A new constituent of electrostatic energy in semiconductors

The concept of electric energy is revisited in detail for semiconductors. We come to the conclusion that the main relationship used to calculate the energy related to the penetration of the electric field in semiconductors is missing a fundamental term. For instance, spatial derivate of the electrostatic energy using the traditional formula fails at giving the correct electrostatic force between semiconductor based capacitor plates, and reveals unambiguously the existence of an extra contribution to the standard electrostatic free energy. The additional term is found to be related to the generation of space charge regions which are predicted when combining electrostatics with semiconductor physics laws, such as for accumulation and inversion layers. On the contrary, no such energy is needed when relying on electrostatics only, as for instance when adopting the so-called full depletion approximation. The same holds for neutral and charged insulators that are still consistent with the customary definition, but these two examples are in fact singular cases. In semiconductors for instance, this additional energy can largely exceed the energy gained by the dipoles, thus becoming the dominant term. This unexpected result clearly asks for a generalization of electrostatic energy in matter in order to reconcile basic concepts of electrostatic energy in the framework of classical physics.