(Color online) Interface energy density (IED) as a function of periodicity of the superlattices, calculated using the formula [E (bulk−ZrN) + E (bul−ScN) − E (ZrN/ScN)]. Convergence is achieved quickly with the 4/4, 6/6 superlattice. Lines are drawn over the data points to show convergence.
(Color online) (a) Electronic structure of the 2/2-ZrN/ScN metal/semiconductor superlattice along the high symmetry directions of the tetragonal Brillouin zone. The symmetry points are Γ (0, 0, 0), X (0, 1/2, 0), M (1/2, 1/2, 0), Z (0, 0, 1/2), R (0, 1/2, 1/2), A (1/2, 1/2, 1/2). A relatively flat band at the Fermi energy along the Γ–Z directions can be observed. (b) The normalized density of states for m/m ZrN/ScN superlattices. (c) The partial densities of states (PDOS) of a typical 2/2 superlattice.
(Color online) (a) Highest occupied and (b) lowest unoccupied electronic states at the Γ point for 2/2 ZrN/ScN metal/semiconductor superlattice.
(Color online) (a) Planer average electrostatic potential (oscillating dashed green line) as a function of perpendicular distance from the (001) interface. Lattice-plane oscillations are evident, and are filtered with the macroscopic averaging technique (long-dashed red line). Vertical dashed black line represents the lattice planes. The difference of microscopic average electroscopic potential between metal and semiconductor side is critical for the estimates of Schottky barrier. (b) Charge transfer from ScN to ZrN layers at the interface of 8/8 superlattices. Zr and N atoms on the ZrN layer at the interface has gained charge (indicated by the positive sign), whereas Sc and N atom on ScN layer has lost charge (shown by the negative sign), resulting in the formation of diploes.
(Color online) Electrical conductivity of (a) ScN, (b) ZrN, and (c) ZrN/ScN metal/semiconductor superlattices. Although the ScN and ZrN show the traditional semiconducting and metallic electrical conducting behavior, respectively, the ZrN/ScN superlattices show interesting linear increase in electrical conductivity with temperature.
(Color online) Seebeck coefficient of (a) ScN and (b) ZrN and ZrN/ScN superlattices. S of superlattices increases with temperature and saturates after 400 K.
Vibrational spectra and phonon density of states of 2/2 ZrN/ScN metal/semiconductor superlattices. Localized phonons, manifested as flat dispersion along the Γ–Z, R–X, and M–A directions are observed.
(Color online) (a) Boltzmann transport based calculations of cross-plane lattice thermal conductivity for bulk materials and superlattices, representing reduction of κ along the cross-plane direction. (b) Cross-plane lattice thermal conductivity as a function of phonon frequencies at different temperatures.
Estimation of Schottky barrier height as a function of the stacking period (it is clear that the value of barrier height converges with the 7/7 and 8/8 superlattices).
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