Simulation of temperature profile for the electron and the lattice systems in laterally structured layered conductors

Abstract

PACS 05.70.Ln -Nonequilibrium and irreversible thermodynamics PACS 44.05.+e -Analytical and numerical techniques PACS 73.63.-b -Electronic transport in nanoscale materials and structures Abstract -Electrons in operating microelectronic semiconductor devices are accelerated by locally varying strong electric field to acquire effective electron temperatures nonuniformly distributing in nanoscales and largely exceeding the temperature of host crystal lattice. The thermal dynamics of electrons and the lattice are hence nontrivial and its understanding at nanoscales is decisively important for gaining higher device performance. Here, we propose and demonstrate that in layered conductors nonequilibrium nature between the electrons and the lattice can be explicitly pursued by simulating the conducting layer by separating it into two physical sheets representing, respectively, the electron-and the lattice-subsystems. We take, as an example of simulating GaAs devices, a 35nm thick 1µm wide U-shaped conducting channel with 15nm radius of curvature at the inner corner of the U-shaped bend, and find a remarkable hot spot to develop due to hot electron generation at the inner corner. The hot spot in terms of the electron temperature achieves a significantly higher temperature and is of far sharper spatial distribution when compared to the hot spot in terms of the lattice temperature. Similar simulation calculation made on a metal (NiCr) narrow lead of the similar geometry shows that a hot spot shows up as well at the inner corner, but its strength and the spatial profiles are largely different from those in semiconductor devices; viz., the amplitude and the profile of the electron system are similar to those of the lattice system, indicating quasi-equilibrium between the two subsystems. The remarkable difference between the semiconductor and the metal is interpreted to be due to the large difference in the electron specific heat, rather than the difference in the electron phonon interaction. This work will provide useful hints to deeper understanding of the nonequilibrium properties of electrical conductors, through a simple and convenient method for modeling nonequilibrium layered conductors.

Quasiadiabatic electron transport in room temperature nanoelectronic devices induced by hot-phonon bottleneck

“…There is a small temperature rise such that ΔT L~1 K at the maximum, where T L = T base + ΔT L and T base = 300.8 K (see "Methods" and Supplementary Fig. 3 and Supplementary Note 3), which is due to a large lattice specific heat and the fact that the heat spreads via lattice thermal conduction 32 .…”

“…8d), demonstrating the hotphonon bottleneck effect. The profile of the lattice temperature T L (x) is broadened due to the lattice thermal conduction 32 , and is theoretically derived from P LO (x) by assuming a symmetric broadening parameter (see Supplementary Note 9). A solid blue line in Fig.…”

Anisotropic Hot-Electron Kinetics Revealed by Terahertz Fluctuation

“…The hotspots of T e at the corners are generated by the current crowding effect; viz., the electric field E is concentrated at the corners, locally enhancing the Joule heating at the corners. ,, The concentrated Joule heating provides distinct peaks in Δ T e at the corners. The corresponding peak in Δ T L is far less prominent because (i) the lattice heat capacity is far larger than that of electrons and (ii) the lattice thermal conductance is much larger than that of conduction electrons in semiconductors. , …”

“…To explicitly know what would be anticipated if the transport were in the simplest linear-response regime, we have carried out simulation calculations on the simplified assumption of a one-carrier transport that is linear and isotropic conduction based [Section S3 in the SI]. A two-temperature model is applied to treat the nonequilibrium system of conduction electrons and the lattice . As the electrical conduction is diffusive and local, the local energy loss rate p ( r ) at a given point r can be viewed as given by the local energy gain rate j ( r )· E ( r ) at the same point r , and the local current density j ( r ) is given locally by the conductivity σ­( r ) and the electric field E ( r ) at the position r ; viz., p ( r ) = j ( r )· E ( r ) and j ( r ) = σ­( r ) E ( r ).…”

“…A two-temperature model is applied to treat the nonequilibrium system of conduction electrons and the lattice. 36 As the electrical conduction is diffusive and local, the local energy loss rate p(r) at a given point r can be viewed as given by the local energy gain rate j(r)•E(r) at the same point r, and the local current density j(r) is given locally by the conductivity σ(r) and the electric field E(r) at the position r; viz., p(r) = j(r)•E(r) and j(r) = σ(r)E(r). To obtain simultaneously both T e and T L , the conductive quantum well is represented by two separated layers: The electron layer representing the electrical conductivity σ(r) and the electron thermal conductivity and the lattice layer representing the lattice thermal conductivity.…”