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Epitaxial (Ti_1−xMg_x)_0.25Al_0.75N(0001)/Al₂O₃(0001) layers are used as a model system to explore how Fermi‐level engineering facilitates structural stabilization of a host matrix despite the intentional introduction of local bonding instabilities that enhance the piezoelectric response. The destabilizing octahedral bonding preference of Ti dopants and the preferred 0.67 nitrogen‐to‐Mg ratio for Mg dopants deteriorate the wurtzite AlN matrix for both Ti‐rich (x< 0.2) and Mg‐rich (x≥ 0.9) alloys. Conversely,x= 0.5 leads to a stability peak with a minimum in the lattice constant ratioc/a, which is caused by a Fermi‐level shift into the bandgap and a trend toward nondirectional ionic bonding, leading to a maximum in the expected piezoelectric stress constante₃₃. The refractive index and the subgap absorption decrease withx, the optical bandgap increases, and the elastic constant along the hexagonal axisC₃₃= 270 ± 14 GPa remains composition independent, leading to an expected piezoelectric constantd₃₃= 6.4 pC N⁻¹atx= 0.5, which is 50% larger than for the pure AlN matrix. Thus, contrary to the typical anticorrelation between stability and electromechanical coupling, the (Ti_1−xMg_x)_0.25Al_0.75N system exhibits simultaneous maxima in the structural stability and the piezoelectric response atx= 0.5.

 

The electron reflection probability r at symmetric twin boundaries Σ3, Σ5, Σ9, and Σ11 is predicted from first principles for the eight most conductive face-centered cubic (fcc) metals. r increases with decreasing interplanar distance of atomic planes parallel to the boundary. This provides the basis for an extrapolation scheme to estimate the reflection probability r r at random grain boundaries, which is relatively small, r r = 0.28–0.39, for Cu, Ag, and Au due to their nearly spherical Fermi surfaces, but approximately two times higher for Al, Ca, Ni, Rh, and Ir with a predicted r r = 0.61–0.72. The metal resistivity in the limit of small randomly oriented grains with fixed average size is expected to be proportional to the materials benchmark quantity ρ o λ × r r /(1 − r r ), where ρ o and λ are the bulk resistivity and bulk electron mean free path, respectively. Cu has the lowest value for this quantity, indicating that all other fcc metals have a higher resistivity in the limit of small randomly oriented grains. Thus, the conductivity benefit of replacement metals for narrow Cu interconnect lines can only be realized if the grains are larger than the linewidth or exhibit symmetric orientation relationships where r < r r .