Lattice thermal conductivity of silicon from empirical interatomic potentials

We present calculations of the lattice thermal conductivity of silicon that incorporate several commonly used empirical models of the interatomic potential. Second- and third-order force constants obtained from these potentials are used as inputs to an exact iterative solution of the inelastic phonon Boltzmann equation, which includes the anharmonic three-phonon scattering as well as isotopic defect and boundary scattering. Comparison of the calculated lattice thermal conductivity with the experiment shows that none of these potentials provides satisfactory agreement. Calculations of the mode Gr\"uneisen parameters and the linear thermal expansion coefficient help elucidate the reasons for this. We also examine a set of parameters for one of these empirical potentials that produces improved agreement with both the measured lattice thermal conductivity and the thermal expansion data.