Thermally Stable Nanotwins: New Heights for Cu Mechanics

Abstract Nanocrystalline and nanotwinned materials achieve exceptional strengths through small grain sizes. Due to large areas of crystal interfaces, they are highly susceptible to grain growth and creep deformation, even at ambient temperatures. Here, ultrahigh strength nanotwinned copper microstructures have been stabilized against high temperature exposure while largely retaining electrical conductivity. By incorporating less than 1 vol% insoluble tungsten nanoparticles by a novel hybrid deposition method, both the ease of formation and the high temperature stability of nanotwins are dramatically enhanced up to at least 400 °C. By avoiding grain coarsening, improved high temperature creep properties arise as the coherent twin boundaries are poor diffusion paths, while some size‐based nanotwin strengthening is retained. Such microstructures hold promise for more robust microchip interconnects and stronger electric motor components.

: High resolution HAADF scanning TEM images of tungsten nanoparticles in the 0.84 vol.% containing nt-Cu film, acquired as drift correction averaged ~30 frame series. A (detail from Figure 1), along with C, is consistent with the <100> view of the A15 phase in E: the occupation density of the atomic columns is indicated (red ring highlighting) as multiples of unit occupation of the un-highlighted columns. The fringes of the crystal planes of the Cu matrix are annotated with white lines. The scale bars are 2 nm long.

Supplementary Material 2: W NP concentration measurements
The number density of W NP was measured by manually counting the nanoparticles on BF-STEM images of Ga + thinned liftout specimens across several regions per sample. A nominal 2% counting error was assumed. The Cu film volume here considered was the product of the area on the BF-STEM image times the sample thickness -the latter measured at each specific imaging and counting location by high resolution SEM using the STEM probe contamination method; a ±2 nm error was considered for each dimension, based on repeated measurement.
Number density was converted to volume density knowing the average W nanoparticle diameter (4.0 nm [11] ) and a conservative error in the mean of measurement by TEM of ±0.1 nm (e.g. 1 nm error per measurement from HR-TEM images, with 1174 particles measured previously [11] ). Counting nanoparticles in the presence of nanotwins presented the complication of contrast from both NP and TBs; the solution was to achieve incident beam conditions per grain which led to low contrast of the matrix/twin volumes and the TBs, see in Supplementary Material 6. For both initial W NP densities, the particle volume fraction in the films was measured in the undeformed as-deposited and 400 °C-annealed states, as well as after hot indentation (higher W NP: 25 & 400 °C; lower: 25 °C) by measuring in a region centred 100 nm below the apex of the indent. The measured values and errors are summarised in Table S1, along with the volumes considered and the particle count to demonstrate counting statistics: due to the restricted size and gradient of the plastic zone below the indent, a reduced number of particles was counted compared to the undeformed state. It should be noted that counting W NP in the deformed condition presented the additional difficulty that dislocation intersections and debris generated additional point features in bright field imaging; use of the atomic number contrast of HAADF images in combination with their BF counterparts facilitated W NP identification. The film in Figure S2A,B is an additional deposition condition to the uniform ones in the main script: it contains variable W NP concentration through the film thickness -highest at the base, lowest in the mid-region and partway between these extremes in the upper layer.
This can be achieved by several methods -varying the W magnetron power, the tolerance in size selectivity of the mass spectrometer-based device [11] and finally the power of the Cu magnetron. In the as-deposited state, the Cu microstructure is columnar -many grains are continuous from substrate to surface. For certain grains, the incident electron beam direction is appropriate to generate contrast on the horizontal nanotwins (see Supplementary Material 6). After annealing at 400 °C, this columnar structure is maintained in the upper region but is entirely lost in the middle layer: grain coarsening to a single crystal has occurred where the W NP content was lowest, equivalently to the 0.84 vs 0.41 vol.% W NP films in the main script.
Contrast in the lowest layer was too poor to assess the microstructure -due to the increased specimen thickness and higher W NP density. Room temperature spherical nanoindentation on this film to ~80% depth serves to demonstrate in Figure S2C the preferential migration of Cu, using the boundaries between differing W NP density layers as visual markers.
Immediately below the indenter, the nanoparticles are seen to accumulate from the upper layer, exemplified by the atomic-number contrast in HAADF, whilst the pile-up material is considerably leaner in W NP. Although the self-diffusivity of copper is substantially greater than that of the insoluble W in the Cu matrix, at room temperature (0.22Tm) and an indentation strain rate of 0.2 s -1 , diffusion-based flow is not expected to control strength: any particle crowding occurs through relatively athermal crystal plasticity. Figure S2: Scanning TEM images of a Cu film with a varying concentration of embedded W NP along the direction of growth -part adapted from [11] . (A) as-deposited film with columnar Cu grains -some grains are correctly orientated for nanotwin contrast (see Supplementary Material 6); (B) the same film after annealing at 400 °C for 2 h; the columnar grains are lost in the middle layer with the lowest W NP density. (C) demonstrates particle crowding in this variable W NP density film below a spherical indent.

Supplementary Material 3: Electrical resistivity analysis
The increased resistivity of nanotwinned Cu compared to oxygen-free high-conductivity copper (OFHC) (1.67 × 10 -8 Ω m [14] ) is known to be due to the supplementary twin boundary content and ~100 nm diameter columnar grains. Considering the 3.58 × 10 -16 and 1.7 × 10 -17 Ω m 2 electrical resistivity of Cu GB [56] and TB [57] , respectively, the latter being half that of an intrinsic stacking fault [58] , the boundary contribution to resistivity here is 0.40 × 10 -8 and 0.53 × 10 -8 Ω m, respectively. Combined, these closely fulfil the 1.18 × 10 -8 Ω m excess of the nt-Cu above the OFHC reference. Addition of W nanoparticles further raised the resistivity to 2.98 × 10 -8 and 3.26 × 10 -8 Ω m, for 0.41 and 0.84 vol.% W NP, respectively -only an extra 0.13 × 10 -8 and 0.42 × 10 -8 Ω m over the tungsten-free film due to conduction electron scattering off the nanoparticle interfaces. Hence, the Cu-Cu boundaries remain the dominant factor in raising the resistivity. Figure S3: Room temperature indentation elastic modulus for the three material Cu film conditions (vol.% W nanoparticles) in the main script as a function of annealing temperature (1 h in vacuum per step, cumulative, except 500 and 600 °C which were each performed on separate samples as single temperature anneals) starting from the as-deposited state, as in Figure 2.

Supplementary Material 5: X-ray diffraction data
XRD data of the nt-Cu films, obtained in Bragg-Brentano geometry at room temperature following successive heat treatments, is given in Figure S4. These were analysed by peakfitting to determine the lattice parameters and hence the thermal-induced relaxation of deposition stresses, as reported in Table S2. A ~0.2% decrease in out-of-plane lattice parameter after annealing at 200 °C is characteristic of relaxation of initial in-plane compressive stress from film deposition.  (111) to (200) at 300 °C (cumulative, as in Figure 2A) and above for the 0.41 vol.% W NP film, whilst the 0.84 vol.% condition revealed no significant textural evolution from (111) -additional W peaks are seen in the latter case; the Mo sample holder and Inconel fixing screws necessary for nanoindentation also occasionally give signals.  Figure S5 reveals partial coarsening of the Cu grains.
TEM imaging of a FIB-thinned cross-section lamella confirms this in Figure S6 and demonstrates that coarsening of the mid-depth of the film is greater than the near-surface region probed by EBSD -and most substantially contributing to the measured hardness. The coarsened grains after 1 h at 500 °C do not present a single dominant out-of-plane texture; the in-plane grain diameter average by grain area is 2.6 ± 2.0 µm, reflecting the distinct bimodality of the grain size distribution of this condition. Furthermore, the average nanotwin thickness of the retained nt-Cu grains is 6.9 ± 1.0 nm, i.e. it has coarsened from the asdeposited value of 4.1 ± 0.3 nm, or that after 1 h at 400 °C: 4.1 ± 0.5 nm.
Annealing for 1 h at 600 °C resulted in near-complete coarsening of the Cu film to a 200 dominant texture with in-plane grain diameters averaging 39 ± 19 µm (area average ± standard deviation), Figure S5.  appear twin-free at a certain viewing angle, by further tilting the sample, the twins in these grain become visible; in contrast, this is not true for those equivalent grains in the peak plasticity zone below the indenter for the tungsten-free film where the nanotwinned microstructure is lost. Figure S7: Illustration of incident beam orientation impact on visibility of nanotwins upon TEM bright field imaging: red arrows indicate in each image in which columns nanotwins are substantially visible, whilst blue arrows indicate appropriate imaging conditions for nanoparticle counting (nanotwin extinction). The scale bar is 100 nm long.

Supplementary Material 8: Strength/hardness calculations
For the lamellar spacing-grain size condition of the present study, the dislocation nucleationlimited regime, Equation 1, applies. A previous study [24] determined the stress concentration factor at a TB-GB intersection to be S* ≈ 1.5/2, which also accounts for the directionality of leading partial dislocations. The Debye frequency at room temperature is 1.3 × 10 13 s -1 (Li et al. [24] ), V* ≈ 5b 3 (within the range predicted previously [8c] ) and ΔU ≈ 1.04 eV (Li et al. [24] )the latter based on empirical data fitting [8b] . Other parameters for Cu at T = 298 K are given in Table S3.
A model of the cutting of dispersed particles by matrix dislocations was developed by Ansell and Lenel [59] . It considers the shear stress exerted locally by a dislocation pile-up on a second phase particle, which shears the particle at a critical stress dependent on the shear modulus of the second phase. The cutting of particles would be expected to lead to a strength increase: where the shear modulus of W, GW, is 164.1 GPa [60] and C is ~30 in the case of dislocationfree particles [59] , which is reasonable for 4 nm W nanoparticles. Values for this stress for the materials in the present study are in Table S4.
The Hall-Petch strength is calculated as follows: TB spacing, λ, is taken as the characteristic Hall-Petch length when considerably smaller than grain size, d, giving a size-based strength: where σ0 (40 MPa [61] ) is the inherent resistance of the Cu lattice to dislocation motion and kHP (61)(62) describes sensitivity to d or λ equally well.
Further strengthening mechanisms were ignored due to the low initial dislocation density outside of the TBs from deposition, hence leading to a minimal strength increase at this scale of nanotwin thickness [63] ; this microstructural refinement also suppresses dislocation pile-up and locking mechanisms [23] . Load transfer to the W NP is also minimal for phase fractions below 1 vol.% [28] , and solution strength of PVD impurities is negligible (e.g. Ar <0.02 at.% [64] , and although O content can range 0 -5 at.% [65] , it is minimised to close to zero [65b] by surface cleanliness, low base pressures and substrate bias [65a] ).  [40] 42.1 b, Burgers vector of ordinary dislocation /nm 0.256 bp, Burgers vector of leading partial dislocation /nm 0.144 ν, Poisson ratio [40] 0.34  Table S1 for each material condition. *In cases where nanotwins exist/remain, the dislocation nucleation stress is the limiting factor at this twin lamella thickness, and hence the Hall Petch stress is superfluous [24] . Similarly, where nanoparticles are present, it is apparent that the stress for dislocation bowing is consistently lower than that for cutting across W NP, i.e. the latter mechanism is not favoured. **For the annealed 0.41 vol.% W NP condition, the film thickness was taken -the lateral grain size now being larger than this.

Supplementary Material 9: Creep flow stress calculations
Calculations of creep and grain boundary sliding flow stresses were based on the following models: Coble creep [66] , i.e. diffusion creep along grain boundaries: where Ω is the volume of a single atom, i.e. a 3 /4, δB is the width of a grain boundary, taken as b, DB0 is the prefactor for grain boundary diffusion and QB is the activation energy of the same process. ̇ is the strain rate -corresponding to the indentation strain rate of 0.2 s -1 here. Blum-Zeng creep [38,67] , i.e. diffusion creep along dislocations, considering the influence of nanocrystalline grain sizes (particularly, the high density of high angle grain boundaries) on the dislocation content within grains at any moment: where α and c are parameters for dislocation interaction with themselves, and the GB, respectively, previously determined for this material [67] .
Sliding of the columnar grain boundaries: where ρm is the density of copper at the melt point, MCu is its molar mass, Tm is its melting temperature and b is the Burgers vector of an ordinary dislocation in Cu, such that b 3 represents the activation volume for single atomic motions. fg is the volume fraction of grain interior, which for columnar grains as here is given by ( − 2 B )⁄ . The fraction of the total strain rate completed by GBS, Ġ BSṫot ⁄ , was given a value of 0.6 -relative to previous studies [25] .
TB annihilation through dislocation motion serving to migrate TBs [26] : where E0 is the GB energy of the Σ3(112) incoherent twin boundary generated upon detwinning, R is the radius of the disconnection semi-loop generated at the Σ3(111) coherent twin interfaces, expressed as a fraction of the grain diameter -identified to be 11% in previous work on this material. h is the width of the coherent twin boundaries, i.e. a single (111) layer: √3 ⁄ . The fraction of the total strain rate completed by detwinning, Ḋ Tṫot ⁄ , was arbitrarily given a value of 0.5, although it should be noted that σdetwinning is not significantly sensitive to this term.
Model lamellar spacings and grain diameters are taken to facilitate comparison with the datasets here, using λ = 4.1 nm and d = 130 nm for the nanotwinned condition, and d = 1000 nm for the untwinned, coarse grained annealed microstructure of the 0.41 and 0 vol.% W NP films following annealing up to 400 °C. In the latter, TB migration for detwinning is, of course, omitted from the calculations.
The complete set of curves for these models and conditions are plotted in Figure S8. The remaining parameters are given in Table S5.

Supplementary Material 10: nt-Cu thin film deposition
The cycles of the nanoparticle generator, which ensure a uniform flow rate with time of the nanoparticles by regularly supplementing the available nucleation sites, are described in Figure S1. Figure S9: Pressure evolution of the main deposition chamber containing the matrix (copper) magnetron during two complete air-leak cycles.