Simulations of “atomistic” effects in nanoscale dopant profiling

The most commonly used method for dopant profiling in semiconductors is scanning capacitance microscopy (SCM). However, the analysis on which SCM is based assumes the dopant atoms are a continuous fluid, and “atomistic” effects caused by the locations of the individual dopant atoms make this assumption invalid at a resolution finer than 10 nm for a dopant concentration of 10
¹⁸
cm
^-3
where there is an average of only 1 atom per pixel. Simulations are presented which include quantum mechanical effects such as the confinement of carriers near the dopant atoms, as well as the discrete nature of the dopant atoms. These simulations suggest that error bars should be used to show the lack of certainty in dopant profiling as such a fine resolution is approached.