Fully macroscopic description of bounded semiconductors with an application to the Si-SiO2interface

A fully macroscopic description of semiconductors is presented which includes the boundary conditions at the surface of the semiconductor that are required for consistency with the usual diffusion-drift current equations. As in all field theories, e.g., electromagnetism, both the boundary conditions and the differential equations are obtained from the same governing integral forms. The new boundary conditions relate the jump discontinuities in the chemical potentials across the interface to the forces exerted by the lattice on the charge carriers which prevent the carriers from leaving the solid. The expressions for the forces in the static case are found and the values of the material surface coefficients appearing therein are obtained from quasistatic metal-oxide-semiconductor capacitance-voltage measurements for some particular Si-Si${\mathrm{O}}_2$ interfaces.