Fractal properties and applications of dendritic filaments in programmable metallization cells

Programmable metallization cell (PMC) technology employs the mechanisms of metal ion transport in solid electrolytes (SE) and electrochemical redox reactions in order to form metallic electrodeposits. When a positive bias is applied to an anode opposite to a cathode, atoms at the anode are oxidized to ions and dissolve into the SE. Under the influence of the electric field, the ions move to the cathode and become reduced to form the electrodeposits. These electrodeposits are filamentary in nature and persistent, and since they are metallic can alter the physical characteristics of the material on which they are formed. PMCs can be used as next generation memories, radio frequency (RF) switches and physical unclonable functions (PUFs).

The morphology of the filaments is impacted by the biasing conditions. Under a relatively high applied electric field, they form as dendritic elements with a low fractal dimension (FD), whereas a low electric field leads to high FD features. Ion depletion effects in the SE due to low ion diffusivity/mobility also influences the morphology by limiting the ion supply into the growing electrodeposit.

Ion transport in SE is due to hopping transitions driven by drift and diffusion force. A physical model of ion hopping with Brownian motion has been proposed, in which the ion transitions are random when time window is larger than characteristic time. The random growth process of filaments in PMC adds entropy to the electrodeposition, which leads to random features in the dendritic patterns. Such patterns has extremely high information capacity due to the fractal nature of the electrodeposits.

In this project, lateral-growth PMCs were fabricated, whose LRS resistance is less than 10Ω, which can be used as RF switches. Also, an array of radial-growth PMCs was fabricated, on which multiple dendrites, all with different shapes, could be grown simultaneously. Those patterns can be used as secure keys in PUFs and authentication can be performed by optical scanning.

A kinetic Monte Carlo (KMC) model is developed to simulate the ion transportation in SE under electric field. The simulation results matched experimental data well that validated the ion hopping model.