  We present a comprehensive investigation of nonequilibrium effects and self
heating in single electron transfer devices based primarily on the Coulomb
blockade effect. During an electron trapping process, a hot electron may be
deposited in a quantum dot or metal island, with an extra energy usually on 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 quilibrium
regime, a hot electron fully gives up its energy to phonons within a pump
cycle. In the nonequilibrium 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
$T_l$. We have calculated the coefficient in the well known $T^5$ 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 and operation frequency and device size for various types of
devices.
