Thermal conductivity of GaAs/AlAs superlattices: The Umklapp process

The thermal conductivity of GaAs/AlAs superlattices limited by the three-phonon Umklapp process and boundary scattering has been studied theoretically based on the model of lattice dynamics with force constant matrix. It was found that the Umklapp relaxation rate approximates BT\omega^2/n with a fitting parameter B. The thermal conductivity increases with the increase of temperature at low temperatures, and would show a peak behaviour at about 60K before falling off at high temperatures. In addition, the thermal conductivity increases with the increase of period thickness of the superlattices.