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A polarized AlN/GaN five barrier heterostructure was grown and characterized for resonant electron emission in a diode configuration. Diodes of this type have extremely high resonant tunneling voltages of ~5 V, which is important for an effective electron emission over the surface gate-electrode vacuum barrier. The surface electrode consists of a carbon nanotube (CNT) network, which is highly conductive and has a good surface potential distribution and electron transparency, which is expected to be higher compared to a thin metal layer. The design proposed in this work aims in demonstrating monochromatic electron emission through the use of a resonant-tunneling configuration, semiconducting surface accelerating layer and a CNT surface gate-electrode.