Nano-volcanic Eruption of Silver

Silver (Ag) is one of the seven metals of antiquity and an important engineering material in the electronic, medical, and chemical industries because of its unique noble and catalytic properties. Ag thin films are extensively used in modern electronics primarily because of their oxidation-resistance. Here we report a novel phenomenon of Ag nano-volcanic eruption that is caused by interactions between Ag and oxygen (O). It involves grain boundary liquation, the ejection of transient Ag-O fluids through grain boundaries, and the decomposition of Ag-O fluids into O2 gas and suspended Ag and Ag2O clusters. Subsequent coating with re-deposited Ag-O and the de-alloying of O yield a conformal amorphous Ag coating. Patterned Ag hillock arrays and direct Ag-to-Ag bonding can be formed by the homogenous crystallization of amorphous coatings. The Ag “nano-volcanic eruption” mechanism is elaborated, shedding light on a new mechanism of hillock formation and new applications of amorphous Ag coatings.


Formation of abundant Ag hillocks and roughened surfaces
Figure S1 (A) shows the optical micrograph of the edge of the "covered" region of a sputtered Ag film after being annealed at 250 °C for 1 h in the ambient atmosphere, and the close--ups of scanning electron micrographs of the "covered" (right) and "uncovered" (left) regions. A clear boundary between the "covered" and "uncovered" regions can be seen with an optical microscope. The different optical properties in the "covered" and "uncovered" regions are attributed from the surface microstructures, that abundant Ag hillocks form in the "covered" region (right), which roughens the surface and induces light scattering. Therefore, although the volume of abundant Ag hillocks are typically 1 to 2 μm 3 , which has been beyond the spatial resolution of visible optics, the formation of abundant Ag hillocks can be clearly identified using a common optical microscope owing to the light scattering.
Figure S1 (C) shows the schematic diagram of using a mask to produce patterned abundant Ag hillocks. The characters of masks are etched out using a laser micro--processing kit; hence, the characters shown in Figs. S1 (B) and (D) are the "uncovered" regions. The patterned abundant Ag hillocks in Figs. S1 (B) and (D) are 3 fabricated in the ambient atmosphere and in an ultra--high vacuum, respectively. For the former, more hillocks are found in the "covered" regions (inverse parts of characters), as shown in the close--up optical images in Fig. S1 (B). However, no hillocks can be found in the "covered" regions when annealing under an ultra--high vacuum, while uniformly formed hillocks can be found in the "uncovered" regions as shown in Fig. S1 (D). As the "Ag nano--volcanic eruption" mechanism being elucidated in the paper, it is not surprising to see this trend. It is also comprehensible that a sharper boundary between "covered" and "uncovered" regions is expected for the process under an ultra--high vacuum; that is, the thermal convection for the process in the ambient atmosphere may not cause blowing out all suspended Ag and Ag2O clusters, so some of them still deposit at the "uncovered" region, resulting in the formation of a thinner amorphous Ag coating and subsequently fewer and smaller hillocks as shown in Fig. S1 (B). On the contrary, the autogenic mixture of suspended Ag and Ag2O clusters and O2 gas may be sucked into "uncovered" regions quickly, so no amorphous Ag coating nor hillocks will form, 4 which leaves a relatively flat surface behind at the "uncovered" regions (characters) as shown in Fig. S1 (D). Optical micrographs of patterned abundant Ag hillocks, which were fabricated with a mask at 250 °C for 1 h in an ultra--high vacuum, and its close--ups in "covered" and "uncovered" regions. 5

Kinetic analyses of abundant Ag hillock formation
Adatom diffusion on free surface is much faster than both grain boundary diffusion and lattice diffusion. We can assume that all Ag atoms that arrive at the free surface would immediately join the hillock growth, as comparing to the mass transfers of Ag from the stressed Ag film to its free surface. The atomic flux (J) driven by stress gradient can be expressed as where Δσ is the stress difference and d is the film thickness, so Δσ/d is the linear stress gradient, D is the diffusivity, T is the temperature, and k is the Boltzmann's constant. 24 The number of atoms (N') transported by the flux in a period of time t and through an area A is or the volume accumulated (V') through the stress--migration is where Ω is the atomic volume. Therefore, the volume accumulated (V') through the stress--migration is Since the atomic flux is contributed by both grain boundary diffusion and lattice diffusion, the accumulated volume through stress--migration can be further expressed as where the subscript l and gb stand for lattice and grain boundary, respectively. For 1 μm--thick sputtered Ag films annealed at 250 °C for an hour, the Δ ( ) ! ! can be estimated to be 8.26×10 !" Pa • s. 12 Additionally, as depicted in Fig. S2, based on the density of hillock nucleation sites (~1.06×10 ! #/mm 2 ) and average grain size of the Ag film (~104 nm) in experiments, 12 and the assumption of width of grain boundary to be 0.5 nm, the average areas of diffusion through lattice (Al) and grain boundary (Agb) per hillock can be estimated to be 9.33×10 !!" m 2 and 9.38×10 !!" m 2 , respectively. By taking Ω, k, T, d, Dl, and Dgb to be 1.71×10 !!" m ! , 1.38×10 !!" J/K, 523.15 K, 10 --6 m, 5.61×10 !!" m 2 /s, and 1.08×10 !!" m 2 /s, respectively, 25,26 the estimated volume of each Ag hillock is ~0.2 μm 3 , which is significantly smaller than the actual abundant Ag hillocks (1~2 μm 3 ) being observed in 7 experiments. 3,6,12,13 Fig. S2: The schematic top--view of the average territory a hillock on the Ag film with columnar grains. 8

Ab initio lattice stability of fcc--Ag and Ag2O under external pressure
The Vienna Ab--initio Simulation Package (VASP) 27  Monkhost--Pack scheme 29 were performed for the 32--atoms Ag supercell 30 and 48--atoms Ag2O supercell, 31 respectively. The numerical integration of the Brillouin zone and the energy cut--off were verified to produce absolute energy convergence to better than 10 −3 eV/atom, with the forces at each atomic site converged to within 10 −2 eV/Å. The dependence of strain energy on external pressure for each phase was calculated based on the total energy difference between the cell stressed structure and the fully relaxed structure. As shown in Fig.  S3, the changes of lattice stability for both fcc--Ag and Ag2O phases are only 0.4 and 0.3 meV/atom, respectively, when the external pressure is as large as 350 MPa, which was much 9 larger than that applied in any of our experiments. Therefore, as expected for most condensed phases, the changes in phase stability for both Ag and Ag2O phases are negligible under very large stresses. Figure S3: Ab initio strain energies of fcc--Ag and Ag2O phases as function of external pressure ranging from 0 to 400 MPa.

Critical temperature on Ag nano--volcanic eruption
Ag--O grain boundary liquation due to the extremely high oxygen partial pressure at the grain boundaries is the first step of the "nano--volcanic eruption". Figure S4 shows the optical micrographs of the sputtered Ag films, which are partially covered with dummy chips and annealed at 100, 120, 130, 140, 145, and 150 °C, respectively, in the ambient pressure for 5 h. After the prolonged annealing time, a clear boundary between the "covered" (right) and "uncovered" (left) regions can only be found in the sample, which was annealed at 150 °C. Evidently there is no nano--volcanic eruption and hillock formation after prolonged annealing at temperatures at or lower than 145 °C and vice versa. This critical temperature of approximately 150 °C is close to the normal decomposition temperature of Ag2O. This finding strongly supports the "nano volcanic eruption" mechanism, as other theories concerning stress migration does not involve a critical temperature for formation of abundant Ag hillocks. Based on this understanding, an even lower processing temperature than 250 °C at as low as 150 °C is theoretically achievable for forming amorphous Ag coating as well as Ag--to--Ag direct bonding.