Proposal of a Simple Numerical Method for Determining the Height of the Schottky Barrier at Metal–Semiconductor Junctions

Abstract

Using a 2-D energy band model for electrons on metal surfaces, the value of surface electrical potential was determined. This potential depends on the work function, the concentration of conduction electrons in the metal, and the electron effective mass in surface 2-D band. The spatial distributions of electrical potential were calculated in thermal equilibrium in cylindrical structures of different semiconductors with Al contacts and considered surface states that accumulate surface charge. The electrical potential difference between the metal surface and the interior of the semiconductor constitutes the Schottky barrier (SB). The results of our calculations are in good agreement with the experimental data and confirm the fact that simple Schottky-Mott theory cannot be used to calculate the height of the SB. Calculations were performed for the structure Hg0.78Cd0.22Te at ${T} =77$ K, as well as CdTe and GaAs at ${T} =300$ K. The estimated effective mass of electrons in the surface 2-D band for aluminum is ${m}_{e}\approx {1.16}{m}_{{0}}$ .