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The benefits of using submicrometer modal-dimension silicon waveguides in realizing high-efficiency parametric Raman wavelength conversion are demonstrated theoretically and experimentally. The combined effects of Raman nonlinearities and free-carrier losses induced by two-photon absorption (TPA) are analyzed using the coupled-mode theory. The analysis indicates that scaling down the lateral dimensions increases the conversion efficiency of the Raman process and reduces the effective lifetime of free carriers and hence ameliorates the free-carrier losses. The feasibility of data conversion is demonstrated by coherent transfer of the analog radio-frequency (RF) signal from Stokes to anti-Stokes channels. The conversion efficiency, and hence signal-to-noise ratio (SNR), and bandwidth of the conversion process are found to be limited by the phase mismatch between the pump, Stokes, and anti-Stokes fields. The dispersion properties of submicrometer waveguides are also studied from the point of view of achieving phase matching and enhancing the conversion efficiency.