgO(001)

interfaces5,55 which is attributed to local epitaxial strain fields, non-uniform charge transfer, and/or

asymmetric covalent bonding that lead to both potential perturbations and localized interface

states. Such data fitting results in p1 = 0.55 ± 0.05 and a curve (not shown) that is undistinguishable

from the (red) curve in Fig. 3. That is, both the in situ and ex situ data at 295 K are well described

by a single mean free path of 19.5±1.0 nm and a surface scattering specularity that decreases from

p1 = 0.55 ± 0.05 in vacuum to p1 = 0 in air. We note that, in principle, it is also possible that p1 is

non-zero in air, which would yield a corresponding p1 > 0.55 in vacuum. However, we believe p1

= 0 in air is the most reasonable assumption, because the measured resistance is relatively

independent of oxidation time, while a continuously growing oxide would be expected to result in

a decreasing scattering specularity if p1 is not already zero. This is further supported by the ex situ

measured ρo×λ product which is identical at 295 and 77 K, suggesting that the surface scattering

specularity is the same when air exposed or immersed in liquid N2. That is, the air exposure of

approximately 2 s between sample removal from the deposition system and immersion into liquid

N2 is sufficient to cause a transition from partially specular (p1 = 0.55) to completely diffuse (p1 =

0) surface scattering.

We now explore if the measured resistivity increase upon air exposure of the three thinnest

samples (d = 6.9, 8.8, and 21.1 nm) can be explained by an increase in the Co surface

roughness15,17,18,50–54 rather than the (above discussed) decrease in specularity. For this purpose,

we envision an as-deposited relatively smooth Co surface which roughens upon air exposure,

leading to the measured increase in ρ. In this case, surface scattering is assumed to remain

completely diffuse and the lower bound fitted mean free path λ = 14.0 ± 0.5 nm from the in situ

data is the value that most aptly describes the data. We note that this mean free path is reasonably

close to the previously reported λ = 11.8 nm from first principles.42 The maximum roughness

resulting from oxidation is obtained from the XRR measurements, more specifically from the

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interface RMS roughness between Co and the surface oxide, which is 0.3 ± 0.1 nm for d = 6.9, 0.3

± 0.1 nm for d = 8.8 nm, and 1.0 ± 0.2 nm for d = 21.1 nm. We emphasize here that these are

maximum values and that we believe the roughening due to oxidation to be smaller, since the

interface between Co and the substrates have comparable roughness values, suggesting that the

measured roughness is primarily determined by the initial substrate roughness. Nevertheless, we

estimate the impact of the measured roughness on the resistivity using the model by Namba,15

which utilizes the quantities d/λ and h/λ, where h is one half of the average peak-to-valley height,

as determined from the measured RMS roughness by 2h . For the three samples under

discussion, Namba’s model predicts negligible resistivity increases (< 1%), suggesting that

roughness cannot explain the resistivity increase. However, recent studies18,72 indicate a stronger

effect of surface roughness on the thin film resistivity than Namba’s model, and propose a step

edge model that predicts a resistivity contribution that is proportional to the RMS roughness

divided by the lateral correlation length ξ of the surface morphology. Unfortunately, ξ cannot be

determined from our XRR data. Thus, inversely, we determine ξ that would be required such that

the increase in ρ upon air exposure could be attributed to the measured roughness. For this purpose,

we estimate the Co ballistic conductance go = 3/(4ρoλ) = 9.42 × 1014 Ω-1m-1 from the free electron

approximation and determine ξ = 1.9, 2.5, and 8.7 nm for d = 6.9, 8.8, and 21.1 nm, respectively.

These ξ values are 1-2 orders of magnitudes smaller than what would be expected, based on

reported values of epitaxial layers with comparable thicknesses.3,17 Thus, we conclude that the

resistivity change upon air exposure cannot be primarily attributed to an increase in the Co surface

roughness.

In summary, our measurements suggest a product ρo×λ = 12.2 × 10-16 Ωm2 for conduction

within the Co basal plane. This value is 82% larger than that for Cu42 and 21% larger and 30%

smaller than that for W(011) and W(001), respectively.26 Based on this comparison and the simple

model described in the introduction that assumes metal-independent surface and grain boundary

scattering coefficients, the line resistances for Co and W are expected to be approximately equal

for any given wire width w, because the ρo×λ products and ρo values are similar for Co and W, but

are larger than that of Cu for all w. Nevertheless, Co lines may exhibit a conductance advantage

over W because (1) we measure a high specularity (p = 0.55 ± 0.05) at the Co-vacuum interface,

while the reported p = 0 for W,11,26 suggesting that Co has a higher chance than W to exhibit

partially specular surface scattering with a suitable barrier/liner material, and (2) Co is expected73

to have a lower grain boundary reflection coefficient R, based on the measured range R = 0.07-0.6

for Co,46–49,74 and R = 0.4-0.67 for W,11,14,75 and (3) Cobalt has a higher potential for grain growth

and defect removal through annealing, because of its 52% lower melting point in comparison to

W.

IV. CONCLUSIONS

Co(0001) layers are sputter deposited on Al2O3(0001) substrates at 300 °C and annealed at

500 °C. They exhibit an epitaxial film-substrate relationship with Co[0001]║Al2O3[0001] and Co[

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0110 ]║Al2O3[ 0211 ] as determined by XRD. TEM analyses confirm the epitaxy and absence of

grain boundaries, while XRR measurements show that the surface and interface roughness are too

small to substantially affect the resistivity. In situ and ex situ transport measurements indicate a

room temperature mean free path λ = 19.5 ± 1.0 nm and partially specular surface scattering with

p = 0.55 ± 0.05 for the as-deposited layers which transitions to completely diffuse scattering (p =

0) after exposure to air. The results indicate that Co exhibits a resistivity scaling that is similar to

that of W, but that Co may outperform the W conductivity for narrow interconnects due to its

potentially higher surface scattering specularity, lower predicted grain boundary reflection

coefficient, and higher potential for grain growth.

ACKNOWLEDGMENTS

The authors acknowledge the NSF under grant No. 1740271, 1740270, and 1712752, the

SRC under tasks 2764 and 2881, and the NY State Empire State Development's Division of

Science, Technology and Innovation (NYSTAR) through Focus Center-NY–RPI Contract

C150117.

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Figures

FIG. 1. Representative (a) reciprocal space map, (b) ω-2θ scan, (c) ϕ-scan for Co 10 11 reflections,

and (d) XRR scan including result from curve fitting (red), from an epitaxial

Co(0001)/Al2O3(0001) layer with thickness d = 36.7 nm.

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FIG. 2. HRTEM micrograph of a Co(0001)-Al2O3(0001) interface taken from a 36.7-nm-thick Co

layer. The inset is the diffraction pattern along the [1010] Co and the [1120] Al2O3 zone axes.

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FIG. 3. Resistivity ρ of epitaxial Co(0001) films vs thickness d, measured in situ (red squares) and

ex situ (gray squares) in vacuum and air at 295 K, and immersed in liquid N2 at 77 K (blue

triangles). Curves are from data fitting using the FS model.

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resistivity scaling and electron surface scattering in...

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