A critical review of published approaches to nanoscale thermal radiation

Radiative heat transfer across nanoscale-thick layers attracts considerable attention because of its importance for modern technology, and also because of the evidence that conventional methods of radiative heat transfer fail at such small scales. This paper analyzes several approaches to this problem that have been proposed since the late 1960s when the first adaptations of the classical Stefan–Boltzmann law of radiative heat transfer to smaller scales were presented. It is shown that while all authors agree that thermal radiation is described by Maxwell’s equations for electrodynamics, the methods of these studies drifted from deductive reasoning based on these equations toward heuristic guesses. This paper identifies critical points of several of these previous studies that are responsible for the lack of a suitable theory of radiative heat transfer across nanoscale layers despite almost 50 years of effort. Among these points are: (1) attempts to describe heat transfer using statistical distributions that are limited to equilibrium systems that cannot produce any heat flux; (2) application of the so-called fluctuation–dissipation theorem when its conditions are not satisfied; (3) the failure to distinguish between different kinds of evanescent fields; (4) an unjustified assumption that resonant surface waves can transfer heat by tunneling.