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