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A fundamental understanding of the mechanisms responsible for the dependence of hole mobility on SiGe channel layer thickness is presented for channel thicknesses down to 1.8 nm. This understanding is critical to the design of strained SiGe p-MOSFETs, as lattice mismatch limits the thickness of SiGe that can be grown on Si and as Ge outdiffusion during processing reduces the Ge fraction. Temperature-dependent measurements are used to extract the phonon-limited mobility as a function of SiGe channel thickness for strained Si0.57Ge0.43 heterostructures on bulk Si. The hole mobility is shown to degrade significantly for channel thickness below 4 nm due to a combination of phonon and interface scattering. Due to the finite nature of the quantum-well barrier, SiGe film thickness fluctuation scattering is not significant in this structure for channel thickness greater than 2.8 nm.