The resistance of copper grain boundaries (GBs) is calculated systematically through a full atomistic quantum approach. A set of twin GBs, including the coherent twin GB, is generated by density functional theory (DFT) total energy relaxation starting from the coincidence site lattice (CSL) model. The atomic structure of the GBs is used to construct two-probe transport junctions for quantum-transport analysis by carrying out DFT within the Green's function formalism. The specific resistivity calculated for the coherent twin GB is found to be quantitatively consistent with the available experimental and theoretical data. The specific resistivity and reflection coefficient of other more complex GBs are predicted. The interfacial energy density and specific resistivity are both found to inversely relate with the planar density of coincidence sites. Comparison of our calculated specific resistivities and reflection coefficients with the corresponding GB-averaged experimental quantities shines light on the microstructure of the samples.

We report first principles analysis of the band gap Eg of ternary group-III nitride InxGa1−xN in both the wurtzite and zincblende form, within the linear muffin-tin orbital (LMTO) density functional theory method. We have implemented the semilocal modified Becke–Johnson (MBJ) exchange potential to accurately determine the band gap. The doping of In atoms into the GaN crystal is handled by the InxGa1−xN alloy model within the coherent potential approximation (CPA). The LMTO-CPA-MBJ approach allows us to predict Eg as a function of arbitrary In concentration x. Quantitative comparison to the experimental data is made.

The resistance of doped single grain boundaries (GBs) in copper is calculated from first principles and systematically compared to its pure single GB equivalent. As a first step, a state-of-the-art ab initio method is used to calculate the resistivity of doped bulk copper for 16 doping elements at concentration 1 at. %. Results are in qualitatively excellent and quantitatively reasonable agreement with the corresponding experimental data, and allow us to determine Ag, Zn, Mg, Pd, Al, and In as best candidates for GB doping. These atoms have a minimal impact on the bulk resistivity, while they also conform to a set of established criteria for alloying with copper. Then, the specific resistivity of six twin GBs is determined for these elements over a wide spectrum of doping concentrations for the submonolayer and the monolayer GB complexions. Reduced resistivity is observed for Zn, Mg, Al, In, and other elements in two high-Σ GBs, and is qualitatively related to the segregation enthalpy as well as to a low number of empty states around the Fermi energy in the boundary plane region of the GB. The results indicate the possibility for a reduced net resistivity in copper interconnects by GB doping.