Forward and reverse current-voltage (I-V) of Ti/Au/n-Al0.33Ga0.67As/n-GaAs/n-Al0.33Ga0.67As multi-quantum well (MQW) Schottky diodes were measured over a range of temperatures from 20 to 400 K by a step of 20 K. The Schottky diodes parameters were then extracted from these characteristics. The Cheung method is used for this purpose, assuming a thermionic conduction mechanism. The extracted ideality factor decrease with increasing temperatures. But their values at low temperatures were found to be unrealistic. In order to explain this uncertainty, three assumptions were explored. Firstly an assumed inhomogeneous barrier height gave better parameters especially the Richardson constant but the ideality factor is still unrealistic at low temperatures. Secondly, by using numerical simulation, it was demonstrated that defects including interface states are not responsible for the apparent unrealistic Schottky diode parameters. The third assumption is the tunnelling mechanism through the barrier in the low temperature range. At these lower temperatures, the tunnelling mechanism was more suitable to explain the extracted parameters values.