Spatially-Complex 2D/3D Geometries and Boundary Conditions in Electron Hydrodynamics

Recent advances in spatially-resolved transport measurements and computational frameworks have revealed that electrons in condensed matter can flow collectively, confirming early theoretical predictions and reinvigorating scientific interest in the field of electron hydrodynamics.

Despite the success of channel flow geometries in differentiating between uniform and parabolic current profiles, they have recently been shown to be insensitive to probing the differences between microscopic scattering processes, highlighting the need for more spatially-complex geometries. Additionally, the importance of boundary conditions, which has long been appreciated for 2D devices, is further underscored as nanoelectronic devices used in experiments have finite thickness, allowing out-of-plane boundaries to influence in-plane current profiles.

Here, we use our spatially-resolved Boltzmann transport framework SpaRTaNS to investigate the effect of spatially-complex 2D and 3D geometries, as-well as common boundary conditions, on the observed current profiles. Specifically, we elucidate how diffusive, absorbing, and specular boundary conditions on the carrier distribution functions relate to the more intuitive no-slip, no-stress, and finite-slip boundary conditions on current profiles. Further, we illustrate how this formalism can naturally be extended to handle transmission and reflection across device interfaces.