Three-dimensional analytical modeling of nanocrystal memory electrostatics

The integration of a two-dimensional distribution of discrete nanoscale floating gates in the nonvolatile memory gate stack produces significant three-dimensional (3D) electrostatic effects in contrast to the conventional flash memory modeling where a one-dimensional (1D) treatment is often sufficient. We have developed an analytical model for 3D electrostatics, which can not only enhance design intuition for device optimization but also provide convenient integration with a Schrödinger solver for self-consistent transport calculations since it is independent of discretization requirements. The model is validated by comparing with a finite-element Maxwell equation solver. The 3D analytical model has a much lower root-mean-square error than the 1D formulation for electrostatic potentials and fields in the tunneling path.