THERMAL-CONDUCTIVITY AND LOCALIZATION IN GLASSES - NUMERICAL STUDY OFA MODEL OF AMORPHOUS-SILICON

Numerical calculations of thermal conductivity kappa(T) are reported f or realistic atomic structure models of amorphous silicon with 1000 at oms and periodic boundary conditions. Using Stillinger-Weber forces, t he vibrational eigenstates are computed by exact diagonalization in ha rmonic approximation. Only the uppermost 3% of the states are localize d. The finite size of the system prevents accurate information about l ow-energy vibrations, but the 98% of the modes with energies above 10 meV are densely enough represented to permit a lot of information to b e extracted. Each harmonic mode has an intrinsic (harmonic) diffusivit y defined by the Kubo formula, which we can accurately calculate for o mega > 10 meV. If the mode could be assigned a wave vector k and a vel ocity v = partial derivative omega/partial derivative k, then Boltzman n theory assigns a diffusivity D(k) = 1/3vl, where l is the mean free path. We find that we cannot define a wave vector for the majority of the states, but the intrinsic harmonic diffusivity is still well-defin ed and has a numerical value similar to what one gets by using the Bol tzmann result, replacing v by a sound velocity and replacing l by an i nteratomic distance a. This appears to justify the notion of a minimum thermal conductivity as discussed by Kittel, Slack, and others. In or der to fit the experimental kappa(T) it is necessary to add a Debye-li ke continuation from 10 meV down to 0 meV. The harmonic diffusivity be comes a Rayleigh omega-4 law and gives a divergent kappa(T) as T-->0. To eliminate this we make the standard assumption of resonant-plus-rel axational absorption from two-level systems (this is an anharmonic eff ect which would lie outside our model even if it did contain two-level systems implicitly). A reasonable fit and explanation then results fo r the behavior of kappa(T) in all temperature regimes. We also study t he effect of increasing the harmonic disorder by substitutional mass d efects (modeling amorphous Si/Ge alloys). The additional disorder incr eases the fraction of localized states, but delocalized states still d ominate. However, the diffusivity of the delocalized states is diminis hed, weakening our faith in any literal interpretation of the minimum conductivity idea.