Finite element simulations of electrostatic dopant potentials in thin semiconductor specimens for electron holography

Two-dimensional finite element simulations of electrostatic dopant potentials in parallel-sided semiconductor specimens that contain p–n junctions are used to assess the effect of the electrical state of the surface of a thin specimen on projected potentials measured using off-axis electron holography in the transmission electron microscope. For a specimen that is constrained to have an equipotential surface, the simulations show that the step in the projected potential across a p–n junction is always lower than would be predicted from the properties of the bulk device, but is relatively insensitive to the value of the surface state energy, especially for thicker specimens and higher dopant concentrations. The depletion width measured from the projected potential, however, has a complicated dependence on specimen thickness. The results of the simulations are of broader interest for understanding the influence of surfaces and interfaces on electrostatic potentials in nanoscale semiconductor devices.