Our percolating devices were fabricated by simple nanoparticle deposition processes (32, 44). Seven-nanometer Sn nanoparticles were deposited between gold electrodes (spacing, 100 μm) on a silicon nitride surface. Deposition was terminated at the onset of conduction, which corresponds to the percolation threshold (28, 44). The deposition takes place in a controlled environment with a well-defined partial pressure of air and humidity, as described in (32). This process leads to controlled coalescence and fabrication of robust structures, which function for many months but which yet allow atomic-scale switching processes to take place unhindered. The individual atomic-scale filaments formed within tunneling gaps exhibit quantized conduction (29), but, as shown in fig. S1 (E and F), the complex percolating-tunneling network comprises many parallel and series paths, and so the device conductance is not quantized.

As described in the discussion of Fig. 4, data from all devices presented here are consistent with criticality. To explore noncritical networks, several devices were fabricated with surface coverages that were either below or above the percolation threshold (see Fig. 1, B and D). In all cases, however, it was not possible to observe avalanches of events. When stimulated, low-coverage devices exhibit a number of irreversible drops in conductance and rapidly become open circuit: Atomic switches can be opened, but the prevalence of large gaps in the network makes closing switches difficult. High-coverage devices exhibit no switching events for small stimulus voltages and exhibit irreversible drops in conductance for larger stimulus voltages due to melting of particles when large currents flow.

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