Volt-current characteristics for tunneling through insulating films

Abstract

Previous theory is extended by including the temperature dependence and image force correction and by a careful consideration of the electron energy ranges which give the main contribution to the tunnel current. The effects on the volt-current characteristic of a non-parabolic energy momentum relation in the insulator, and a conduction-band-edge effective electron mass in the insulator which differs from that in the outer metal layers, have both been derived. The published experimental dependence of the tunnel current on voltage and temperature, for Al-Al₂O₃-Al sandwiches, is in reasonable agreement with the theory if the effective electron mass in the insulator is about a quarter of the free electron mass and the metal-insulator work function, for a 48 Å thick film, is about 1.1 eV. Contrary to previous theory, it is predicted that the deviations (by about five per cent) from the zero temperature and zero bias ohmic resistance will occur for temperatures in excess of about 150°K and voltages in excess of about 0.1 V.