Temperature dependence of the Fowler–Nordheim current in metal-oxide-degenerate semiconductor structures

A comprehensive study of the temperature dependence of the Fowler–Nordheim (F–N) tunnel emission in a metal-oxide-semiconductor structure is conducted both theoretically and experimentally. The theoretical variations with temperature of the F–N emission is analyzed both for metallic and degenerate semiconductor cathode materials. The influence of the electron concentration of a degenerate semiconductor on the amplitude of the F–N current is demonstrated. A new analytical formula for the F–N current temperature dependence is derived from the exact expressions using the Sommerfeld expansion. This new analytical approximation proves to be much more efficient than the previous analytical formula developed by Good and Müller [Field Emission, Handbuch der Physik, Vol. 21 (Springer, Berlin, 1956)] and may be very useful for F–N current computer-aided-design-oriented numerical simulation. The experimental study of the F–N current in MOS capacitors clearly demonstrates the strong impact of temperature on the F–N emission above 250 °C. It is also shown that the pre-exponential and the exponential F–N coefficients can still be determined as a function of temperature. The relative variation with temperature of the experimental F–N current data can be well interpreted by the exact F–N emission formula provided that the temperature dependence of the semiconductor (metal) -oxide barrier height Φb is well accounted for by a quasilinear function of temperature. The absolute amplitude of the F–N current can also be satisfactorily predicted by the exact F–N theory while adjusting the semiconductor electron concentration.