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 ([1overline{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.

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