Generalized nonequilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

Electron transport properties of nanoelectronics can be significantly influenced by the inevitable and randomly distributed impurities/defects. For theoretical simulation of disordered nanoscale electronics, one is interested in both the configurationally averaged transport property and its statistical fluctuation that tells device-to-device variability induced by disorder. However, due to the lack of an effective method to do disorder averaging under the nonequilibrium condition, the important effects of disorders on electron transport remain largely unexplored or poorly understood. In this work, we report a general formalism of Green's function based nonequilibrium effective medium theory to calculate the disordered nanoelectronics. In this method, based on a generalized coherent potential approximation for the Keldysh nonequilibrium Green's function, we developed a generalized nonequilibrium vertex correction method to calculate the average of a two-Keldysh-Green's-function correlator. We obtain nine nonequilibrium vertex correction terms, as a complete family, to express the average of any two-Green's-function correlator and find they can be solved by a set of linear equations. As an important result, the averaged nonequilibrium density matrix, averaged current, disorder-induced current fluctuation, and averaged shot noise, which involve different two-Green's-function correlators, can all be derived and computed in an effective and unified way. To test the general applicability of this method, we applied it to compute the transmission coefficient and its fluctuation with a square-lattice tight-binding model and compared with the exact results and other previously proposed approximations. Our results show very good agreement with the exact results for a wide range of disorder concentrations and energies. In addition, to incorporate with density functional theory to realize first-principles quantum transport simulation, we have also derived a general form of conditionally averaged nonequilibrium Green's function for multicomponent disorders.

Figure 1

Physical model for a two-probe nanoelectronic device with disorders. (a) The central device region with disorders is sandwiched by two semi-infinite leads. (b) The effects of the leads are turned into the self-energies so that the central device region becomes calculable.

Figure 2

(a) The time contour starts from $-\infty$, passes through $t$ and $t^{\prime }$, and finally returns to $-\infty$. (b) Four possible combinations of $t$ and $t^{\prime }$ on the time contour.

Figure 3

Diagrammatic representation of $\langle GCG\rangle$. The thick line and thin line represent $G$ and $\overline{G}$, respectively. The dashed line represents the interaction with the disorders (red dots). The blue dot represents a vertex $C$.

Figure 4

Numerical results of a nanoribbon with a lattice tight-binding model containing $3\times 3$ disordered sites as shown in inset of (a). The left column—(a), (c), (e), and (g)—and the right column—(b), (d), (f), and (h)—show the averaged transmission coefficients and the corresponding fluctuations with disorder concentrations $x=0.01,0.1,0.3,0.5$, respectively.

Figure 5

(a) A fully disorder averaged system. (b) A conditionally averaged system. (c) Schematic illustration of CPA with SSA.