Ab initio description of transport in nanostructures including electron-phonon coupling

Abstract

The ongoing trends toward miniaturization and exploitation of non-classical degrees of freedom severely challenge the available methods for the theoretical description of electronic devices, because in realistic situations both quantum-mechanical effects as well as phase-breaking scattering events must be taken into account. The objective of this work is to assist the endeavor to improve electronic and spintronic appliances by implementing a numerical scheme making predictive nanoscale device modeling from first principles affordable.A thorough mathematical and physical discussion regarding the treatment of phase-breaking scattering events - particularly those due to the electron-phonon interaction - in ab initio electronic transport calculations yields the basis for the advocated computational scheme. This method is characterized by the usage of suitable additional self-energies in the Keldysh formulation of the non-equilibrium Green´s function formalism (NEGF) as implemented in a Korringa-Kohn-Rostoker (KKR) electronic structure code. The evaluation of the transmission probability is performed by means of the Landauer-Büttiker theory. Depending on the problem at hand, we propose two methods to obtain the necessary energy-resolved electron-phonon self-energies: In case of non-magnetic metals, a wave-vector integration of bulk self-energies obtained from third-party codes is introduced. Alternatively, we describe a self-energy fitting procedure to spin-resolved ab initio resistivity data. If the effects of thermal expansion are taken into account (e.g., in the framework of the Debye-Grüneisen theory), we show that the suggested method provides very accurate results for the temperature-dependence of electronic transport properties in both complex nanostructures as well as bulk-like macroscopic devices up to very high temperatures.We verify the correctness of the implementation and study the validity of the calculational scheme by carefully analyzing the required numerical precisions in the bulk-like metallic systems copper, aluminum, and - to some extent - iron. The electron-phonon induced electron linewidth is calculated. Subsequently, we evaluate the temperature-dependent resistivity and compare to both experimental data and to results obtained using other methods based on first principles, notably the lowest-order variational approximation (LOVA) to the Boltzmann formalism and the alloy analogy. For all three materials we find the Landauer formula to be valid in the considered temperature regime of up to 900 K. Further, in the limit of macroscopic device lengths, Ohm´s law emerges. In the studies on copper and aluminum, the strong influence of thermal expansion on the resistivity is traced back to the vibrational degrees of freedom. This provides evidence for the validity of the quasi-harmonic approximation in case of simple metals and illustrates the importance of accurate phonon calculations. We argue that GGA exchange-correlation functionals are hence to be preferred over local approximations if experimental lattice constants are used. In the low temperature regime, however, small deviations of the Fermi surface triangulation used in the wave-vector integration determine the accuracy of the results.In order to study the applicability of the proposed method in the context of complex nanostructures, the understanding of the mechanisms giving rise to resonant tunneling in Fe/MgO double barrier magnetic tunnel junctions is confirmed and improved: The strong localization of Δ1 quantum well states mimics the one-dimensional situation and induces strong asymmetric peaks in the energy-resolved transmission. These peaks are palmed off with increasing temperature and become more symmetric in energy. We show that the resonant behavior in the current-voltage characteristics reduces likewise and in accordance with experimental data. This is related to an increase of the electron linewidth on the one hand, and a broadening of the electron distribution functions on the other hand. Further, and still in accordance with the experiment, phase-breaking scattering in the metallic leads is found to decrease the resistance of the device.