Here, we report the thermal conductivity measurement of B-doped Si nanowires with δ dopant modulation on the surface using the self-heated 3ω method, which resembles the thermal dissipation in operating electronic devices. The thermal conductivity for δ-modulated Si nanowires of 45 nm diameter (∼23 W/m K) is found to agree well with that of non-doped Si nanowires reported previously, which is attributed to the dominant surface boundary scattering and the highly confined dopant distribution at the surface. Furthermore, through a length dependent study of the thermal conductivity (κ) from 400 nm to 4 μm, we found an apparent length dependence of κ at L < 2 μm. The phenomenon could not be simply interpreted by solely considering the ballistic effect in thermal transport, but can be accounted for by including the additional resistive processes that are associated with the thermalization of joule-heating emitted phonons, which opts in to suppress the thermal conductivity of nano-systems under the ballistic thermal transport regime.
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