  The mechanisms causing the reduction in lattice thermal conductivity in
highly P- and B-doped Si are looked into in detail. Scattering rates of phonons
by point defects, as well as by electrons, are calculated from first
principles. Lattice thermal conductivities are calculated considering these
scattering mechanisms both individually and together. It is found that at low
carrier concentrations and temperatures phonon scattering by electrons is
dominant and can reproduce the experimental thermal conductivity reduction.
However, at higher doping concentrations the scattering rates of phonons by
point defects dominate the ones by electrons except for the lowest phonon
frequencies. Consequently, phonon scattering by point defects contributes
substantially to the thermal conductivity reduction in Si at defect
concentrations above $10^{19}$ cm$^{-3}$ even at room temperature. Only when,
phonon scattering by both point defects and electrons are taken into account,
excellent agreement is obtained with the experimental values at all
temperatures.
