Given that the step edge is vulnerable to oxidation because surface steps act as the dominant source of Cu adatoms for oxide growth on surface terraces2,11, oxidation resistance requires that surface step edges are avoided6,12,13. In this regard, the close-packed Cu(111) surface is superior to other Cu surfaces14,15 and our experimental demonstration thus used a single-crystal Cu(111) film (SCCF) grown by atomic sputtering epitaxy (ASE)16 to show that a tightly coordinated flat surface can remain semi-permanently stable against oxidation. Theoretical calculations show the atomic-scale oxidation-resistant mechanism of the flat copper surface from the perspective of the likely pathways for oxygen atoms into the viable structures of the copper surface with a discovery of the self-regulated protection layer at elevated oxygen coverages. The implication is that the atomically flat surface of the SCCF shows oxidation-resistant properties owing to the high energy barrier for oxygen infiltration and self-regulation owing to high oxygen coverages.

Flatness of Cu(111) surface

The surface and structural characteristics of a 110-nm-thick SCCF with an ultraflat surface (see Extended Data Fig. 1 for a large-scale characterization) are examined using high-resolution (scanning) transmission electron microscopy (HR(S)TEM) combined with geometrical phase analysis (GPA)17,18 (Fig. 1). The cross-sectional (S)TEM images (Fig. 1a, e) show that the copper film grew along the [111] direction, thus creating an exposed surface (111) plane with mono-atomic step-edge structures. Typical multi-atomic step edges and intrinsic defects such as grain boundaries and stacking faults are rarely detected. It is remarkable that the outermost copper surface layer has the same atomic configuration as the interior copper without evidence of surface relaxation or structural changes by surface oxidation, even at the step-edge positions. To examine the local strain behaviour near the surface region, lattice distortions along the in-plane (x) and out-of-plane (y) directions relative to the inside of the SCCF were measured by the GPA technique (Fig. 1b, c). The resulting strain field maps (Exx and Eyy) clearly show that no noticeable changein lattice strain is observed throughout the entire surface region. This means that the SCCF has a nearly perfect atomic structure up to its outermost surface layer without any structural defects, such as vacancies or dislocations. The simulated HRTEM image using an amorphous carbon/flat copper surface model matches well with the experimental HRTEM image (Fig. 1a). By comparing the layer spacings of the (111) stacking planes (d(111) = 0.21 nm) between the simulated and experimental images (Fig. 1d), it is evident that the Cu surface is undistorted and ultraflat, and has the same structure as bulk Cu. Annular dark-field (ADF) and annular bright-field (ABF) STEM images of the SCCF surface are complementary to the HRTEM observation results (Fig. 1e). We can discriminate this remarkable ultraflat surface structure of the SCCF from that of the conventional polycrystalline Cu thin film (PCCF) and the Cu(111) surface of a bulk Cu single crystal with a notable oxidized copper layer on top of them (Extended Data Fig. 2 and Fig. 3). Notably, we found that the SCCF sample maintained its ultraflat and pristine surface even after more than a year of air exposure (Fig. 2a–d), suggesting that our SCCF has exceptional oxidation-resistant properties (also see Extended Data Fig. 4 for a large-scale scanning tunnelling microscope (STM) topography).

Fig. 1: Surface of a single-crystal copper thin film grown by ASE.
figure 1

a, Cross-sectional HRTEM image of the surface region of the copper thin film observed in the \([1\overline{1}0]\) orientation. The simulated HRTEM image and the corresponding model of the carbon–copper supercell are presented alongside the experimental HRTEM image. Scale bar is 2 nm. b, c, In-plane (Exx) and out-of-plane (Eyy) strain field maps obtained by GPA for the experimental HRTEM image. The reference area of Cu chosen for GPA is marked by the white square boxes in each map. Note that complex patterns for parts of the carbon film are shaded by a grey colour for clarity, as those are not relevant for the strain behaviour of the SCCF. Scale bars are 2 nm. d, Comparison of the experimental and simulated intensity profiles obtained along the out-of-plane direction for (111) layer spacings (d(111) = 0.21 nm). e, Simultaneously acquired ADF-STEM and ABF-STEM images for the surface region of the copper thin film. Scale bars are 2 nm.

Source data

Fig. 2: Long-term oxidation resistance and structural stability of the SCCF surface.
figure 2

a, Low-magnification BF-TEM image of the SCCF sample exposed to ambient air at room temperature for about 1 year (top). The result shows that the atomically flat surface morphology over the entire SCCF film has remained almost unchanged. HRTEM image of the surface region (marked by a red rectangle in the top panel) of the 1-year-old SCCF sample (bottom). The sample was oriented in the \([1\overline{1}0]\) direction. Scale bars are 100 nm (top) and 2 nm (bottom). b, Comparison of the intensity profiles for the (111) plane between the as-deposited (red) and 1-year-old (blue) samples. c, EBSD map showing perfect alignment along the (111) plane. Scale bar is 3 μm. d, IPF with a sole spot associated with the (111) plane. The inset image is the enlarged image of the sole-spot area. e, HRTEM image of the surface region of the 3-year-old SCCF sample observed in the \([1\overline{1}0]\) orientation (top) and in-plane (Exx, middle) and out-of-plane (Eyy, bottom) strain field maps obtained by GPA for the HRTEM image of the 3-year-old SCCF sample. Scale bars are 2 nm. f, FFT patterns of region 1 (top), region 2 (middle) and both regions (bottom). g, Thermogravimetric analysis for the PCCF and SCCF samples with different surface roughness. r.m.s., root mean square.

Source data

The low-magnification bright-field TEM (BF-TEM) image (Fig. 2a, top) and the cross-sectional HRTEM image (Fig. 2a, bottom) show that the mono-atomic step-edge structure is maintained even after a year. The two intensity profiles for the (111) plane between the as-deposited (red) and the 1-year-old (blue) samples (Fig. 2b) show a change in the planar spacing of the (111) planes up to the uppermost surface layer, and they agree well with each other, suggesting that no notable oxidation has occurred even in the SCCF under long-term exposure to air. The electron backscatter diffraction (EBSD) map (Fig. 2c) and inverse pole figure (IPF) (Fig. 2d) show that no misalignment of crystal lattices deviating from the (111) plane has occurred after a year. Oxidized portions were rare on the 3-year-old SCCF sample oriented along \([1\overline{1}0]\) in the HRTEM image, although they were found on the sample edge where the sample was cut (Fig. 2e, top). The resulting strain field maps (Exx and Eyy) prepared using the GPA technique (Fig. 2e, middle and bottom) show that the overlayer (region 1) has a new lattice structure that is mismatched with the SCCF. The fast Fourier transform (FFT) patterns of region 1 (Fig. 2f, top), region 2 (Fig. 2f, middle) and both regions (Fig. 2f, bottom) indicate that the two regions belong to the Cu2O and Cu phases, respectively, and suggest that part of the surface is oxidized. However, the oxidized surface only reaches a few Cu2O layers, which is thin compared with the thickness of natural oxide layers in polycrystalline Cu (Extended Data Fig. 2). Comparative thermogravimetric analysis of PCCF and SCCF samples having different surface roughness clearly demonstrates that the SCCF with mono-atomic step edges shows exceptional resistance to initial oxidation at elevated temperatures compared with the other samples (Fig. 2g).

Growth condition for the flat surface

The flatness of a surface is decisively influenced by the interface structure between the film and the substrate19,20, which can be relaxed by structural defects such as dislocations. The interface structure between the Cu film and the Al2O3 substrate is characterized by HR(S)TEM (Fig. 3). The overall interface structure viewed at the \([11\overline{2}]\) orientation of the Cu film and the FFT pattern of the imageshow that the crystallographic orientation relationship (OR) is \({(111)}_{{\rm{Cu}}}{[11\overline{2}]}_{{\rm{Cu}}}//{(001)}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}{[110]}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) (Fig. 3a, b). The copper lattices seem to flawlessly adjoin with the Al2O3 substrate without interfacial misfit defects, suggesting that the Cu film grows metamorphically on the substrate21 (Extended Data Fig. 5). The enlarged image of the interface (Fig. 3c) shows a detailed lattice mismatch between the two materials. The in-plane atomic distance mismatch \(f\)((\({{d}_{{\rm{O}}-{\rm{O}}}^{[\bar{1}20]}}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}-{d}_{{\rm{Cu}}-{\rm{Cu}}}^{[\bar{1}10]}\))/\({{d}_{{\rm{O}}-{\rm{O}}}^{[\bar{1}20]}}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\)) between Cu atoms in the film and O atoms in Al2O3 is estimated to be 6.9%. However, considering the extended atomic distance mismatch (EADM)22,23, the large mechanical misfit strain can be relieved if the mismatch for a relatively long period of atomic distance is extremely small. The EADM is defined as (ID − ID′)/ID′, in which D and D′ are the Cu–Cu distance in the Cu (111) epilayer and the O–O distance in the substrate, respectively, and I and I′ are smallest non-reducible integers determined by the relation D:D′ ~ I:I′. Given the DCu-Cu \((14\times {d}_{{\rm{Cu}}-{\rm{Cu}}}^{[\overline{1}10]})\) interatomic spacing (3.578 nm) of Cu atoms in the film and the \({D{\prime} }_{{\rm{O}}-{\rm{O}}}\) \((13\times {d}_{{\rm{O}}-{\rm{O}}}^{[\overline{1}20]})\) interatomic spacing (3.575 nm) of O atoms in Al2O3, the EADM of the Cu–Al2O3 interface is about 0.1% (Fig. 3c). The light-element-sensitive ABF-STEM imaging24 (Fig. 3d) shows that the interface model of Cu grown on the oxygen-terminated Al2O3 surface matches well with the experimental heterostructure. The inverted intensity profile obtained across the interface (Fig. 3e) clearly corroborates the presence of an oxygen layer between the Cu and Al layers, thus indicating the existence of Cu–O interactions at the interface, which can be stabilized on a typical Al2O3 surface terminated with oxygen25. Owing to the in-plane lattice mismatch, a large-scale interference pattern, that is, a moiré pattern26, can be observed in the plane view of the Cu–Al2O3 heterostructure (Fig. 3f). Indeed, the hexagonal moiré pattern with a dimension (dm) of 1.83 nm is observed owing to the different in-plane lattice periodicities in the vertical OR of [111]Cu//[001]Al2O3, which is confirmed by the FFT pattern analysis (inset in Fig. 3f). The simulated moiré pattern generated by the epitaxy model of Cu–Al2O3 with the same OR is consistent with the experimental moiré pattern, showing the repeating large-scale contrast feature (Fig. 3g, h). This vertical OR observation corroborates our EADM analysis and indicates that the growth mechanism of the SCCF on the Al2O3 substrate can be understood on the basis of the large-scale mismatch epitaxial relationship, rather than the atomic-scale lattice interrelation. The detailed chemical nature of the SCCF at the surface and the interface regions are investigated by the combined spectroscopic approaches of energy-dispersive X-ray spectroscopy (EDX), electron energy loss spectroscopy (EELS) in ADF-STEM imaging mode and X-ray photoelectron spectroscopy27,28 (Extended Data Fig. 6).

Fig. 3: Interface structure and crystallographic relation.
figure 3

a, Cross-sectional HRTEM image of the Cu–Al2O3 heterointerface having the orientation relation of \({(111)}_{{\rm{Cu}}}{[11\overline{2}]}_{{\rm{Cu}}}//{(001)}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}{[110]}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\). Scale bar is 2 nm. b, A composite pattern of FFTs for the regions of Cu and Al2O3 in the HRTEM image. c, Enlarged HRTEM image for the region marked by the dashed box in a. Scale bar is 1 nm. d, ABF-STEM image and superimposed atomic model of the Cu–Al2O3 heterointerface. Scale bar is 5 Å. e, Inverted intensity profile obtained across the interface between Cu and Al2O3 in d. f, Plan-view HRTEM image of the Cu–Al2O3 heterointerface. The inset is the FFT pattern of the HRTEM image. Scale bar is 2 nm. g, h, Side view (g) and plan view (h) of the deduced epitaxy model of Cu grown on an Al2O3 substrate. The yellow diamonds with unit length of dm in f and h indicate the 2D unit cell of the moiré pattern.

Calculation of oxidation resistance

We can understand the exceptional oxidation resistance of our films using a microscopic model of copper oxidation on the basis of first-principles density functional theory (DFT) calculations29,30,31. The main reason for the suppression of oxidation is that our atomically flat film is free of one critical feature, namely, multi-atomic step edges, as shown in Fig. 4. The energy profile in Fig. 4a shows that the penetration of an O atom through a pristine Cu(111) surface needs an activation energy of more than 1.4 eV (Fig. 4b), and the O atom becomes stable only in the second subsurface interlayer space with a further energy barrier of 1.3 eV (Fig. 4c). One of the main reasons for the strong resistance of a flat surface to oxidation is that, when Cu atoms are oxidized, the out-of-plane distance between Cu layers increases from 2.10 to 2.48 Å, and the volume expands by 18% (Extended Data Fig. 7). The volume increase is even more pronounced in the early stage of oxidation: the Cu layer distance in the monolayer of Cu2O on the Cu surface is 3.26 Å, and the volume is greater by 55% (Extended Data Fig. 7). Given that one exposed Cu surface is insufficient to initiate the oxidation process, we examine a structure wherein two crystallographically different planes meet, namely, the edge of a multi-atomic step. Notably O2 molecules physisorbed on a Cu(111) surface readily dissociate into O ions with a small activation energy of 0.027 eV (Extended Data Fig. 8). Figure 4d–f shows the initiation of oxidation on the edge of such multi-atomic steps according to our DFT calculation; Fig. 4a shows that there is a critical difference between a mono-atomic step and a multi-atomic step in terms of the oxidation resistance. Whereas the penetration of O atoms at a bi-atomic and tri-atomic step is an exothermic reaction (ΔE = −0.90 and −0.86 eV, respectively) with smaller activation energies (Ea = 0.97 and 0.71 eV, respectively), the penetration of O at the edge of a mono-atomic step is highly endothermic (ΔE = +0.80 eV), requiring a much larger activation energy (Ea = 1.56 eV), and shows strong oxidation resistance. Our DFT calculation indicates that, as the coverage of oxygen increases, the incremental adsorption energy for the next O atom becomes smaller and eventually becomes negative beyond 50% of oxygen coverage, rendering the adsorption process energetically unfavourable (Fig. 4g). This self-regulation of oxygen suppresses further adsorption of O atoms on an ultraflat Cu surface at elevated oxygen coverages and increasingly enhances the oxidation resistance of the surface. Our microscopic model of oxidation is well supported by HRTEM images, which show that atomically flat Cu thin films with occasional presence of mono-atomic steps are highly resistant to oxidation over an extended period (≥3 years) (Fig. 2), whereas Cu films with multi-atomic steps show substantial oxidation (Extended Data Figs. 2 and 3). The oxidation resistance of a Cu(111) surface is greatly affected by the type of surface defects32,33,34,35, which suggests that an atomically flat Cu(111) surface without multi-atom steps is essential to achieve strong oxidation resistance.

Fig. 4: Theoretical analysis and a model of oxidation of the copper surface.
figure 4

af, Energy profile of an O atom along various penetration paths (a): from the Cu(111) surface into the first Cu substrate interstitial layer (black solid circles) (b); from the first to the second Cu substrate interstitial layer (black open circles) (c); from the outside to the inside of the mono-atomic step edge (red solid circles) (d); from the outside to the inside of the bi-atomic step edge (blue open squares) (e); and from the outside to the inside of the tri-atomic step edge (pink open squares) (f). Blue spheres represent Cu atoms in the bulk or substrate, green spheres represent Cu atoms in the steps and dark blue spheres represent Cu atoms on the step edge. Orange spheres represent adsorbed O atoms and red spheres represent O atoms infiltrating into the interstitial region. Panel f also shows the initiation of oxidation on the edge of a multi-atomic step: (1) given a pristine step edge and ambient oxygen conditions, (2) two O atoms (orange spheres) adsorb on each side of the Cu on the edge (Cu-1, dark blue sphere); (3) the third adsorbed O atom (O-2, red sphere) causes the local structure of Cu-1 to be similar to that of Cu in a monolayer of \({{\rm{Cu}}}_{2}{\rm{O}}\), and the expansion of volume causes Cu-1 to move upward and open a pathway for O-2; and (4) O-2 passes through the opening and binds with Cu atoms in the next row to push those Cu atoms upward to sustain the oxidation process. g, Incremental adsorption energy of O atom as a function of oxygen coverage of the fcc sites on the Cu(111) surface. The red and blue shading in a and g represents the endothermic and exothermic reactions, respectively.

Source data


ASE for the preparation of single-crystal Cu thin films

Cu thin films were grown as nearly defect-free and grain-boundary-free single crystals using the ASE technique achieved by addressing the problems of conventional sputter systems16. Because the ASE system controlling atomic-level growth is very sensitive to environmental factors, it requires three key instrumental modifications compared with a commercially available sputtering system. First, we used a single-crystal target instead of a polycrystalline one; second, all conducting wires of the wiring network were replaced with single-crystal copper wires; finally, a mechanical noise-reduction system was installed to suppress the mechanical vibrations from the surroundings. The idea of this technology is on the basis of completely eliminating the noise caused by electron-grain boundary scattering in the conduction network in the device, which, to our knowledge, has been completely ignored until now. Once the system was appropriately constructed, we confirmed that the quality of the Cu films was greatly improved, with a high level of reproducibility. The schematic diagram of the ASE system with the three key features is shown in Extended Data Fig. 9a and the detailed descriptions are as follows.

Single-crystal Cu sputtering target

For a polycrystalline target with a high density of surface steps and grain boundaries, atoms on the edges or grain boundaries have a lower binding energy than that of atoms arranged on a flat plane of the grain. Hence the atoms at the structural defects are prone to being sputtered as atomic clusters for the RF power set to remove atoms from a flat plane, which will eventually be deposited on the substrate as randomly oriented clusters. To realize the practicability of ASE growth, the use of a single-crystal Cu target with a (111) surface is essential because Cu atoms are sputtered from the target as individual atoms. Thus the uniform stacking of Cu atoms on the substrate is empirically achieved for the growth of an ultraflat film. The single-crystal Cu(111) target can be obtained from the single-crystal Cu ingot grown by the Czochralski method by cutting using wire electrical discharge machining as a 6-mm-thick disc with a 2-inch diameter (see the two images on the upper-left side of Extended Data Fig. 9a). Even though Cu single-crystal ingots are commercially available, we grew them using our own apparatus in this study, and there were no differences between the two in the resulting improvement of film quality.

Electrical noise reduction using single-crystal Cu wires

To reduce electrical noise interference, we replaced the electrical networks made of conducting wires in conventional sputtering systems with single-crystal Cu wires as much as possible (see the three images on the lower-left side of Extended Data Fig. 9a). The effectiveness of this modification was previously demonstrated in a Hall measurement kit with circuitry and connecting components made of single-crystal Cu, notably improving the measurement precision of the electrical coefficients, such as carrier density and mobility36. Single-crystal Cu wires can be prepared by the wire electrical discharge machining cutting of a single-crystal Cu disc in a spiral manner, as reported in our previous study37. To ensure further reduction of electrical noise, we replaced a typical RF power cable with a single crystal. To monitor how effectively the single-crystal power cable improves the RF power stability in the sputtering system, we measured the change in the RF power over time with and without the single-crystal Cu power cable (Extended Data Fig. 10a, b). Single-crystal wiring has already been adapted in the sputtering system used in the test. Therefore it is evident that the output RF power is more stabilized in a narrower power range (12.61 ± 0.005 W) after changing the original power cable to a single crystal. Although the RF power stability of the sputtering system before modification is also of good quality compared with the conventional ones, we empirically confirmed that such a level of stability is not sufficient for the growth of the Cu film with an atomic-level flatness.

Mechanical noise reduction using mechanical diodes

Although mechanical noise is not the main source of interference in the ASE system, the electrical noise reduction on the basis of the single-crystal Cu wiring cannot be effective unless the mechanical noise is effectively screened. After the tests to reduce the mechanical noise with several choices, including absorbers, barriers, vibration isolators and vibration dampers, we found that the application of a mechanical diode consisting of a set of metal spikes and pads is very effective and economical in shielding the mechanical interferences transmitted through the wall and the floor. As depicted in Extended Data Fig. 9a, we designed mechanical diodes and installed them on every device, including the chamber and the vacuum pumps. The growth of the atomically flat metal films was not successful without this shield against mechanical noise.

To verify the reproducibility of our ASE approach for the growth of the ultraflat Cu(111) film, we measured the root mean square (r.m.s.) roughness of many samples as a function of the film thickness and compared these values with those of the samples grown by a conventional sputtering system equipped with only the single-crystal Cu target (Extended Data Fig. 10c). The averaged r.m.s. value for the 29 samples grown by the ASE system was estimated to be around 0.20 ± 0.1 nm (red dashed line), which is similar to the planar spacing of Cu(111). Notably, it can be further decreased to about 0.17 ± 0.1 nm (purple dashed line) when considering thinner Cu films below 35 nm, suggesting their reliable applications to ultrathin electronic devices. However, the averaged r.m.s. value for the samples grown by the conventional sputtering system equipped with the single-crystal Cu target was around 0.66 ± 0.2 nm, which is good but not enough for the growth of the ultraflat Cu films with only the mono-atomic steps.

Optimized sputtering conditions using the ASE system

A double-side polished (001) Al2O3 wafer with a thickness of 430 μm was used as the substrate material. The optimized deposition temperature and RF (13.56 MHz in frequency) power were about 170 °C and 30 W, respectively, and varied slightly, depending on the ASE systems. The target-to-substrate distance was set at 95 mm. The base pressure was maintained at under 2 × 10−7 torr and the working pressure at 5.4 × 10−3 torr with an Ar gas flow of 50 sccm. Ar gas with a purity of 99.9999% (6N) was used. The relationship between the deposition time and the thickness of the thin film (or the average growth rate) was determined from the average deposition time of a 200-nm-thick film grown under the optimum conditions. The determined average growth rate of roughly 4.3 nm min−1 is fairly reliable above a film thickness of 10 nm. The kinetic energy of sputtered Cu atoms depends on the incident ion energy of Ar+ and the binding energy of Cu atoms at the surface of the target. The crystallographically different surfaces of Cu have different surface binding energies (Eb,Cu), which were reported to be 4.62, 4.26 and 4.65 eV for the Cu(100), Cu(110) and Cu(111) planes, respectively38. Considering the potential energy (\({E}_{{{\rm{Ar}}}^{+}}=15{\rm{eV}}\)) of the accelerated Ar+ ion at the maximum current of 1 A in our ASE equipment, the kinetic energy of the sputtered Cu atoms can be narrowly distributed at around 10.35 eV, which is roughly calculated from \({E}_{{{\rm{Ar}}}^{+}}-{E}_{{\rm{b}},{\rm{Cu}}(111)}\) in the case of the Cu(111) single-crystal target used in this study. By contrast, in the case of polycrystalline Cu target dominantly having a mixture of Cu(100), Cu(110) and Cu(111) exposed planes at the surface, the kinetic energy of the sputtered Cu atoms is expected to be spread between 10.35 and 10.74 eV. When considering the surface defects and grain boundaries at the target, the kinetic energy would be distributed more widely up to 11.52 eV (ref. 39). The radial distribution of the incident flux of the sputtered Cu atoms at the substrate is known to determine the uniformity of the deposition thickness of Cu film40. To check the thickness uniformity of the grown SCCF, we measured the thickness at five different points from centre to edge in a 2-inch wafer using an atomic force microscope (AFM). As a result, the thickness uniformity was estimated to be about 99.8% (Extended Data Fig. 9b, c). This result suggests that the diffusive flux of Cu atoms is purely uniform at the position of the substrate. Note that the substrate of our system is rotated at 30 rpm.

Structural and chemical characterizations

X-ray diffraction θ–2θ measurements were performed using a PANalytical Empyrean Series 2 instrument equipped with a Cu source (40 kV, 30 mA). Data were collected in the range 20° < 2θ < 90°, with a step size of 0.0167° and a dwell time of 0.5 s per point in all cases. AFM measurements were carried out using an XE-100 system (Park Systems, Inc.). Scanning electron microscopy, EBSD, pole figure (PF) and IPF measurements were performed with a Zeiss Supra 40VP with a scanning electron microprobe. An STM surface analysis was conducted using a custom-built STM system installed at the University of Ulsan, Korea. Electron-transparent cross-sectional TEM samples were prepared by the Ga ion beam milling and lift-out method in focused ion beam systems (FIB, Helios NanoLab 450, FEI and AURIGA CrossBeam Workstation, Carl Zeiss) and the possible damaged surface layers on the samples were removed by subsequent low-energy Ar ion beam surface milling at 700 eV for 15 min (Model 1040 NanoMill, Fischione). The plan-view TEM specimen was prepared by mechanical polishing and dimple grinding, followed by ion milling with Ar ions. Double Cs-corrected (S)TEM systems (JEM-ARM200CF, JEOL) equipped with EELS (Quantum ER965, Gatan) and EDX (JED-2300T, JEOL) were used for atomic-scale structure imaging and chemical analysis of the samples at an accelerating voltage of 200 kV. The inner and outer angle ranges for ADF-STEM and ABF-STEM imaging were 45–180 and 12–24 mrad, respectively. The HRTEM, ADF-STEM and ABF-STEM images were denoised by a local 2D difference image filter that is implemented in commercial software (HREM-Filters Pro, HREM Research Inc.). The HRTEM simulation was carried out for the amorphous carbon/copper \([1\overline{1}0]\) supercell structure (4.8 × 4.8 nm2) using the multislice method, which is implemented in the commercial software MacTempas (Total Resolution LLC), with the following microscope and imaging parameters: accelerating voltage (V = 200 kV), spherical aberration coefficient (Cs = 0.4 μm), chromatic aberration coefficient (Cc = 1.1 mm), convergence semi-angle (α = 0.5 mrad), sample thickness (t = 20.5 nm) and defocus (Δf = +14 nm). The simulated HRTEM image was estimated to have a correlation of 0.98 with the experimental HRTEM image as a cross-correlation factor. For the quantitative analysis of local strain components in the copper thin film, the GPA technique was used, which allows mapping two-dimensional local displacement fields by analysing the phase shift between non-collinear Fourier components of the lattice vectors g1 and g2. For EELS measurements of the Cu–Al2O3 interface and the Cu surface, the core-loss EELS spectra of the Cu L edge were obtained from the interface to the Cu surface using the line scan function of the scanning step (0.72 nm) for a 37.83-nm length with an energy dispersion of 0.5 eV pix−1 and a dwell time of 2.0 s pix−1. For core-loss EELS spectrum imaging for the comparison of surface structures between the SCCF and the PCCF samples, surface regions of both samples were selected by 20 × 16 pixels that can be translated as 9.87 × 7.9 nm2 and scanned with the step size of 0.493 nm to obtain EELS spectrum imaging dataset. The selected range of energy loss was set to be 477–988 eV including O K and Cu L2,3 edges. Nanoscale STEM-EDX maps of the constituent elements of the Cu–Al2O heterostructure were obtained for a 256 × 256 pixel resolution with a high-efficiency dual silicon drift detector X-ray detector system having a wide collection window of 100 mm2 for each detector, and the sample drift during the acquisition was corrected by tracking the reference area assigned at the acquisition setup.

Thermogravimetric analysis for the PCCF and SCCF samples with different surface roughness

The thermal mass change was measured using a thermogravimetric measurement system (TG-DTA 2000S, MAC Science). We prepared two SCCF samples with different values of surface roughness and a PCCF sample. The gravimetric changes of the three samples were measured in the temperature range from room temperature to 700 °C at a heating rate of 20 °C min−1 under air atmosphere. The two SCCF samples with different values of r.m.s. roughness, that is, 0.3 nm (SCCF-0.3, corresponding to a mono-atomic step) and 0.7 nm (SCCF-0.7, corresponding to a bi-atomic or tri-atomic step), were tested to ascertain the effect of the surface steps on oxidation in comparison with the PCCF sample (blue) (r.m.s. roughness around 10 nm). Although the SCCF sample with a roughness of 0.3 nm (red) was synthesized by ASE and had an ultraflat surface with occasional mono-atomic steps, the SCCF sample with a roughness of 0.7 nm (green), which was synthesized using a single-crystal target in a conventional sputtering system, had occasional multi-atomic steps of 2 or 3 atomic layers in height.

Theoretical calculations

All ab initio total energy calculations and geometry optimizations were performed with DFT in the generalized gradient approximation Perdew–Burke–Ernzerhof functional29 and with the projected augmented-plane-wave method30, as implemented by Kresse and Joubert31. The Cu substrate was represented by slabs of six layers with the theoretical equilibrium lattice constant. A vacuum length of 15 Å was used, and the bottom two layers of the slab were fixed in their bulk positions. The electron wave functions were expanded in a plane-wave basis set with a cut-off energy of 400 eV. The Brillouin zone for the slabs was sampled using k-point sets equivalent to at least a (5 × 5 × 1) Monkhorst–Pack grid41 for the primitive fcc unit cell. The climbing image-nudged elastic band method42 was used to calculate activation energies. The local atomic charge was computed using Bader’s charge decomposition method43, which divides the total volume into individual atomic volumes for each atom as the one containing a single charge density maximum and separated from the other volumes by a zero-flux surface of the gradients of the charge density magnitude. The incremental adsorption energy of an oxygen atom as a function of oxygen coverage \(\Theta =n/{n}_{0}\) for n O atoms on n0 fcc sites on a Cu(111) substrate is calculated as the energy change when a further O atom is adsorbed on the substrate, \({E}_{{\rm{ad}}}(n)=E[{\rm{Cu}}+(n+1){\rm{O}}]-E[{\rm{Cu}}+n{\rm{O}}]-\frac{1}{2}E[{{\rm{O}}}_{2}],\) in which E[Cu + nO] is the total energy of n oxygen atoms on the Cu substrate and E[O2] is the total energy of an isolated oxygen molecule.