In this paper, we perform, by means of Monte Carlo simulations and experimental measurements, a geometry optimization of GaN-based nano-diodes for broadband Terahertz direct detection (in terms of responsivity) and mixing (in terms of output power). The capabilities of the so-called self-switching diode (SSD) are analyzed for different dimensions of the channel at room temperature. Signal detection up to the 690 GHz limit of the experimental setup has been achieved at zero bias. The reduction of the channel width increases the detection responsivity, while the reduction in length reduces the responsivity but increases the cutoff frequency. In the case of heterodyne detection an intrinsic bandwidth of at least 100 GHz has been found. The intermediate frequency (IF) power increases for short SSDs, while the optimization in terms of the channel width is a trade-off between a higher non-linearity (obtained for narrow SSDs) and a large current level (obtained for wide SSDs). Moreover, the RF performance can be improved by biasing, with optimum performances reached, as expected, when the DC non-linearity is maximum.