The calculation of the thermal conductivity using the Callaway model for several semiconductors

Abstract

In this work, we have developed a Matlab code for calculating the thermal conductivity as a function of the temperature using Callaway’s model. Using this model, the thermal conductivities of Silicon and Diamond are been calculated and these calculations are in agreement with other paper results, in addition to this, the thermal conductivities of low dimensional structures as well as bulk materials are demonstrated. The Callaway model was used in calculating the thermal conductivities of the two variants of both Silicon and Diamond. Based on the simulations that were carried it, it was observed that; thermal conductivity of enriched diamond was found to be greater as compared to that of natural diamond. The calculated thermal conductivity of isotopically pure and natural silicon indicates that the pure sample has a higher thermal conductivity, for example, natural silicon has a thermal conductivity of around 2.8 W/cm-K at 200 K, while isotopically pure silicon has a thermal conductivity of about 4 W/cm-K. The thermal conductivity ratio is 1.42. Thermal conductivity is reduced by 30% due to isotope scattering. A comparison of the Callaway and holland models showed that they have similar relaxation times but better temperature thermal conductivity would be obtained using Holland’s model. Diamond's thermal conductivity (900–2320 Wm-1K-1) and hardness are its most important properties. It was established that the conductivity of synthetic single diamond crystals prepared isotopically enriched in 12C has a better thermal conductivity at 300K (33 Wcm-1K-1) as compared to pure diamond (24–25 Wcm-1K-1), and to Si’s 1.5 that because the diamond has excellent physical qualities and the synthetic single diamond conductivity is made up of microcrystallites of diamonds with diameters on the order of 2 μm, phonon boundary scattering is projected to be high.