Efficient solution algorithm of non-equilibrium Green’s functions in atomistic tight binding representation

INTRODUCTION With the shrinking dimension of electronic devices, quantum transport attracts increasing interest. The non-equilibrium Green’s function (NEGF) formalism [1] provides a very general framework for quantum transport, but it is numerically expensive when applied on atomistic tight binding representations. So far, computational burden (in memory and CPU time) limits the maximum diameter of nanowires that are solvable within atomistic NEGF to about 8nm. Several methods are developed to reduce the numerical costs. However, these methods are either limited to effective mass model [2] or to small cross-sections perpendicular to the transport direction [3]. In this work, it is demonstrated how to apply the concept of low rank approximation [4] to the NEGF method in atomistic tight binding representation. Using this method, transport in a 12nm squared Si nanowire is solved. METHOD All electrons are represented in atomistic multi band tight binding models. If a device consists of several millions of atoms, tight binding descriptions yield millions of electronic states. Only a small fraction of these states contribute to charge transport. In this method, the NEGF equations of the tight binding Hilbert space of rank N are transformed into a Hilbert space of rank n that is spanned by only these relevant states. The maximum achievable speed up is given by (n/N) and the maximum reduction of required memory by (n/N). First, the energy dependent contact selfenergies are calculated within the transfer matrix method of [5] and folded into the device Hamiltonian to represent an open system through the nonhermitian Hamiltonians H(E) for each considered energy E. For every H(E), those n right sided eigenstates are calculated that have eigenvalues closest to E. These eigenstates represent the n columns of a rectangular transformation matrix T (N rows and n columns). The NEGF equations are transformed by T into the smaller Hilbert space and solved therein.