Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation

A review and perspective is presented of the classical, semiclassical and fully quantum routes to the simulation of electrothermal phenomena in ultrascaled silicon nanowire fieldeffect transistors. It is shown that the physics of ultrascaled devices requires at least a coupled electron quantum transport semiclassical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires selfconsistency with the Poisson equation and that the electronic LDOS must be determined within at least the selfconsistent Born approximation. To bring in this description and to provide the energy resolved local carrier distributions it is necessary to adopt the nonequilibrium Green function (NEGF) formalism, briefly surveyed here. The NEGF approach describes quantum coherent and dissipative transport, Pauli exclusion and nonequilibrium conditions inside the device. There are two extremes of NEGF used in the community. The most fundamental is based on coupled equations for the Green functions electrons and phonons that are computed at the atomically resolved level within the nanowire channel and into the surrounding device structure using a tight binding Hamiltonian. It has the advantage of treating both the nonequilibrium heat flow within the electron and phonon systems even when the phonon energy distributions are not described by a temperature model. The disadvantage is the grand challenge level of computational complexity. The second approach, that we focus on here, is more useful for fast multiple simulations of devices important for TCAD (Technology Computer Aided Design). It retains the fundamental quantum transport model for the electrons but subsumes the description of the energy distribution of the local phonon subsystem statistics into a semiclassical Fourier heat equation that is sourced by the local heat dissipation from the electron system. It is shown that this selfconsistent approach retains the salient features of the fullscale approach. For focus, we outline our electrothermal simulations for a typical narrow Si nanowire gate allaround fieldeffect transistor. The selfconsistent Born approximation is used to describe electronphonon scattering as the source of heat dissipation to the lattice. We calculated the effect of the device selfheating on the current voltage characteristics. Our fast and simpler methodology closely reproduces the results of a more fundamental computeintensive calculations in which the phonon system is treated on the same footing as the electron system. We computed the local power dissipation and "local lattice temperature" profiles. We compared the selfheating using hot electron heating and the Joule heating, i.e., assuming the electron system was in local equilibrium with the potential. Our simulations show that at low bias the source region of the device has a tendency to cool down for the case of the hot electron heating but not for the case of Joule heating. Our methodology opens the possibility of studying thermoelectricity at nanoscales in an accurate and computationally efficient way. At nanoscales, coherence and hot electrons play a major role. It was found that the overall behaviour of the electron system is dominated by the local density of states and the scattering rate. Electrons leaving the simulated drain region were found to be far from equilibrium.