Comparison of Analytical and Numerical Resolution Functions in Sputter   Depth Profiling
  Quantification of sputter depth profiles is frequently done by fitting the convolution integral over concentration and depth resolution function. For a thin delta layer, there exist analytical solutions. The analytical depth resolution functions of two popular approaches, that of the MRI model and that of Dowsett and coworkers are compared. It is concluded that the analytical depth resolution function of the MRI model gives the correct location of a buried delta layer with respect to the measured profile, and a clear description of the information depth in AES, XPS and SIMS. Both analytical solutions can be extended to larger layer thickness. But they are less flexible with respect to physical parameters which are not constant with concentration or sputtered depth, such as detection sensitivity, atomic mixing, roughness or preferential sputtering. For these cases, numerical solutions have to be used. 
S. Hofmann, Y. Liu, J.Y. Wang, J. Kovac
cond-mat.mtrl-sci