An Extra Electrostatic Energy in Semiconductors and its Impact in Nanostructures

TL;DR

This paper reveals an additional electrostatic energy component in semiconductors arising from space charge regions, which significantly impacts force calculations in nanostructures like MEMS and NEMS, challenging traditional electrostatic energy definitions.

Contribution

It introduces a revised concept of electrostatic energy in semiconductors accounting for space charge effects, improving accuracy in nanostructure force and energy calculations.

Findings

Standard electrostatic energy formulas fail in semiconductors with space charge regions.

The extra energy can dominate over dipole energy in semiconductors.

Incorrect force predictions occur when using traditional electrostatics in nanostructures.

Abstract

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.