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A numerical model of a new type of resonant-tunnelling diode based on electron resonant-tunnelling emission from silicon cathode with SiOx-Si multilayer coating has been developed. The model is founded on joint numerical solution of the Schrodinger and Poisson equations system for the time-independent electron wave function, electric field, current and voltage and a small-signal analysis of the last three alternating components. Emitter accumulation layer and contacts presence and an electron delay in a coating quantum well and in a diode transit layer were taken into account. The investigations have shown presence of a negative resistance microwave frequency band for the diode with the electron transit angle from 0 to 2pi/3. The upper frequency of the band is 1012 GHz when resonant tunnelling occurs through the highest resonant level in a quantum well.