In this work we present a theoretical study based on time-domain Monte Carlo (MC) simulations of GaN-based Self-Switching Diodes (SSDs) oriented to the experimental achievement and control of the sub-THz Gunn-oscillations potentially provided by these devices. With this aim, an analysis of the frequency performance of SSDs connected to a resonant RLC parallel circuit, is reported here. V-shaped SSDs have been found to be more efficient, in terms of the DC to AC conversion efficiency η, than similar square-shape ones. Indeed, a value of η of at least 0.80%, can be achieved with appropriate RLC elements, even when considering heating effects. When the influence of parasitic elements such as the crosstalk capacitance Ctalk is evaluated, MC simulations have shown that the resonant circuit must contain a capacitance C higher than Ctalk in order to obtain experimentally useful values of η. This condition can be reached by integrating a sufficiently high number N of parallel SSDs in the fabricated devices. MC simulations have also shown that when several diodes are fabricated in parallel the oscillations of all the SSDs are not synchronized, but this problem is solved by the attachment of a resonant RLC tank.