Efficient Ab-Initio Electron Transport Calculations for Heterostructures by the Nonequilibrium Green’s Function Method

Figure 2

(a) Flowchart of DFT-NEGF calculations with parallelization by MPI. The calculation process surrounded by the dashed line corresponds to the calculations of the Green’s functions, which are the central and most time consuming parts of the present formalism. The Green’s functions are calculated independently for various sets of complex/real energies and 2D Bloch wave vectors, whose processes are assigned to multicore processor by MPI. During the calculations of the Green’s functions, the density matrix is partially calculated by integration with respect to the energy and the wave vectors in each core. After the calculations of the density matrix in each core are completed, the Hamiltonian matrix is constructed by summing the elements with communication among MPI processes, and then all the matrix elements of the density matrix are obtained. (b) Elapsed time and speed-up ratio of total elapsed time resulting from the parallelization by the MPI in the ab-initio electron transport calculations for an Al(100)-Si(100)-Al(100) heterostructure. The speed-up ratio is calculated as , where and are the elapsed times for serial and parallel computing, respectively. The number of discretized grid points in the calculations are , , and . For reference, the ideal speed-up ratio is also represented by the green dotted line. The calculation speed increased linearly while lagging slightly behind the ideal speed-up ratio.

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