In this paper, we report on the fabrication of micrometre and nanometre-sized resonant tunnelling diode (RTD) devices which may be used as excitable neuromorphic spike generators. The fabrication processes using photolithography were applied for micro-sized RTDs, while for nano-RTDs the fabrication was optimised to achieve accurate nano-sized mesas through a multi-exposure step based on e-beam lithography. The results show a large decrease in the peak currents from 41 mA to 27 A for micro- and nano-RTDs, respectively, peak and valley voltages of around 0.6 V and 0.8 V and a peak to valley current ratio of around 2.4. For the smallest fabricated RTD of 300 nm diameter, the expected energy consumption per oscillation cycle (if used in an oscillator) will be 1.55 fJ. DC characterisation of the devices show that the nano-RTDs are stable and have smooth current voltage (I-V) characteristics compared with micro-RTDs. The nano-RTD technology could be employed to realise highly sensitive photodetectors that can be operated as spike generators and so they could underpin the development of energy efficient neuromorphic computing.