First-principles quantum transport method for disordered nanoelectronics: Disorder-averaged transmission, shot noise, and device-to-device variability

Because disorders are inevitable in realistic nanodevices, the capability to quantitatively simulate the disorder effects on electron transport is indispensable for quantum transport theory. Here, we report a unified and effective first-principles quantum transport method for analyzing effects of chemical or substitutional disorder on transport properties of nanoelectronics, including averaged transmission coefficient, shot noise, and disorder-induced device-to-device variability. All our theoretical formulations and numerical implementations are worked out within the framework of the tight-binding linear muffin tin orbital method. In this method, we carry out the electronic structure calculation with the density functional theory, treat the nonequilibrium statistics by the nonequilbrium Green's function method, and include the effects of multiple impurity scattering with the generalized nonequilibrium vertex correction (NVC) method in coherent potential approximation (CPA). The generalized NVC equations are solved from first principles to obtain various disorder-averaged two-Green's-function correlators. This method provides a unified way to obtain different disorder-averaged transport properties of disordered nanoelectronics from first principles. To test our implementation, we apply the method to investigate the shot noise in the disordered copper conductor, and find all our results for different disorder concentrations approach a universal Fano factor $1/3$. As the second test, we calculate the device-to-device variability in the spin-dependent transport through the disordered Cu/Co interface and find the conductance fluctuation is very large in the minority spin channel and negligible in the majority spin channel. Our results agree well with experimental measurements and other theories. In both applications, we show the generalized nonequilibrium vertex corrections play a determinant role in electron transport simulation. Our results demonstrate the effectiveness of the first-principles generalized CPA-NVC for atomistic analysis of disordered nanoelectronics, extending the capability of quantum transport simulation.

Figure 1

Schematic illustration of a two-probe device. The central scattering region containing atomic disorders (white spheres) is sandwiched by the left and right semi-infinite electrodes. Applying an external bias drives the central device out of equilibrium.

Figure 2

Transmission and shot noise versus the length of disordered layers $L$ (atomic layer) for ${\mathrm{Cu}/\mathrm{Cu}}_{1-x}{\mathrm{Va}}_x/\mathrm{Cu}$. (Left column) The averaged transmission $\mathrm{Tr}\left[\langle \widehat{T}\rangle \right]$. (a), (c), and (e) are for $x=0.025,x=0.05$, and $x=0.1$, respectively. (Right column) The averaged shot noise $2\mathrm{Tr}[\langle \widehat{T}\rangle -\langle {\widehat{T}}^2\rangle ]$. (b), (d), and (f) are for $x=0.025,x=0.05$, and $x=0.1$, respectively. (Note that the GNVC contribution is negative and its absolute value is plotted.)

Figure 3

Fano factor versus the number of disordered layers $L$ (atomic layer) for ${\mathrm{Cu}/\mathrm{Cu}}_{1-x}{\mathrm{Va}}_x/\mathrm{Cu}$ structure. The red, blue, and green lines are for $x=0.025,x=0.05$, and $x=0.1$, respectively. The horizontal dash line is the theoretical value of $1/3$ universal Fano factor for disordered conductors.

Figure 4

Conductance and its fluctuation versus disorder concentration $x$ for ${\mathrm{Cu}/\mathrm{Cu}}_{1-x}{\mathrm{Co}}_x/\mathrm{Co}$ structure: (a) for single disordered layer and (b) for double disordered layers. The midpoint of the vertical line is the averaged transmission coefficient $\langle T\rangle$; the half of the vertical line equals the transmission fluctuation $\delta T$.