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Large band-to-band tunneling (BTBT) leakage currents can ultimately limit the scalability of high-mobility (small-bandgap) materials. This paper presents a novel heterostructure double-gate FET (DGFET) that can significantly reduce BTBT leakage currents while retaining its high mobility, making it suitable for scaling into the sub-20-nm regime. In particular, through one-dimensional Poisson-Schrodinger, full-band Monte Carlo, and detailed BTBT simulations, the tradeoffs between carrier transport, electrostatics, and BTBT leakage in high-mobility sub-20-nm Si-strained SiGe-Si (high germanium concentration) heterostructure PMOS DGFETs are thoroughly analyzed. The results show a dramatic (>100×) reduction in BTBT and an excellent electrostatic control of the channel while maintaining very high drive currents and switching frequencies in these nanoscale transistors.