Molecular-dynamics simulation of thermal conductivity in amorphous silicon

The temperature-dependent thermal conductivity ~(T) of amorphous silicon has been calculated from equilibrium molecular-dynamics simulations using the time correlations of the heat flux operator in which anharmonicity is explicitly incorporated. The Stillinger-Weber two- and three-body Si potential and the Wooten-Weaire-Winer a-Si model were utilized. The calculations correctly predict an increasing thermal conductivity at low temperatures (below 400 K). The ~(T), for T) 400 K, is affected by the thermally generated coordination-defect states. Comparisons to both experiment and previous calculations will be described. I. INTRODUCTION In spite of extensive studies, a number of outstanding problems do remain in understanding the lowtemperature properties of amorphous materials. Among the intriguing features have been the linear specific heat of glasses, which is generally believed to be due to the presence of localized two-level states. The nature of the vibrational modes in glasses and the excess vibrational density of states at low frequencies is also an interesting aspect. In this paper we study the thermal conductivity of amorphous materials, using amorphous silicon as a prototype. The temperature-dependent behavior of the thermal conductivity is amorphous materials has the following three characteristic regimes. (1) At low temperatures (T( 1 K), tc( T) is proportional to T', which was explained by Anderson, Halperin, and Varma' as being due to the scattering from localized two-level states; (2) at intermediate temperature (1 ( T ( 30 K), a plateau was seen, which has attracted many theoretical investigations; (3) at high temperature (T ~ 30 K), where tc(T) increases smoothly to a limiting value, in contrast to the crystalline insulators where it decreases with 1/T. Birch and Clark and Kittel gave qualitative explanations of regime (3) using the kinetic formula tc=Cvl/3 that is applicable only in the Boltzmann regime where one can assign velocities U to propagating modes. Allen and Feldman (AF) have examined the validity of the kinetic formula in their recent calculation of the thermal conductivity in amorphous silicon. Cahill and Pohl argued, based on Einstein model, that regime (3) can be explained by locally uncorrelated harmonic oscillators with relaxation times of the order of the period of vibration. However, this model is only valid in the limit of highly disordered crystals. In this study we will study regime (3) with a different approach from previous works. There exist many theoretical models for the structure of amorphous Si. A convenient theoretical model is the four-coordinated Wooten-Winer-Weaire (WWW) a-Si model. Biswas et al. obtained a vibrational density of states for the WWW model that agreed well with experiment. They have also obtained amorphous silicon configurations with molecular-dynamics (MD) simulations by cooling the molten silicon configuration. It is also known that Stillinger-Weber (SW) potential is valid for a wide range of properties of a-Si. Since the WWW model has only four-coordinated silicon atoms, this will be a more convenient starting point for the thermal-conductivity calculations than molecular dynamics models of a-Si (Ref. 8) that have coordination defects. In addition, the use of the WWW model together with the SW Si potential allows a direct comparison with the recent calculation of Allen and Feldman. Allen and Feldman have used the novel procedure of using the Kubo formula for calculating thermal conductivity in a-Si. Matrix elements of the heat-current operator were calculated between harmonic vibrational states. Although the zero-temperature WWW structure was used, the temperature entered through the quantum occupation of the vibrational states. AF obtained a tc(T) that increases in temperature up to 300 K and then saturates at a value close to experiment. Low-temperature values (T (300 K) for tc(T) were significantly smaller than experiment. We present in this paper an alternate approach that explicitly incorporates anharmonicities and accounts for temperature-dependent structural changes. Theoretical techniques developed by AF have served as a useful guide in the present work.