Secondary electron doping contrast: Theory based on scanning electron microscope and Kelvin probe force microscopy measurements

The secondary electron emission flux in a scanning electron microscope is a powerful tool for delineation of electrically active dopant concentration, built-in potentials, and surface electric fields in semiconductor junctions. In all the secondary electron images of $p\text{-}n$ junctions, the $p$ -doped regions appear brighter than $n$ -doped regions. We present a theory for the doping contrast in $p\text{-}n$ junctions that is based on the secondary electron emission yield and surface band bending extracted from Kelvin probe force microscopy measurements. We show that the contrast is governed by the secondary electron escape depth, and their escape probability which is related to the secondary electron energy distribution and the effective electron affinity. It is found that the escape depth is the main factor determining the dopant contrast, and the escape probability has a smaller effect. In addition, our theory explains the logarithmic dependence of the measured contrast on the acceptor concentration in silicon reported by many groups.