text: The Debye length has become increasingly significant in the modeling of solid state devices as improvements in lithographic technologies have enabled smaller geometries.
  The Debye length of semiconductors is given:
  where
  * ε is the dielectric constant,
  * k is the Boltzmann constant,
  * T is the absolute temperature in kelvins,
  * q is the elementary charge, and
  * N is the net density of dopants (either donors or acceptors).
  When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants.  Instead, a measure of the profile of the doping gradients provides an "effective" profile that better matches the profile of the majority carrier density.
  In the context of solids, Thomas–Fermi screening length may be required instead of Debye length.