Active layer thickness variation in highly-doped amorphous indium-gallium-zinc oxide thin film transistors with molybdenum-chromium contacts is studied to reveal parametric dependencies under both channel length and gate-contact overlap length scaling. Devices with thickness variations from 5 nm to 30 nm, channel length variation from 3 µm to 100 µm and gate-contact overlap length variation from 1 µm to 10 µm were fabricated, characterized and analyzed. Analysis from a field effect transistor perspective show typical thickness variation trends where threshold voltage shifts positively, subthreshold slope improves and I on /I off ratio increases as the active layer thickness is scaled down. Peculiar observations like extremely low saturation voltage, insensitivity towards channel length variations, two different slopes in the subthreshold region and peaks in the transconductance characteristics can be explained only by invoking the principle of Schottky transistor operation. Thinner devices exhibit high field Schottky operation with barrier lowering which causes monotonously increasing transconductance, while thicker devices show low field behavior with no barrier lowering signified by peaks with saturated behavior of transconductance. Channel length modulates this dependence of transconductance on thickness. Sensitivity towards gate-contact overlap length scaling increases with thickness. Devices with active layer thickness of 5 nm can withstand overlap length scaling up to 5 µm without transconductance degradation, while devices of 10 nm thickness can withstand overlap length scaling only upto 10 µm. Devices of 30 nm thickness show contact limited operation even at 10 µm overlap length. Conventional FET operating principles cannot explain these observations and the phenomenon of Schottky contact transistor operation has been invoked. The results point towards a thin borderline in low dimensional transistors, differentiating a FET from Schottky contact transistors, through a field dependent barrier lowering mechanism, which is modulated by active layer thickness, channel length and gate contact overlap length.