  This work revisits the classical concept of electric energy and suggests that
the common definition is likely to generate large errors when dealing with
nanostructures. For instance, deriving the electrostatic energy in
semiconductors using the traditional formula fails at giving the correct
electrostatic force between capacitor plates and reveals the existence of an
extra contribution to the standard electrostatic energy. This additional energy
is found to proceed from the generation of space charge regions which are
predicted when combining electrostatics laws with semiconductor statistics,
such as for accumulation and inversion layers. On the contrary, no such energy
exists when relying on electrostatics only, as for instance when adopting the
so-called full depletion approximation. The same holds for charged or neutral
insulators that are still consistent with the customary definition, but which
are in fact singular cases. In semiconductors, this additional free energy can
largely exceed the energy gained by the dipoles, thus becoming the dominant
term. Consequently, erroneous electrostatic forces in nanostructure systems
such as for MEMS and NEMS as well as incorrect energy calculations are expected
using the standard definition. This unexpected result clearly asks for a
generalization of electrostatic energy in matter in order to reconcile basic
concepts and to prevent flawed force evaluation in nanostructures with
electrical charges.
