The Stability Of Transportation Of The Electron Gas Under External Voltage

The property of electrons in non-equilibrium state has been received extensive attention in the condensed matter physics research field. The Thomas-Fermi-Dirac (TFD) model has well application in the study of the properties of electron gas under non-equilibrium state and the density functional theory of electron gas under equilibrium state. In molecular electronics, the study of the current formed by quantum electron transportation and the inherent electron properties put forward a question that whether density functional theory in the presence of external voltage applies and when applies.In this paper, we made a further research on the kinetic energy density and exchange energy density of uniform electron gas under external voltage. To be explicit, by calculating the exchange energy density of a series of Fermi radius and voltage using Monte Carlo integration method and polynomial fitting, we obtained the relationship of exchange intensity, Fermi radius and translation vector: ex=-1/4π3(a0kf4+a1kf3Δk+a2kf2Δk2+a3kf1Δk3+a4Δk4+a5Δk5/kf).Where the coefficient ai(i=0,1,2,3,4,5) respectively equals 1.0000,-1.7256, 1.4739,-0.44774,-0.20066,0.13256; the function relationship of transportation vector Δk, Fermi radius, electron density in non-equilibrium and the total electron density is: ρn=ρt-ρe=1/π2·[kf2/2Δk-Δk3/6] kf3=3π2ρt.This result has proved that in the presence of external voltage, when the electrons are under non-equilibrium state, the properties of the uniform electron gas cannot be determined solely by total electron density, but by total electron density and non-equilibrium state density-the electron density of carriers- jointly. Using correction function containing correction factor η and kinetic energy density kTFD exchange energy density exTFD of electron gas for TFD model under equilibrium state to describe the kinetic energy density and exchange energy density of electrons under non-equilibrium state, we obtain k(η)=(1+5/3(η)2)kTFD(ρt).Because there also exists a relationship among external voltage, transportation vector and total electron density:Vb=h2Δk2/2ρteme, we can draw a conclusion that kinetic energy density and exchange energy density is determined by external voltage and total electron density jointly.