Heat Transfer in Nanoelectronics by Quantum Mechanics

Abstract

Today, the transient Fourier heat conduction equation is not considered valid for the derivation of temperatures from the dissipation of Joule heat in nanoelectronics because the dimension of the circuit element is comparable to the mean free path of phonon energy carriers. Instead, the Boltzmann transport equation (BTE) for ballistic transport based on the scattering of phonons within the element is thought to govern heat transfer. However, phonons respond at acoustic frequencies in times on the order of 10–100 ps, and therefore the BTE would not have meaning if the Joule heat is conserved by a faster mechanism. Unlike phonons with response times limited by acoustic frequencies, heat transfer in nanoelectronics based on QED induced heat transfer conserves Joule heat in times < 1 fs by the creation of EM radiation at optical frequencies. QED stands for quantum electrodynamics. In effect, QED heat transfer negates thermal conduction in nanoelectronics because Joule heat is conserved well before phonons respond. QED induced heat transfer finds basis in Planck’s QM given by the Einstein-Hopf relation in terms of temperature and EM confinement of the atom as a harmonic oscillator. QM stands for quantum mechanics and EM for electromagnetic. Like the Fourier equation, the BTE is based on classical physics allowing the atom in nanoelectronic circuit elements to have finite heat capacity, thereby conserving Joule heat by an increase in temperature. QM differs by requiring the heat capacity of the atom to vanish. Conservation of Joule heat therefore proceeds by QED inducing the creation of excitons (hole and electron pairs) inside the circuit element by the frequency up-conversion of Joule heat to the element’s TIR confinement frequency. TIR stands for total internal reflection. Under the electric field across the element, the excitons separate to produce a positive space charge of holes that reduce the electrical resistance or upon recombination are lost by the emission of EM radiation to the surroundings. TIR confinement of EM radiation is the natural consequence of the high surface to volume ratio of the nanoelectronic circuit elements that concentrates Joule heat almost entirely in their surface, the surfaces coinciding with the TIR mode shape of the QED radiation. TIR confinement is not permanent, present only during the absorption of Joule heat. Charge creation aside, QM requires nanoelectronics circuit elements to remain at ambient temperature while dissipating Joule heat by QED radiation to the surroundings. Hot spots do not occur provided the RI of the circuit element is greater than the substrate or surroundings. RI stands for refractive index. In this paper, QED radiation is illustrated with memristors, PC-RAM devices, and 1/ f noise in nanowires, the latter of interest as the advantage of QM in avoiding hot spots in nanoelectronics may be offset by the noise from the holes created in the circuit elements by QED induced radiation.