A contribution to the theory of the space-charge region in thin semiconductor monocrystalline films

The potential distribution in films the thickness of which is equal to or smaller than the Debye length is derived from Poisson's equation under general boundary conditions. It is shown that there exist three basic forms of this distribution depending on the densities and character of charges on both surfaces, on the geometrical thickness of the thin film and on the Debye length of the semiconductor.Notation E_S1,E_S2 dimensionless surface field intensities - F₁F₂ space-charge functions - L_D Debye length - k Boltzmann's constant - n_b bulk electron density - N_S1,N_S2 concentration of surface charges - p_b bulk hole density - q electron charge - T absolute temperature - thickness of thin film measured in Debye lengths - coordinate perpendicular to the surface measured in Debye lengths - ₀ permittivity of free space - _s relative permittivity of semiconductor - dimensionless potential (multiples of kT/q) - E_cb energy of bulk conduction-band edge - E_c energy of conduction-band edge - E_i energy line that runs parallel to band edges and coincides in the bulk (assumed homogeneous) withE_ib, the intrinsic Fermi level - E_v energy of valence-band edge - E_vd energy of bulk valence-band edge - V potential