In PROMIS we support two different types of quantities, linear and exponential quantities. Exponential quantities, such as dopant concentrations vary by several orders of magnitude, typically, but cannot assume negative values. Linear quantities, like the electrostatic potential may assume positive and negative values, but usually have less dynamic range than the exponential quantities.
For linear quantities the gradient criterion compares the variation of the quantities' values at neighboring grid points with their value range in linear scale. For exponential quantities, the values are compared in logarithmic scale. We determine the value range for each quantity separately (3.6-16).
Then, the criterion 
, for inserting grid lines near the vertical
position 
is calculated from (3.6-17) for linear quantities
and from (3.6-18) for exponential quantities. For exponential
quantities concentration values below a certain value 
are ignored in
the gradient criterion. This is particularly essential if the
initial profile for the diffusion is taken from measurements or Monte Carlo
simulations.
For the decision if the grid line may be deleted we
use (3.6-19) and (3.6-20) for linear and
exponential quantities, respectively.
