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In this work we investigate the effect of various structural geometry on the field enhancement factor of an individual carbon nanotube (CNT) field emitter. We employ a computational model, that has been experimentally verified, to investigate the influence of system component geometry. Our results show that, in certain cases, the influences of support length and anode-cathode separation distance are of comparable magnitude. Additionally, the effect of CNT radius dominates the system electrostatics as compared to other structural geometries, such as anode-cathode distance, the cathode structure supporting the CNT emitter and the length of the emitter.