Heat transfer in nanoelectronics by quantum mechanics

Heat transfer began in macroscopic bodies with classical physics in Fourier's transient heat conduction equation based on the notions of heat capacity by Lavoisier and Laplace. Theories of Einstein's characteristic vibrations and Debye's normal modes identified phonons as the heat carriers in Fourier's equation. Einstein and Debye could have but did not include the photons in Planck's theory of blackbody radiation as additional heat carriers. Since then, heat transfer by phonons alone has served well in deriving the thermal response of macroscopic bodies. However, unphysical findings for the thermal response of nanostructures suggest that Fourier's equation needs to be modified at the nanoscale. Proposed modifications include vanishing heat capacity as required by quantum mechanics and conservation of absorbed energy by frequency up-conversion to the total internal reflection resonance of the nanostructure by quantum electrodynamics, the consequence of which in nanoelectronics is charge creation instead of an increase in temperature. Nanoelectronics (memristors, Ovshinsky Effect, and 1/f noise) are discussed with extensions to heat dissipation in nanocomputing.