Density-gradient theory: a macroscopic approach to quantum confinement and tunneling in semiconductor devices

Density-gradient theory provides a macroscopic approach to modeling quantum transport that is particularly well adapted to semiconductor device analysis and engineering. After some introductory observations, the basis of the theory in macroscopic and microscopic physics is summarized, and its scattering-dominated and scattering-free versions are introduced. Remarks are also given about the underlying mathematics and numerics. A variety of applications of the theory to both quantum confinement and quantum tunneling situations are then reviewed. In doing so, particular emphasis is put on understanding the range of validity of the theory and on its unexpected power as a phenomenology. The article closes with a few comments about the future.