Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials. These advantages include ease of implementation, implementation on highly parallel systems, and great flexibility for describing partially periodic systems. One limitation of this approach, shared by other electronic structure methods, is the slow convergence of interatomic forces when compared to total energies. For real space methods, this requires a fine grid to converge a solution of the Kohn–Sham problem, which is accompanied by concurrent increase in memory and additional matrix-vector multiplications. Here we introduce a method to expedite the computation of interatomic forces by employing a high order integration technique. We demonstrate the usefulness of this technique by calculating accurate bond lengths and vibrational frequencies for molecules and nanocrystals without using fine real space grids.

Highlights•We examined the role of quantum confinement in Schottky barriers.•We found for thin films that structural relaxations dominate interfacial energies.•We consider new methods to describe structure of lattice-mismatched interfaces.Schottky barriers form when semiconductors are in contact with metal overlayers establishing a common Fermi level. Few theoretical studies of these materials exist as electronic structure calculations are computationally intensive for mismatched interfaces. We explicitly model a Pb(111) film on a Si(111) substrate. For thick Pb overlayers, we find a bulk regime where the Fermi level is pinned. For thin film regimes (less than five overlayers), structural relaxations dominate the interfacial energy as charge transfer is suppressed by quantum confinement. In this case, the Schottky barrier height follows the trend of the metal work function.

It is well known that the activation energy of dopants in semiconducting nanomaterials is higher than in bulk materials owing to dielectric mismatch and quantum confinement. This quenches the number of free charge carriers in nanomaterials. Though higher doping concentration can compensate for this effect, there is no clear criterion on what the doping concentration should be. Using P-doped Si[110] nanowires as the prototypical system, we address this issue by establishing a doping limit by first-principles electronic structure calculations. We examine how the doped nanowires respond to charging using an effective capacitance approach. As the nanowire gets thinner, the interaction range of the P dopants shortens and the doping concentration can increase concurrently. Hence, heavier doping can remain nondegenerate for thin nanowires.

Highlights•We examined the role of quantum confinement in Schottky barriers.•We found for thin films that structural relaxations dominate interfacial energies.•We consider new methods to describe structure of lattice-mismatched interfaces.Schottky barriers form when semiconductors are in contact with metal overlayers establishing a common Fermi level. Few theoretical studies of these materials exist as electronic structure calculations are computationally intensive for mismatched interfaces. We explicitly model a Pb(111) film on a Si(111) substrate. For thick Pb overlayers, we find a bulk regime where the Fermi level is pinned. For thin film regimes (less than five overlayers), structural relaxations dominate the interfacial energy as charge transfer is suppressed by quantum confinement. In this case, the Schottky barrier height follows the trend of the metal work function.

Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials. These advantages include ease of implementation, implementation on highly parallel systems, and great flexibility for describing partially periodic systems. One limitation of this approach, shared by other electronic structure methods, is the slow convergence of interatomic forces when compared to total energies. For real space methods, this requires a fine grid to converge a solution of the Kohn–Sham problem, which is accompanied by concurrent increase in memory and additional matrix-vector multiplications. Here we introduce a method to expedite the computation of interatomic forces by employing a high order integration technique. We demonstrate the usefulness of this technique by calculating accurate bond lengths and vibrational frequencies for molecules and nanocrystals without using fine real space grids.