Supplementary Figures

Supplementary Figure 1: Mass-spectroscopy measurements during sample preparation. The mass-spectrometry meaurements have been performed in a close proximity to the ZnO(0001) sample surface during the final cycle of the surface preparation (annealing).


Supplementary Note 2: XPS escape depth and elemental ratios
We would like to point out that the escape depth for 2p electrons in Cu at the given photon energy is ∼3.6 ML, which means that the signal from the interior atoms in the 2-4 ML high 3D Cu nanoparticles is attenuated compared to the situation where the Cu atoms are spread as a layer of adsorbates or film over the surface. Note that the XPS signal ratios are given instead of absolute intensities in order to cancel out a possible fluctuation of the X-Ray source intensity, although the absolute intensity trends are also fully consistent with the described sequence. The absolute integral intensity of the Cu 2p peak also increased to about the half of the initial value at the end of range II, while the Zn 2p intensity remained virtually constant after a pronounced drop at the end of range I. Moreover, the Cu/Zn ratio (see Supplementary Figure 2) increases from 0.028 at 475 K to 0.041 at 560 K (the end of range II), which is larger than the initial value of 0.036 after Cu deposition. The increase of the Cu/O ratio could in principle be affected by loss of oxygen. This process is however unlikely at the moderate temperature in range II and the TPD measurements confirmed that the Cu/O, Zn/O, and Cu/Zn ratios were not affected by a loss of species (e.g. Zn or O) from the surface since we did not observe desorption of any of the species within range II (O was emitted above 630 K, Zn above 715 K, and Cu above 750 K).

Supplementary Note 3: Hydrogen in the crystal
Our TPD and XPS measurements confirmed that the crystals we used for the experiments are chemically pure and did not contain any significant traces of impurities except for hydrogen. The TPD measurements (see Supplementary Figure 1

Supplementary Note 6: Reliability of the PBE functional
We note that the PBE method does not describe the charge transition level for V O accurately. Therefore, the ionization of the oxygen vacancy with this method serves as a qualitative indication, rather than as an absolute prediction.
We would also like to note that the PBE functional underestimates the ZnO band gap; thus, in reality the adsorbed Cu atom need not necessarily act as a donor on the 1/4 vacancy reconstruction (although Cu was indeed found to become positively charged on ZnO(0001) at low coverage in Ref. 8).

Supplementary Note 7: The coverage of Cu chosen in our experiments
Here we would like to additionally point out that the 3D Cu NPs completely disappear from the surface and transform into a finely dispersed 2D layer due to their small coverage (0.3 ML), which was chosen to clearly demonstrate the effect. In case of higher coverages in the range from one to few MLs one can expect significant coarsening of 3D NPs accompanied by their partial wetting of the ZnO(0001) and disappearance of some amount of Cu (proportional to the available surface area) as it converts into the finely dispersed phase. Some of the phenomena indeed have been observed 9 but not fully understood as was outlined in the introduction.

Supplementary Note 8: The effect of local Cu-induced band bending on the STM scan profiles
The depressions around Cu NPs, which arise due the local band bending, could be observed laterally by STM for most of the as-grown NPs. The observed width of such depressions is approximately 0.7-1.5 nm for 1-3 nm wide particles as determined from STM cross-section profiles (like the one depicted in Supplementary Figure 5 (b)), taking into account the tip broadening effect. This value corresponds to at least 2-3 double layers of ZnO, which means that the depletion layer would be sufficiently deep to overlap with the subsurface defects region. Although, it is also important to note that the width of the depressions is significantly smaller than the estimated width of the depletion layer. The width of the depletion layer for a nanoparticle on an oxide substrate can be obtained from the following , where D is the depletion layer width and r m is the radius of a nanoparticle 10,11 . For a 1 nm particle, density of donor states N d = 2×10 17 cm −3 , and V BB = 0.4 V (as estimated from the XPS O 2p leading edge analysis), the depletion layer width D = 8.9 nm, which is also very close to the Debye length estimated above.
There can be several reasons why the observed width of the depression region is smaller than the depletion layer width. However, the main reason is that the measured width of the depressions around NPs is a bias dependent quantity as it has been demonstrated in detail on a similar Cu/Pt(110) system by Carroll et al. 12 . Therefore, the charge depletion layer around Cu NPs could not be fully visualized in our apparent height empty state STM images.

Supplementary Discussion
The dispersed particles appearing in range II could also be due to CuZn alloying, but such a scenario would require the migration of Zn interstitials as a driving force and can therefore be ruled out based on the observed XPS trends, which show no Zn enrichment in ranges I and II. Furthermore, the theoretically predicted formation energy for Zn interstitials in n-type ZnO is very high (∼6 eV, Ref. 2), which should lead to low concentrations, in agreement with our experimental observations. In range III, however, Zn interstitials could form during Cu bulk in-diffusion, according to the substitutional mechanism proposed by Qiu et al. 13 . Since Zn interstitials are highly mobile 2 , we tentatively conclude that the Zn/O ratio increase in range III is caused by two factors, namely Cu bulk in-diffusion and Cu-Zn alloying at the surface.

Experimental procedures
The samples for the STM and XPS measurements have been prepared in a UHV chamber with the base pressure below 1.5×10 −10 mbar. We used Zn-face EPI polished ZnO(0001) crystals from MTI Corp., which were in-situ cleaned by up to 20 times repeated cycles of Ar + ion sputtering at 1 keV (15 min) and annealing up to 780 K (15 min). We also performed mass-spectroscopy measurements in a close proximity to the surface during the final cycles of sample preparation. The temperature was monitored by a standard K-type thermocouple attached to one side of the sample and was simultaneously cross-checked by a pyrometer.
The two temperature readings coincided only in a narrow range around 500 K but could be reproducibly linked by the empirically determined relation