Over the past few years vacuum electronics is becoming one of the most promising directions of modern nanoelectronics, which is connected with the progress in the development of triode semiconductor devices with nanoscale vacuum channel, demonstrating the high performance, resistance to the radiation and aggressive environment, and low power consumption [1-3]. With a decrease of the minimum topological size the important issue is to find the optimal performance of the vacuum triode, providing a stable field emission, taking into account the variation in geometry of the triode structure during the transition to the submicron design rules. In this work the simulation models describing the field-emission characteristics of the three different types of field-emission triode structures with nanoscale vacuum channel are presented: a) for the planar geometry of the cathode and grid electrodes, b) for the vertical geometry of the cathode and with the circular aperture of grid electrode, and c) for the planar geometry of the cathode in the case of isolated grid electrode. Based on these models, the geometrical parameters of the triode structures, allowing achieving maximum amplification of the electric field on the cathode surface with the variation of the cathode radius, the "cathode-anode" and "cathode grid" distances, are found which determines the tendency of the parametric change of the field emission in the process of scaling. As the minimum size of the vacuum triode, the technological design standards typical for the modern microelectronics industry was used in the range from 90 to 22 nm (90 nm, 65 nm, 45 nm, 32 nm and 22 nm).