Parameters affecting the accuracy of oxide thickness prediction in thin metal–oxide–semiconductor structures

Abstract

On the basis of the solution of the time dependent Schrödinger equation within the framework of the effective mass theory, a complete quantum mechanical electron tunneling through a biased square potential model with abrupt interfaces was deduced. Barriers of 3 eV height and widths up to 140 Å were investigated. Current density–voltage ( J– V) curves were computed for Al/SiO 2/ n +Si structure. The computed J– V curves exhibited oscillations at applied voltages above (Fowler–Nordheim tunneling) and below (direct tunneling) 3 V. For oxide thickness estimation, the position of the oscillation extrema from this quantum mechanical model were fitted to a wave interference formula and showed excellent agreement for oxide layer widths less than 50 Å. However, a systematic deviation appeared for layers larger than 50 Å. We show that the electron energy distribution at the injection layer and the electron effective mass on layers other than the oxide layer are important parameters for accurate oxide thickness estimation.