Effects of subconduction band excitations on thermal conductance at metal-metal interfaces
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DOS of Al and Cu as a function of energy relative to the Fermi energy. Since metal composites in equilibrium must have the same Fermi energy, we shift the Cu DOS so that the Fermi energy aligns with Al. The - and -band in Cu are shown separately for clarity.
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(a) TBC predictions for a flux of electrons in Al crossing an Al/Cu interface (Al/Cu) and for a flux of electrons in Cu crossing a Cu/Al interface (Cu/Al). Also shown in this figure is the prediction using Eq. (5) extended to high temperatures. The eTBC clearly deviates from the linear trend predicted from the low temperature theory as temperature increases. At intermediately high temperatures, the eTBC from Cu/Al is lower than from Al/Cu due to the large number of holes in the Cu -band. Much greater temperatures, however, cause greater transport from Cu to Al as the great number of electrons participating in the transport mitigates their lower transmission probability. (b) Transmission probability as a function of energy for the cases shown in (a) for and 10 000 K. At 300 K, the transmission probabilities are nearly identical since only states around the Fermi energy are available and Cu and Al have similar shaped Fermi surfaces. In contrast, as temperature is increased to introduce holes in the Cu -band, the number of available states for transmission of the Al thermal flux increases near the maxima of this -band.
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