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This paper studies the impact of high-mobility materials on the performance and energy efficiency of near- and sub-threshold CMOS logic circuits by means of analytical equations and experimental data on SiGe pMOSFETs. The introduction of high-mobility materials is shown to improve the energy-performance trade-off in near-threshold circuits more than in above-threshold circuits, since the benefits of higher mobility are degraded at higher longitudinal and transversal electric fields. On the other hand, results show that high-mobility materials do not exhibit any advantage in terms of the energy-performance trade-off in sub-threshold logic circuits. This is explained by the fact that the benefits brought by the larger mobility of SiGe or other alternative materials can be obtained by tuning the threshold voltage of conventional Si devices.