Testing the Equivalence between Spatial Averaging and Temporal Averaging in Highly Dilute Solutions

Thermal scanning probe lithography-a review

Fundamental aspects and state-of-the-art results of thermal scanning probe lithography (t-SPL) are reviewed here. t-SPL is an emerging direct-write nanolithography method with many unique properties which enable original or improved nano-patterning in application fields ranging from quantum technologies to material science. In particular, ultrafast and highly localized thermal processing of surfaces can be achieved through the sharp heated tip in t-SPL to generate high-resolution patterns. We investigate t-SPL as a means of generating three types of material interaction: removal, conversion, and addition. Each of these categories is illustrated with process parameters and application examples, as well as their respective opportunities and challenges. Our intention is to provide a knowledge base of t-SPL capabilities and current limitations and to guide nanoengineers to the best-fitting approach of t-SPL for their challenges in nanofabrication or material science. Many potential applications of nanoscale modifications with thermal probes still wait to be explored, in particular when one can utilize the inherently ultrahigh heating and cooling rates.

Explaining the Transition from Diffusion Limited to Reaction Limited Surface Assembly of Molecular Species through Spatial Variations

Surface assembly is often decomposed into two classes: diffusion and reaction limited processes. The transition between the two cases is complex because the dynamics are so different. In this article, we simulate, explain, and experimentally discuss the evolution of the spatial distribution for surface assemblies with diffusion limited and reaction limited processes. Explicitly, we demonstrate that diffusion limited and reaction limited processes show some temporal differences, but more importantly, we show that the spatial arrangements are different enough to discriminate between the two cases. Using fundamental properties, such as the diffusion constant, we calculate the evolution of the spatial profile and derive from physical, heuristic models the assembly rate for reaction and diffusion limited processes based on the individual particle's interactions with the surface. Finally, we confirm the spatial profile differences between diffusion and reaction limited cases by experimentally measuring the surface assembly between two molecules of similar size, but having different assembly routes. Unique to our description is that we have derived and simulated everything through the particle picture in place of ensemble descriptions such as the diffusion equation, and we show the equivalence between our heuristic formulas and those derived from the diffusion equation.