Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors

The isotope effect on the lattice thermal conductivity for group IV and group III-V semiconductors is calculated using the Debye-Callaway model modified to include both transverse and longitudinal phonon modes explicitly. The frequency and temperature dependences of the normal and umklapp phonon-scattering rates are kept the same for all compounds. The model requires as adjustable parameters only the longitudinal and transverse phonon Gr\"uneisen constants and the effective sample diameter. The model can quantitatively account for the observed isotope effect in diamond and germanium but not in silicon. The magnitude of the isotope effect is predicted for silicon carbide, boron nitride, and gallium nitride. In the case of boron nitride the predicted increase in the room-temperature thermal conductivity with isotopic enrichment is in excess of 100%. Finally, a more general method of estimating normal phonon-scattering rate coefficients for other types of solids is presented.