Non-equilibrium effects and self-heating in single-electron Coulomb blockade devices

We present a comprehensive investigation of non-equilibrium effects and self-heating in single electron transfer devices based primarily on the Coulomb blockade effect. During an electron trapping process, a hot electron maybe deposited in a quantum dot or metal island, with an extra energy usually of the order of the Coulomb charging energy, which is much higher than the temperature in typical experiments. The hot electron may relax through three channels: tunneling back and forth to the feeding lead (or island), emitting phonons, and exciting background electrons. Depending on the magnitudes of the rates in the latter two channels relative to the device operation frequency and to each other, the system may be in one of three different regimes: equilibrium, non-equilibrium, and self-heating (partial equilibrium). In the equilibrium regime, a hot electron fully gives up its energy to phonons within a pump cycle. In the non-equilibrium regime, the relaxation is via tunneling with a distribution of characteristic rates; the approach to equilibrium goes like a power law of time (frequency) instead of an exponential. This channel is plagued completely in the continuum limit of the single-electron levels. In the self-heating regime, the hot electron thermalizes quickly with background electrons, whose temperature T_e is elevated above the lattice temperature T_ol. We have calculated the coefficient in the well-known T⁵ law of energy dissipation rate, and compared the results to experimental values for aluminum and copper islands and for a two-dimensional semiconductor quantum dot. Moreover, we have obtained different scaling relations between the electron temperature, the operation frequency and device size for various types of devices.