text: In semiconductor physics, this equation is called the drift–diffusion equation. The word "drift" is related to drift current and drift velocity. The equation is normally written:
  where
  * and  are the concentrations (densities) of electrons and holes, respectively,
  * is the elementary charge,
  * and  are the electric currents due to electrons and holes respectively,
  * and  are the corresponding "particle currents" of electrons and holes respectively,
  * represents carrier generation and recombination ( for generation of electron-hole pairs,  for recombination.)
  * is the electric field vector
  * and  are electron and hole mobility.
  The diffusion coefficient and mobility are related by the Einstein relation as above:
  where  is the Boltzmann constant and  is absolute temperature. The drift current and diffusion current refer separately to the two terms in the expressions for , namely:
  This equation can be solved together with Poisson's equation numerically.
  An example of results of solving the drift diffusion equation is shown on the right. When light shines on the center of semiconductor, carriers are generated in the middle and diffuse towards two ends. The drift–diffusion equation is solved in this structure and electron density distribution is displayed in the figure. One can see the gradient of carrier from center towards two ends.