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Alloy scattering in a sSi/Si0.5Ge0.5/strained Silicon on Insulator (SOI) (sSOI) quantum-well (QW) p-MOSFET is investigated by hole density modulation through applying back-gate biases. The hole mobility under negative back-gate biases is found degraded by intensified alloy scattering at low electrical field because more holes are distributed in the bulk Si0.5Ge0.5. At higher electrical field, the higher density of holes populated at the Si/ Si0.5Ge0.5 interface and less holes in the bulk Si0.5Ge0.5 result in less pronounced alloy scattering, leading to mobility enhancement under negative back-gate biases. This confirms experimentally that alloy scattering does not play a significant role in the hole mobility of sSi/ Si0.5Ge0.5/sSOI QW p-MOSFETs under normal operating mode.