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We present a model which deepens into the role that normal scattering has onthe thermal conductivity in semiconductor bulk, micro and nanoscale samples.Thermal conductivity as a function of the temperature undergoes a smoothtransition from a kinetic to a collective regime that depends on the importanceof normal scattering events. We demonstrate that in this transition, the keypoint to fit experimental data is changing the way to perform the average onthe scattering rates. We apply the model to bulk Si with different isotopiccompositions obtaining an accurate fit. Then we calculate the thermalconductivity of Si thin films and nanowires by only introducing the effectivesize as additional parameter. The model provides a better prediction of thethermal conductivity behavior valid for all temperatures and sizes above 30 nmwith a single expression. Avoiding the introduction of confinement or quantumeffects, the model permits to establish the limit of classical theories in thestudy of the thermal conductivity in nanoscopic systems.

From kinetic to collective behavior in thermal transport on semiconductors and semiconductor nanostructures