Theory of Non-equilibrium Vertex Correction

For realistic nanostructures, there are inevitably some degree of disorder such as impurity atoms, imperfect lattices, surface roughness, etc.. For situations where disorder locate randomly in the nanostructure, any calculated quantum transport results should be averaged over disorder distributions. A brute force approach is to generate many disorder configurations, calculate each of them, and then average the results. For atomistic first principles modeling, such a brute force averaging is computationally prohibitive - if not impossible, to perform. It is therefore very important and useful to develop a theoretical framework where the disorder averaging is done analytically before atomic first principles analysis is carried out.;We have applied the NEGF-DFT-NVC method to investigate several important problems associated with disorder scattering in nano-electronic device systems. These include interface roughness scattering in Fe/vacuum/Fe magnetic tunnel junctions; the diffusive scattering of carriers due to oxygen vacancies in Fe/MgO/Fe magnetic tunnel junctions; the surface roughness scattering that enhances resistivity of copper interconnect wires; and effects of barrier layer coating for Cu interconnects. Our investigations reveal very important role played by the atomic level defects and impurities to both equilibrium and nonequilibrium quantum transport properties, and results compare favorably with the corresponding experimental data.;In this thesis, we have developed such a first principles non-equilibrium quantum transport theory and its associated modeling software for predicting disorder scattering in nano-electronic devices. Our theoretical formalism is based on carrying out density functional theory (DFT) within the Keldysh non-equilibrium Green's function (NEGF) framework, and a non-equilibrium vertex correction (NVC) theory for handling disorder configurational average at the non-equilibrium density matrix level. In our theory, we use the coherent potential approximation to calculate disorder averaging of the device Hamiltonian and one particle Green's functions, and use NVC to calculate correlated multiple impurity scattering at the non-equilibrium density matrix level. After the NEGF-DFT-NVC self-consistent calculation is converged, we calculate the transmission coefficients by a second, unavoidable, vertex correction. The NEGF-DFT-NVC theory allows us to predict non-equilibrium quantum transport properties of nanoelectronic devices with atomistic disorder from first principles without any phenomenological parameters. The theory and implementation details are presented.