Simulating radial dendrite growth

The formation of dendrites in materials is usually seen as a failure-inducing defect in devices. Naturally, most research views dendrites as a problem needing a solution while focusing on process control techniques and post-mortem analysis of various stress patterns with the ultimate goal of total suppression of the structures. However, programmable metallization cell (PMC) technology embraces dendrite formation in chalcogenide glasses by utilizing the nascent conductive filaments as its core operative element. Furthermore, exciting More-than-Moore capabilities in the realms of device watermarking and hardware encryption schema are made possible by the random nature of dendritic branch growth. While dendritic structures have been observed and are well-documented in solid state materials, there is still no satisfactory theoretical model that can provide insight and a better understanding of how dendrites form. Ultimately, what is desired is the capability to predict the final structure of the conductive filament in a PMC device so that exciting new applications can be developed with PMC technology.

This thesis details the results of an effort to create a first-principles MATLAB simulation model that uses configurable physical parameters to generate images of dendritic structures. Generated images are compared against real-world samples. While growth has a significant random component, there are several reliable characteristics that form under similar parameter sets that can be monitored such as the relative length of major dendrite arms, common branching angles, and overall growth directionality.

The first simulation model that was constructed takes a Newtonian perspective of the problem and is implemented using the Euler numerical method. This model has several shortcomings stemming majorly from the simplistic treatment of the problem, but is highly performant. The model is then revised to use the Verlet numerical method, which increases the simulation accuracy, but still does not fully resolve the issues with the theoretical background. The final simulation model returns to the Euler method, but is a stochastic model based on Mott-Gurney’s ion hopping theory applied to solids. The results from this model are seen to match real samples the closest of all simulations.