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First order Raman spectra of Si nanocrystals exhibit large shift and width, strongly exceeding the theoretical calculated values. The disagreement between theory and experiment is dramatically increasing for the smallest nanocrystal sizes. Here, we present a novel theoretical approach showing one-, two-, or three-dimensional quantum effects, due to the limited size of the corresponding coordinate of the quantum structure. The method can be applied to nanosized layers, quantum wires and/or quantum dots. The agreement of the present theory with experimental data is dramatically improved.

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