We have investigated effects of the vertical scaling on electrical properties in extremely thin-body InAs-on-insulator (-OI) metal-oxide-semiconductor field-effect transistors (MOSFETs). It is found that the body thickness (T-body) scaling provides better short channel effect (SCE) control, whereas the T-body scaling also causes the reduction of the mobility limited by channel thickness fluctuation (delta T-body) scattering (mu(fluctuation)). Also, in order to achieve better SCEs control, the thickness of InAs channel layer (T-channel) scaling is more favorable than the thickness of MOS interface buffer layer (T-buffer) scaling from a viewpoint of a balance between SCEs control and mu(fluctuation) reduction. These results indicate necessity of quantum well channel structure in InAs-OI MOSFETs and these should be considered in future transistor design. (C) 2014 AIP Publishing LLC.