We have designed and grown high-electron-mobility heterostructures that use InAsySb1 - y group V alloys as a channel material and that can be used in high-speed transistors and magnetic held sensors. The group V alloys were formed by modulating As-2 and Sb-2 beams during growth. The composition was controlled by changing the group V shutter cycle. The electron mobility-in the InAsySb1 - y channel, which is only 20-30 nm thick and is sandwiched between Al0.15In0.85Sb high-resistivity barrier layers, was increased to 28 000 cm(2) V-1 s(-1) at room temperature by reducing the lattice mismatch between the channel layer and the barrier layer. This mobility is an order of magnitude greater than that of the strained Al0.158In0.85Sb/InSb/Al0.15In0.85Sb heterostructure grown as a reference. The electron mobility in the InAsySb1 - y channel sandwiched between Al0.5Ga0.5Sb barrier layers was also increased from 19 500 cm(2) V-1 s(-1) (y=1.0) to 24 500 cm(2) V-1 s(-1) (y=0.86) at room temperature by reducing the lattice mismatch between the channel layer and the barrier layer. These increases in mobility indicate that the lattice mismatch must be reduced in order to achieve a high electron mobility of such heterostructures grown mismatched on GaAs substrates.